Daily Papers

Automated segmentation of retinal optical coherence tomography (OCT) images has become an important recent direction in machine learning for medical applications. We hypothesize that the anatomic structure of layers and their high-frequency variation in OCT images make retinal OCT a fitting choice for extracting spectral-domain features and combining them with spatial domain features. In this work, we present Upsilon-Net, an architecture that combines the frequency domain features with the image domain to improve the segmentation performance of OCT images. The results of this work demonstrate that the introduction of two branches, one for spectral and one for spatial domain features, brings a very significant improvement in fluid segmentation performance and allows outperformance as compared to the well-known U-Net model. Our improvement was 13% on the fluid segmentation dice score and 1.9% on the average dice score. Finally, removing selected frequency ranges in the spectral domain demonstrates the impact of these features on the fluid segmentation outperformance.

The main challenge in vision-and-language navigation (VLN) is how to understand natural-language instructions in an unseen environment. The main limitation of conventional VLN algorithms is that if an action is mistaken, the agent fails to follow the instructions or explores unnecessary regions, leading the agent to an irrecoverable path. To tackle this problem, we propose Meta-Explore, a hierarchical navigation method deploying an exploitation policy to correct misled recent actions. We show that an exploitation policy, which moves the agent toward a well-chosen local goal among unvisited but observable states, outperforms a method which moves the agent to a previously visited state. We also highlight the demand for imagining regretful explorations with semantically meaningful clues. The key to our approach is understanding the object placements around the agent in spectral-domain. Specifically, we present a novel visual representation, called scene object spectrum (SOS), which performs category-wise 2D Fourier transform of detected objects. Combining exploitation policy and SOS features, the agent can correct its path by choosing a promising local goal. We evaluate our method in three VLN benchmarks: R2R, SOON, and REVERIE. Meta-Explore outperforms other baselines and shows significant generalization performance. In addition, local goal search using the proposed spectral-domain SOS features significantly improves the success rate by 17.1% and SPL by 20.6% for the SOON benchmark.

This work identifies anisotropic parameter distributions as a fundamental barrier to training large language models (LLMs) with low-bit quantization: a few dominant singular values create wide numerical ranges that conflict with the inherent bias of block-wise quantization. This bias disproportionately preserves high-magnitude values while discarding smaller ones, causing training instability and low model performance. This work introduces Metis, a training framework that combines (i) spectral decomposition with random embedding to efficiently disentangle dominant from long-tail components, compressing broad distributions into quantization-friendly narrow ranges; (ii) adaptive learning rates in the spectral domain to amplify underrepresented directions and better capture diverse features critical for performance; and (iii) a dual-range regularizer that jointly constrains numerical precision and parameter range distribution, ensuring stable, unbiased low-bit training. With Metis, FP8 training surpasses FP32 baselines, and FP4 training achieves accuracy comparable to FP32, paving the way for robust and scalable LLM training under advanced low-bit quantization. The code implementation for Metis is available at: https://github.com/typename-yyf/Metis-quantization.

Recent advances in synthetic speech have made audio deepfakes increasingly realistic, posing significant security risks. Existing detection methods that rely on a single modality, either raw waveform embeddings or spectral based features, are vulnerable to non spoof disturbances and often overfit to known forgery algorithms, resulting in poor generalization to unseen attacks. To address these shortcomings, we investigate hybrid fusion frameworks that integrate self supervised learning (SSL) based representations with handcrafted spectral descriptors (MFCC , LFCC, CQCC). By aligning and combining complementary information across modalities, these fusion approaches capture subtle artifacts that single feature approaches typically overlook. We explore several fusion strategies, including simple concatenation, cross attention, mutual cross attention, and a learnable gating mechanism, to optimally blend SSL features with fine grained spectral cues. We evaluate our approach on four challenging public benchmarks and report generalization performance. All fusion variants consistently outperform an SSL only baseline, with the cross attention strategy achieving the best generalization with a 38% relative reduction in equal error rate (EER). These results confirm that joint modeling of waveform and spectral views produces robust, domain agnostic representations for audio deepfake detection.

Recent studies show that self-attentions behave like low-pass filters (as opposed to convolutions) and enhancing their high-pass filtering capability improves model performance. Contrary to this idea, we investigate existing convolution-based models with spectral analysis and observe that improving the low-pass filtering in convolution operations also leads to performance improvement. To account for this observation, we hypothesize that utilizing optimal token mixers that capture balanced representations of both high- and low-frequency components can enhance the performance of models. We verify this by decomposing visual features into the frequency domain and combining them in a balanced manner. To handle this, we replace the balancing problem with a mask filtering problem in the frequency domain. Then, we introduce a novel token-mixer named SPAM and leverage it to derive a MetaFormer model termed as SPANet. Experimental results show that the proposed method provides a way to achieve this balance, and the balanced representations of both high- and low-frequency components can improve the performance of models on multiple computer vision tasks. Our code is available at https://doranlyong.github.io/projects/spanet/{https://doranlyong.github.io/projects/spanet/}.

Parkinsons disease (PD) alters cortical neural dynamics, yet reliable non-invasive electrophysiological biomarkers remain elusive. This study examined whether interpretable EEG features capturing complementary aspects of neural dynamics can discriminate Parkinsonian neural states. A comprehensive set of interpretable features was extracted and grouped into Standard descriptors (spectral power, phase synchronization, time-domain statistics) and Dynamical descriptors (aperiodic activity, cross-frequency coupling, scale-free dynamics, neuronal avalanche statistics, and instantaneous frequency measures). A multi-head attention transformer classifier was trained using strict LOSO validation. Group-level comparisons were performed to identify electrophysiological differences associated with disease and medication state. Standard feature sets achieved strongest performance in discriminating medication states (PDoff vs PDon), whereas Dynamical performed competitively in contrasts between PD patients and healthy controls. Random feature ablation analyses indicated that Dynamical descriptors provide complementary information distributed across features while correlation analysis revealed low redundancy within both feature sets. Group-level comparisons revealed medication-sensitive reductions in delta power and voltage variance, modulation of neuronal avalanche statistics, persistent increases in theta phase synchronization in PD patients, and disease-related alterations in cross-frequency interactions. Traditional spectral and synchronization features primarily reflect medication-related neural modulation, whereas dynamical descriptors reveal broader alterations in cortical network organization associated with disease but also with medication. These findings support multivariate EEG representations as a promising framework for developing non-invasive biomarkers of PD.

3D Gaussian Splatting (3DGS) enables real-time, photorealistic novel view synthesis, making it a highly attractive representation for model-based video tracking. However, leveraging the differentiability of the 3DGS renderer "in the wild" remains notoriously fragile. A fundamental bottleneck lies in the compact, local support of the Gaussian primitives. Standard photometric objectives implicitly rely on spatial overlap; if severe camera misalignment places the rendered object outside the target's local footprint, gradients strictly vanish, leaving the optimizer stranded. We introduce SpectralSplats, a robust tracking framework that resolves this "vanishing gradient" problem by shifting the optimization objective from the spatial to the frequency domain. By supervising the rendered image via a set of global complex sinusoidal features (Spectral Moments), we construct a global basin of attraction, ensuring that a valid, directional gradient toward the target exists across the entire image domain, even when pixel overlap is completely nonexistent. To harness this global basin without introducing periodic local minima associated with high frequencies, we derive a principled Frequency Annealing schedule from first principles, gracefully transitioning the optimizer from global convexity to precise spatial alignment. We demonstrate that SpectralSplats acts as a seamless, drop-in replacement for spatial losses across diverse deformation parameterizations (from MLPs to sparse control points), successfully recovering complex deformations even from severely misaligned initializations where standard appearance-based tracking catastrophically fails.

In the face of the deep learning model's vulnerability to domain shift, source-free domain adaptation (SFDA) methods have been proposed to adapt models to new, unseen target domains without requiring access to source domain data. Although the potential benefits of applying data augmentation to SFDA are attractive, several challenges arise such as the dependence on prior knowledge of class-preserving transformations and the increase in memory and computational requirements. In this paper, we propose Source-free Domain Adaptation Through the Lens of Data Augmentation (SF(DA)^2), a novel approach that leverages the benefits of data augmentation without suffering from these challenges. We construct an augmentation graph in the feature space of the pretrained model using the neighbor relationships between target features and propose spectral neighborhood clustering to identify partitions in the prediction space. Furthermore, we propose implicit feature augmentation and feature disentanglement as regularization loss functions that effectively utilize class semantic information within the feature space. These regularizers simulate the inclusion of an unlimited number of augmented target features into the augmentation graph while minimizing computational and memory demands. Our method shows superior adaptation performance in SFDA scenarios, including 2D image and 3D point cloud datasets and a highly imbalanced dataset.

Recently, learning-based algorithms have achieved promising performance on cross-spectral image patch matching, which, however, is still far from satisfactory for practical application. On the one hand, a lack of large-scale dataset with diverse scenes haunts its further improvement for learning-based algorithms, whose performances and generalization rely heavily on the dataset size and diversity. On the other hand, more emphasis has been put on feature relation in the spatial domain whereas the scale dependency between features has often been ignored, leading to performance degeneration especially when encountering significant appearance variations for cross-spectral patches. To address these issues, we publish, to be best of our knowledge, the largest visible and Long-wave Infrared (LWIR) image patch matching dataset, termed VL-CMIM, which contains 1300 pairs of strictly aligned visible and LWIR images and over 2 million patch pairs covering diverse scenes such as asteroid, field, country, build, street and water.In addition, a multi-domain feature relation learning network (MD-FRN) is proposed. Input by the features extracted from a four-branch network, both feature relations in spatial and scale domains are learned via a spatial correlation module (SCM) and multi-scale adaptive aggregation module (MSAG), respectively. To further aggregate the multi-domain relations, a deep domain interactive mechanism (DIM) is applied, where the learnt spatial-relation and scale-relation features are exchanged and further input into MSCRM and SCM. This mechanism allows our model to learn interactive cross-domain feature relations, leading to improved robustness to significant appearance changes due to different modality.

Large language models are increasingly adapted to downstream tasks through fine-tuning. Full supervised fine-tuning (SFT) and parameter-efficient fine-tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), are two dominant approaches. While PEFT methods are widely used for their computational efficiency, the implications of their configurations (e.g., rank) remain under-explored in downstream Q&A tasks and generalisation. In this work, we perform a comprehensive evaluation across multiple reasoning and recall datasets, conducting a rank sweep to quantify the trade-off between SFT and PEFT. We also compare the accuracy of PEFT and SFT models across in-domain and out-of-domain adaptation, highlighting distinct generalisation behaviour and task-specific forgetting. We demonstrate that LoRA achieves competitive and in some cases superior performance compared to SFT, particularly on reasoning tasks at specific rank values. Additionally, we analyze the internal representations via spectral features and layer-wise attention structures, offering insights into representational drift and structural changes in attention patterns.

Generating realistic time series data is important for many engineering and scientific applications. Existing work tackles this problem using generative adversarial networks (GANs). However, GANs are often unstable during training, and they can suffer from mode collapse. While variational autoencoders (VAEs) are known to be more robust to these issues, they are (surprisingly) less often considered for time series generation. In this work, we introduce Koopman VAE (KVAE), a new generative framework that is based on a novel design for the model prior, and that can be optimized for either regular and irregular training data. Inspired by Koopman theory, we represent the latent conditional prior dynamics using a linear map. Our approach enhances generative modeling with two desired features: (i) incorporating domain knowledge can be achieved by leverageing spectral tools that prescribe constraints on the eigenvalues of the linear map; and (ii) studying the qualitative behavior and stablity of the system can be performed using tools from dynamical systems theory. Our results show that KVAE outperforms state-of-the-art GAN and VAE methods across several challenging synthetic and real-world time series generation benchmarks. Whether trained on regular or irregular data, KVAE generates time series that improve both discriminative and predictive metrics. We also present visual evidence suggesting that KVAE learns probability density functions that better approximate empirical ground truth distributions.

Understanding the interaction of neural and cardiac systems during cognitive activity is critical to advancing physiological computing. Although EEG has been the gold standard for assessing mental workload, its limited portability restricts its real-world use. Widely available ECG through wearable devices proposes a pragmatic alternative. This research investigates whether ECG signals can reliably reflect cognitive load and serve as proxies for EEG-based indicators. In this work, we present multimodal data acquired from two different paradigms involving working-memory and passive-listening tasks. For each modality, we extracted ECG time-domain HRV metrics and Catch22 descriptors against EEG spectral and Catch22 features, respectively. We propose a cross-modal XGBoost framework to project the ECG features onto EEG-representative cognitive spaces, thereby allowing workload inferences using only ECG. Our results show that ECG-derived projections expressively capture variation in cognitive states and provide good support for accurate classification. Our findings underpin ECG as an interpretable, real-time, wearable solution for everyday cognitive monitoring.

We present AERO, a audio super-resolution model that processes speech and music signals in the spectral domain. AERO is based on an encoder-decoder architecture with U-Net like skip connections. We optimize the model using both time and frequency domain loss functions. Specifically, we consider a set of reconstruction losses together with perceptual ones in the form of adversarial and feature discriminator loss functions. To better handle phase information the proposed method operates over the complex-valued spectrogram using two separate channels. Unlike prior work which mainly considers low and high frequency concatenation for audio super-resolution, the proposed method directly predicts the full frequency range. We demonstrate high performance across a wide range of sample rates considering both speech and music. AERO outperforms the evaluated baselines considering Log-Spectral Distance, ViSQOL, and the subjective MUSHRA test. Audio samples and code are available at https://pages.cs.huji.ac.il/adiyoss-lab/aero

Semantic segmentation of remote sensing imagery demands precise spatial boundaries and robust intra-class consistency, challenging conventional hierarchical models. To address limitations arising from spatial domain feature fusion and insufficient receptive fields, this paper introduces SAIP-Net, a novel frequency-aware segmentation framework that leverages Spectral Adaptive Information Propagation. SAIP-Net employs adaptive frequency filtering and multi-scale receptive field enhancement to effectively suppress intra-class feature inconsistencies and sharpen boundary lines. Comprehensive experiments demonstrate significant performance improvements over state-of-the-art methods, highlighting the effectiveness of spectral-adaptive strategies combined with expanded receptive fields for remote sensing image segmentation.

The integration of new modalities enhances the capabilities of multimodal large language models (MLLMs) but also introduces additional vulnerabilities. In particular, simple visual jailbreaking attacks can manipulate open-source MLLMs more readily than sophisticated textual attacks. However, these underdeveloped attacks exhibit extremely limited cross-model transferability, failing to reliably identify vulnerabilities in closed-source MLLMs. In this work, we analyse the loss landscape of these jailbreaking attacks and find that the generated attacks tend to reside in high-sharpness regions, whose effectiveness is highly sensitive to even minor parameter changes during transfer. To further explain the high-sharpness localisations, we analyse their feature representations in both the intermediate layers and the spectral domain, revealing an improper reliance on narrow layer representations and semantically poor frequency components. Building on this, we propose a Feature Over-Reliance CorrEction (FORCE) method, which guides the attack to explore broader feasible regions across layer features and rescales the influence of frequency features according to their semantic content. By eliminating non-generalizable reliance on both layer and spectral features, our method discovers flattened feasible regions for visual jailbreaking attacks, thereby improving cross-model transferability. Extensive experiments demonstrate that our approach effectively facilitates visual red-teaming evaluations against closed-source MLLMs.

Within the graph learning community, conventional wisdom dictates that spectral convolutional networks may only be deployed on undirected graphs: Only there could the existence of a well-defined graph Fourier transform be guaranteed, so that information may be translated between spatial- and spectral domains. Here we show this traditional reliance on the graph Fourier transform to be superfluous and -- making use of certain advanced tools from complex analysis and spectral theory -- extend spectral convolutions to directed graphs. We provide a frequency-response interpretation of newly developed filters, investigate the influence of the basis used to express filters and discuss the interplay with characteristic operators on which networks are based. In order to thoroughly test the developed theory, we conduct experiments in real world settings, showcasing that directed spectral convolutional networks provide new state of the art results for heterophilic node classification on many datasets and -- as opposed to baselines -- may be rendered stable to resolution-scale varying topological perturbations.

Recent works have established that AI models introduce spectral artifacts into generated images and propose approaches for learning to capture them using labeled data. However, the significant differences in such artifacts among different generative models hinder these approaches from generalizing to generators not seen during training. In this work, we build upon the key idea that the spectral distribution of real images constitutes both an invariant and highly discriminative pattern for AI-generated image detection. To model this under a self-supervised setup, we employ masked spectral learning using the pretext task of frequency reconstruction. Since generated images constitute out-of-distribution samples for this model, we propose spectral reconstruction similarity to capture this divergence. Moreover, we introduce spectral context attention, which enables our approach to efficiently capture subtle spectral inconsistencies in images of any resolution. Our spectral AI-generated image detection approach (SPAI) achieves a 5.5% absolute improvement in AUC over the previous state-of-the-art across 13 recent generative approaches, while exhibiting robustness against common online perturbations. Code is available on https://mever-team.github.io/spai.

Given the importance of remote sensing, surprisingly little attention has been paid to it by the representation learning community. To address it and to establish baselines and a common evaluation protocol in this domain, we provide simplified access to 5 diverse remote sensing datasets in a standardized form. Specifically, we investigate in-domain representation learning to develop generic remote sensing representations and explore which characteristics are important for a dataset to be a good source for remote sensing representation learning. The established baselines achieve state-of-the-art performance on these datasets.

In this paper, we propose a speed-up approach for subclass discriminant analysis and formulate a novel efficient multi-view solution to it. The speed-up approach is developed based on graph embedding and spectral regression approaches that involve eigendecomposition of the corresponding Laplacian matrix and regression to its eigenvectors. We show that by exploiting the structure of the between-class Laplacian matrix, the eigendecomposition step can be substituted with a much faster process. Furthermore, we formulate a novel criterion for multi-view subclass discriminant analysis and show that an efficient solution for it can be obtained in a similar to the single-view manner. We evaluate the proposed methods on nine single-view and nine multi-view datasets and compare them with related existing approaches. Experimental results show that the proposed solutions achieve competitive performance, often outperforming the existing methods. At the same time, they significantly decrease the training time.

Whitening loss offers a theoretical guarantee against feature collapse in self-supervised learning (SSL) with joint embedding architectures. Typically, it involves a hard whitening approach, transforming the embedding and applying loss to the whitened output. In this work, we introduce Spectral Transformation (ST), a framework to modulate the spectrum of embedding and to seek for functions beyond whitening that can avoid dimensional collapse. We show that whitening is a special instance of ST by definition, and our empirical investigations unveil other ST instances capable of preventing collapse. Additionally, we propose a novel ST instance named IterNorm with trace loss (INTL). Theoretical analysis confirms INTL's efficacy in preventing collapse and modulating the spectrum of embedding toward equal-eigenvalues during optimization. Our experiments on ImageNet classification and COCO object detection demonstrate INTL's potential in learning superior representations. The code is available at https://github.com/winci-ai/INTL.

Graph neural networks aim to learn representations for graph-structured data and show impressive performance, particularly in node classification. Recently, many methods have studied the representations of GNNs from the perspective of optimization goals and spectral graph theory. However, the feature space that dominates representation learning has not been systematically studied in graph neural networks. In this paper, we propose to fill this gap by analyzing the feature space of both spatial and spectral models. We decompose graph neural networks into determined feature spaces and trainable weights, providing the convenience of studying the feature space explicitly using matrix space analysis. In particular, we theoretically find that the feature space tends to be linearly correlated due to repeated aggregations. Motivated by these findings, we propose 1) feature subspaces flattening and 2) structural principal components to expand the feature space. Extensive experiments verify the effectiveness of our proposed more comprehensive feature space, with comparable inference time to the baseline, and demonstrate its efficient convergence capability.

Time-domain surveys such as the Zwicky Transient Facility (ZTF) have opened a new frontier in the discovery and characterization of transients. While photometric light curves provide broad temporal coverage, spectroscopic observations remain crucial for physical interpretation and source classification. However, existing spectral analysis methods -- often reliant on template fitting or parametric models -- are limited in their ability to capture the complex and evolving spectra characteristic of such sources, which are sometimes only available at low resolution. In this work, we introduce SpectraNet, a deep convolutional neural network designed to learn robust representations of optical spectra from transients. Our model combines multi-scale convolution kernels and multi-scale pooling to extract features from preprocessed spectra in a hierarchical and interpretable manner. We train and validate SpectraNet on low-resolution time-series spectra obtained from the Spectral Energy Distribution Machine (SEDM) and other instruments, demonstrating state-of-the-art performance in classification. Furthermore, in redshift prediction tasks, SpectraNet achieves a root mean squared relative redshift error of 0.02, highlighting its effectiveness in precise regression tasks as well.

Linearization of attention using various kernel approximation and kernel learning techniques has shown promise. Past methods used a subset of combinations of component functions and weight matrices within the random feature paradigm. We identify the need for a systematic comparison of different combinations of weight matrices and component functions for attention learning in Transformer. Hence, we introduce Spectraformer, a unified framework for approximating and learning the kernel function in the attention mechanism of the Transformer. Our empirical results demonstrate, for the first time, that a random feature-based approach can achieve performance comparable to top-performing sparse and low-rank methods on the challenging Long Range Arena benchmark. Thus, we establish a new state-of-the-art for random feature-based efficient Transformers. The framework also produces many variants that offer different advantages in accuracy, training time, and memory consumption. Our code is available at: https://github.com/cruiseresearchgroup/spectraformer .

Dimensionality reduction is critical for deploying dense retrieval systems at scale, yet mainstream post-hoc methods face a fundamental trade-off: principal component analysis (PCA) preserves dominant variance but underutilizes representational capacity, while whitening enforces isotropy at the cost of amplifying noise in the heavy-tailed eigenspectrum of retrieval embeddings. Intermediate spectral scaling methods unify these extremes by reweighting dimensions with a power coefficient γ, but treat γ as a fixed hyperparameter that requires task-specific tuning. We show that the optimal scaling strength γ is not a global constant: it varies systematically with target dimensionality k and is governed by the signal-to-noise ratio (SNR) of the retained subspace. Based on this insight, we propose Spectral Tempering (SpecTemp), a learning-free method that derives an adaptive γ(k) directly from the corpus eigenspectrum using local SNR analysis and knee-point normalization, requiring no labeled data or validation-based search. Extensive experiments demonstrate that Spectral Tempering consistently achieves near-oracle performance relative to grid-searched γ^*(k) while remaining fully learning-free and model-agnostic. Our code is publicly available at https://anonymous.4open.science/r/SpecTemp-0D37.

Domain Generalization (DG) is a fundamental challenge for machine learning models, which aims to improve model generalization on various domains. Previous methods focus on generating domain invariant features from various source domains. However, we argue that the domain variantions also contain useful information, ie, classification-aware information, for downstream tasks, which has been largely ignored. Different from learning domain invariant features from source domains, we decouple the input images into Domain Expert Features and noise. The proposed domain expert features lie in a learned latent space where the images in each domain can be classified independently, enabling the implicit use of classification-aware domain variations. Based on the analysis, we proposed a novel paradigm called Domain Disentanglement Network (DDN) to disentangle the domain expert features from the source domain images and aggregate the source domain expert features for representing the target test domain. We also propound a new contrastive learning method to guide the domain expert features to form a more balanced and separable feature space. Experiments on the widely-used benchmarks of PACS, VLCS, OfficeHome, DomainNet, and TerraIncognita demonstrate the competitive performance of our method compared to the recently proposed alternatives.

In this paper, we present a Hybrid Spectral Denoising Transformer (HSDT) for hyperspectral image denoising. Challenges in adapting transformer for HSI arise from the capabilities to tackle existing limitations of CNN-based methods in capturing the global and local spatial-spectral correlations while maintaining efficiency and flexibility. To address these issues, we introduce a hybrid approach that combines the advantages of both models with a Spatial-Spectral Separable Convolution (S3Conv), Guided Spectral Self-Attention (GSSA), and Self-Modulated Feed-Forward Network (SM-FFN). Our S3Conv works as a lightweight alternative to 3D convolution, which extracts more spatial-spectral correlated features while keeping the flexibility to tackle HSIs with an arbitrary number of bands. These features are then adaptively processed by GSSA which per-forms 3D self-attention across the spectral bands, guided by a set of learnable queries that encode the spectral signatures. This not only enriches our model with powerful capabilities for identifying global spectral correlations but also maintains linear complexity. Moreover, our SM-FFN proposes the self-modulation that intensifies the activations of more informative regions, which further strengthens the aggregated features. Extensive experiments are conducted on various datasets under both simulated and real-world noise, and it shows that our HSDT significantly outperforms the existing state-of-the-art methods while maintaining low computational overhead. Code is at https: //github.com/Zeqiang-Lai/HSDT.

In this paper, we propose SPECTRUM, a temporal-frequency synergistic model that unlocks the untapped potential of multi-domain representation learning for online handwriting verification (OHV). SPECTRUM comprises three core components: (1) a multi-scale interactor that finely combines temporal and frequency features through dual-modal sequence interaction and multi-scale aggregation, (2) a self-gated fusion module that dynamically integrates global temporal and frequency features via self-driven balancing. These two components work synergistically to achieve micro-to-macro spectral-temporal integration. (3) A multi-domain distance-based verifier then utilizes both temporal and frequency representations to improve discrimination between genuine and forged handwriting, surpassing conventional temporal-only approaches. Extensive experiments demonstrate SPECTRUM's superior performance over existing OHV methods, underscoring the effectiveness of temporal-frequency multi-domain learning. Furthermore, we reveal that incorporating multiple handwritten biometrics fundamentally enhances the discriminative power of handwriting representations and facilitates verification. These findings not only validate the efficacy of multi-domain learning in OHV but also pave the way for future research in multi-domain approaches across both feature and biometric domains. Code is publicly available at https://github.com/NiceRingNode/SPECTRUM.

Several recent studies advocate the use of spectral discriminators, which evaluate the Fourier spectra of images for generative modeling. However, the effectiveness of the spectral discriminators is not well interpreted yet. We tackle this issue by examining the spectral discriminators in the context of perceptual image super-resolution (i.e., GAN-based SR), as SR image quality is susceptible to spectral changes. Our analyses reveal that the spectral discriminator indeed performs better than the ordinary (a.k.a. spatial) discriminator in identifying the differences in the high-frequency range; however, the spatial discriminator holds an advantage in the low-frequency range. Thus, we suggest that the spectral and spatial discriminators shall be used simultaneously. Moreover, we improve the spectral discriminators by first calculating the patch-wise Fourier spectrum and then aggregating the spectra by Transformer. We verify the effectiveness of the proposed method twofold. On the one hand, thanks to the additional spectral discriminator, our obtained SR images have their spectra better aligned to those of the real images, which leads to a better PD tradeoff. On the other hand, our ensembled discriminator predicts the perceptual quality more accurately, as evidenced in the no-reference image quality assessment task.

Domain generalization (DG) is a principal task to evaluate the robustness of computer vision models. Many previous studies have used normalization for DG. In normalization, statistics and normalized features are regarded as style and content, respectively. However, it has a content variation problem when removing style because the boundary between content and style is unclear. This study addresses this problem from the frequency domain perspective, where amplitude and phase are considered as style and content, respectively. First, we verify the quantitative phase variation of normalization through the mathematical derivation of the Fourier transform formula. Then, based on this, we propose a novel normalization method, PCNorm, which eliminates style only as the preserving content through spectral decomposition. Furthermore, we propose advanced PCNorm variants, CCNorm and SCNorm, which adjust the degrees of variations in content and style, respectively. Thus, they can learn domain-agnostic representations for DG. With the normalization methods, we propose ResNet-variant models, DAC-P and DAC-SC, which are robust to the domain gap. The proposed models outperform other recent DG methods. The DAC-SC achieves an average state-of-the-art performance of 65.6% on five datasets: PACS, VLCS, Office-Home, DomainNet, and TerraIncognita.

Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being sampled onto a uniform physical grid suffer significant aliasing error and information loss. Moreover, signals can exist in different topological structures as, for example, points, lines, surfaces and volumes. It has been challenging to analyze signals with mixed topologies (for example, point cloud with surface mesh). To this end, we develop mathematical formulations for Non-Uniform Fourier Transforms (NUFT) to directly, and optimally, sample nonuniform data signals of different topologies defined on a simplex mesh into the spectral domain with no spatial sampling error. The spectral transform is performed in the Euclidean space, which removes the translation ambiguity from works on the graph spectrum. Our representation has four distinct advantages: (1) the process causes no spatial sampling error during the initial sampling, (2) the generality of this approach provides a unified framework for using CNNs to analyze signals of mixed topologies, (3) it allows us to leverage state-of-the-art backbone CNN architectures for effective learning without having to design a particular architecture for a particular data structure in an ad-hoc fashion, and (4) the representation allows weighted meshes where each element has a different weight (i.e., texture) indicating local properties. We achieve results on par with the state-of-the-art for the 3D shape retrieval task, and a new state-of-the-art for the point cloud to surface reconstruction task.

This paper studies sequence modeling for prediction tasks with long range dependencies. We propose a new formulation for state space models (SSMs) based on learning linear dynamical systems with the spectral filtering algorithm (Hazan et al. (2017)). This gives rise to a novel sequence prediction architecture we call a spectral state space model. Spectral state space models have two primary advantages. First, they have provable robustness properties as their performance depends on neither the spectrum of the underlying dynamics nor the dimensionality of the problem. Second, these models are constructed with fixed convolutional filters that do not require learning while still outperforming SSMs in both theory and practice. The resulting models are evaluated on synthetic dynamical systems and long-range prediction tasks of various modalities. These evaluations support the theoretical benefits of spectral filtering for tasks requiring very long range memory.

Image datasets are essential not only in validating existing methods in computer vision but also in developing new methods. Most existing image datasets focus on trichromatic intensity images to mimic human vision. However, polarization and spectrum, the wave properties of light that animals in harsh environments and with limited brain capacity often rely on, remain underrepresented in existing datasets. Although spectro-polarimetric datasets exist, these datasets have insufficient object diversity, limited illumination conditions, linear-only polarization data, and inadequate image count. Here, we introduce two spectro-polarimetric datasets: trichromatic Stokes images and hyperspectral Stokes images. These novel datasets encompass both linear and circular polarization; they introduce multiple spectral channels; and they feature a broad selection of real-world scenes. With our dataset in hand, we analyze the spectro-polarimetric image statistics, develop efficient representations of such high-dimensional data, and evaluate spectral dependency of shape-from-polarization methods. As such, the proposed dataset promises a foundation for data-driven spectro-polarimetric imaging and vision research. Dataset and code will be publicly available.

Spectral analysis provides one of the most effective paradigms for information-preserving dimensionality reduction, as simple descriptions of naturally occurring signals are often obtained via few terms of periodic basis functions. In this work, we study deep neural networks designed to harness the structure in frequency domain for efficient learning of long-range correlations in space or time: frequency-domain models (FDMs). Existing FDMs are based on complex-valued transforms i.e. Fourier Transforms (FT), and layers that perform computation on the spectrum and input data separately. This design introduces considerable computational overhead: for each layer, a forward and inverse FT. Instead, this work introduces a blueprint for frequency domain learning through a single transform: transform once (T1). To enable efficient, direct learning in the frequency domain we derive a variance-preserving weight initialization scheme and investigate methods for frequency selection in reduced-order FDMs. Our results noticeably streamline the design process of FDMs, pruning redundant transforms, and leading to speedups of 3x to 10x that increase with data resolution and model size. We perform extensive experiments on learning the solution operator of spatio-temporal dynamics, including incompressible Navier-Stokes, turbulent flows around airfoils and high-resolution video of smoke. T1 models improve on the test performance of FDMs while requiring significantly less computation (5 hours instead of 32 for our large-scale experiment), with over 20% reduction in average predictive error across tasks.

Unsupervised semantic segmentation is a long-standing challenge in computer vision with great significance. Spectral clustering is a theoretically grounded solution to it where the spectral embeddings for pixels are computed to construct distinct clusters. Despite recent progress in enhancing spectral clustering with powerful pre-trained models, current approaches still suffer from inefficiencies in spectral decomposition and inflexibility in applying them to the test data. This work addresses these issues by casting spectral clustering as a parametric approach that employs neural network-based eigenfunctions to produce spectral embeddings. The outputs of the neural eigenfunctions are further restricted to discrete vectors that indicate clustering assignments directly. As a result, an end-to-end NN-based paradigm of spectral clustering emerges. In practice, the neural eigenfunctions are lightweight and take the features from pre-trained models as inputs, improving training efficiency and unleashing the potential of pre-trained models for dense prediction. We conduct extensive empirical studies to validate the effectiveness of our approach and observe significant performance gains over competitive baselines on Pascal Context, Cityscapes, and ADE20K benchmarks.

Foundation models have triggered a paradigm shift in computer vision and are increasingly being adopted in remote sensing, particularly for multispectral imagery. Yet, their potential in hyperspectral imaging (HSI) remains untapped due to the absence of comprehensive and globally representative hyperspectral datasets. To close this gap, we introduce SpectralEarth, a large-scale multi-temporal dataset designed to pretrain hyperspectral foundation models leveraging data from the Environmental Mapping and Analysis Program (EnMAP). SpectralEarth comprises 538,974 image patches covering 415,153 unique locations from more than 11,636 globally distributed EnMAP scenes spanning two years of archive. Additionally, 17.5% of these locations include multiple timestamps, enabling multi-temporal HSI analysis. Utilizing state-of-the-art self-supervised learning (SSL) algorithms, we pretrain a series of foundation models on SpectralEarth. We integrate a spectral adapter into classical vision backbones to accommodate the unique characteristics of HSI. In tandem, we construct four downstream datasets for land-cover and crop-type mapping, providing benchmarks for model evaluation. Experimental results support the versatility of our models, showcasing their generalizability across different tasks and sensors. We also highlight computational efficiency during model fine-tuning. The dataset, models, and source code will be made publicly available.

Utilizing hyperspectral remote sensing technology enables the extraction of fine-grained land cover classes. Typically, satellite or airborne images used for training and testing are acquired from different regions or times, where the same class has significant spectral shifts in different scenes. In this paper, we propose a Bi-directional Domain Adaptation (BiDA) framework for cross-domain hyperspectral image (HSI) classification, which focuses on extracting both domain-invariant features and domain-specific information in the independent adaptive space, thereby enhancing the adaptability and separability to the target scene. In the proposed BiDA, a triple-branch transformer architecture (the source branch, target branch, and coupled branch) with semantic tokenizer is designed as the backbone. Specifically, the source branch and target branch independently learn the adaptive space of source and target domains, a Coupled Multi-head Cross-attention (CMCA) mechanism is developed in coupled branch for feature interaction and inter-domain correlation mining. Furthermore, a bi-directional distillation loss is designed to guide adaptive space learning using inter-domain correlation. Finally, we propose an Adaptive Reinforcement Strategy (ARS) to encourage the model to focus on specific generalized feature extraction within both source and target scenes in noise condition. Experimental results on cross-temporal/scene airborne and satellite datasets demonstrate that the proposed BiDA performs significantly better than some state-of-the-art domain adaptation approaches. In the cross-temporal tree species classification task, the proposed BiDA is more than 3\%sim5\% higher than the most advanced method. The codes will be available from the website: https://github.com/YuxiangZhang-BIT/IEEE_TCSVT_BiDA.

The recent surge in contrast-based graph self-supervised learning has prominently featured an intensified exploration of spectral cues. Spectral augmentation, which involves modifying a graph's spectral properties such as eigenvalues or eigenvectors, is widely believed to enhance model performance. However, an intriguing paradox emerges, as methods grounded in seemingly conflicting assumptions regarding the spectral domain demonstrate notable enhancements in learning performance. Through extensive empirical studies, we find that simple edge perturbations - random edge dropping for node-level and random edge adding for graph-level self-supervised learning - consistently yield comparable or superior performance while being significantly more computationally efficient. This suggests that the computational overhead of sophisticated spectral augmentations may not justify their practical benefits. Our theoretical analysis of the InfoNCE loss bounds for shallow GNNs further supports this observation. The proposed insights represent a significant leap forward in the field, potentially refining the understanding and implementation of graph self-supervised learning.

In this work we introduce KERNELIZED TRANSFORMER, a generic, scalable, data driven framework for learning the kernel function in Transformers. Our framework approximates the Transformer kernel as a dot product between spectral feature maps and learns the kernel by learning the spectral distribution. This not only helps in learning a generic kernel end-to-end, but also reduces the time and space complexity of Transformers from quadratic to linear. We show that KERNELIZED TRANSFORMERS achieve performance comparable to existing efficient Transformer architectures, both in terms of accuracy as well as computational efficiency. Our study also demonstrates that the choice of the kernel has a substantial impact on performance, and kernel learning variants are competitive alternatives to fixed kernel Transformers, both in long as well as short sequence tasks.

We introduce Domain-specific Masks for Generalization, a model for improving both in-domain and out-of-domain generalization performance. For domain generalization, the goal is to learn from a set of source domains to produce a single model that will best generalize to an unseen target domain. As such, many prior approaches focus on learning representations which persist across all source domains with the assumption that these domain agnostic representations will generalize well. However, often individual domains contain characteristics which are unique and when leveraged can significantly aid in-domain recognition performance. To produce a model which best generalizes to both seen and unseen domains, we propose learning domain specific masks. The masks are encouraged to learn a balance of domain-invariant and domain-specific features, thus enabling a model which can benefit from the predictive power of specialized features while retaining the universal applicability of domain-invariant features. We demonstrate competitive performance compared to naive baselines and state-of-the-art methods on both PACS and DomainNet.

Discrete speech representations have garnered recent attention for their efficacy in training transformer-based models for various speech-related tasks such as automatic speech recognition (ASR), translation, speaker verification, and joint speech-text foundational models. In this work, we present a comprehensive analysis on building ASR systems with discrete codes. We investigate different methods for codec training such as quantization schemes and time-domain vs spectral feature encodings. We further explore ASR training techniques aimed at enhancing performance, training efficiency, and noise robustness. Drawing upon our findings, we introduce a codec ASR pipeline that outperforms Encodec at similar bit-rate. Remarkably, it also surpasses the state-of-the-art results achieved by strong self-supervised models on the 143 languages ML-SUPERB benchmark despite being smaller in size and pretrained on significantly less data.

Domain Generalization aims to develop models that can generalize to novel and unseen data distributions. In this work, we study how model architectures and pre-training objectives impact feature richness and propose a method to effectively leverage them for domain generalization. Specifically, given a pre-trained feature space, we first discover latent domain structures, referred to as pseudo-domains, that capture domain-specific variations in an unsupervised manner. Next, we augment existing classifiers with these complementary pseudo-domain representations making them more amenable to diverse unseen test domains. We analyze how different pre-training feature spaces differ in the domain-specific variances they capture. Our empirical studies reveal that features from diffusion models excel at separating domains in the absence of explicit domain labels and capture nuanced domain-specific information. On 5 datasets, we show that our very simple framework improves generalization to unseen domains by a maximum test accuracy improvement of over 4% compared to the standard baseline Empirical Risk Minimization (ERM). Crucially, our method outperforms most algorithms that access domain labels during training.

Hyperspectral image (HSI) classification is widely used for the analysis of remotely sensed images. Hyperspectral imagery includes varying bands of images. Convolutional Neural Network (CNN) is one of the most frequently used deep learning based methods for visual data processing. The use of CNN for HSI classification is also visible in recent works. These approaches are mostly based on 2D CNN. Whereas, the HSI classification performance is highly dependent on both spatial and spectral information. Very few methods have utilized the 3D CNN because of increased computational complexity. This letter proposes a Hybrid Spectral Convolutional Neural Network (HybridSN) for HSI classification. Basically, the HybridSN is a spectral-spatial 3D-CNN followed by spatial 2D-CNN. The 3D-CNN facilitates the joint spatial-spectral feature representation from a stack of spectral bands. The 2D-CNN on top of the 3D-CNN further learns more abstract level spatial representation. Moreover, the use of hybrid CNNs reduces the complexity of the model compared to 3D-CNN alone. To test the performance of this hybrid approach, very rigorous HSI classification experiments are performed over Indian Pines, Pavia University and Salinas Scene remote sensing datasets. The results are compared with the state-of-the-art hand-crafted as well as end-to-end deep learning based methods. A very satisfactory performance is obtained using the proposed HybridSN for HSI classification. The source code can be found at https://github.com/gokriznastic/HybridSN.

In recent years, large language models (LLMs) have transformed natural language understanding through vast datasets and large-scale parameterization. Inspired by this success, we present SpecCLIP, a foundation model framework that extends LLM-inspired methodologies to stellar spectral analysis. Stellar spectra, akin to structured language, encode rich physical and chemical information about stars. By training foundation models on large-scale spectral datasets, our goal is to learn robust and informative embeddings that support diverse downstream applications. As a proof of concept, SpecCLIP involves pre-training on two spectral types--LAMOST low-resolution and Gaia XP--followed by contrastive alignment using the CLIP (Contrastive Language-Image Pre-training) framework, adapted to associate spectra from different instruments. This alignment is complemented by auxiliary decoders that preserve spectrum-specific information and enable translation (prediction) between spectral types, with the former achieved by maximizing mutual information between embeddings and input spectra. The result is a cross-spectrum framework enabling intrinsic calibration and flexible applications across instruments. We demonstrate that fine-tuning these models on moderate-sized labeled datasets improves adaptability to tasks such as stellar-parameter estimation and chemical-abundance determination. SpecCLIP also enhances the accuracy and precision of parameter estimates benchmarked against external survey data. Additionally, its similarity search and cross-spectrum prediction capabilities offer potential for anomaly detection. Our results suggest that contrastively trained foundation models enriched with spectrum-aware decoders can advance precision stellar spectroscopy.

Hyperspectral pansharpening is receiving a growing interest since the last few years as testified by a large number of research papers and challenges. It consists in a pixel-level fusion between a lower-resolution hyperspectral datacube and a higher-resolution single-band image, the panchromatic image, with the goal of providing a hyperspectral datacube at panchromatic resolution. Thanks to their powerful representational capabilities, deep learning models have succeeded to provide unprecedented results on many general purpose image processing tasks. However, when moving to domain specific problems, as in this case, the advantages with respect to traditional model-based approaches are much lesser clear-cut due to several contextual reasons. Scarcity of training data, lack of ground-truth, data shape variability, are some such factors that limit the generalization capacity of the state-of-the-art deep learning networks for hyperspectral pansharpening. To cope with these limitations, in this work we propose a new deep learning method which inherits a simple single-band unsupervised pansharpening model nested in a sequential band-wise adaptive scheme, where each band is pansharpened refining the model tuned on the preceding one. By doing so, a simple model is propagated along the wavelength dimension, adaptively and flexibly, with no need to have a fixed number of spectral bands, and, with no need to dispose of large, expensive and labeled training datasets. The proposed method achieves very good results on our datasets, outperforming both traditional and deep learning reference methods. The implementation of the proposed method can be found on https://github.com/giu-guarino/R-PNN

Currently, prominent Transformer architectures applied on graphs and meshes for shape analysis tasks employ traditional attention layers that heavily utilize spectral features requiring costly eigenvalue decomposition-based methods. To encode the mesh structure, these methods derive positional embeddings, that heavily rely on eigenvalue decomposition based operations, e.g. on the Laplacian matrix, or on heat-kernel signatures, which are then concatenated to the input features. This paper proposes a novel approach inspired by the explicit construction of the Hodge Laplacian operator in Discrete Exterior Calculus as a product of discrete Hodge operators and exterior derivatives, i.e. (L := star_0^{-1} d_0^T star_1 d_0). We adjust the Transformer architecture in a novel deep learning layer that utilizes the multi-head attention mechanism to approximate Hodge matrices star_0, star_1 and star_2 and learn families of discrete operators L that act on mesh vertices, edges and faces. Our approach results in a computationally-efficient architecture that achieves comparable performance in mesh segmentation and classification tasks, through a direct learning framework, while eliminating the need for costly eigenvalue decomposition operations or complex preprocessing operations.

While the harmonic function solution performs well in many semi-supervised learning (SSL) tasks, it is known to scale poorly with the number of samples. Recent successful and scalable methods, such as the eigenfunction method focus on efficiently approximating the whole spectrum of the graph Laplacian constructed from the data. This is in contrast to various subsampling and quantization methods proposed in the past, which may fail in preserving the graph spectra. However, the impact of the approximation of the spectrum on the final generalization error is either unknown, or requires strong assumptions on the data. In this paper, we introduce Sparse-HFS, an efficient edge-sparsification algorithm for SSL. By constructing an edge-sparse and spectrally similar graph, we are able to leverage the approximation guarantees of spectral sparsification methods to bound the generalization error of Sparse-HFS. As a result, we obtain a theoretically-grounded approximation scheme for graph-based SSL that also empirically matches the performance of known large-scale methods.

The push to train ever larger neural networks has motivated the study of initialization and training at large network width. A key challenge is to scale training so that a network's internal representations evolve nontrivially at all widths, a process known as feature learning. Here, we show that feature learning is achieved by scaling the spectral norm of weight matrices and their updates like texttt{fan-out/fan-in}, in contrast to widely used but heuristic scalings based on Frobenius norm and entry size. Our spectral scaling analysis also leads to an elementary derivation of maximal update parametrization. All in all, we aim to provide the reader with a solid conceptual understanding of feature learning in neural networks.

This work studies the generalization issue of face anti-spoofing (FAS) models on domain gaps, such as image resolution, blurriness and sensor variations. Most prior works regard domain-specific signals as a negative impact, and apply metric learning or adversarial losses to remove them from feature representation. Though learning a domain-invariant feature space is viable for the training data, we show that the feature shift still exists in an unseen test domain, which backfires on the generalizability of the classifier. In this work, instead of constructing a domain-invariant feature space, we encourage domain separability while aligning the live-to-spoof transition (i.e., the trajectory from live to spoof) to be the same for all domains. We formulate this FAS strategy of separability and alignment (SA-FAS) as a problem of invariant risk minimization (IRM), and learn domain-variant feature representation but domain-invariant classifier. We demonstrate the effectiveness of SA-FAS on challenging cross-domain FAS datasets and establish state-of-the-art performance.

Handling out-of-distribution samples is a long-lasting challenge for deep visual models. In particular, domain generalization (DG) is one of the most relevant tasks that aims to train a model with a generalization capability on novel domains. Most existing DG approaches share the same philosophy to minimize the discrepancy between domains by finding the domain-invariant representations. On the contrary, our proposed method called POEM acquires a strong DG capability by learning domain-invariant and domain-specific representations and polarizing them. Specifically, POEM cotrains category-classifying and domain-classifying embeddings while regularizing them to be orthogonal via minimizing the cosine-similarity between their features, i.e., the polarization of embeddings. The clear separation of embeddings suppresses domain-specific features in the domain-invariant embeddings. The concept of POEM shows a unique direction to enhance the domain robustness of representations that brings considerable and consistent performance gains when combined with existing DG methods. Extensive simulation results in popular DG benchmarks with the PACS, VLCS, OfficeHome, TerraIncognita, and DomainNet datasets show that POEM indeed facilitates the category-classifying embedding to be more domain-invariant.

Spectral imaging offers promising applications across diverse domains, including medicine and urban scene understanding, and is already established as a critical modality in remote sensing. However, variability in channel dimensionality and captured wavelengths among spectral cameras impede the development of AI-driven methodologies, leading to camera-specific models with limited generalizability and inadequate cross-camera applicability. To address this bottleneck, we introduce CARL, a model for Camera-Agnostic Representation Learning across RGB, multispectral, and hyperspectral imaging modalities. To enable the conversion of a spectral image with any channel dimensionality to a camera-agnostic representation, we introduce a novel spectral encoder, featuring a self-attention-cross-attention mechanism, to distill salient spectral information into learned spectral representations. Spatio-spectral pre-training is achieved with a novel feature-based self-supervision strategy tailored to CARL. Large-scale experiments across the domains of medical imaging, autonomous driving, and satellite imaging demonstrate our model's unique robustness to spectral heterogeneity, outperforming on datasets with simulated and real-world cross-camera spectral variations. The scalability and versatility of the proposed approach position our model as a backbone for future spectral foundation models. Code and model weights are publicly available at https://github.com/IMSY-DKFZ/CARL.

Polynomial filters, a kind of Graph Neural Networks, typically use a predetermined polynomial basis and learn the coefficients from the training data. It has been observed that the effectiveness of the model is highly dependent on the property of the polynomial basis. Consequently, two natural and fundamental questions arise: Can we learn a suitable polynomial basis from the training data? Can we determine the optimal polynomial basis for a given graph and node features? In this paper, we propose two spectral GNN models that provide positive answers to the questions posed above. First, inspired by Favard's Theorem, we propose the FavardGNN model, which learns a polynomial basis from the space of all possible orthonormal bases. Second, we examine the supposedly unsolvable definition of optimal polynomial basis from Wang & Zhang (2022) and propose a simple model, OptBasisGNN, which computes the optimal basis for a given graph structure and graph signal. Extensive experiments are conducted to demonstrate the effectiveness of our proposed models.

Hyperspectral image denoising is unique for the highly similar and correlated spectral information that should be properly considered. However, existing methods show limitations in exploring the spectral correlations across different bands and feature interactions within each band. Besides, the low- and high-level features usually exhibit different importance for different spatial-spectral regions, which is not fully explored for current algorithms as well. In this paper, we present a Mixed Attention Network (MAN) that simultaneously considers the inter- and intra-spectral correlations as well as the interactions between low- and high-level spatial-spectral meaningful features. Specifically, we introduce a multi-head recurrent spectral attention that efficiently integrates the inter-spectral features across all the spectral bands. These features are further enhanced with a progressive spectral channel attention by exploring the intra-spectral relationships. Moreover, we propose an attentive skip-connection that adaptively controls the proportion of the low- and high-level spatial-spectral features from the encoder and decoder to better enhance the aggregated features. Extensive experiments show that our MAN outperforms existing state-of-the-art methods on simulated and real noise settings while maintaining a low cost of parameters and running time.

We introduce a novel framework that directly learns a spectral basis for shape and manifold analysis from unstructured data, eliminating the need for traditional operator selection, discretization, and eigensolvers. Grounded in optimal-approximation theory, we train a network to decompose an implicit approximation operator by minimizing the reconstruction error in the learned basis over a chosen distribution of probe functions. For suitable distributions, they can be seen as an approximation of the Laplacian operator and its eigendecomposition, which are fundamental in geometry processing. Furthermore, our method recovers in a unified manner not only the spectral basis, but also the implicit metric's sampling density and the eigenvalues of the underlying operator. Notably, our unsupervised method makes no assumption on the data manifold, such as meshing or manifold dimensionality, allowing it to scale to arbitrary datasets of any dimension. On point clouds lying on surfaces in 3D and high-dimensional image manifolds, our approach yields meaningful spectral bases, that can resemble those of the Laplacian, without explicit construction of an operator. By replacing the traditional operator selection, construction, and eigendecomposition with a learning-based approach, our framework offers a principled, data-driven alternative to conventional pipelines. This opens new possibilities in geometry processing for unstructured data, particularly in high-dimensional spaces.

Plant traits such as leaf carbon content and leaf mass are essential variables in the study of biodiversity and climate change. However, conventional field sampling cannot feasibly cover trait variation at ecologically meaningful spatial scales. Machine learning represents a valuable solution for plant trait prediction across ecosystems, leveraging hyperspectral data from remote sensing. Nevertheless, trait prediction from hyperspectral data is challenged by label scarcity and substantial domain shifts (\eg across sensors, ecological distributions), requiring robust cross-domain methods. Here, we present GreenHyperSpectra, a pretraining dataset encompassing real-world cross-sensor and cross-ecosystem samples designed to benchmark trait prediction with semi- and self-supervised methods. We adopt an evaluation framework encompassing in-distribution and out-of-distribution scenarios. We successfully leverage GreenHyperSpectra to pretrain label-efficient multi-output regression models that outperform the state-of-the-art supervised baseline. Our empirical analyses demonstrate substantial improvements in learning spectral representations for trait prediction, establishing a comprehensive methodological framework to catalyze research at the intersection of representation learning and plant functional traits assessment. All code and data are available at: https://github.com/echerif18/HyspectraSSL.

The asymptotically precise estimation of the generalization of kernel methods has recently received attention due to the parallels between neural networks and their associated kernels. However, prior works derive such estimates for training by kernel ridge regression (KRR), whereas neural networks are typically trained with gradient descent (GD). In the present work, we consider the training of kernels with a family of spectral algorithms specified by profile h(lambda), and including KRR and GD as special cases. Then, we derive the generalization error as a functional of learning profile h(lambda) for two data models: high-dimensional Gaussian and low-dimensional translation-invariant model. Under power-law assumptions on the spectrum of the kernel and target, we use our framework to (i) give full loss asymptotics for both noisy and noiseless observations (ii) show that the loss localizes on certain spectral scales, giving a new perspective on the KRR saturation phenomenon (iii) conjecture, and demonstrate for the considered data models, the universality of the loss w.r.t. non-spectral details of the problem, but only in case of noisy observation.

The foundation model has recently garnered significant attention due to its potential to revolutionize the field of visual representation learning in a self-supervised manner. While most foundation models are tailored to effectively process RGB images for various visual tasks, there is a noticeable gap in research focused on spectral data, which offers valuable information for scene understanding, especially in remote sensing (RS) applications. To fill this gap, we created for the first time a universal RS foundation model, named SpectralGPT, which is purpose-built to handle spectral RS images using a novel 3D generative pretrained transformer (GPT). Compared to existing foundation models, SpectralGPT 1) accommodates input images with varying sizes, resolutions, time series, and regions in a progressive training fashion, enabling full utilization of extensive RS big data; 2) leverages 3D token generation for spatial-spectral coupling; 3) captures spectrally sequential patterns via multi-target reconstruction; 4) trains on one million spectral RS images, yielding models with over 600 million parameters. Our evaluation highlights significant performance improvements with pretrained SpectralGPT models, signifying substantial potential in advancing spectral RS big data applications within the field of geoscience across four downstream tasks: single/multi-label scene classification, semantic segmentation, and change detection.

Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general framework which unifies many existing GNN models from the view of parameterized decomposition and filtering, and show how it helps to enhance the flexibility of GNNs while alleviating the smoothness and amplification issues of existing models. Essentially, we show that the extensively studied spectral graph convolutions with learnable polynomial filters are constrained variants of this formulation, and releasing these constraints enables our model to express the desired decomposition and filtering simultaneously. Based on this generalized framework, we develop models that are simple in implementation but achieve significant improvements and computational efficiency on a variety of graph learning tasks. Code is available at https://github.com/qslim/PDF.

Advanced interpretation of hyperspectral remote sensing images benefits many precise Earth observation tasks. Recently, visual foundation models have promoted the remote sensing interpretation but concentrating on RGB and multispectral images. Due to the varied hyperspectral channels,existing foundation models would face image-by-image tuning situation, imposing great pressure on hardware and time resources. In this paper, we propose a tuning-free hyperspectral foundation model called HyperFree, by adapting the existing visual prompt engineering. To process varied channel numbers, we design a learned weight dictionary covering full-spectrum from 0.4 sim 2.5 , mum, supporting to build the embedding layer dynamically. To make the prompt design more tractable, HyperFree can generate multiple semantic-aware masks for one prompt by treating feature distance as semantic-similarity. After pre-training HyperFree on constructed large-scale high-resolution hyperspectral images, HyperFree (1 prompt) has shown comparable results with specialized models (5 shots) on 5 tasks and 11 datasets.Code and dataset are accessible at https://rsidea.whu.edu.cn/hyperfree.htm.

We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral coefficients. In contrast to current machine learning approaches which enforce PDE constraints by minimizing the numerical quadrature of the residuals in the spatiotemporal domain, we leverage Parseval's identity and introduce a new training strategy through a spectral loss. Our spectral loss enables more efficient differentiation through the neural network, and substantially reduces training complexity. At inference time, the computational cost of our method remains constant, regardless of the spatiotemporal resolution of the domain. Our experimental results demonstrate that our method significantly outperforms previous machine learning approaches in terms of speed and accuracy by one to two orders of magnitude on multiple different problems. When compared to numerical solvers of the same accuracy, our method demonstrates a 10times increase in performance speed.

Multi-spectral imagery plays a crucial role in diverse Remote Sensing applications including land-use classification, environmental monitoring and urban planning. These images are widely adopted because their additional spectral bands correlate strongly with physical materials on the ground, such as ice, water, and vegetation. This allows for more accurate identification, and their public availability from missions, such as Sentinel-2 and Landsat, only adds to their value. Currently, the automatic analysis of such data is predominantly managed through machine learning models specifically trained for multi-spectral input, which are costly to train and support. Furthermore, although providing a lot of utility for Remote Sensing, such additional inputs cannot be used with powerful generalist large multimodal models, which are capable of solving many visual problems, but are not able to understand specialized multi-spectral signals. To address this, we propose a training-free approach which introduces new multi-spectral data in a Zero-Shot-only mode, as inputs to generalist multimodal models, trained on RGB-only inputs. Our approach leverages the multimodal models' understanding of the visual space, and proposes to adapt to inputs to that space, and to inject domain-specific information as instructions into the model. We exemplify this idea with the Gemini2.5 model and observe strong Zero-Shot performance gains of the approach on popular Remote Sensing benchmarks for land cover and land use classification and demonstrate the easy adaptability of Gemini2.5 to new inputs. These results highlight the potential for geospatial professionals, working with non-standard specialized inputs, to easily leverage powerful multimodal models, such as Gemini2.5, to accelerate their work, benefiting from their rich reasoning and contextual capabilities, grounded in the specialized sensor data.

Accurate classification of hyperspectral imagery (HSI) is often frustrated by the tension between high-dimensional spectral data and the extreme scarcity of labeled training samples. While hierarchical models like LoLA-SpecViT have demonstrated the power of local windowed attention and parameter-efficient fine-tuning, the quadratic complexity of standard Transformers remains a barrier to scaling. We introduce VP-Hype, a framework that rethinks HSI classification by unifying the linear-time efficiency of State-Space Models (SSMs) with the relational modeling of Transformers in a novel hybrid architecture. Building on a robust 3D-CNN spectral front-end, VP-Hype replaces conventional attention blocks with a Hybrid Mamba-Transformer backbone to capture long-range dependencies with significantly reduced computational overhead. Furthermore, we address the label-scarcity problem by integrating dual-modal Visual and Textual Prompts that provide context-aware guidance for the feature extraction process. Our experimental evaluation demonstrates that VP-Hype establishes a new state of the art in low-data regimes. Specifically, with a training sample distribution of only 2\%, the model achieves Overall Accuracy (OA) of 99.69\% on the Salinas dataset and 99.45\% on the Longkou dataset. These results suggest that the convergence of hybrid sequence modeling and multi-modal prompting provides a robust path forward for high-performance, sample-efficient remote sensing.

Detecting fake images is becoming a major goal of computer vision. This need is becoming more and more pressing with the continuous improvement of synthesis methods based on Generative Adversarial Networks (GAN), and even more with the appearance of powerful methods based on Diffusion Models (DM). Towards this end, it is important to gain insight into which image features better discriminate fake images from real ones. In this paper we report on our systematic study of a large number of image generators of different families, aimed at discovering the most forensically relevant characteristics of real and generated images. Our experiments provide a number of interesting observations and shed light on some intriguing properties of synthetic images: (1) not only the GAN models but also the DM and VQ-GAN (Vector Quantized Generative Adversarial Networks) models give rise to visible artifacts in the Fourier domain and exhibit anomalous regular patterns in the autocorrelation; (2) when the dataset used to train the model lacks sufficient variety, its biases can be transferred to the generated images; (3) synthetic and real images exhibit significant differences in the mid-high frequency signal content, observable in their radial and angular spectral power distributions.

Time series data, characterized by its intrinsic long and short-range dependencies, poses a unique challenge across analytical applications. While Transformer-based models excel at capturing long-range dependencies, they face limitations in noise sensitivity, computational efficiency, and overfitting with smaller datasets. In response, we introduce a novel Time Series Lightweight Adaptive Network (TSLANet), as a universal convolutional model for diverse time series tasks. Specifically, we propose an Adaptive Spectral Block, harnessing Fourier analysis to enhance feature representation and to capture both long-term and short-term interactions while mitigating noise via adaptive thresholding. Additionally, we introduce an Interactive Convolution Block and leverage self-supervised learning to refine the capacity of TSLANet for decoding complex temporal patterns and improve its robustness on different datasets. Our comprehensive experiments demonstrate that TSLANet outperforms state-of-the-art models in various tasks spanning classification, forecasting, and anomaly detection, showcasing its resilience and adaptability across a spectrum of noise levels and data sizes. The code is available at https://github.com/emadeldeen24/TSLANet

We propose a novel spectral generative modeling framework for natural language processing that jointly learns a global time varying Fourier dictionary and per token mixing coefficients, replacing the ubiquitous self attention mechanism in transformer architectures. By enforcing reconstruction losses in both the time domain (embedding reconstruction) and the frequency domain (via Short Time Fourier Transform magnitude matching) alongside a standard language modeling objective, and fitting a Gaussian Mixture Model (GMM) prior over the learned mixing vectors, our approach achieves competitive perplexity and generation quality on standard benchmarks such as WikiText2 and Penn Treebank. In contrast to the quadratic computation complexity of self attention, our method operates with linear complexity, delivering substantial efficiency gains. We demonstrate that spectral dictionary models can achieve competitive performance compared to transformer baselines while significantly reducing inference latency and memory footprint, offering a compelling alternative for scalable language modeling.

With the advent of new spectroscopic surveys from ground and space, observing up to hundreds of millions of galaxies, spectra classification will become overwhelming for standard analysis techniques. To prepare for this challenge, we introduce a family of deep learning tools to classify features in one-dimensional spectra. As the first application of these Galaxy Spectra neural Networks (GaSNets), we focus on tools specialized at identifying emission lines from strongly lensed star-forming galaxies in the eBOSS spectra. We first discuss the training and testing of these networks and define a threshold probability, PL, of 95% for the high quality event detection. Then, using a previous set of spectroscopically selected strong lenses from eBOSS, confirmed with HST, we estimate a completeness of ~80% as the fraction of lenses recovered above the adopted PL. We finally apply the GaSNets to ~1.3M spectra to collect a first list of ~430 new high quality candidates identified with deep learning applied to spectroscopy and visually graded as highly probable real events. A preliminary check against ground-based observations tentatively shows that this sample has a confirmation rate of 38%, in line with previous samples selected with standard (no deep learning) classification tools and follow-up by Hubble Space Telescope. This first test shows that machine learning can be efficiently extended to feature recognition in the wavelength space, which will be crucial for future surveys like 4MOST, DESI, Euclid, and the Chinese Space Station Telescope (CSST).

Hyperspectral object tracking using snapshot mosaic cameras is emerging as it provides enhanced spectral information alongside spatial data, contributing to a more comprehensive understanding of material properties. Using transformers, which have consistently outperformed convolutional neural networks (CNNs) in learning better feature representations, would be expected to be effective for Hyperspectral object tracking. However, training large transformers necessitates extensive datasets and prolonged training periods. This is particularly critical for complex tasks like object tracking, and the scarcity of large datasets in the hyperspectral domain acts as a bottleneck in achieving the full potential of powerful transformer models. This paper proposes an effective methodology that adapts large pretrained transformer-based foundation models for hyperspectral object tracking. We propose an adaptive, learnable spatial-spectral token fusion module that can be extended to any transformer-based backbone for learning inherent spatial-spectral features in hyperspectral data. Furthermore, our model incorporates a cross-modality training pipeline that facilitates effective learning across hyperspectral datasets collected with different sensor modalities. This enables the extraction of complementary knowledge from additional modalities, whether or not they are present during testing. Our proposed model also achieves superior performance with minimal training iterations.

Entropy and mutual information in neural networks provide rich information on the learning process, but they have proven difficult to compute reliably in high dimensions. Indeed, in noisy and high-dimensional data, traditional estimates in ambient dimensions approach a fixed entropy and are prohibitively hard to compute. To address these issues, we leverage data geometry to access the underlying manifold and reliably compute these information-theoretic measures. Specifically, we define diffusion spectral entropy (DSE) in neural representations of a dataset as well as diffusion spectral mutual information (DSMI) between different variables representing data. First, we show that they form noise-resistant measures of intrinsic dimensionality and relationship strength in high-dimensional simulated data that outperform classic Shannon entropy, nonparametric estimation, and mutual information neural estimation (MINE). We then study the evolution of representations in classification networks with supervised learning, self-supervision, or overfitting. We observe that (1) DSE of neural representations increases during training; (2) DSMI with the class label increases during generalizable learning but stays stagnant during overfitting; (3) DSMI with the input signal shows differing trends: on MNIST it increases, while on CIFAR-10 and STL-10 it decreases. Finally, we show that DSE can be used to guide better network initialization and that DSMI can be used to predict downstream classification accuracy across 962 models on ImageNet. The official implementation is available at https://github.com/ChenLiu-1996/DiffusionSpectralEntropy.

Domain Generalization (DG) is a critical area that focuses on developing models capable of performing well on data from unseen distributions, which is essential for real-world applications. Existing approaches primarily concentrate on learning domain-invariant features, which assume that a model robust to variations in the source domains will generalize well to unseen target domains. However, these approaches neglect a deeper analysis at the parameter level, which makes the model hard to explicitly differentiate between parameters sensitive to domain shifts and those robust, potentially hindering its overall ability to generalize. In order to address these limitations, we first build a covariance-based parameter sensitivity analysis framework to quantify the sensitivity of each parameter in a model to domain shifts. By computing the covariance of parameter gradients across multiple source domains, we can identify parameters that are more susceptible to domain variations, which serves as our theoretical foundation. Based on this, we propose Domain-Sensitive Parameter Regularization (DSP-Reg), a principled framework that guides model optimization by a soft regularization technique that encourages the model to rely more on domain-invariant parameters while suppressing those that are domain-specific. This approach provides a more granular control over the model's learning process, leading to improved robustness and generalization to unseen domains. Extensive experiments on benchmarks, such as PACS, VLCS, OfficeHome, and DomainNet, demonstrate that DSP-Reg outperforms state-of-the-art approaches, achieving an average accuracy of 66.7\% and surpassing all baselines.

Hyperspectral image classification remains a challenging task due to the high dimensionality of spectral data, significant inter-band redundancy, and the limited availability of annotated samples. While recent transformer-based models have improved the global modeling of spectral-spatial dependencies, their scalability and adaptability under label-scarce conditions remain limited. In this work, we propose LoLA-SpecViT(Low-rank adaptation Local Attention Spectral Vision Transformer), a lightweight spectral vision transformer that addresses these limitations through a parameter-efficient architecture tailored to the unique characteristics of hyperspectral imagery. Our model combines a 3D convolutional spectral front-end with local window-based self-attention, enhancing both spectral feature extraction and spatial consistency while reducing computational complexity. To further improve adaptability, we integrate low-rank adaptation (LoRA) into attention and projection layers, enabling fine-tuning with over 80\% fewer trainable parameters. A novel cyclical learning rate scheduler modulates LoRA adaptation strength during training, improving convergence and generalisation. Extensive experiments on three benchmark datasets WHU-Hi LongKou, WHU-Hi HongHu, and Salinas demonstrate that LoLA-SpecViT consistently outperforms state-of-the-art baselines, achieving up to 99.91\% accuracy with substantially fewer parameters and enhanced robustness under low-label regimes. The proposed framework provides a scalable and generalizable solution for real-world HSI applications in agriculture, environmental monitoring, and remote sensing analytics. Our code is available in the following https://github.com/FadiZidiDz/LoLA-SpecViT{GitHub Repository}.

Recent advances in vision-language models (VLMs) have demonstrated remarkable zero-shot capabilities, yet adapting these models to specialized domains remains a significant challenge. Building on recent theoretical insights suggesting that independently trained VLMs are related by a canonical transformation, we extend this understanding to the concept of domains. We hypothesize that image features across disparate domains are related by a canonicalized geometric transformation that can be recovered using a small set of anchors. Few-shot classification provides a natural setting for this alignment, as the limited labeled samples serve as the anchors required to estimate this transformation. Motivated by this hypothesis, we introduce BiCLIP, a framework that applies a targeted transformation to multimodal features to enhance cross-modal alignment. Our approach is characterized by its extreme simplicity and low parameter footprint. Extensive evaluations across 11 standard benchmarks, including EuroSAT, DTD, and FGVCAircraft, demonstrate that BiCLIP consistently achieves state-of-the-art results. Furthermore, we provide empirical verification of existing geometric findings by analyzing the orthogonality and angular distribution of the learned transformations, confirming that structured alignment is the key to robust domain adaptation. Code is available at https://github.com/QuantitativeImagingLaboratory/BilinearCLIP

In recent years, the emergence of Transformers with self-attention mechanism has revolutionized the hyperspectral image (HSI) classification. However, these models face major challenges in computational efficiency, as their complexity increases quadratically with the sequence length. The Mamba architecture, leveraging a state space model (SSM), offers a more efficient alternative to Transformers. This paper introduces the Spatial-Spectral Morphological Mamba (MorpMamba) model in which, a token generation module first converts the HSI patch into spatial-spectral tokens. These tokens are then processed by morphological operations, which compute structural and shape information using depthwise separable convolutional operations. The extracted information is enhanced in a feature enhancement module that adjusts the spatial and spectral tokens based on the center region of the HSI sample, allowing for effective information fusion within each block. Subsequently, the tokens are refined through a multi-head self-attention which further improves the feature space. Finally, the combined information is fed into the state space block for classification and the creation of the ground truth map. Experiments on widely used HSI datasets demonstrate that the MorpMamba model outperforms (parametric efficiency) both CNN and Transformer models. The source code will be made publicly available at https://github.com/MHassaanButt/MorpMamba.

Hyperspectral images (HSIs) often suffer from diverse and unknown degradations during imaging, leading to severe spectral and spatial distortions. Existing HSI restoration methods typically rely on specific degradation assumptions, limiting their effectiveness in complex scenarios. In this paper, we propose MP-HSIR, a novel multi-prompt framework that effectively integrates spectral, textual, and visual prompts to achieve universal HSI restoration across diverse degradation types and intensities. Specifically, we develop a prompt-guided spatial-spectral transformer, which incorporates spatial self-attention and a prompt-guided dual-branch spectral self-attention. Since degradations affect spectral features differently, we introduce spectral prompts in the local spectral branch to provide universal low-rank spectral patterns as prior knowledge for enhancing spectral reconstruction. Furthermore, the text-visual synergistic prompt fuses high-level semantic representations with fine-grained visual features to encode degradation information, thereby guiding the restoration process. Extensive experiments on 9 HSI restoration tasks, including all-in-one scenarios, generalization tests, and real-world cases, demonstrate that MP-HSIR not only consistently outperforms existing all-in-one methods but also surpasses state-of-the-art task-specific approaches across multiple tasks. The code and models will be released at https://github.com/ZhehuiWu/MP-HSIR.

This work studies Hyperspectral image (HSI) super-resolution (SR). HSI SR is characterized by high-dimensional data and a limited amount of training examples. This exacerbates the undesirable behaviors of neural networks such as memorization and sensitivity to out-of-distribution samples. This work addresses these issues with three contributions. First, we observe that HSI SR and RGB image SR are correlated and develop a novel multi-tasking network to train them jointly so that the auxiliary task RGB image SR can provide additional supervision. Second, we propose a simple, yet effective data augmentation routine, termed Spectral Mixup, to construct effective virtual training samples to enlarge the training set. Finally, we extend the network to a semi-supervised setting so that it can learn from datasets containing only low-resolution HSIs. With these contributions, our method is able to learn from heterogeneous datasets and lift the requirement for having a large amount of HD HSI training samples. Extensive experiments on four standard datasets show that our method outperforms existing methods significantly and underpin the relevance of our contributions. Code has been made available at https://github.com/kli8996/HSISR.

Cross-Domain Few-Shot Object Detection (CD-FSOD) aims to detect novel objects with only a handful of labeled samples from previously unseen domains. While data augmentation and generative methods have shown promise in few-shot learning, their effectiveness for CD-FSOD remains unclear due to the need for both visual realism and domain alignment. Existing strategies, such as copy-paste augmentation and text-to-image generation, often fail to preserve the correct object category or produce backgrounds coherent with the target domain, making them non-trivial to apply directly to CD-FSOD. To address these challenges, we propose Domain-RAG, a training-free, retrieval-guided compositional image generation framework tailored for CD-FSOD. Domain-RAG consists of three stages: domain-aware background retrieval, domain-guided background generation, and foreground-background composition. Specifically, the input image is first decomposed into foreground and background regions. We then retrieve semantically and stylistically similar images to guide a generative model in synthesizing a new background, conditioned on both the original and retrieved contexts. Finally, the preserved foreground is composed with the newly generated domain-aligned background to form the generated image. Without requiring any additional supervision or training, Domain-RAG produces high-quality, domain-consistent samples across diverse tasks, including CD-FSOD, remote sensing FSOD, and camouflaged FSOD. Extensive experiments show consistent improvements over strong baselines and establish new state-of-the-art results. Codes will be released upon acceptance.

In hyperspectral image classification (HSIC), most deep learning models rely on opaque spectral-spatial feature mixing, limiting their interpretability and hindering understanding of internal decision mechanisms. We present physical spectrum-aware white-box mHC, named ES-mHC, a hyper-connection framework that explicitly models interactions among different electromagnetic spectrum groupings (residual stream in mHC) interactions using structured, directional matrices. By separating feature representation from interaction structure, ES-mHC promotes electromagnetic spectrum grouping specialization, reduces redundancy, and exposes internal information flow that can be directly visualized and spatially analyzed. Using hyperspectral image classification as a representative testbed, we demonstrate that the learned hyper-connection matrices exhibit coherent spatial patterns and asymmetric interaction behaviors, providing mechanistic insight into the model internal dynamics. Furthermore, we find that increasing the expansion rate accelerates the emergence of structured interaction patterns. These results suggest that ES-mHC transforms HSIC from a purely black-box prediction task into a structurally transparent, partially white-box learning process.

While spectral-based optimizers like Muon operate directly on the spectrum of updates, standard adaptive methods such as AdamW do not account for the global spectral structure of weights and gradients, leaving them vulnerable to two empirical issues in large language model (LLM) training: (i) the optimizer updates can have large spectral norms, potentially destabilizing training and degrading generalization; (ii) stochastic gradient noise can exhibit sparse spectral spikes, with a few dominant singular values much larger than the rest. We propose SPECTRA, a general framework addressing these by (i) post-spectral clipping of updates to enforce spectral-norm constraints; (ii) optional pre-spectral clipping of gradients to suppress spectral noise spikes. We prove that post-clipping constitutes a Composite Frank-Wolfe method with spectral-norm constraints and weight regularization, recovering Frobenius and ell_{infty}-norm regularization with SGD-based and sign-based methods. We further analyze how pre-clipping mitigates sparse spectral spikes. We propose efficient soft spectral clipping via Newton-Schulz iterations, avoiding expensive SVD. Experiments on LLM pretraining show SPECTRA uniformly improves validation loss for various optimizers, including AdamW, Signum, and AdEMAMix, with the best-performing variants achieving state-of-the-art results. Models trained with SPECTRA exhibit smaller weight norms, confirming the link between spectral clipping and regularization.

Single hyperspectral image super-resolution (single-HSI-SR) aims to restore a high-resolution hyperspectral image from a low-resolution observation. However, the prevailing CNN-based approaches have shown limitations in building long-range dependencies and capturing interaction information between spectral features. This results in inadequate utilization of spectral information and artifacts after upsampling. To address this issue, we propose ESSAformer, an ESSA attention-embedded Transformer network for single-HSI-SR with an iterative refining structure. Specifically, we first introduce a robust and spectral-friendly similarity metric, \ie, the spectral correlation coefficient of the spectrum (SCC), to replace the original attention matrix and incorporates inductive biases into the model to facilitate training. Built upon it, we further utilize the kernelizable attention technique with theoretical support to form a novel efficient SCC-kernel-based self-attention (ESSA) and reduce attention computation to linear complexity. ESSA enlarges the receptive field for features after upsampling without bringing much computation and allows the model to effectively utilize spatial-spectral information from different scales, resulting in the generation of more natural high-resolution images. Without the need for pretraining on large-scale datasets, our experiments demonstrate ESSA's effectiveness in both visual quality and quantitative results.

In this paper, we study the diffusability (learnability) of variational autoencoders (VAE) in latent diffusion. First, we show that pixel-space diffusion trained with an MSE objective is inherently biased toward learning low and mid spatial frequencies, and that the power-law power spectral density (PSD) of natural images makes this bias perceptually beneficial. Motivated by this result, we propose the Spectrum Matching Hypothesis: latents with superior diffusability should (i) follow a flattened power-law PSD (Encoding Spectrum Matching, ESM) and (ii) preserve frequency-to-frequency semantic correspondence through the decoder (Decoding Spectrum Matching, DSM). In practice, we apply ESM by matching the PSD between images and latents, and DSM via shared spectral masking with frequency-aligned reconstruction. Importantly, Spectrum Matching provides a unified view that clarifies prior observations of over-noisy or over-smoothed latents, and interprets several recent methods as special cases (e.g., VA-VAE, EQ-VAE). Experiments suggest that Spectrum Matching yields superior diffusion generation on CelebA and ImageNet datasets, and outperforms prior approaches. Finally, we extend the spectral view to representation alignment (REPA): we show that the directional spectral energy of the target representation is crucial for REPA, and propose a DoG-based method to further improve the performance of REPA. Our code is available https://github.com/forever208/SpectrumMatching.

Automated polyp segmentation is essential for early diagnosis of colorectal cancer, yet developing robust models remains challenging due to limited annotated data and significant performance degradation under domain shift. Although semi-supervised learning (SSL) reduces annotation requirements, existing methods rely on generic augmentations that ignore polyp-specific structural properties, resulting in poor generalization to new imaging centers and devices. To address this, we introduce Frequency Prior Guided Matching (FPGM), a novel augmentation framework built on a key discovery: polyp edges exhibit a remarkably consistent frequency signature across diverse datasets. FPGM leverages this intrinsic regularity in a two-stage process. It first learns a domain-invariant frequency prior from the edge regions of labeled polyps. Then, it performs principled spectral perturbations on unlabeled images, aligning their amplitude spectra with this learned prior while preserving phase information to maintain structural integrity. This targeted alignment normalizes domain-specific textural variations, thereby compelling the model to learn the underlying, generalizable anatomical structure. Validated on six public datasets, FPGM establishes a new state-of-the-art against ten competing methods. It demonstrates exceptional zero-shot generalization capabilities, achieving over 10% absolute gain in Dice score in data-scarce scenarios. By significantly enhancing cross-domain robustness, FPGM presents a powerful solution for clinically deployable polyp segmentation under limited supervision.

The Invariant Risk Minimization (IRM) principle was first proposed by Arjovsky et al. [2019] to address the domain generalization problem by leveraging data heterogeneity from differing experimental conditions. Specifically, IRM seeks to find a data representation under which an optimal classifier remains invariant across all domains. Despite the conceptual appeal of IRM, the effectiveness of the originally proposed invariance penalty has recently been brought into question. In particular, there exists counterexamples for which that invariance penalty can be arbitrarily small for non-invariant data representations. We propose an alternative invariance penalty by revisiting the Gramian matrix of the data representation. We discuss the role of its eigenvalues in the relationship between the risk and the invariance penalty, and demonstrate that it is ill-conditioned for said counterexamples. The proposed approach is guaranteed to recover an invariant representation for linear settings under mild non-degeneracy conditions. Its effectiveness is substantiated by experiments on DomainBed and InvarianceUnitTest, two extensive test beds for domain generalization.

Non-linear activation functions are crucial in Convolutional Neural Networks. However, until now they have not been well described in the frequency domain. In this work, we study the spectral behavior of ReLU, a popular activation function. We use the ReLU's Taylor expansion to derive its frequency domain behavior. We demonstrate that ReLU introduces higher frequency oscillations in the signal and a constant DC component. Furthermore, we investigate the importance of this DC component, where we demonstrate that it helps the model extract meaningful features related to the input frequency content. We accompany our theoretical derivations with experiments and real-world examples. First, we numerically validate our frequency response model. Then we observe ReLU's spectral behavior on two example models and a real-world one. Finally, we experimentally investigate the role of the DC component introduced by ReLU in the CNN's representations. Our results indicate that the DC helps to converge to a weight configuration that is close to the initial random weights.

Large language models and deep neural networks achieve strong performance but suffer from reliability issues and high computational cost. This thesis proposes a unified framework based on spectral geometry and random matrix theory to address both problems by analyzing the eigenvalue structure of hidden activations. The first contribution, EigenTrack, is a real-time method for detecting hallucinations and out-of-distribution behavior in language and vision-language models using spectral features and their temporal dynamics. The second contribution, RMT-KD, is a principled compression method that identifies informative spectral components and applies iterative knowledge distillation to produce compact and efficient models while preserving accuracy. Together, these results show that spectral statistics provide interpretable and robust signals for monitoring uncertainty and guiding compression in large-scale neural networks.

In this paper we introduce Feature Gradients, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e., in mini-batches) and in linear time and space with respect to both the number of features D and the sample size N . This, along with a discrete-to-continuous relaxation of the search domain, allows for an efficient, gradient-based search algorithm among feature subsets for very large datasets. Crucially, our algorithm is capable of finding higher-order correlations between features and targets for both the N > D and N < D regimes, as opposed to approaches that do not consider such interactions and/or only consider one regime. We provide experimental demonstration of the algorithm in small and large sample-and feature-size settings.

We propose a fully spectral, neuro\-symbolic reasoning architecture that leverages Graph Signal Processing (GSP) as the primary computational backbone for integrating symbolic logic and neural inference. Unlike conventional reasoning models that treat spectral graph methods as peripheral components, our approach formulates the entire reasoning pipeline in the graph spectral domain. Logical entities and relationships are encoded as graph signals, processed via learnable spectral filters that control multi-scale information propagation, and mapped into symbolic predicates for rule-based inference. We present a complete mathematical framework for spectral reasoning, including graph Fourier transforms, band-selective attention, and spectral rule grounding. Experiments on benchmark reasoning datasets (ProofWriter, EntailmentBank, bAbI, CLUTRR, and ARC-Challenge) demonstrate improvements in logical consistency, interpretability, and computational efficiency over state\-of\-the\-art neuro\-symbolic models. Our results suggest that GSP provides a mathematically grounded and computationally efficient substrate for robust and interpretable reasoning systems.

Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored the multiscale architectures and various operator designs, they are limited to learning the operators as a whole in the coordinate space. In real physical science problems, PDEs are complex coupled equations with numerical solvers relying on discretization into high-dimensional coordinate space, which cannot be precisely approximated by a single operator nor efficiently learned due to the curse of dimensionality. We present Latent Spectral Models (LSM) toward an efficient and precise solver for high-dimensional PDEs. Going beyond the coordinate space, LSM enables an attention-based hierarchical projection network to reduce the high-dimensional data into a compact latent space in linear time. Inspired by classical spectral methods in numerical analysis, we design a neural spectral block to solve PDEs in the latent space that approximates complex input-output mappings via learning multiple basis operators, enjoying nice theoretical guarantees for convergence and approximation. Experimentally, LSM achieves consistent state-of-the-art and yields a relative gain of 11.5% averaged on seven benchmarks covering both solid and fluid physics. Code is available at https://github.com/thuml/Latent-Spectral-Models.

Deep functional maps have recently emerged as a powerful tool for solving non-rigid shape correspondence tasks. Methods that use this approach combine the power and flexibility of the functional map framework, with data-driven learning for improved accuracy and generality. However, most existing methods in this area restrict the learning aspect only to the feature functions and still rely on axiomatic modeling for formulating the training loss or for functional map regularization inside the networks. This limits both the accuracy and the applicability of the resulting approaches only to scenarios where assumptions of the axiomatic models hold. In this work, we show, for the first time, that both in-network regularization and functional map training can be replaced with data-driven methods. For this, we first train a generative model of functional maps in the spectral domain using score-based generative modeling, built from a large collection of high-quality maps. We then exploit the resulting model to promote the structural properties of ground truth functional maps on new shape collections. Remarkably, we demonstrate that the learned models are category-agnostic, and can fully replace commonly used strategies such as enforcing Laplacian commutativity or orthogonality of functional maps. Our key technical contribution is a novel distillation strategy from diffusion models in the spectral domain. Experiments demonstrate that our learned regularization leads to better results than axiomatic approaches for zero-shot non-rigid shape matching. Our code is available at: https://github.com/daidedou/diffumatch/

Molecular structure elucidation from spectra is a foundational problem in chemistry, with profound implications for compound identification, synthesis, and drug development. Traditional methods rely heavily on expert interpretation and lack scalability. Pioneering machine learning methods have introduced retrieval-based strategies, but their reliance on finite libraries limits generalization to novel molecules. Generative models offer a promising alternative, yet most adopt autoregressive SMILES-based architectures that overlook 3D geometry and struggle to integrate diverse spectral modalities. In this work, we present DiffSpectra, a generative framework that directly infers both 2D and 3D molecular structures from multi-modal spectral data using diffusion models. DiffSpectra formulates structure elucidation as a conditional generation process. Its denoising network is parameterized by Diffusion Molecule Transformer, an SE(3)-equivariant architecture that integrates topological and geometric information. Conditioning is provided by SpecFormer, a transformer-based spectral encoder that captures intra- and inter-spectral dependencies from multi-modal spectra. Extensive experiments demonstrate that DiffSpectra achieves high accuracy in structure elucidation, recovering exact structures with 16.01% top-1 accuracy and 96.86% top-20 accuracy through sampling. The model benefits significantly from 3D geometric modeling, SpecFormer pre-training, and multi-modal conditioning. These results highlight the effectiveness of spectrum-conditioned diffusion modeling in addressing the challenge of molecular structure elucidation. To our knowledge, DiffSpectra is the first framework to unify multi-modal spectral reasoning and joint 2D/3D generative modeling for de novo molecular structure elucidation.

This work introduces ILIAS, a new test dataset for Instance-Level Image retrieval At Scale. It is designed to evaluate the ability of current and future foundation models and retrieval techniques to recognize particular objects. The key benefits over existing datasets include large scale, domain diversity, accurate ground truth, and a performance that is far from saturated. ILIAS includes query and positive images for 1,000 object instances, manually collected to capture challenging conditions and diverse domains. Large-scale retrieval is conducted against 100 million distractor images from YFCC100M. To avoid false negatives without extra annotation effort, we include only query objects confirmed to have emerged after 2014, i.e. the compilation date of YFCC100M. An extensive benchmarking is performed with the following observations: i) models fine-tuned on specific domains, such as landmarks or products, excel in that domain but fail on ILIAS ii) learning a linear adaptation layer using multi-domain class supervision results in performance improvements, especially for vision-language models iii) local descriptors in retrieval re-ranking are still a key ingredient, especially in the presence of severe background clutter iv) the text-to-image performance of the vision-language foundation models is surprisingly close to the corresponding image-to-image case. website: https://vrg.fel.cvut.cz/ilias/

Time series classification (TSC) on multivariate time series is a critical problem. We propose a novel multi-view approach integrating frequency-domain and time-domain features to provide complementary contexts for TSC. Our method fuses continuous wavelet transform spectral features with temporal convolutional or multilayer perceptron features. We leverage the Mamba state space model for efficient and scalable sequence modeling. We also introduce a novel tango scanning scheme to better model sequence relationships. Experiments on 10 standard benchmark datasets demonstrate our approach achieves an average 6.45% accuracy improvement over state-of-the-art TSC models.

Hyperspectral images (HSI) provide rich spectral information that contributed to the successful performance improvement of numerous computer vision tasks. However, it can only be achieved at the expense of images' spatial resolution. Hyperspectral image super-resolution (HSI-SR) addresses this problem by fusing low resolution (LR) HSI with multispectral image (MSI) carrying much higher spatial resolution (HR). All existing HSI-SR approaches require the LR HSI and HR MSI to be well registered and the reconstruction accuracy of the HR HSI relies heavily on the registration accuracy of different modalities. This paper exploits the uncharted problem domain of HSI-SR without the requirement of multi-modality registration. Given the unregistered LR HSI and HR MSI with overlapped regions, we design a unique unsupervised learning structure linking the two unregistered modalities by projecting them into the same statistical space through the same encoder. The mutual information (MI) is further adopted to capture the non-linear statistical dependencies between the representations from two modalities (carrying spatial information) and their raw inputs. By maximizing the MI, spatial correlations between different modalities can be well characterized to further reduce the spectral distortion. A collaborative l_{2,1} norm is employed as the reconstruction error instead of the more common l_2 norm, so that individual pixels can be recovered as accurately as possible. With this design, the network allows to extract correlated spectral and spatial information from unregistered images that better preserves the spectral information. The proposed method is referred to as unregistered and unsupervised mutual Dirichlet Net (u^2-MDN). Extensive experimental results using benchmark HSI datasets demonstrate the superior performance of u^2-MDN as compared to the state-of-the-art.

We present a machine sound dataset to benchmark domain generalization techniques for anomalous sound detection (ASD). Domain shifts are differences in data distributions that can degrade the detection performance, and handling them is a major issue for the application of ASD systems. While currently available datasets for ASD tasks assume that occurrences of domain shifts are known, in practice, they can be difficult to detect. To handle such domain shifts, domain generalization techniques that perform well regardless of the domains should be investigated. In this paper, we present the first ASD dataset for the domain generalization techniques, called MIMII DG. The dataset consists of five machine types and three domain shift scenarios for each machine type. The dataset is dedicated to the domain generalization task with features such as multiple different values for parameters that cause domain shifts and introduction of domain shifts that can be difficult to detect, such as shifts in the background noise. Experimental results using two baseline systems indicate that the dataset reproduces domain shift scenarios and is useful for benchmarking domain generalization techniques.

Geospatial raster data, such as that collected by satellite-based imaging systems at different times and spectral bands, hold immense potential for enabling a wide range of high-impact applications. This potential stems from the rich information that is spatially and temporally contextualized across multiple channels and sensing modalities. Recent work has adapted existing self-supervised learning approaches for such geospatial data. However, they fall short of scalable model architectures, leading to inflexibility and computational inefficiencies when faced with an increasing number of channels and modalities. To address these limitations, we introduce Low-rank Efficient Spatial-Spectral Vision Transformer with three key innovations: i) the LESS Attention Block that approximates high-dimensional spatial-spectral attention through Kronecker's product of the low-dimensional spatial and spectral attention components; ii) the Continuous Positional-Channel Embedding Layer that preserves both the continuity and physical characteristics of each spatial-spectral patch; and iii) the Perception Field Mask that exploits local spatial dependencies by constraining attention to neighboring patches. To evaluate the proposed innovations, we construct GFM-Bench, which serves as a comprehensive benchmark for such geospatial raster data. We pretrain LESS ViT using a Hyperspectral Masked Autoencoder framework with integrated positional and channel masking strategies. Experimental results demonstrate that our proposed method achieves competitive performance against state-of-the-art multi-modal geospatial foundation models while outperforming them on cross-satellite generalization tasks with higher computational efficiency. The flexibility and extensibility of our framework make it a promising direction for future geospatial data analysis tasks that involve a wide range of modalities and channels.

Deep representations across modalities are inherently intertwined. In this paper, we systematically analyze the spectral characteristics of various semantic and pixel encoders. Interestingly, our study uncovers a highly inspiring and rarely explored correspondence between an encoder's feature spectrum and its functional role: semantic encoders primarily capture low-frequency components that encode abstract meaning, whereas pixel encoders additionally retain high-frequency information that conveys fine-grained detail. This heuristic finding offers a unifying perspective that ties encoder behavior to its underlying spectral structure. We define it as the Prism Hypothesis, where each data modality can be viewed as a projection of the natural world onto a shared feature spectrum, just like the prism. Building on this insight, we propose Unified Autoencoding (UAE), a model that harmonizes semantic structure and pixel details via an innovative frequency-band modulator, enabling their seamless coexistence. Extensive experiments on ImageNet and MS-COCO benchmarks validate that our UAE effectively unifies semantic abstraction and pixel-level fidelity into a single latent space with state-of-the-art performance.

Diabetic Retinopathy (DR), induced by diabetes, poses a significant risk of visual impairment. Accurate and effective grading of DR aids in the treatment of this condition. Yet existing models experience notable performance degradation on unseen domains due to domain shifts. Previous methods address this issue by simulating domain style through simple visual transformation and mitigating domain noise via learning robust representations. However, domain shifts encompass more than image styles. They overlook biases caused by implicit factors such as ethnicity, age, and diagnostic criteria. In our work, we propose a novel framework where representations of paired data from different domains are decoupled into semantic features and domain noise. The resulting augmented representation comprises original retinal semantics and domain noise from other domains, aiming to generate enhanced representations aligned with real-world clinical needs, incorporating rich information from diverse domains. Subsequently, to improve the robustness of the decoupled representations, class and domain prototypes are employed to interpolate the disentangled representations while data-aware weights are designed to focus on rare classes and domains. Finally, we devise a robust pixel-level semantic alignment loss to align retinal semantics decoupled from features, maintaining a balance between intra-class diversity and dense class features. Experimental results on multiple benchmarks demonstrate the effectiveness of our method on unseen domains. The code implementations are accessible on https://github.com/richard-peng-xia/DECO.

CNN-based generative modelling has evolved to produce synthetic images indistinguishable from real images in the RGB pixel space. Recent works have observed that CNN-generated images share a systematic shortcoming in replicating high frequency Fourier spectrum decay attributes. Furthermore, these works have successfully exploited this systematic shortcoming to detect CNN-generated images reporting up to 99% accuracy across multiple state-of-the-art GAN models. In this work, we investigate the validity of assertions claiming that CNN-generated images are unable to achieve high frequency spectral decay consistency. We meticulously construct a counterexample space of high frequency spectral decay consistent CNN-generated images emerging from our handcrafted experiments using DCGAN, LSGAN, WGAN-GP and StarGAN, where we empirically show that this frequency discrepancy can be avoided by a minor architecture change in the last upsampling operation. We subsequently use images from this counterexample space to successfully bypass the recently proposed forensics detector which leverages on high frequency Fourier spectrum decay attributes for CNN-generated image detection. Through this study, we show that high frequency Fourier spectrum decay discrepancies are not inherent characteristics for existing CNN-based generative models--contrary to the belief of some existing work--, and such features are not robust to perform synthetic image detection. Our results prompt re-thinking of using high frequency Fourier spectrum decay attributes for CNN-generated image detection. Code and models are available at https://keshik6.github.io/Fourier-Discrepancies-CNN-Detection/

Unlabeled data is a key component of modern machine learning. In general, the role of unlabeled data is to impose a form of smoothness, usually from the similarity information encoded in a base kernel, such as the epsilon-neighbor kernel or the adjacency matrix of a graph. This work revisits the classical idea of spectrally transformed kernel regression (STKR), and provides a new class of general and scalable STKR estimators able to leverage unlabeled data. Intuitively, via spectral transformation, STKR exploits the data distribution for which unlabeled data can provide additional information. First, we show that STKR is a principled and general approach, by characterizing a universal type of "target smoothness", and proving that any sufficiently smooth function can be learned by STKR. Second, we provide scalable STKR implementations for the inductive setting and a general transformation function, while prior work is mostly limited to the transductive setting. Third, we derive statistical guarantees for two scenarios: STKR with a known polynomial transformation, and STKR with kernel PCA when the transformation is unknown. Overall, we believe that this work helps deepen our understanding of how to work with unlabeled data, and its generality makes it easier to inspire new methods.

Spatial-Spectral Mamba (SSM) improves computational efficiency and captures long-range dependencies, addressing Transformer limitations. However, traditional Mamba models overlook rich spectral information in HSIs and struggle with high dimensionality and sequential data. To address these issues, we propose the SSM with multi-head self-attention and token enhancement (MHSSMamba). This model integrates spectral and spatial information by enhancing spectral tokens and using multi-head attention to capture complex relationships between spectral bands and spatial locations. It also manages long-range dependencies and the sequential nature of HSI data, preserving contextual information across spectral bands. MHSSMamba achieved remarkable classification accuracies of 97.62\% on Pavia University, 96.92\% on the University of Houston, 96.85\% on Salinas, and 99.49\% on Wuhan-longKou datasets. The source code is available at https://github.com/MHassaanButt/MHA\_SS\_Mamba{GitHub}.

Large Language Models (LLMs) have demonstrated remarkable performance across various tasks but remain prone to hallucinations. Detecting hallucinations is essential for safety-critical applications, and recent methods leverage attention map properties to this end, though their effectiveness remains limited. In this work, we investigate the spectral features of attention maps by interpreting them as adjacency matrices of graph structures. We propose the LapEigvals method, which utilises the top-k eigenvalues of the Laplacian matrix derived from the attention maps as an input to hallucination detection probes. Empirical evaluations demonstrate that our approach achieves state-of-the-art hallucination detection performance among attention-based methods. Extensive ablation studies further highlight the robustness and generalisation of LapEigvals, paving the way for future advancements in the hallucination detection domain.

Recent advancements in learning latent codes derived from high-dimensional shapes have demonstrated impressive outcomes in 3D generative modeling. Traditionally, these approaches employ a trained autoencoder to acquire a continuous implicit representation of source shapes, which can be computationally expensive. This paper introduces a novel framework, spectral-domain diffusion for high-quality shape generation SpoDify, that utilizes singular value decomposition (SVD) for shape encoding. The resulting eigenvectors can be stored for subsequent decoding, while generative modeling is performed on the eigenfeatures. This approach efficiently encodes complex meshes into continuous implicit representations, such as encoding a 15k-vertex mesh to a 512-dimensional latent code without learning. Our method exhibits significant advantages in scenarios with limited samples or GPU resources. In mesh generation tasks, our approach produces high-quality shapes that are comparable to state-of-the-art methods.

We present Manifold Diffusion Fields (MDF), an approach to learn generative models of continuous functions defined over Riemannian manifolds. Leveraging insights from spectral geometry analysis, we define an intrinsic coordinate system on the manifold via the eigen-functions of the Laplace-Beltrami Operator. MDF represents functions using an explicit parametrization formed by a set of multiple input-output pairs. Our approach allows to sample continuous functions on manifolds and is invariant with respect to rigid and isometric transformations of the manifold. Empirical results on several datasets and manifolds show that MDF can capture distributions of such functions with better diversity and fidelity than previous approaches.

Semidefinite programming is a fundamental problem class in convex optimization, but despite recent advances in solvers, solving large-scale semidefinite programs remains challenging. Generally the matrix functions involved are spectral or unitarily invariant, i.e., they depend only on the eigenvalues or singular values of the matrix. This paper investigates how spectral matrix cones -- cones defined from epigraphs and perspectives of spectral or unitarily invariant functions -- can be used to enhance first-order conic solvers for semidefinite programs. Our main result shows that projecting a matrix can be reduced to projecting its eigenvalues or singular values, which we demonstrate can be done at a negligible cost compared to the eigenvalue or singular value decomposition itself. We have integrated support for spectral matrix cone projections into the Splitting Conic Solver (SCS). Numerical experiments show that SCS with this enhancement can achieve speedups of up to an order of magnitude for solving semidefinite programs arising in experimental design, robust principal component analysis, and graph partitioning.

Learning feature representations of geographical space is vital for any machine learning model that integrates geolocated data, spanning application domains such as remote sensing, ecology, or epidemiology. Recent work mostly embeds coordinates using sine and cosine projections based on Double Fourier Sphere (DFS) features -- these embeddings assume a rectangular data domain even on global data, which can lead to artifacts, especially at the poles. At the same time, relatively little attention has been paid to the exact design of the neural network architectures these functional embeddings are combined with. This work proposes a novel location encoder for globally distributed geographic data that combines spherical harmonic basis functions, natively defined on spherical surfaces, with sinusoidal representation networks (SirenNets) that can be interpreted as learned Double Fourier Sphere embedding. We systematically evaluate the cross-product of positional embeddings and neural network architectures across various classification and regression benchmarks and synthetic evaluation datasets. In contrast to previous approaches that require the combination of both positional encoding and neural networks to learn meaningful representations, we show that both spherical harmonics and sinusoidal representation networks are competitive on their own but set state-of-the-art performances across tasks when combined. We provide source code at www.github.com/marccoru/locationencoder

Time series domain adaptation stands as a pivotal and intricate challenge with diverse applications, including but not limited to human activity recognition, sleep stage classification, and machine fault diagnosis. Despite the numerous domain adaptation techniques proposed to tackle this complex problem, they primarily focus on domain adaptation from a single source domain. Yet, it is more crucial to investigate domain adaptation from multiple domains due to the potential for greater improvements. To address this, three important challenges need to be overcome: 1). The lack of exploration to utilize domain-specific information for domain adaptation, 2). The difficulty to learn domain-specific information that changes over time, and 3). The difficulty to evaluate learned domain-specific information. In order to tackle these challenges simultaneously, in this paper, we introduce PrOmpt-based domaiN Discrimination (POND), the first framework to utilize prompts for time series domain adaptation. Specifically, to address Challenge 1, we extend the idea of prompt tuning to time series analysis and learn prompts to capture common and domain-specific information from all source domains. To handle Challenge 2, we introduce a conditional module for each source domain to generate prompts from time series input data. For Challenge 3, we propose two criteria to select good prompts, which are used to choose the most suitable source domain for domain adaptation. The efficacy and robustness of our proposed POND model are extensively validated through experiments across 50 scenarios encompassing four datasets. Experimental results demonstrate that our proposed POND model outperforms all state-of-the-art comparison methods by up to 66% on the F1-score.

Previous research has shown that the principal singular vectors of a pre-trained model's weight matrices capture critical knowledge. In contrast, those associated with small singular values may contain noise or less reliable information. As a result, the LoRA-based parameter-efficient fine-tuning (PEFT) approach, which does not constrain the use of the spectral space, may not be effective for tasks that demand high representation capacity. In this study, we enhance existing PEFT techniques by incorporating the spectral information of pre-trained weight matrices into the fine-tuning process. We investigate spectral adaptation strategies with a particular focus on the additive adjustment of top singular vectors. This is accomplished by applying singular value decomposition (SVD) to the pre-trained weight matrices and restricting the fine-tuning within the top spectral space. Extensive speaker verification experiments on VoxCeleb1 and CN-Celeb1 demonstrate enhanced tuning performance with the proposed approach. Code is released at https://github.com/lizhepolyu/SpectralFT.

Despite their many desirable properties, Gaussian processes (GPs) are often compared unfavorably to deep neural networks (NNs) for lacking the ability to learn representations. Recent efforts to bridge the gap between GPs and deep NNs have yielded a new class of inter-domain variational GPs in which the inducing variables correspond to hidden units of a feedforward NN. In this work, we examine some practical issues associated with this approach and propose an extension that leverages the orthogonal decomposition of GPs to mitigate these limitations. In particular, we introduce spherical inter-domain features to construct more flexible data-dependent basis functions for both the principal and orthogonal components of the GP approximation and show that incorporating NN activation features under this framework not only alleviates these shortcomings but is more scalable than alternative strategies. Experiments on multiple benchmark datasets demonstrate the effectiveness of our approach.

Vision-language foundation models (VLFMs) promise zero-shot and retrieval understanding for Earth observation. While operational satellite systems often lack full multi-spectral coverage, making RGB-only inference highly desirable for scalable deployment, the adoption of VLFMs for satellite imagery remains hindered by two factors: (1) multi-spectral inputs are informative but difficult to exploit consistently due to band redundancy and misalignment; and (2) CLIP-style text encoders limit semantic expressiveness and weaken fine-grained alignment. We present SATtxt, a spectrum-aware VLFM that operates with RGB inputs only at inference while retaining spectral cues learned during training. Our framework comprises two stages. First, Spectral Representation Distillation transfers spectral priors from a frozen multi-spectral teacher to an RGB student via a lightweight projector. Second, Spectrally Grounded Alignment with Instruction-Augmented LLMs bridges the distilled visual space and an expressive LLM embedding space. Across EuroSAT, BigEarthNet, and ForestNet, SATtxt improves zero-shot classification on average by 4.2%, retrieval by 5.9%, and linear probing by 2.7% over baselines, showing an efficient path toward spectrum-aware vision-language learning for Earth observation. Project page: https://ikhado.github.io/sattxt/

What sorts of structure might enable a learner to discover classes from unlabeled data? Traditional approaches rely on feature-space similarity and heroic assumptions on the data. In this paper, we introduce unsupervised learning under Latent Label Shift (LLS), where we have access to unlabeled data from multiple domains such that the label marginals p_d(y) can shift across domains but the class conditionals p(x|y) do not. This work instantiates a new principle for identifying classes: elements that shift together group together. For finite input spaces, we establish an isomorphism between LLS and topic modeling: inputs correspond to words, domains to documents, and labels to topics. Addressing continuous data, we prove that when each label's support contains a separable region, analogous to an anchor word, oracle access to p(d|x) suffices to identify p_d(y) and p_d(y|x) up to permutation. Thus motivated, we introduce a practical algorithm that leverages domain-discriminative models as follows: (i) push examples through domain discriminator p(d|x); (ii) discretize the data by clustering examples in p(d|x) space; (iii) perform non-negative matrix factorization on the discrete data; (iv) combine the recovered p(y|d) with the discriminator outputs p(d|x) to compute p_d(y|x) ; forall d. With semi-synthetic experiments, we show that our algorithm can leverage domain information to improve upon competitive unsupervised classification methods. We reveal a failure mode of standard unsupervised classification methods when feature-space similarity does not indicate true groupings, and show empirically that our method better handles this case. Our results establish a deep connection between distribution shift and topic modeling, opening promising lines for future work.

Spherical CNNs generalize CNNs to functions on the sphere, by using spherical convolutions as the main linear operation. The most accurate and efficient way to compute spherical convolutions is in the spectral domain (via the convolution theorem), which is still costlier than the usual planar convolutions. For this reason, applications of spherical CNNs have so far been limited to small problems that can be approached with low model capacity. In this work, we show how spherical CNNs can be scaled for much larger problems. To achieve this, we make critical improvements including novel variants of common model components, an implementation of core operations to exploit hardware accelerator characteristics, and application-specific input representations that exploit the properties of our model. Experiments show our larger spherical CNNs reach state-of-the-art on several targets of the QM9 molecular benchmark, which was previously dominated by equivariant graph neural networks, and achieve competitive performance on multiple weather forecasting tasks. Our code is available at https://github.com/google-research/spherical-cnn.

Hyperspectral target detection (HTD) aims to identify specific materials based on spectral information in hyperspectral imagery and can detect extremely small objects, some of which occupy a smaller than one-pixel area. However, existing HTD methods are developed based on per-pixel binary classification, which limits the feature representation capability for instance-level objects. In this paper, we rethink the hyperspectral target detection from the point object detection perspective, and propose the first specialized network for hyperspectral multi-class point object detection, SpecDETR. Without the visual foundation model of the current object detection framework, SpecDETR treats each pixel in input images as a token and uses a multi-layer Transformer encoder with self-excited subpixel-scale attention modules to directly extract joint spatial-spectral features from images. During feature extraction, we introduce a self-excited mechanism to enhance object features through self-excited amplification, thereby accelerating network convergence. Additionally, SpecDETR regards point object detection as a one-to-many set prediction problem, thereby achieving a concise and efficient DETR decoder that surpasses the state-of-the-art (SOTA) DETR decoder. We develop a simulated hyperSpectral Point Object Detection benchmark termed SPOD, and for the first time, evaluate and compare the performance of current object detection networks and HTD methods on hyperspectral point object detection. Extensive experiments demonstrate that our proposed SpecDETR outperforms SOTA object detection networks and HTD methods. Our code and dataset are available at https://github.com/ZhaoxuLi123/SpecDETR.

We show that deep neural networks trained across diverse tasks exhibit remarkably similar low-dimensional parametric subspaces. We provide the first large-scale empirical evidence that demonstrates that neural networks systematically converge to shared spectral subspaces regardless of initialization, task, or domain. Through mode-wise spectral analysis of over 1100 models - including 500 Mistral-7B LoRAs, 500 Vision Transformers, and 50 LLaMA-8B models - we identify universal subspaces capturing majority variance in just a few principal directions. By applying spectral decomposition techniques to the weight matrices of various architectures trained on a wide range of tasks and datasets, we identify sparse, joint subspaces that are consistently exploited, within shared architectures across diverse tasks and datasets. Our findings offer new insights into the intrinsic organization of information within deep networks and raise important questions about the possibility of discovering these universal subspaces without the need for extensive data and computational resources. Furthermore, this inherent structure has significant implications for model reusability, multi-task learning, model merging, and the development of training and inference-efficient algorithms, potentially reducing the carbon footprint of large-scale neural models.

Despite the non-autoregressive potential of diffusion language models (dLLMs), existing decoding strategies demonstrate positional bias, failing to fully unlock the potential of arbitrary generation. In this work, we delve into the inherent spectral characteristics of dLLMs and present the first frequency-domain analysis showing that low-frequency components in hidden states primarily encode global structural information and long-range dependencies, while high-frequency components are responsible for characterizing local details. Based on this observation, we propose FourierSampler, which leverages a frequency-domain sliding window mechanism to dynamically guide the model to achieve a "structure-to-detail" generation. FourierSampler outperforms other inference enhancement strategies on LLADA and SDAR, achieving relative improvements of 20.4% on LLaDA1.5-8B and 16.0% on LLaDA-8B-Instruct. It notably surpasses similarly sized autoregressive models like Llama3.1-8B-Instruct.

Despite the recent visually-pleasing results achieved, the massive computational cost has been a long-standing flaw for diffusion probabilistic models (DPMs), which, in turn, greatly limits their applications on resource-limited platforms. Prior methods towards efficient DPM, however, have largely focused on accelerating the testing yet overlooked their huge complexity and sizes. In this paper, we make a dedicated attempt to lighten DPM while striving to preserve its favourable performance. We start by training a small-sized latent diffusion model (LDM) from scratch, but observe a significant fidelity drop in the synthetic images. Through a thorough assessment, we find that DPM is intrinsically biased against high-frequency generation, and learns to recover different frequency components at different time-steps. These properties make compact networks unable to represent frequency dynamics with accurate high-frequency estimation. Towards this end, we introduce a customized design for slim DPM, which we term as Spectral Diffusion (SD), for light-weight image synthesis. SD incorporates wavelet gating in its architecture to enable frequency dynamic feature extraction at every reverse steps, and conducts spectrum-aware distillation to promote high-frequency recovery by inverse weighting the objective based on spectrum magni tudes. Experimental results demonstrate that, SD achieves 8-18x computational complexity reduction as compared to the latent diffusion models on a series of conditional and unconditional image generation tasks while retaining competitive image fidelity.

Invariance learning methods aim to learn invariant features in the hope that they generalize under distributional shifts. Although many tasks are naturally characterized by continuous domains, current invariance learning techniques generally assume categorically indexed domains. For example, auto-scaling in cloud computing often needs a CPU utilization prediction model that generalizes across different times (e.g., time of a day and date of a year), where `time' is a continuous domain index. In this paper, we start by theoretically showing that existing invariance learning methods can fail for continuous domain problems. Specifically, the naive solution of splitting continuous domains into discrete ones ignores the underlying relationship among domains, and therefore potentially leads to suboptimal performance. To address this challenge, we then propose Continuous Invariance Learning (CIL), which extracts invariant features across continuously indexed domains. CIL is a novel adversarial procedure that measures and controls the conditional independence between the labels and continuous domain indices given the extracted features. Our theoretical analysis demonstrates the superiority of CIL over existing invariance learning methods. Empirical results on both synthetic and real-world datasets (including data collected from production systems) show that CIL consistently outperforms strong baselines among all the tasks.

We establish a new theoretical framework for learning under multi-class, instance-dependent label noise. This framework casts learning with label noise as a form of domain adaptation, in particular, domain adaptation under posterior drift. We introduce the concept of relative signal strength (RSS), a pointwise measure that quantifies the transferability from noisy to clean posterior. Using RSS, we establish nearly matching upper and lower bounds on the excess risk. Our theoretical findings support the simple Noise Ignorant Empirical Risk Minimization (NI-ERM) principle, which minimizes empirical risk while ignoring label noise. Finally, we translate this theoretical insight into practice: by using NI-ERM to fit a linear classifier on top of a self-supervised feature extractor, we achieve state-of-the-art performance on the CIFAR-N data challenge.

Diffusion models are a strong backbone for visual generation, but their inherently sequential denoising process leads to slow inference. Previous methods accelerate sampling by caching and reusing intermediate outputs based on feature distances between adjacent timesteps. However, existing caching strategies typically rely on raw feature differences that entangle content and noise. This design overlooks spectral evolution, where low-frequency structure appears early and high-frequency detail is refined later. We introduce Spectral-Evolution-Aware Cache (SeaCache), a training-free cache schedule that bases reuse decisions on a spectrally aligned representation. Through theoretical and empirical analysis, we derive a Spectral-Evolution-Aware (SEA) filter that preserves content-relevant components while suppressing noise. Employing SEA-filtered input features to estimate redundancy leads to dynamic schedules that adapt to content while respecting the spectral priors underlying the diffusion model. Extensive experiments on diverse visual generative models and the baselines show that SeaCache achieves state-of-the-art latency-quality trade-offs.

Face anti-spoofing (FAS) based on domain generalization (DG) has been recently studied to improve the generalization on unseen scenarios. Previous methods typically rely on domain labels to align the distribution of each domain for learning domain-invariant representations. However, artificial domain labels are coarse-grained and subjective, which cannot reflect real domain distributions accurately. Besides, such domain-aware methods focus on domain-level alignment, which is not fine-grained enough to ensure that learned representations are insensitive to domain styles. To address these issues, we propose a novel perspective for DG FAS that aligns features on the instance level without the need for domain labels. Specifically, Instance-Aware Domain Generalization framework is proposed to learn the generalizable feature by weakening the features' sensitivity to instance-specific styles. Concretely, we propose Asymmetric Instance Adaptive Whitening to adaptively eliminate the style-sensitive feature correlation, boosting the generalization. Moreover, Dynamic Kernel Generator and Categorical Style Assembly are proposed to first extract the instance-specific features and then generate the style-diversified features with large style shifts, respectively, further facilitating the learning of style-insensitive features. Extensive experiments and analysis demonstrate the superiority of our method over state-of-the-art competitors. Code will be publicly available at https://github.com/qianyuzqy/IADG.

This thesis addresses two persistent and closely related challenges in modern deep learning, reliability and efficiency, through a unified framework grounded in Spectral Geometry and Random Matrix Theory (RMT). As deep networks and large language models continue to scale, their internal behavior becomes increasingly opaque, leading to hallucinations, fragile generalization under distribution shift, and growing computational and energy demands. By analyzing the eigenvalue dynamics of hidden activations across layers and inputs, this work shows that spectral statistics provide a compact, stable, and interpretable lens on model behavior, capable of separating structured, causal representations from noise-dominated variability. Within this framework, the first contribution, EigenTrack, introduces a real-time method for detecting hallucinations and out-of-distribution behavior in large language and vision-language models. EigenTrack transforms streaming activations into spectral descriptors such as entropy, variance, and deviations from the Marchenko-Pastur baseline, and models their temporal evolution using lightweight recurrent classifiers, enabling early detection of reliability failures before they appear in model outputs while offering interpretable insight into representation dynamics. The second contribution, RMT-KD, presents a principled approach to compressing deep networks via random matrix theoretic knowledge distillation. By interpreting outlier eigenvalues in activation spectra as carriers of task-relevant information, RMT-KD progressively projects networks onto lower-dimensional subspaces through iterative self-distillation, yielding significantly more compact and energy-efficient models while preserving accuracy and dense, hardware-friendly structure.

We present AstroCLIP, a strategy to facilitate the construction of astronomical foundation models that bridge the gap between diverse observational modalities. We demonstrate that a cross-modal contrastive learning approach between images and optical spectra of galaxies yields highly informative embeddings of both modalities. In particular, we apply our method on multi-band images and optical spectra from the Dark Energy Spectroscopic Instrument (DESI), and show that: (1) these embeddings are well-aligned between modalities and can be used for accurate cross-modal searches, and (2) these embeddings encode valuable physical information about the galaxies -- in particular redshift and stellar mass -- that can be used to achieve competitive zero- and few- shot predictions without further finetuning. Additionally, in the process of developing our approach, we also construct a novel, transformer-based model and pretraining approach for processing galaxy spectra.

In this paper, we prove representation bottlenecks of a cascaded convolutional decoder network, considering the capacity of representing different frequency components of an input sample. We conduct the discrete Fourier transform on each channel of the feature map in an intermediate layer of the decoder network. Then, we introduce the rule of the forward propagation of such intermediate-layer spectrum maps, which is equivalent to the forward propagation of feature maps through a convolutional layer. Based on this, we find that each frequency component in the spectrum map is forward propagated independently with other frequency components. Furthermore, we prove two bottlenecks in representing feature spectrums. First, we prove that the convolution operation, the zero-padding operation, and a set of other settings all make a convolutional decoder network more likely to weaken high-frequency components. Second, we prove that the upsampling operation generates a feature spectrum, in which strong signals repetitively appears at certain frequencies.

Inspired by recent development of artificial satellite, remote sensing images have attracted extensive attention. Recently, noticeable progress has been made in scene classification and target detection.However, it is still not clear how to describe the remote sensing image content with accurate and concise sentences. In this paper, we investigate to describe the remote sensing images with accurate and flexible sentences. First, some annotated instructions are presented to better describe the remote sensing images considering the special characteristics of remote sensing images. Second, in order to exhaustively exploit the contents of remote sensing images, a large-scale aerial image data set is constructed for remote sensing image caption. Finally, a comprehensive review is presented on the proposed data set to fully advance the task of remote sensing caption. Extensive experiments on the proposed data set demonstrate that the content of the remote sensing image can be completely described by generating language descriptions. The data set is available at https://github.com/201528014227051/RSICD_optimal