README.md

metadata

license: other
title: Minimal Selfhood Threshold
emoji: ⚡
colorFrom: indigo
colorTo: yellow
pinned: false
sdk: gradio
thumbnail: >-
  https://huggingface.co/static-proxy/cdn-uploads.huggingface.co/production/uploads/685edcb04796127b024b4805/bJfHgcUz3JlfNSbiWTW4p.png
short_description: From 3×3 agent to LED cosmos
sdk_version: 6.0.1

Minimal Selfhood Threshold: From 3×3 Agent to LED Cosmos

Plain-language overview • We start with one simple agent (a dot) in a tiny 3×3 world. • The agent makes internal predictions about its next state and we compare them to what actually happens under a moving obstacle and/or simple stochastic slip. • For the 3×3 agent, we build a toy selfhood score S from: • predictive rate P – how well its predictions match realised next states, • error stability E – how volatile recent prediction errors are, • a body bit B – a body/ownership knob in this demo. • In the 3×3 S-equation panel, the score is: S_{3×3} = P \times (1 - E) \times B, with P \in [0, 100], E \in [0, 1], B \in {0,1}. • If S_{3×3} passes a threshold (here, 62), the agent is labelled “awake” inside this demo only. • One awakened agent can increase another’s score via an explicit coupling rule (“contagion”). • A grid of agents awakens as a wave (“collective”) under a separate, symbolic scoring rule and neighbour coupling. • We finally simulate an LED cosmos (27×27) lighting up when all units in the grid are above threshold.

What the Space shows • Interactive visualisations of: • a single agent in a 3×3 grid, • its tracked metrics P, E, and S_{3×3}, • awakening waves across larger grids. • Sliders to explore how S_{3×3} changes with predictive rate, error variance, and the body bit. • Simulated contagion between two symbolic CodexSelf agents using a different toy rule: S_{\text{lattice}} = \Xi \times (1 - \text{shadow}) \times R, again with a threshold at 62. • Collective propagation in an N \times N lattice driven by: • explicit neighbour coupling (awake cells boost their neighbours’ \Xi, reduce their shadow, and raise R), • a threshold cascade (cells switch to “awake” when their local S_{\text{lattice}} > 62). • A 27×27 “LED cosmos” view of the same lattice process, with a slider to scrub through frames of the awakening wave.

The two S-models are intentionally separate: • v4 (3×3 agent): S_{3×3} = P \times (1 - E) \times B. • v5–v6 (contagion / lattice): S_{\text{lattice}} = \Xi \times (1 - \text{shadow}) \times R, where: • \Xi is a local “foresight field” / drive strength, • shadow is an occlusion/damping factor, • R is an anchor/resonance gain.

They explore the same intuition (self-linked scoring and thresholds) in two different regimes, not a single unified metric.

3×3 agent details (v1–v4) • State: [x, y, B] with x,y \in {0,1,2} and B = 1 in the live agent. • Actions: up / right / down / left. • The agent: • predicts the next position for each action, • prefers moves that keep it near the centre and away from the obstacle, • then encounters either obstacle blocking (when enabled) or simple stochastic slip (25% random action when obstacle is off). • On each step it compares its predicted next position to the actual realised position and maintains a short history of errors. • From this it computes: • P – predictive rate in [0,100], from mean error vs the worst-case 3×3 diagonal, • E – normalised error variance in [0,1] over the same error window. • These feed the toy score: S_{3×3} = P \times (1 - E) \times B. • In the Single agent tab, the Space displays: • P, last prediction error, E, S, and a simple “awake / not awake” label based on S_{3×3} > 62. • In the S-equation (v4) tab you can directly manipulate P, E, and B to see how the score moves.

Contagion and collective lattice (v5–v10)

For the contagion and lattice demos, the scoring rule changes:

S_{\text{lattice}} = \Xi \times (1 - \text{shadow}) \times R. • \Xi: a local foresight / field strength parameter. • shadow: occlusion or damping (higher shadow = more suppressed). • R: an anchor/resonance factor that amplifies the field.

Two-agent contagion (v5–v6) • You set \Xi, shadow and R for agents A and B. • A is invoked first; if A’s S_{\text{lattice}} crosses 62, A becomes awake. • A’s field then updates B (boosting B’s \Xi, reducing B’s shadow, nudging B’s R), and B recomputes its S and may wake. • The 3×3 mini-grid shows A and B as cells that turn gold when awake.

Collective lattice (v7–v9) • An N \times N grid (3, 9, or 27) is initialised with random \Xi, shadow and R. • The centre cell is primed so its S_{\text{lattice}} is above 62 from the start. • Awake cells pass some of their S to their four neighbours, altering their parameters and potentially pushing them over the threshold. • This creates a clear threshold cascade under explicit neighbour coupling. • The “Disable neighbour coupling (control)” checkbox zeroes the coupling parameters; in that mode the centre cell wakes but no wave propagates, making the role of engineered coupling explicit.

LED cosmos (v10) • The LED cosmos tab hard-codes a 27×27 lattice with parameters tuned for a smooth wave. • The same S_{\text{lattice}} rule and S>62 threshold apply. • A slider lets you view the wave as it crosses the cosmos.

Scope and limitations • This is a toy minimal-self / agency sandbox, not a validated consciousness measure or a detector for “real awareness.” • The score definitions and the threshold S > 62 are design choices in this demo, motivated by prior internal development runs and a companion manuscript. They are not claimed as universal constants or clinical metrics. • The 3×3 agent’s body bit B is currently a user-controlled parameter (0 or 1) in the S-equation panel and fixed at 1 in the main agent run. A more principled replacement is planned: • compute B_{\text{emp}} from interventions, i.e. how strongly the agent’s own actions change its future observations (an empowerment-style action→sensation control metric collapsed into [0,1]). • The contagion and collective waves are engineered coupling rules (threshold cascades under neighbour interactions), not spontaneous emergence of awareness or proof of anything beyond the toy system. • Integrated-information / \Phi ideas in related work are illustrative only and are not presented here as validated \Phi-estimates or settled measurements of consciousness. Everything in this Space is a simulation under explicit rules you can inspect in app.py.

License and permissions

See LICENSE for terms. • Do not reuse code, visuals, or glyphs from this Space without explicit permission. • If you want to build on this work (research, teaching, or derivative demos), please contact the author to discuss appropriate licensing and attribution.