ghca

A study of local timescales in Greenberg–Hastings cellular automata, and an exploratory program using GH excitable dynamics as the substrate for a reward-driven learning mechanism on a graph.

Two strands

1. Lattice GH cellular automata (original). Excitable-media dynamics on a 2D lattice with an (active, passive) refractory cycle, plus tools to enumerate which initial configurations self-sustain ("persistence probability" over (active, passive) parameter space).

2. Learning on a GH network (in progress). GH dynamics generalised to an arbitrary weighted graph, with per-node timescales, as the substrate for a learning mechanism. The framing is inside-out (Buzsáki): the medium generates its own repertoire of dynamical patterns, and a strict scalar reward (Sutton) selects and stabilises a subset through action. Memory, attention and executive function are treated as categories read out from one homogeneous substrate, not as built-in modules.

Files

File	Purpose
ghca_main.py	Lattice GH substrate: Population class, run, plot, animate
ghca_core.py	Encode/embed integer configurations, run + animate
ghca_plot.py	Persistence-probability maps over (active, passive) space
ghca_net.py	GH dynamics on a graph: per-node timescales, weighted-threshold excitation, spontaneous firing, homeostatic threshold; topology builders and order-parameter observables
ghca_learn.py	Reward-modulated learner: eligibility-trace conduction (Line A) and timescale (Line B) plasticity, order-parameter critic, layered-graph builder
ghca_causal.py	Causal instrumentation (C-series): partial-observation S_obs, wave variables W=f(S), and do(S) / do(W) / do(θ) intervention operators
experiments/e0_characterization.py	E0 — substrate characterisation (find the self-sustaining band)
experiments/e1_conditioning.py	E1 — stimulus→response conditioning (A-vs-B dissociation)
experiments/e2_delayed_response.py	E2 — delayed response / working memory (τ-controlled memory)
experiments/e2_information.py	E2 addendum — memory as a τ-tuned information-destruction rate
experiments/e3_timed_response.py	E3 — timed response (identity × latency double dissociation)
experiments/e3_factored_credit.py	E3 composition study — factored credit + curriculum vs shared reward
experiments/e4_attention.py	E4 — selective attention as biased WTA by wave annihilation
experiments/e5_executive.py	E5 — executive control / task switching (a slow-loop option gates fast routing)
experiments/e6_horde.py	E6 — emergent categories (three GVF demons read one frozen substrate)
experiments/c0_instrumentation.py	C0 — instrument the causal variables (W=f(S), partial spikes)
experiments/c1_graph_certificates.py	C1 — validate Theorem-1 epiphenomenality certificate on known SCMs
experiments/c2_fat_handed.py	C2 — do(W) is fat-handed when W=f(S) (achievable-band of behaviour)
experiments/c3_do_theta.py	C3 — do(θ) (timescales/couplings) is the well-posed causal handle
experiments/c4_outcome_relativity.py	C4 — outcome-relativity & degeneracy (causal-emergence cap)
result/	Saved simulation outputs (.npy) and experiment data

Documentation

• docs/learning_experiments.md — the full design: substrate spec, strict-reward learning framework, the two parallel plasticity lines (conduction weights vs local timescales), input/cue/feedback formats, hyperparameters, and the staged experiment series E0–E6.
• docs/e0_results.md — findings from E0 (substrate characterisation): range-1 fixates, the live threshold band widens with range (threshold-range scaling), an organised spiral band at r=2/a=6/θ≈4, and the dominant loop period tracking τ (period = 1.00·τ + 0.95, r = 0.9992).
• docs/e1_results.md — findings from E1 (conditioning): a strict scalar reward carves the stimulus→action mapping; the predicted dissociation holds (Line A = 0.91, Line B = 0.35 ≤ chance, A+B = 0.86 final accuracy over 6 seeds).
• docs/e2_results.md — findings from E2 (working memory): memory is a τ-controlled reentrant loop; the dissociation inverts — Line A retains only at zero delay, Line B learns τ below the loop transit time and holds memory to D=200. Needs a shared regional timescale (per-node τ hits a weakest-link problem).
• docs/e3_results.md — findings from E3 (timed response): double dissociation confirmed — Line A learns identity (wrong timing), Line B learns timing (not identity). New open problem: naive A+B interferes (both worse than either alone) under a single shared reward — later decomposed: factored credit removes the below-chance collapse (to ≈chance), a slow-first curriculum adds a marginal bimodal lift (joint composition on 1/5 seeds) — direction supported, magnitude not established at n=5.
• docs/e4_results.md — findings from E4 (attention): selective attention as biased winner-take-all by wave annihilation — a textbook psychometric (accuracy 0.96 at modest bias), the annihilation locus linear in the bias, achieved with zero inhibitory nodes.
• docs/e5_results.md — findings from E5 (executive control): a persistent reentrant loop (the E2 mechanism) acts as an option that gates fast routing — switching 0.89 vs 0.20 when the loop is ablated, post-switch accuracy consolidating 0.57→0.92, single-rule routing spared by the ablation (0.87 vs 0.86). The discriminator localises the loop's role to holding the rule across a block.
• docs/e6_results.md — findings from E6 (emergent categories): three GVF demons on one frozen substrate, reading the same feature vector, predict distinct questions well above baseline (memory R²=0.62, attention forecast 0.84, executive R²=0.98); their readouts are near-orthogonal and a generic probe matches an own-region oracle — memory/attention/executive are questions asked of one machine, not modules.
• docs/causal_experiments.md — C-series plan: using the substrate (where W = f(S) is explicit) as a synthetic-SCM testbed for the spike-wave causal question (arXiv:2511.06602) — validate the paper's certificates on ground truth, then show do(W) is fat-handed under real constitution and do(θ) is the well-posed handle.
• docs/c0_results.md — findings from C0: W=f(S) verified; the wave carries info beyond partial spikes for a collective code (growing as observation gets sparser) but not for a labeled-line code — informativeness is structure-dependent.
• docs/c1_results.md — findings from C1: on six canonical graphs the Theorem-1 certificate matches ground-truth do(W) — including the confounded case (association without causation) and front-door (causal despite an observed mediator).
• docs/c2_results.md — findings from C2 (headline): when W=f(S) is constituted, one do(W=w) admits a huge behavioural band (33 σ) for a micro-reading behaviour vs ~0 for a collective one — do(W) is fat-handed and its causal verdict depends on the realization.
• docs/c3_results.md — findings from C3: do(θ) (timescales/couplings) is the well-posed handle — single-valued reproducible response, intervention ambiguity 0.014 σ vs do(W)'s 33 σ; θ is exactly what plasticity acts on.
• docs/c4_results.md — findings from C4: the causal role is (handle, outcome)-relative (do(θ) matrix is diagonal); the wave is the natural causal variable only where behaviour is collective (macro- sufficiency 1.03 vs 0.11 — causal emergence).
• docs/synthesis.md — tying note: the E-series and C-series are one argument — θ (timescales, couplings) is both the variable the learner adapts and the only well-posed causal handle; spikes and waves are two readouts of one parameterised dynamics.

Progress

• E0 — substrate characterisation and operating point (see results)
• E1 — stimulus→response conditioning (A-vs-B dissociation confirmed)
• E2 — delayed response / working memory (dissociation inverts: B critical)
• E3 — timed response (double dissociation confirmed; A+B interference decomposed: factored credit removes the below-chance reward-conflation collapse 0.11→0.48, a slow-first curriculum adds a marginal, bimodal lift to 0.56 with genuine joint composition on 1/5 seeds — direction supported, magnitude not established at n=5; substrate-resonance capped)
• E4 — selective attention as biased WTA by wave annihilation (psychometric accuracy 0.96 at modest bias; zero inhibitory nodes)
• E5 — executive control / task switching: a persistent loop (E2 mechanism) as an option gating routing (switching 0.89 vs ablated 0.20; switch cost consolidates 0.57→0.92; single-rule spared 0.87 vs 0.86)
• E6 — emergent categories (Horde/GVF readout): three demons on one frozen substrate predict distinct questions (memory R²=0.62, attention 0.84, executive R²=0.98), near-orthogonal, no dedicated wiring — E-series complete

C-series (constitution & causality of spike–wave duality — see docs/causal_experiments.md):

• C0 — instrument the causal variables (W=f(S); wave informative beyond partial spikes for a collective code only)
• C1 — certificate validated on ground truth (all 6 canonical graphs agree; confounded & front-door as key cases)
• C2 — do(W) is fat-handed for a constituted W=f(S) (achievable band 33σ vs ~0)
• C3 — do(θ) is the well-posed causal handle (ambiguity 0.014σ vs 33σ; θ→W→B)
• C4 — outcome-relativity (diagonal do(θ) matrix) & degeneracy (macro-sufficiency 1.03 vs 0.11) — C-series complete

Both series are complete. See docs/synthesis.md for how the E-series and C-series tie together into one argument.

Reproduce

python3 -m pip install numpy matplotlib scipy networkx scikit-learn
python3 experiments/e0_characterization.py    # writes docs/figures/e0_*.png, result/e0/
python3 experiments/e5_executive.py           # writes docs/figures/e5_*.png, result/e5/
python3 experiments/e6_horde.py               # writes docs/figures/e6_horde.png, result/e6/

Each experiments/*.py is self-contained and writes its figures to docs/figures/ and data to result/.