Papers
Research across cognition, computation, and the structure of meaning.
Distilling the Local Rule: Surface Minimisation as an Emergent Property
Replacing the global Nambu-Goto watcher with a purely local, distilled update rule whose emergent behaviour minimises wiring surface and sits at criticality — and testing whether it is a law (scale-invariant) or a fit
Danyiel Colin2026-0610 sections last modified Jun 2026The prototype enforced its geometry: a global watcher solved the surface problem and moved the nodes there, so 'the substrate minimises wiring surface' was true by construction. This paper earns it. We distil a purely local update rule f_theta — each cell reading only its own state and the relative geometry of its immediate neighbours, never the global action or any population statistic — that reproduces surface descent, then run it with the watcher off and measure the result. The discovery machinery (the factory) is strictly offline and is the only place the surface action S appears: behavioural cloning of the watcher's per-node displacement plus a differentiable rollout that backpropagates S through a multi-step geometry rollout. The runtime body (the chassis) carries the frozen theta and no global term; the rule is rotation-equivariant and translation-invariant by construction, built from relative neighbour vectors with no absolute frame, and radius-truncated through a spatial hash, so locality is physical rather than merely intended. Two properties then emerge with no global term at runtime. Surface minimisation: a naive clone oscillates — it descends on barely half its passes — and a decentralised backtracking gate applied in Gauss-Seidel order restores clean monotone descent (99% of passes, surface removed matching the watcher's own). Quasi-criticality: 0001's sub-critical reading was an artifact of a constant DC drive, and once the operating point is calibrated the watcher-free chassis sits at branching ratio ~0.9 — but this is a tuned operating point, not self-organised criticality (a later sweep of dynamic depressing synapses found no parameter-free regime). The realistic reading of the topology is a cost-pole one: at scale the rule's grown geometry does read more critical than a frozen lattice (0.87 vs 0.75), but the causal chain 'wiring economy grows a small-world that drives criticality' is confounded — a static-lattice rewire is already small-world, and a degree-matched random graph reaches the same branching ratio — so surface minimisation is a cost prior here, not the generator. The holographic precondition, retested on a clean toroidal boundary with a controls-validated mutual-information estimator (the dimensionality-robust ones fail a known-volume-law control), reads volume-law — the expected thermal default of an idle quasi-critical net — which relocates the live area-law question to the dynamical phase under an encoding/FEP task. The same chassis, scaled and ported to async event-driven execution, becomes v0.2. A second pass then audits not whether the structure descends but how it moves, and finds the inherited teacher remodels like a seizure — add-only, global, on the activity timescale (32 edges per pass, zero pruning, a 25-tick cadence inside the 11-tick avalanche band), violating the slow-drive/fast-relaxation axiom of self-organised criticality. We retime it per-neuron (lognormal periods — desynchronisation, not mere slowing) and make it activity-gated and balanced (a local calcium-coincidence set-point with formation/elimination turnover and tag-and-capture consolidation), then re-distil that teacher, so the local rule inherits breathing rather than seizing structure. The fix exposes that structure and function are one controller (postsynaptic calcium to CaMKII) with two readouts — the volatile synaptic weight and the durable wiring — and it earns a result: a causal double dissociation in which the connectivity layout alone decodes a past stimulus, the decode following the gate rather than the operating point (invariant across a 3.3x branching-ratio sweep; an ablated network at higher criticality still cannot decode), with the gated memory-bearing structure reaching the in-vivo reverberating regime at scale. The layout is the memory.
foundationalcomputationneuroscienceneural-cellular-automatanambu-gotolocal-ruledistillationscale-invariancesurface-optimizationself-organizationstructural-plasticitycalcium-gatingstructural-memoryPSI-E1The Spiking Prototype: a Nambu-Goto-Enforced Substrate and What It Does (Not) Achieve
v0.1 — a 3-D LIF/ALIF blob with node-placed functional plasticity, two slow homeostats, Dale's-law E/I balance, and a global surface-minimisation watcher; the honest baseline the local-rule programme must beat
Danyiel Colin2026-065 sections last modified Jun 2026Criticality and Nambu-Goto surface minimisation are emergent global properties: neither may be enforced from outside at runtime without making the result circular. This paper presents v0.1, a deliberately honest prototype that enforces the geometry anyway — a global watcher slides the free interior of a 3-D embedding down the gradient of the physical-network surface action S = Σ π w L and rewires by proximity — so there is a working substrate and a measured baseline. The atomic unit is a leaky integrate-and-fire neuron with spike-frequency adaptation; its functional plasticity lives on the node (a learnable membrane time constant and threshold), not on O(E) edges, and its synapses are scalar weights under local STDP behind a three-factor interface. Excitability is regulated by two slow, literature-grounded homeostats — Triesch intrinsic plasticity (threshold) and Turrigiano synaptic scaling (weight) — over a Dale's-law excitatory/inhibitory balance. We justify each choice and then test the substrate honestly. Across 36 runs (sizes, seeds, and ablation arms) the watcher minimises surface every pass; the population is alive and rate-regulated; and the branching ratio σ_MR sits sub-critical at ≈0.32, tight across seeds — the expected negative under globally-enforced geometry. The load-bearing finding is a clean discriminator: ablate the homeostat and σ_MR collapses to ≈1.0 (synchrony), so excitability regulation, not the geometry, is what keeps the substrate measurable. v0.1's job is to establish the substrate and prove its central property is not an artefact of its regulator — and to make the case that the enforced geometry must instead be *earned* by a local rule, which is the next paper.
foundationalcomputationneurosciencespiking-neural-networkLIFcriticalitynambu-gotohomeostasisSTDPself-organizationnode-migrationPSI-E1substrate