Wilson-Cowan source and polyglot fidelity evidence

This page records the scientific boundary, equations, five-runtime parity, failure atomicity, and controlled benchmark used to promote WilsonCowanUnit to the polyglot-complete catalogue.

Scientific scope

Wilson and Cowan (1972) derive coupled coarse-grained equations for excitatory and inhibitory population activities. Their final population equations include response functions and availability/refractory factors. The maintained SC-NeuroCore model uses the common normalised reduction

[ \tau_e\dot E=-E+S(w_{ee}E-w_{ei}I+I_{ext}),\qquad \tau_i\dot I=-I+S(w_{ie}E-w_{ii}I), ]

with a shifted logistic satisfying (S(0)=0). It omits the paper's explicit availability/refractory multipliers and does not expose an independent inhibitory external input. This scope is declared in the Python model, paired schemas, descriptor, and public documentation.

Primary source: Wilson and Cowan 1972, doi:10.1016/S0006-3495(72)86068-5.

Numerical contract

Every runtime evaluates the same four RK4 stages from the same pre-step E/I pair and commits both candidates together. The branch-stable logistic avoids overflow at finite saturation inputs. Configuration requires finite, non-negative weights; positive time constants, steepness, and dt; finite theta; and E/I values inside the normalised [-beta, 1] state envelope, where beta = logistic(-a * theta). The shifted response itself remains in [-beta, 1-beta]; accepting the saturated initial boundary 1 is safe because the relaxation term immediately points inward.

The public batch accepts one constant excitatory current. Existing raw native parity tests additionally exercise varying drive vectors. All native batch surfaces validate the whole contract before caller-visible writes.

Executable parity matrix

Runtime	Executed surface	Enrolled result
Python	public scalar and atomic batch	reference
Rust engine	PyO3 modular batch	complete trace within 1e-9
Rust safety	independently compiled module	RK4 reference, saturation boundary, and atomic errors; 7/7 tests
Julia	simulate_wilson_cowan! through JuliaCall	complete trace within 1e-9
Go	generated C-shared ABI	complete trace within 1e-9
Mojo	exported shared-library C ABI	complete trace within 1e-8

The controlled trajectory starts from E=0.1, I=0.05, uses the default weights, time constants, shifted sigmoid, and dt=0.1, then applies I_ext=1.5 for 100,000 RK4 steps. The Python canonical interleaved E/I trace has SHA-256 0033492a00af00c389e88bee83b5a48cad74137f311a4bfb36e9882c42b6c50e.

The focused tests also cover sigmoid asymptotes, quiescent, driven, and sustained oscillatory regimes, an RK4-versus-Euler discriminator, empty batches, explicit-unavailable backends, malformed native results, corrupted mutable state, invalid external drive, and Go/Mojo contracts whose caller buffers must remain unchanged.

Generated-RTL co-simulation

tests/test_cosim_wilson_cowan.py first proves that the authored TOML and JSON schemas are structurally identical and that both reproduce the maintained hand RK4 trajectory within 1e-15. It then generates the production Q32.32 Verilog module and executes it with Icarus/Verilog over 96 mixed-drive samples:

• 8 samples at I_ext=0;
• 16 each at I_ext=1.5, 3.0, and 5.0;
• 8 at I_ext=-1.0;
• 32 sinusoidally varied samples centred at 2.0.

The measured maximum absolute error across both public E/I outputs is 0.019371701775768302, below the declared 0.021 envelope. Both rates remain inside the normalised Wilson-Cowan state envelope and every spike_out value is zero. The test asserts Icarus availability instead of skipping, so missing hardware tooling fails the lane closed.

Controlled benchmark

benchmarks/bench_wilson_cowan.py measures the complete 100,000-step E/I trace through each public dispatcher five times after warm-up. It fails if any runtime is absent, standalone Rust-safety tests fail, or a trajectory or final- state delta exceeds 1e-9 for Rust/Julia/Go or 1e-8 for Mojo.

The committed artefact records every raw sample, exact source and native-binary hashes, tool versions, affinity, load, and parity deltas. It is single-logical- CPU, non-exclusive local regression evidence, not production, cross-host, hardware, or universal-ranking evidence.

The exact measured timing table is reproduced in Benchmark Comparison. The dedicated wilson-cowan-rk4-five-backend-local-regression evidence gate rejects missing backends, source drift, parity drift, or missing numerical timing records. The aggregate 2026-07-14 gate report evaluates this Wilson-Cowan gate with zero Wilson-Cowan failures. Its overall status remains red because 68 source-hash drifts belong to older benchmark artefacts elsewhere in the repository; those inherited failures are retained in the report rather than suppressed.

Boundaries

• E and I are continuous normalised population activities, not spikes.
• The maintained equations are an explicit normalised reduction, not a verbatim reproduction of the paper's availability/refractory factors.
• Only the excitatory population receives an exposed external drive.
• RK4 is a maintained numerical choice, not a method prescribed by the paper.
• The benchmark is local non-exclusive regression evidence.
• Generated Q32.32 trajectory execution is H1 co-simulation evidence only.
• No formal equivalence, synthesis, timing, device, PPA, or production-speed result is claimed.

Reproduction

Bash

rustc --edition 2021 --test \
  src/sc_neurocore/accel/rust/safety/wilson_cowan.rs \
  -o /tmp/wilson_cowan_tests
/tmp/wilson_cowan_tests

PYTHONPATH=bridge:src:. .venv/bin/python -m pytest -q \
  tests/test_model_wilson_cowan.py \
  tests/test_wilson_cowan_accel_dispatch_contracts.py \
  tests/test_wilson_cowan_backends.py \
  tests/test_bench_wilson_cowan.py \
  tests/test_cosim_wilson_cowan.py

taskset -c 4 env PYTHONPATH=bridge:src:. .venv/bin/python \
  benchmarks/bench_wilson_cowan.py \
  --json benchmarks/results/bench_wilson_cowan.json