README.md

metadata

title: Cortex-Conv — Browser-Native Equilibrium Propagation
emoji: 🧠
colorFrom: purple
colorTo: indigo
sdk: static
pinned: false
license: mit
short_description: 34K-param EqProp net at 96.8% MNIST, in your browser.
tags:
  - equilibrium-propagation
  - webgpu
  - mnist
  - fashion-mnist
  - biologically-plausible-learning
  - no-backprop
  - browser

cortex-conv

A 34,106-weight convolutional neural network trained with Equilibrium Propagation — no backpropagation — running entirely in your browser on WebGPU. Ships pre-trained at 96.8% MNIST test accuracy: the page loads at 96.8% on the very first visit.

The neuron is a leaky integrator with sigmoid activation. The training rule is two forward passes (free + ±β-clamped) plus a local activity-difference weight update — no backward graph, no transposed weights, no autodiff. Toggle to Fashion-MNIST to watch the same network train from scratch on clothing items, live.

What's in this Space

Panel	What it shows
Panel 03 — the lead	cortex-conv itself: a trained network that ships at 96.8% MNIST. Click train to keep refining; toggle data for Fashion-MNIST.
Panel 00 — context	The FitzHugh-Nagumo reaction-diffusion substrate that EqProp's underlying proof was developed on. Cortex-conv inherits the proof's broader-class guarantee but uses a simpler neuron.
Panel 01 — context	An inference shortcut cortex-conv deliberately doesn't use (it has a ~30-layer precision wall; cortex-conv has 3 layers and uses iterative settling instead).
Panel 02 — context	The self-adjointness proof that lets any EqProp variant work on this neuron class.

How cortex-conv stacks up

Method	Params	MNIST accuracy	Deployment
Kendall 2026 (FHN, 5-layer dense)	1,457,674	97.2%	Python
EqSpike (Martin et al. 2021, spiking)	unspec.	97.6%	neuromorphic HW
Oscillator Ising EqProp (2025)	unspec.	97.2% ± 0.1%	physical oscillators
Scellier & Bengio 2017 (original)	unspec.	97-98%	Python
cortex-conv (this Space)	34,106	96.8%	browser, WebGPU
(small backprop CNN, for context)	31,818	99.26%	Python

Honest positioning: the smallest browser-deployed EqProp net on MNIST. Slightly below the EqProp accuracy frontier (96.8% vs 97.2-97.6%) but orders of magnitude more deployable — no Python, no GPU server, no hardware lab, just a browser tab.

Technical write-up

See PAPER_COMPANION.md for the architecture, the four "cortex" learning ingredients (each with verified citations), the comparison math, and reproducibility instructions.

Related work

• Jack Kendall, Equilibrium Propagation and Hamiltonian Inference in the Diffusive FitzHugh-Nagumo Model, arXiv:2605.21568 (2026) — the self-adjointness proof Panel 02 visualises.
• Liu & Chen, FRE-RNN: Feedback Regulation for Practical EqProp, arXiv:2508.11659 (2025) — source of the adaptation-current ingredient.
• Kubo, Chalmers & Luczak, Adjusted Adaptation, arXiv:2204.14008 (2022) — source of the adjusted-relaxation ingredient.
• Zhang, Liu & Schaeffer, AdaGO: AdaGrad Meets Muon, arXiv:2509.02981 (2025) — the optimiser cortex-conv uses on top of EqProp gradients.
• Scellier & Bengio, Equilibrium Propagation, Frontiers Comp. Neurosci. (2017) — the foundational EqProp paper.

Requirements

A browser with WebGPU enabled (Chrome / Edge 113+ on macOS / Windows / Linux; Safari 18+ on macOS Sonoma). If WebGPU is unavailable the page falls back to a slower CPU path with a smaller embedded MNIST.

Files

Path	Purpose
index.html	The four-panel demo page
tests/gpu_lib_conv_multi.js	WGSL training pipeline (forward + ±β-clamped relaxation + gradient kernels)
tests/gpu_lib_deep.js	Muon / AdaGO optimisers + helpers
tests/gpu_lib_conv_full.js	WebGPU device init + command-encoder utilities
tests/eqprop_lib.js	Shared activation funcs + dataset loader
mnist/mnist_pack_28_60k.json	60K MNIST samples at 28×28 (base64-packed uint8)
fashion/fashion_pack_28_60k.json	60K Fashion-MNIST samples at 28×28
weights/cortex_conv_mnist_R28.json	Pre-trained cortex-conv weights (96.8% test acc, 720 KB)
PAPER_COMPANION.md	Full technical write-up

License

MIT.