A short paper showing that gradient descent on network weights induces kernel descent in the space of neural activities, governed by a neural-tangent-kernel-style Gram matrix on internal neurons.
Key result: When the kernel is diagonally dominant (wide networks), each neuron's activity change is approximately proportional to the negative loss gradient with respect to that neuron's activity — converting untestable claims about synaptic learning rules into testable predictions about observable activity changes.
Install uv, then run the complete dependency graph from the repository root:
uv run snakemake --cores 1This regenerates seeded simulation outputs, publication-ready figures,
manuscript assets, and the compiled paper. The Snakemake dependency graph is
the authoritative provenance record.
To rebuild one step, use uv run snakemake --cores 1 --forcerun <rule_name>.
Snakefile— the executable workflow and artifact lineageanalysis/— one explicit entrypoint per workflow stepdata/generated/— machine-generated intermediatesresults/— final scientific tables and figurespaper/activity_dynamics.tex— manuscript sourcepaper/activity_dynamics.pdf— compiled paperindex.html— static interactive demo for GitHub Pages
Launch the interactive demo — the runnable demo is the static browser page in index.html, served directly by GitHub Pages with no install or build step. Adjust width, depth, and learning rate to see how the kernel and diagonal approximation behave.