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.
activity_dynamics.tex— Paper sourceactivity_dynamics.pdf— Compiled PDFgen_figures.py— Python script to generate figuresindex.html— Live interactive demo page served directly by 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.