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 figuresactivity_ntk_demo.jsx— Interactive demo source (React/JSX)
Launch the interactive demo — runs in your browser, no install needed. Adjust width, depth, and learning rate to see how the kernel and diagonal approximation behave.