INTERACTIVE FIGURE 1A dense layer and its unit-net analog
ordinary dense layer W ∈ ℝ — any sign, any scale
hover a neuron (n1\u2013n5) to see its row \u2014 raw weight values appear on the edges
unit-net layer z = Pa − Na — Σ row(P) = 1, N ∈ [0,1]
hover a neuron (n1\u2013n5) \u2014 P shares (green) and \u2212N (rust) appear on the edges
excitation (+)inhibition (−)budget bar, ticked at 1.0
Same connectivity, two coordinate systems. On the left, each neuron's incoming row lives on whatever
scale training left it — hover different neurons and watch Σ|w| swing by ~40×, which is why "this weight is big" carries
no meaning across neurons. On the right the invariant is structural: every neuron's excitation stacks to exactly
1.000 (the black-ticked bar), every inhibitory synapse is ≤ 1, and edge thicknesses are comparable everywhere in the
figure. Each budget bar is the neuron's whole P row laid end to end: one green segment per input, in input order
(a1…a6), so a segment's length is that input's share of the budget and the white lines are the boundaries between
shares — hover the neuron and the same numbers appear on its edges. Resample as many times as you like — the segments
reshuffle, but the bar always fills to exactly the 1.0 tick.