Figure impossibility · A Small Switch in a Vast Machine

Figure viewer

Back to article ↩

← Back to article

One scalar weight moves the two activation changes along the descending line (δw,−δw). The equal-positive request (+d,+d) is visibly off that line. — A shared-weight constraint · Exact mathematical model
One weight moves the two inputs in opposite directions, so it cannot shift both positively. This exact counterexample assumes a bias-free linear model; an editable bias changes what is possible.
Settings, scope and source files
Exact counterexample $h_w(x)=wx$ at $x=\pm1$ . A shared weight update yields $(\delta w,-\delta w)$ , so the direct request $(+d,+d)$ is unreachable for $d\ne0$ . An editable bias would change this conclusion.
Source asset (original) ↧ Source asset (GIF) ↧ Source asset (MP4) ↧