What you're seeing. A real multilayer network (4 → 4 → 4 → 4) with tanh hidden
units and a sigmoid output; a bit reads as 1 once its output passes 0.5. The answer chips
show the correct bits, so you can see the gap.
- Addition is the one you can realistically reach by hand — drag the output-bit wires
and biases until the answer chips turn green.
- Multiplication and division are nonlinear. The network can learn them to 100%
(only 16 cases to fit), but you'll almost never find the weights by hand — that's what
Train is for. One press gets most of the way; press again to converge.
- Train addition to 100%, then switch operation: the wires that solved
+ are
useless for ×. Each task needs its own shape.
- Compression rounds every weight to a coarse grid. Slide it down and watch the wires
snap to fewer thicknesses while accuracy falls. Training still runs in full precision; the
slider squeezes the result afterward.