spirals — optimizers, checkpointing, resume, inference

Two-spirals classification (the classic Lang & Witbrock task, 400 points) with a 2-64-64-2 tanh MLP, trained full-batch for 2000 steps — once per optimizer: SGD (Nesterov momentum), AdamW, Muon, APOLLO, and APOLLO-Mini, plus a final adamw-groups run that composes param groups (decay / no-decay), a warmup-cosine lr schedule, and global-norm gradient clipping — the standard LLM training recipe in miniature (main.zig).

For every optimizer the demo:

1. trains, checkpointing model + optimizer state at the halfway step (under /tmp/fucina-spirals-*, deleted at the end);
2. restores that checkpoint into a fresh model + optimizer, retrains the second half, and demands bit-identical final parameters — the process exits nonzero on any non-bit-exact resume;
3. reloads the final weights into a gradient-free constant model (the inference path) and reports its accuracy.

Muon/APOLLO routing: hidden matrices take the matrix path, the classifier head goes to the AdamW fallback, biases auto-route to the fallback.

No weights, no flags:

zig build spirals -Doptimize=ReleaseFast

Each [name] block prints final loss/accuracy and the resume max |delta param| (must be bit-exact); the five plain-optimizer blocks also print the from-checkpoint inference accuracy. The adamw-groups run stops at the resume proof — its point is that the schedule factor is a pure function of the step, so the composed set replays bit-exactly.

Shared knobs

The ReleaseFast/-Dcpu build discipline and global thread/BLAS knobs are shared machinery — see docs/RUNNING-MODELS.md. This demo takes no arguments.