spb/forge Public MIT

- optimizer "adamw" | "muon": Newton-Schulz orthogonalized momentum on 2-D
  hidden matrices (composed from the existing matmul kernels on Metal),
  AdamW kept for embeddings/head/1-D params; muon_lr follows the lr schedule
- schedule "cosine" | "wsd": warmup-stable-decay with 1-sqrt cooldown,
  extendable runs, wsd_decay_frac
- gpt-50m base config + Muon+WSD and MobileLLM-style deep-and-thin variants

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

A complete transformer training stack with no ML dependencies: tensors,
autograd, hand-written Metal kernels, flash attention (forward and backward),
AdamW, BPE tokenizer, checkpointing and generation. Architecture is fully
config-driven — the same binary trains 12M to 205M parameter models.

Every Metal kernel is validated against a CPU reference (85 parity checks,
<=1e-4, most bit-exact), gradients against central finite differences, and
each optimization was accepted only after the training loss trajectory stayed
numerically unchanged.

Measured findings (M5 Max, documented in RESEARCH.md and paper/forge.tex):

- `constant constexpr` for MSL tile constants declares an address-space
  variable, not a compile-time constant. Loops stop unrolling and every
  matrix accumulator spills: 0.82 -> 10.21 TFLOPS once switched to enums.
- That defect is invisible in the AIR at every -O level, because unrolling
  happens in the driver back end. Benchmark; do not read the IR.
- Register pressure, not bandwidth, dominates attention backward. Guided by
  measured spill counts, three restructurings took it 107 -> 7.05 ms (15.2x).
- On M5, mpp::tensor_ops::matmul2d reaches 51.5 TFLOPS with f16 operands vs
  10.6 for a tuned simdgroup_matrix kernel (4.9x), verified numerically.
  f16 on the simdgroup path alone is worth only +18-22%.
- Concurrent dispatch for the optimizer sweep: +22% on the 100M config.

Trained the 12.2M config for one epoch over 19.14M TinyStories tokens:
loss 8.40 -> 2.99, validation 3.009, perplexity 20.27, ~38.2k tokens/sec.