PRD — Single --depth N knob auto-derives every pretrain HP

Goal

tinygpt train --depth 12 ... should auto-derive d_model, n_heads, d_mlp, peak_lr, batch_size, and total_steps from compute- optimal scaling laws. UX win — most users don’t want to tune 6 hyperparameters when the depth alone implies a reasonable point.

karpathy/nanochat ships this exact pattern. We borrow the surface.

Why now

• B6 (Mac app demo) wants a 1-click train flow. Six hyperparameter fields in the app are six bugs waiting to happen. --depth is the right abstraction.
• TinyGPT users currently hand-set d_model / n_heads / etc. via ModelConfig presets. Presets work for ~5 named sizes; everything in between is hand-tuning.
• Cheap to add — a single function that maps depth → ModelConfig + TrainSchedule.

Scope — in

• Sources/TinyGPTModel/DepthDerivation.swift — deriveHP(depth: Int) -> (config: ModelConfig, schedule: TrainSchedule) per the scaling laws documented in nanochat’s recipe + the Chinchilla compute- optimal corner.
• tinygpt train --depth N flag — when set, overrides individual HP flags (with a warning if conflicting flags are also passed).
• Documented table in docs/training_guide.md mapping depth → derived HPs, so users can verify what they’re getting.

Scope — out

• Width independent of depth. V1 is depth-driven; aspect-ratio tuning is V2.
• µ-Transfer (µP) for HP transfer across scales. Bigger arc; defer.
• Recipe presets for non-Chinchilla regimes (longer-than- compute-optimal training, etc.). V1 = Chinchilla corner.

Files to touch

Acceptance criteria

• tinygpt train --depth 12 --corpus shakespeare.txt --steps 1000 runs with auto-derived HPs and reports them in the banner.
• Derivation matches nanochat’s curve to ±10% on the chinchilla- optimal points.
• Existing recipe paths (explicit d_model / n_heads / etc.) unchanged.

Reference patterns

• karpathy/nanochat — direct inspiration.
• Chinchilla, Hoffmann et al. 2022 — the compute-optimal curve. Cite.

Open questions

• Whether the derivation hits the Chinchilla corner or a slightly over-trained corner for small models. Recommendation: add a --regime {chinchilla,overtrained} flag, default chinchilla.