ADR: StoryLM-0 NLL ∘ decoder train step

Context

Section 14 SGDs the embedding table from seed ones on the logits. Section 10 already has VJPs for the NLL composition. Section 11 already allows one SGD composition per tensor. Neither slice put NLL and every decoder weight in one program.

Mean reduction of [B, T] NLL is unspecified. Next-token shift inside the graph is unspecified.

Decision

Specify the composition in 15-nll-decoder-train.md:

• Differentiated body = decoder let-spine + Section 9 NLL. Primal is per-token NLL. Seed ones is sum of token NLLs, not mean.
• token_ids and targets are discrete I64 parameters.
• After projection, apply Section 11 SGD to {token_embedding, wq, wk, wv, wo, lm_head}. Bind and discard mask / scale cotangents.
• The wrapper returns the constructed tuple (nll, emb', wq', wk', wv', wo', lm') under the existing Section 12 multi-result ABI.

No new operator.

Consequences

• storylm0_nll_step.kina is the host numeric instance.
• AdamW, mean NLL, in-graph target shift, sampling, and KV-cache remain later sections.