feat(coordinator): add the SPEC §3.5 alternative heads (R10 ablation parity)

[minion1227]

The gap

SPEC §1.3 invariant R10 — "linear head ≥ all other head variants overall" (Table 3) — is the justification for shipping a plain linear routing head. The verifier for R10 is already merged (analysis/head_variants.py, #352): hand it a {variant: {benchmark: score}} table and it reports the overall ranking and the R10 verdict.

But nothing in src/ could ever produce a non-linear head, so the table it grades had to be typed in by hand from the paper. coordinator/ contains only head.py (LinearHead). This PR is the producer.

Four coordinator.head config knobs — type, hidden_dim, include_stop_action, factorize — also had zero readers anywhere in src/, so editing them silently did nothing.

What's here

coordinator/heads.py adds low-rank, sparse, block-diagonal-2 and block-diagonal-10 per SPEC §3.5. Each maps h → z and splits into the same two logit groups the linear head uses (z[:n_models] agent, z[n_models:] role, one softmax each), so a variant is a drop-in replacement at the decision boundary. param_counts() produces the params mapping the merged R10 verifier already accepts, for Table 3's efficiency column.

head           params        (at our n_a=6, d_h=1024)
low_rank       14,420
sparse          7,170
linear          6,144
block_diag_2    3,072
block_diag_10   1,024

Two SPEC problems this surfaced

Reproducing Table 3 exactly turned up two inconsistencies. Both are documented and pinned by tests rather than quietly worked around — flagging them is the point, since R10 is graded against these numbers.

1. Low-rank is internally inconsistent. A low-rank head is U ∈ R^{r×d_h} plus V ∈ R^{n_a×r} (σ is fixed, not a parameter) = r·(d_h + n_a). At the paper's d_h=1024, n_a=10 and the stated r=14, that is 14,476 — not the tabled 20,680, which requires r=20. The two cannot both hold.

This keeps the stated hyperparameter r=14 as the default, on the grounds that a hyperparameter is the more direct claim and silently switching to r=20 to make a derived total match would hide the conflict. Pass rank=20 to reproduce the table. Pinned by test_lowrank_rank14_contradicts_spec_table3.

2. d_h=1024 is not divisible by 10. SPEC's headline variant — block-diag-10, "one block per logit", "exact 10× reduction" to 1,024 params — is unconstructible with equal input chunks at the paper's own shape (1024/10 = 102.4).

The resolution: B must divide n_a (output logits split cleanly into blocks) but need not divide d_h. Inputs are partitioned into B contiguous near-equal chunks summing to exactly d_h (e.g. 103,103,103,103,102,…). Because the chunk sizes sum to d_h, the count is exactly (n_a/B)·d_h — no rounding, at any d_h — reproducing both 5,120 and 1,024. Requiring B | d_h instead would make the paper's own headline variant impossible to build.

Every other Table 3 count (linear 10,240; sparse 11,266; block-diag-2 5,120; block-diag-10 1,024) is reproduced exactly at the paper's shape.

Sparse's ρ carries no gradient, stated plainly

SPEC defines k = max(1, ⌊d_h·(1−σ(ρ))⌋). A floor to an integer has zero derivative almost everywhere, so ∂L/∂ρ is structurally zero however the mask is relaxed — the Gumbel relaxation makes which edges survive differentiable, not how many. ρ is kept as a parameter because SPEC's +2 counts it and because the gradient-free optimizers this repo actually uses for the head (sep-CMA-ES, Random Search) can search it. test_sparse_rho_has_no_gradient_path asserts this rather than hiding it. Only τ is gradient-trainable of the two.

Why it's low-risk

• Purely additive. params.py and policy.py are untouched. make_spec() computes n_head = n_a·d_h, which is linear-only and feeds the frozen submission dimension — wiring a variant into that path would change n_total and break submission, so this deliberately does not. Tests pin make_spec().n_total == 13312 and that policy still builds LinearHead.
• No default changes. from_config on the shipped configs/trinity.yaml reproduces exactly today's linear head (test_from_config_builds_the_shipped_config_unchanged).
• The registry reuses the shipped head, it does not re-implement it: make_head("linear") returns head.py's LinearHead, pinned identical by test_registry_linear_matches_head_py.
• Dead knobs are now honoured or rejected, never silently ignored: hidden_dim != 0, include_stop_action, and a non-two_softmax factorize each raise with an explanation, since no SPEC §3.5 head implements them.

Verification

• pytest tests/ -q → 1911 passed, 0 failed (81 new)
• ruff check src/ scripts/repo_governance/ → clean; mypy src/trinity/coordinator/heads.py → clean
• End-to-end: param_counts() feeding the merged analyze_heads() verifier returns the R10 verdict

Tests import torch lazily inside the test bodies and parametrize over a literal variant list (pinned against the registry by test_variants_list_matches_registry), because pytest imports test modules at collection time — a module-scope torch import would break test_shaped_fitness.py::test_no_torch_imported regardless of filename.

Note on CI: main has unresolved merge-conflict markers in src/trinity/analysis/__init__.py (introduced by dc15f97), so the package does not import and this PR is red on the merge commit. This branch touches no file in analysis/, and the 1911-passed run above was taken with those markers resolved locally.

The fix is not contested: #402, #405, #407, #408 and #403 all rewrite that file to the byte-identical result (every one is index 9916618..6865bc2), so merging any one of them repairs main and the rest become no-ops on that file. Note that #407 / #408 / #403 are already green — they touch that file for their own feature and resolved it in passing. Only PRs that don't touch it (this one, #415, #412) are red.

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