PHASE6_HETERO_POS.md

Phase 6 — heterogeneous positional bias: content–position balance ties, the temperature knob hurts

A final orthogonal probe (2026-06-23) closes the applied attention arc by testing the only axis the earlier bake-offs had not: per-head content↔position balance. The verdict re-confirms the Phase-5 selection — learnable-ALiBi (one learnable linear slope per head, nothing else) is the hypothesis to ship.

Why this experiment

The GPU bake-off winner, learnable-ALiBi, learned per-head slopes spanning ~125× (0.68 → 0.005), with the flattest heads going essentially NoPE-like. So its +8% was never "a better distance curve" — it was the model self-organizing into sharp-local heads plus near-global content-only heads. Every variant that added more distance shape (Calabi–Yau curve, log-curvature, Fourier features) overfit and lost at scale. The untried, orthogonal axis is to make that local↔global mixture explicit: give each head a learnable content scale c_h so it can choose how much weight the content score q·k carries relative to the positional penalty −a_h·d:

score_h(i,j) = c_h · (q_i · k_j)/√D  −  a_h · (i − j)        [content_balance]

Hypothesis: making the local↔NoPE mixture explicit (learnable slope a_h and learnable content scale c_h) should modestly improve perplexity and — the real prize — improve length extrapolation, without the overfit that killed "more shape". A per-head softmax temperature τ_h was added as an extra-knob ablation. Pre-committed KILL: if content_balance gives no extrapolation gain over alibi_learn.

Schemes: alibi_fixed (baseline), alibi_learn (the bake-off winner / control), nope (content-only sanity), content_balance (the hypothesis), cb_softmax_temp (content_balance + per-head temperature).

GPU result (NVIDIA L4, 2026-06-23, full preset)

Trained from scratch on real WikiText-2 (Salesforce/wikitext, wikitext-2-raw-v1), d_model 512 / 8 layers / 8 heads, ctx 512, 4000 steps, batch 24, γ-L2 1e-3, val early-stop. Primary metric: validation perplexity at 1×/2×/4×/8× the training context (length extrapolation; lower is better).

mode	1× (512)	2× (1024)	4× (2048)	8× (4096)
alibi_fixed	3.705	3.623	3.577	3.513
alibi_learn (control / winner)	3.651	3.559	3.500	3.429
nope	10.290	10.845	11.571	12.311
content_balance (hypothesis)	3.642	3.548	3.488	3.428
cb_softmax_temp (+ temperature)	3.732	3.659	3.599	3.548

content_balance vs alibi_learn @4×: +0.35% (and +0.17% @8×).

Verdict — KILL the extra knobs; learnable-ALiBi stands

1. content_balance ties alibi_learn within noise (+0.35% @4×, +0.17% @8×). The learnable content scales settled near 1.0 with a mild upward drift toward the flatter/global heads (c ≈ 0.79 → 0.93 across the slope-ordered heads) — the model does want global heads to lean a little more on content, but the effect is marginal and does not clear a meaningful margin. KILL per the pre-committed criterion (no extrapolation gain over alibi_learn).
2. The softmax-temperature knob regresses — cb_softmax_temp is worse than plain alibi_learn at every length (3.732 vs 3.651 @1×). This is the recurring Phase-4/5 pattern once more: extra parameters hurt at scale. Notably the local screen (d128/L3, 800 steps) had crowned cb_softmax_temp the best scheme — another instance of a short, small screen rewarding the highest-capacity variant that then loses when properly trained.
3. nope collapses and gets worse with length (10.3 → 12.3), the expected sanity check that the positional penalty is doing real work.

What this adds to the arc

Phase 6 was the last orthogonal axis left to try — not more distance shape (Phases 4–5 closed that), but content/position mixing. It lands in the same place: adaptability beats added structure, but only up to the single learnable slope. Once each head can pick its own slope, an explicit content-balance knob is redundant (the model already realizes the local↔global split through the slope alone) and a temperature knob is actively harmful.

Selected hypothesis (final): a learnable per-head linear positional bias (learnable-ALiBi) — one slope per head, no log-curvature, no Calabi–Yau sequence, no content scale, no temperature. It is the robust GPU-scale winner across every bake-off (Phases 4, 5, 6), passes the §5 gate at +8.1% over the best baseline, and extrapolates flat where learned-absolute positions collapse.

Artifacts: 4_ai_hardware_attention/cy_sieve_hetero_pos.py (experiment), gpu_phase_runs/hetero_pos_gpu_20260623.json + .log (GPU run), gpu_phase_runs/hetero_pos_local_20260623.json (local screen). See also PHASE5_FINAL_BAKEOFF.md and CYSIEVE_JOURNEY.md.