Per pearl_controller_anchors_isv_driven, every controller anchor/target/
cap derives from a tracked signal, not hardcoded constants. The σ-only
revert kept Kendall σ as a free Adam-learned scalar — that violated ISV
discipline and fought Adam's m/√v normalization
(pearl_adam_normalizes_loss_weights).
Single source of truth for both per-horizon controllers:
log_sigma_h[h] ← max(log(0.5), 0.5 * log(loss_ema[h]))
Kendall equilibrium (∂L/∂log σ = 0 ⟹ σ_h² = mean_bce_h)
in closed form. Asymmetric floor at log(0.5) prevents
collapse. No Adam state, no gradient delay.
lambda[h] ← clamp(1.0, 2.0, 1.0 + Z_SCALE_ISV * z_h)
Z_SCALE_ISV = (LAMBDA_CEILING - LAMBDA_FLOOR) / z_max_ema
Adaptive scale auto-uses the full clamp envelope:
the historical-max-z horizon maps exactly to
LAMBDA_CEILING. Replaces hardcoded Z_SCALE=0.5 which
rarely engaged on real data (max observed λ ~1.04).
Both anchor on the same ISV (loss_ema). z_max_ema is a new single-scalar
EMA state tracking max |z| across horizons, with first-obs bootstrap.
Removes:
- opt_log_sigma AdamW optimizer (σ no longer learned)
- grad_log_sigma_h_d memset (BCE kernel writes; output ignored — kept
only to preserve BCE kernel signature)
Kernel signature change (horizon_ema_and_lambda):
+z_max_ema [1] (read+write EMA state)
+log_sigma_h [5] (closed-form output, overwrite)
Discipline:
- First-obs bootstrap (sentinel <= 0) per pearl_first_observation_bootstrap
- Permanent floor (max(real, floor)) per pearl_blend_formulas_must_have_permanent_floor
- Asymmetric clamp per pearl_audit_unboundedness_for_implicit_asymmetry
- Z-score normalisation per pearl_zscore_normalization_for_magnitude_asymmetric_signals
- No nvrtc, no atomicAdd, no host branches in graph capture
All 9 perception_overfit tests pass — including
horizon_ema_and_lambda_track_after_training which validates the kernel
end-to-end through 64 K-loop iterations of capture/replay.
Submit local smoke; cluster A/B vs σ-only baseline (0.7506/0.7519) and
vs Phase 1+2+3 (0.7749/0.7591) follows once the perf-only 3-fold A/B
confirms no regression at b23f8f2ef.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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