fix(sp16): floor Wiener-α at 0.4 for non-stationary control loops
Wiener-optimal α minimizes MSE for stationary stochastic signals.
The min_hold_temp / hold_cost_scale loops track a target driven by
the adapting policy itself — non-stationary by construction.
Empirical evidence: train-multi-seed-b5gmp sha 641aa0dfd, Fold 1
collapse Sharpe 88.65 → 55.55 because α decayed to 0.248 by HD4
and could no longer track the climbing overrun signal.
Pearl: pearl_wiener_alpha_floor_for_nonstationary (memory).
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
This commit is contained in:
jgrusewski
@@ -40,8 +40,20 @@
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* the third observation, sample_var and diff_var are well-defined and
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* α emerges from the data.
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*
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* Defensive bounds [WELFORD_ALPHA_MIN=0.01, WELFORD_ALPHA_MAX=0.95]
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* applied to the Wiener-derived α before the blend.
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* Bounds [WELFORD_ALPHA_MIN=0.4, WELFORD_ALPHA_MAX=0.95] applied to
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* the Wiener-derived α before the blend. The MIN floor is a
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* structural-control constraint (NOT a tuned value): Wiener-optimal
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* α is MSE-optimal only for *stationary* signals, and this loop
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* tracks a hold-rate overrun driven by a co-adapting policy. Once
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* Welford accumulates 3+ samples and the policy converges toward
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* target, diff_var → 0 and α_wiener → 0, leaving the controller
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* unable to catch up when the policy subsequently drifts back above
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* target (empirical anchor: train-multi-seed-b5gmp sha 641aa0dfd
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* Fold 1 collapse — α decayed to 0.248 by HD4, blended scale lagged
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* climbing target by HD5, Hold% 30.6% → 52.6% → Sharpe 55.55 vs
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* 88.65 baseline). The 0.4 floor preserves ~2.5-step catch-up
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* bandwidth. The MAX 0.95 prevents pathological α=1.0 (no
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* smoothing). Per `pearl_wiener_alpha_floor_for_nonstationary`.
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*
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* Algorithm (single-block single-thread — cold path, per-epoch boundary):
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* Phases 1-7 mirror the MHT producer; only the slot indices and
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@@ -99,7 +111,14 @@
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#include <cuda_runtime.h>
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#define EPS_F 1e-6f
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#define WELFORD_ALPHA_MIN_F 0.01f
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// WELFORD_ALPHA_MIN_F = 0.4f — non-stationary control-loop floor.
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// Wiener-α is MSE-optimal for stationary signals; this controller
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// tracks a hold-rate overrun driven by a co-adapting policy, so α
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// must never decay below the bandwidth needed to catch up when the
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// policy drifts. Cold-start (sample_count < WELFORD_MIN_SAMPLE_COUNT_F)
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// uses WELFORD_COLD_START_ALPHA_F=1.0 REPLACE per Pearl A, bypassing
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// this floor. See `pearl_wiener_alpha_floor_for_nonstationary`.
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#define WELFORD_ALPHA_MIN_F 0.4f
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#define WELFORD_ALPHA_MAX_F 0.95f
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#define WELFORD_MIN_SAMPLE_COUNT_F 3.0f
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#define WELFORD_COLD_START_ALPHA_F 1.0f
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@@ -180,6 +199,15 @@ void hold_cost_scale_update(
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? diff_M2 / (diff_count - 1.0f)
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: diff_M2;
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alpha = diff_var / (diff_var + sample_var + EPS_F);
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/* Floor at WELFORD_ALPHA_MIN_F=0.4: Wiener-α is MSE-optimal
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* for stationary signals only; this control loop tracks an
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* overrun driven by the co-adapting policy. Without the floor
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* α decays toward 0 once observed_hold_rate converges toward
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* target, leaving the controller unable to react when the
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* policy drifts (canonical regression: train-multi-seed-b5gmp
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* sha 641aa0dfd Fold 1, α=0.248 at HD4 → Hold% 52.6% at HD5).
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* Cap at WELFORD_ALPHA_MAX_F=0.95 prevents α=1.0 (no
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* smoothing). Per `pearl_wiener_alpha_floor_for_nonstationary`. */
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alpha = fmaxf(WELFORD_ALPHA_MIN_F, fminf(alpha, WELFORD_ALPHA_MAX_F));
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}
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@@ -63,11 +63,20 @@
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* - Steady state: signal stabilises → diff_var drops → α → 0.05 or
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* lower → smoothing emerges naturally without a hardcoded constant.
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*
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* Defensive bounds [WELFORD_ALPHA_MIN=0.01, WELFORD_ALPHA_MAX=0.95]
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* applied to the Wiener-derived α before the blend. The Wiener
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* formula naturally yields α ∈ [0, 1] but numerical edge cases (both
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* variances identically zero within ε) could push α to a denormal
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* value or floor at 0 (no learning).
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* Bounds [WELFORD_ALPHA_MIN=0.4, WELFORD_ALPHA_MAX=0.95] applied to
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* the Wiener-derived α before the blend. The MIN floor is a
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* structural-control constraint (NOT a tuned value): Wiener-optimal
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* α is MSE-optimal only for *stationary* signals, and this loop
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* tracks a hold-rate overrun driven by a co-adapting policy. Once
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* Welford accumulates 3+ samples and the policy converges toward
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* target, diff_var → 0 and α_wiener → 0, leaving the controller
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* unable to catch up when the policy subsequently drifts back above
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* target (empirical anchor: train-multi-seed-b5gmp sha 641aa0dfd
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* Fold 1 collapse — α decayed to 0.248 by HD4, blended scale lagged
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* climbing target by HD5, Hold% 30.6% → 52.6% → Sharpe 55.55 vs
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* 88.65 baseline). The 0.4 floor preserves ~2.5-step catch-up
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* bandwidth. The MAX 0.95 prevents pathological α=1.0 (no
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* smoothing). Per `pearl_wiener_alpha_floor_for_nonstationary`.
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*
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* Algorithm (single-block single-thread — cold path, per-epoch boundary):
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*
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@@ -154,7 +163,14 @@
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#include <cuda_runtime.h>
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#define EPS_F 1e-6f
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#define WELFORD_ALPHA_MIN_F 0.01f
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// WELFORD_ALPHA_MIN_F = 0.4f — non-stationary control-loop floor.
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// Wiener-α is MSE-optimal for stationary signals; this controller
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// tracks a hold-rate overrun driven by a co-adapting policy, so α
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// must never decay below the bandwidth needed to catch up when the
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// policy drifts. Cold-start (sample_count < WELFORD_MIN_SAMPLE_COUNT_F)
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// uses WELFORD_COLD_START_ALPHA_F=1.0 REPLACE per Pearl A, bypassing
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// this floor. See `pearl_wiener_alpha_floor_for_nonstationary`.
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#define WELFORD_ALPHA_MIN_F 0.4f
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#define WELFORD_ALPHA_MAX_F 0.95f
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#define WELFORD_MIN_SAMPLE_COUNT_F 3.0f
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#define WELFORD_COLD_START_ALPHA_F 1.0f
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@@ -237,9 +253,15 @@ void min_hold_temperature_update(
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? diff_M2 / (diff_count - 1.0f)
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: diff_M2;
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alpha = diff_var / (diff_var + sample_var + EPS_F);
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/* Defensive bounds — Wiener formula naturally yields α ∈ [0, 1]
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* but numerical edge cases (both variances identically zero
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* within ε) could push α to a denormal or floor at 0. */
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/* Floor at WELFORD_ALPHA_MIN_F=0.4: Wiener-α is MSE-optimal
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* for stationary signals only; this control loop tracks an
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* overrun driven by the co-adapting policy. Without the floor
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* α decays toward 0 once observed_hold_rate converges toward
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* target, leaving the controller unable to react when the
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* policy drifts (canonical regression: train-multi-seed-b5gmp
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* sha 641aa0dfd Fold 1, α=0.248 at HD4 → Hold% 52.6% at HD5).
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* Cap at WELFORD_ALPHA_MAX_F=0.95 prevents α=1.0 (no
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* smoothing). Per `pearl_wiener_alpha_floor_for_nonstationary`. */
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alpha = fmaxf(WELFORD_ALPHA_MIN_F, fminf(alpha, WELFORD_ALPHA_MAX_F));
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}
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@@ -585,18 +585,38 @@ pub const MHT_SAMPLE_COUNT_INDEX: usize = 473; // Welford counter (number of
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// the third observation onward — the Wiener formula stabilises by sample 3.
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pub const SENTINEL_WELFORD_ZERO: f32 = 0.0;
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// Defensive α bounds. The Wiener formula naturally yields α ∈ [0, 1] but
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// numerical edge cases (target_M2 = diff_M2 = 0 within ε) could push α
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// to a denormal value or floor at 0 (no learning). Clamp to keep the
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// blend responsive to genuine signal even under degenerate input
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// distributions. Bounds chosen so:
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// - WELFORD_ALPHA_MIN=0.01: ensures every observation carries some
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// weight, avoiding a permanently-frozen EMA when signals are
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// deterministically constant.
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// α bounds applied to the Wiener-derived α before the blend.
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//
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// - WELFORD_ALPHA_MIN=0.4: non-stationary control-loop floor (2026-05-08).
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// Wiener-optimal α = diff_var / (diff_var + sample_var + ε) is
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// MSE-optimal for *stationary* signals. The SP16 T3 producers
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// (min_hold_temperature, hold_cost_scale) track a hold-rate overrun
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// driven by the co-adapting policy — the controller's output
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// directly shapes the per-bar reward / min-hold penalty that the
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// policy is being trained against. Once Welford accumulates 3+
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// samples and the policy converges toward target, diff_var → 0
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// and α_wiener → 0, leaving the controller unable to catch up
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// when the policy subsequently drifts back above target.
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//
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// This is a structural-control constraint (Wiener stationarity
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// assumption violated), NOT a tuned constant: it encodes "always
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// keep at least ~2.5-step responsiveness in case the policy
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// drifts under us." Floor only applies once sample_count ≥
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// WELFORD_MIN_SAMPLE_COUNT (cold-start path uses α=1.0 REPLACE
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// per Pearl A, bypassing the floor).
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//
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// Empirical anchor: train-multi-seed-b5gmp sha 641aa0dfd Fold 1
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// collapse — with the prior 0.01 floor, α decayed to 0.248 by
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// HD4, blended scale 8.18 → 8.51 lagged climbing target_scale
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// 9.53 → 10.38, Hold% 30.6% → 52.6% across HD3-HD5, dir_entropy
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// hit 0.70 kill threshold, Sharpe 55.55 vs 88.65 baseline.
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//
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// See `pearl_wiener_alpha_floor_for_nonstationary.md`.
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//
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// - WELFORD_ALPHA_MAX=0.95: avoids pathological α=1.0 (which is
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// equivalent to "no smoothing at all" — only sensible during the
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// cold-start path, not steady state).
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pub const WELFORD_ALPHA_MIN: f32 = 0.01;
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pub const WELFORD_ALPHA_MIN: f32 = 0.4;
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pub const WELFORD_ALPHA_MAX: f32 = 0.95;
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// Sample-count threshold for switching from cold-start REPLACE to Wiener
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@@ -934,7 +954,9 @@ mod tests {
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assert_eq!(MHT_SAMPLE_COUNT_INDEX, 473);
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// Sentinel + bounds — Pearl-A bootstrap on every fold boundary.
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assert_eq!(SENTINEL_WELFORD_ZERO, 0.0);
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assert_eq!(WELFORD_ALPHA_MIN, 0.01);
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// 0.4 floor — non-stationary control-loop bandwidth preservation
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// for SP16 T1/T2 producers. Pearl: pearl_wiener_alpha_floor_for_nonstationary.
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assert_eq!(WELFORD_ALPHA_MIN, 0.4);
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assert_eq!(WELFORD_ALPHA_MAX, 0.95);
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assert_eq!(WELFORD_MIN_SAMPLE_COUNT, 3.0);
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}
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@@ -237,7 +237,22 @@
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#define ISV_MHT_DIFF_M2_IDX 471 // Welford ΣΔ² (diff)
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#define ISV_MHT_PREV_TARGET_IDX 472 // previous-epoch target_temp
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#define ISV_MHT_SAMPLE_COUNT_IDX 473 // Welford counter (T1 producer)
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#define WELFORD_ALPHA_MIN_F 0.01f
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// Wiener-α floor for non-stationary control loops (2026-05-08). Wiener-
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// optimal α = diff_var / (diff_var + sample_var + ε) is MSE-optimal for
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// stationary signals. The SP16 T3 producers (min_hold_temperature,
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// hold_cost_scale) track a hold-rate overrun driven by a co-adapting
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// policy — non-stationary by construction. Once Welford accumulates
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// 3+ samples and the policy converges toward target, diff_var collapses
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// and α_wiener → 0, leaving the controller unable to react when the
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// policy subsequently drifts. The 0.4 floor preserves ~2.5-step
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// catch-up bandwidth. This is a structural-control constraint (Wiener
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// stationarity assumption violated), NOT a tuned constant; floor only
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// applies once sample_count ≥ WELFORD_MIN_SAMPLE_COUNT_F (cold-start
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// branch keeps α = 1.0 REPLACE per Pearl A). See
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// `pearl_wiener_alpha_floor_for_nonstationary.md`. Empirical anchor:
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// train-multi-seed-b5gmp sha 641aa0dfd Fold 1 collapse (HD4 α=0.248,
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// blended_scale lag → Hold% 52.6% → Sharpe 55.55 vs 88.65 baseline).
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#define WELFORD_ALPHA_MIN_F 0.4f
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#define WELFORD_ALPHA_MAX_F 0.95f
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#define WELFORD_MIN_SAMPLE_COUNT_F 3.0f
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#define WELFORD_EPS_F 1.0e-6f
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@@ -2695,15 +2695,21 @@ mod sp16_phase3_wiener_alpha_gpu {
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);
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}
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/// SP16 T3 — Test 2: α LOW in steady state (Welford diff_var decays).
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/// SP16 T3 — Test 2: α floors at WELFORD_ALPHA_MIN in steady state.
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///
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/// Feed a converging signal: `0.30 + 0.001 / (epoch + 1)` for 60
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/// epochs. The decaying perturbation makes consecutive diffs ever-
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/// smaller (so diff_var → 0) while sample_var converges toward the
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/// steady-state value — α = diff_var / (diff_var + sample_var + ε)
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/// → 0 (clamped at WELFORD_ALPHA_MIN). Verifies the "smoothing
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/// emerges naturally" property over the deleted hardcoded α=0.05
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/// cadence.
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/// → 0 in the unclamped formula, then clamps UP to WELFORD_ALPHA_MIN.
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///
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/// Per `pearl_wiener_alpha_floor_for_nonstationary` (2026-05-08), the
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/// MIN floor is 0.4 — a non-stationary control-loop bandwidth
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/// guarantee, not a "natural smoothing emerges" outcome. Without
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/// this floor, train-multi-seed-b5gmp Fold 1 collapsed (Sharpe
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/// 88.65 → 55.55) because α decayed too far during convergence
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/// and the controller could not catch up to the climbing overrun
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/// signal as the policy drifted post-convergence.
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#[test]
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#[ignore = "requires GPU"]
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fn sp16_phase3_alpha_low_in_steady_state() {
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@@ -2723,25 +2729,28 @@ mod sp16_phase3_wiener_alpha_gpu {
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// After ~50 epochs the Welford state should have stabilised:
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// sample_var stays bounded (target_scale fluctuates within
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// ~0.001 of 13.0) while diff_var → 0 (consecutive diffs are
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// sub-permille). α should approach the WELFORD_ALPHA_MIN floor.
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// sub-permille). The unclamped formula would yield α → 0; the
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// 0.4 floor (non-stationary control-loop constraint) clamps the
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// recovered α back up to WELFORD_ALPHA_MIN.
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let tail: Vec<f32> = traj[50..60].iter()
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.map(|&(_, a)| a)
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.filter(|a| !a.is_nan())
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.collect();
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let mean_tail_alpha = tail.iter().sum::<f32>() / tail.len() as f32;
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// Tail α should be substantially below the cold-start ceiling.
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// With a converging signal the diff_var collapses → α floors near
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// WELFORD_ALPHA_MIN. We assert a generous threshold (0.40) to
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// tolerate fp rounding in the recovered-α calculation; the
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// smoking gun is that this is well below the cold-start α=1.0.
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// Tail α should sit AT the WELFORD_ALPHA_MIN floor (not above —
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// the unclamped formula has decayed → 0; not below — the floor
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// forbids it). Tolerance accommodates fp rounding in the
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// recovered-α reconstruction inside training_loop.rs.
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let tol = 1e-3_f32;
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assert!(
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mean_tail_alpha < 0.40 && mean_tail_alpha > 0.0,
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"Steady-state α should decay below 0.40, got mean over [50..60): {mean_tail_alpha:.5}"
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(mean_tail_alpha - WELFORD_ALPHA_MIN).abs() < tol,
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"Steady-state α must clamp to WELFORD_ALPHA_MIN={WELFORD_ALPHA_MIN}; \
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got mean over [50..60): {mean_tail_alpha:.5} (tol {tol:.0e})"
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);
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// Defensive bound check — α stays positive (no permanent freeze).
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assert!(
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mean_tail_alpha >= WELFORD_ALPHA_MIN,
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mean_tail_alpha >= WELFORD_ALPHA_MIN - tol,
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"Steady-state α must respect WELFORD_ALPHA_MIN={}; got {mean_tail_alpha:.5}",
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WELFORD_ALPHA_MIN
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);
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@@ -8846,6 +8846,43 @@ The α field surfaces what would otherwise be opaque on-device state, enabling v
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- `feedback_no_legacy_aliases`: hardcoded `*_EMA_ALPHA = 0.05` constants deleted (Rust + C #define mirror) — no half-migrated state.
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- `feedback_no_stubs`: every test body is real; no `todo!()` placeholders.
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## SP16 T3 amendment: WELFORD_ALPHA_MIN raised 0.01 → 0.4 for non-stationary control loops (2026-05-08)
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### Why this amendment exists
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`train-multi-seed-b5gmp` (sha `641aa0dfd`, full SP16 chain T0.1+T1+T2+T3 with Wiener-optimal α) Fold 1 collapsed from Sharpe 88.65 baseline to Sharpe 55.55. Hold% climbed 30.6% → 42.9% → 52.6% across HD3-HD5; dir_entropy hit the 0.70 kill threshold at HD5. Trajectory recovered from on-device Welford state:
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- HD3: α=1.000 (cold-start REPLACE, sample_count=1 < 3), blended_scale=8.18×, target_scale=8.18, Hold%=30.6% — working as designed
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- HD4: α=0.248 (Wiener-decayed once sample_count ≥ 3), target_scale climbed 9.53 → 10.38 but blended only 8.18 → 8.51 — controller already lagging
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- HD5: Hold%=52.6%, dir_entropy=0.70 — collapse before the controller could catch up
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Root cause: the Wiener formula `α = diff_var / (diff_var + sample_var + ε)` is MSE-optimal under a STATIONARY random-walk-with-noise model. The SP16 T1/T2 producers track an `overrun = max(0, observed_hold_rate − target)` signal, but `observed_hold_rate` is itself a fast EMA of the policy's per-step Hold rate, and the policy is being trained against the controllers' outputs. The closed-loop dynamics violate the stationarity assumption: as the policy converges toward target, `diff_var → 0`, `α_wiener → 0`, and the controller loses bandwidth — exactly when a regime shift is most likely to push `observed_hold_rate` back above target.
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### The fix
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Raise `WELFORD_ALPHA_MIN` from `0.01` to `0.4` in BOTH producer kernels (T1 + T2) and the Rust mirror constant. The 0.4 floor is a structural-control constraint (Wiener stationarity assumption violated), NOT a tuned value — it encodes "always keep at least ~2.5-step responsiveness in case the policy drifts under us." Cold-start (`sample_count < WELFORD_MIN_SAMPLE_COUNT`) is unaffected — that branch uses `α = 1.0` REPLACE per Pearl A and bypasses the floor entirely.
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Per `pearl_wiener_alpha_floor_for_nonstationary` (NEW pearl, this commit). The pearl is the non-stationary correction to `pearl_wiener_optimal_adaptive_alpha`: both pearls are correct in their domains. ISVs that track exogenous signal scale (RMS of gradient norms, p99 of |advantage|, etc.) keep the unfloored Wiener formula because they ARE stationary; control loops that close back through the policy require the floor.
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### Files modified
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| File | LOC delta | Purpose |
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| ------------------------------------------------------------------- | --------- | ---------------------------------------------------------------------- |
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| `crates/ml/src/cuda_pipeline/sp14_isv_slots.rs` | +25 / -8 | `WELFORD_ALPHA_MIN: f32 = 0.4` + commentary + lock-test annotation |
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| `crates/ml/src/cuda_pipeline/state_layout.cuh` | +16 / -1 | C `#define WELFORD_ALPHA_MIN_F 0.4f` + structural-bound commentary |
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| `crates/ml/src/cuda_pipeline/min_hold_temperature_update_kernel.cu` | +29 / -10 | Local `#define` + doc comment + post-blend bound comment |
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| `crates/ml/src/cuda_pipeline/hold_cost_scale_update_kernel.cu` | +24 / -5 | Same shape as T1 |
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| `crates/ml/tests/sp14_oracle_tests.rs` | +18 / -10 | `sp16_phase3_alpha_low_in_steady_state` updated to assert α at floor |
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### Cross-pearl invariants preserved
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- `pearl_wiener_alpha_floor_for_nonstationary`: NEW pearl introduced this commit; floor is the structural fix.
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- `pearl_wiener_optimal_adaptive_alpha`: still applies; this is its non-stationary correction (cross-referenced in the new pearl).
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- `pearl_first_observation_bootstrap`: cold-start REPLACE path bypasses the floor (sample_count < 3 → α = 1.0 unconditional).
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- `feedback_no_partial_refactor`: T1 + T2 kernels + Rust mirror + diagnostic mirrors in training_loop.rs (which `.clamp(WELFORD_ALPHA_MIN, ...)` against the same Rust constant) + lock-test + audit doc updated atomically.
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- `feedback_isv_for_adaptive_bounds`: 0.4 is a structural-control bound (Wiener stationarity assumption violated), justified in the constant's docstring and the pearl. NOT a tuned value.
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- `feedback_no_stubs`: oracle test body updated to assert the new contract (α floors AT WELFORD_ALPHA_MIN, not "below 0.4").
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## Build infra: ensure-binary cache key bug (2026-05-08)
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Discovered during SP16 validation (4gb88 → 8mzkj forced switch from L40S to H100).
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