cascade-heat9-var4-throughput-svcal

Heat9 is Heat8 plus one mathematical update only. It preserves Heat8's family and curriculum weights, rates, throughput optimizations, Numba kernels, batching, prefetch behavior, requirements, and all unrelated generator logic.

Stochastic-volatility calibration

Only stochastic-volatility rows inside _integrated change. For multiplier v_t = exp(clip(h_t, -2, 2)), Heat9 applies

v_t / sqrt((1-r) + r mean_prefix(v_t^2)),

where r = T / (T + 512) and T = min(L, 512).

The exponential is convex, so even centered h_t gives E[v_t^2] > 1. The empirical-Bayes correction shrinks the finite-prefix second moment toward one, reducing inflation without flattening the path: every multiplier in a row is scaled by one common normalizer, preserving relative volatility clustering.

Local CR1 evidence over 2026-07-16 through 2026-07-24 improved from 0.093705 to 0.085861 (8.4% lower), with every date improved. That result was derived from Var5 and does not guarantee transfer to Heat8/Var4.

Heat8 evidence and scope

The 2026-07-25 Heat8 analysis scored 0.290859, with MASE 0.997074 and MWSQL 0.084847 over 462 windows. The 07-25 pool expanded from 292 to 462 windows, primarily because healthcare grew from 13 to 140. Relative to Heat3 (MASE 1.167845, MWSQL 0.083478), Heat8's weakness is point error rather than quantile loss. This correction targets over-dispersed integrated gradients and calibration, not domain-specific overfitting.

The expected throughput impact is tiny because integrated mass is 9% and its stochastic-volatility fraction is 30%, affecting about 2.7% of rows. Benchmark it nevertheless.

Benchmark methodology

Measure generation only: instantiate each generator with the same seeds, consume the same complete batch sequence, and exclude import and Numba JIT warmup. Use multiple repetitions and report median total points divided by elapsed wall time. Do not include model training.

Throughput is only a systems check. A production-faithful paired Heat8/Heat9 training-quality A/B with identical trainer configuration, hardware, seeds, and evaluation is required before deployment. Heat9 is not a guaranteed improvement.

Validate

uv run ruff check generators/07-26/cascade-heat9
uv run cascade verify generators/07-26/cascade-heat9 --chain-toml chain.toml