# Critical Damping as a Momentum Schedule: Multi-Seed Validation, a Hybrid Recipe, and an Exhaustive Negative Result on Surgical Layer Selection

Source: [Critical Damping as a Momentum Schedule: Multi-Seed Validation, a Hybrid Recipe, and an Exhaustive Negative Result on Surgical Layer Selection](<https://www.sota2.com/research/paper/69cca66e0636e5bf4afcba5e>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-07-15T05:00:05.882Z

Authors: Ivan Pasichnyk

Published: 2026-03-30T18:53:03.000Z

## Abstract

The critical damping condition of the damped harmonic oscillator model of SGD with momentum (Qian, 1999) yields a momentum schedule with no tuned hyperparameters: mu(t) = 1 - 2\*sqrt(alpha(t)). Across five seeds on ResNet-18/CIFAR-10 (200-epoch cosine schedule) it reaches 90% test accuracy 2.34x faster than constant mu=0.9 (range 1.71-2.86x, 5/5 seeds, one-sided paired t-test p=4e-4), at the cost of a real final-accuracy deficit of 0.46 pp (5/5 seeds, p=0.009). A short-schedule control rules out a schedule-length artifact: compressed baselines either pay 0.5-0.9 pp of accuracy or stay slower to 90% at equal accuracy. A hybrid recipe -- critical-damping momentum until 90%, then constant mu=0.9 -- removes the deficit and keeps the speedup: 95.45 +/- 0.05% final accuracy at 2.4x faster progress to 90% (n=5). The speedup generalizes across architectures (VGG-16 without skip connections: 1.72x, n=3); on CIFAR-100 early gains persist (2-4x to mid-training thresholds) but the accuracy cost grows (-1.7 pp), compressing the accuracy-matched gain to 1.14x. We also report an exhaustive negative result on surgical layer selection. Version 2 of this paper claimed that gradient attribution on misclassified images selects which layers to retrain; running the identical correction protocol on all 35 combinations of 3-of-7 layer groups ranks the selected triple 11th of 35 (exact p=0.31) -- no better than random. What survives is weaker but real: combinations containing the top-ranked layer outperform the rest (+6.2 vs -1.4 mean net error reduction), and the bottom of the gradient-norm ranking reliably predicts the most harmful interventions (down to -20 net errors). Gradient attribution on errors is a harm-avoidance signal, not a selector of repair targets. We release the full 35-combination landscape as a baseline for layer-selection claims.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Image Classification on Surgical correction experiment dataset (train milestones)](<https://www.sota2.com/research/sota/image-classification-on-surgical-correction-experiment-dataset-train-milestones.md>): Image Classification; Surgical correction experiment dataset (train milestones); Best Accuracy: 95.36.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2603.28921>)

[PDF](<https://arxiv.org/pdf/2603.28921.pdf>)