---
license: mit
tags:
- icml2026-repro
- single-index-models
- gradient-descent
- theory-reproduction
---

# Reproduction results — "Full-Batch Gradient Descent Outperforms One-Pass SGD" (ICML 2026 #26332)

Raw and aggregated results for an independent reproduction of
[arXiv:2602.02431](https://arxiv.org/abs/2602.02431) /
[OpenReview QItZDBVCT0](https://openreview.net/forum?id=QItZDBVCT0).

All numbers were produced locally on 2x NVIDIA RTX 4000 Ada with the scripts in the
reproduction logbook (`scripts/sim.py`, `scripts/sweep_spherical.py`,
`scripts/sweep_online_sgd.py`, `scripts/sweep_squared_gd.py`, `scripts/spectral_audit.py`,
`scripts/thm32_bound.py`).

| file | contents |
|---|---|
| `sweep_quad.csv` | full-batch spherical GD, σ(z)=z², per-run squared overlap (Claim 1) |
| `sweep_trunc.csv` | full-batch spherical GD, σ(z)=min(z²,8) (Claims 2/5) |
| `sweep_smooth.csv` | same with the C^∞ truncation of paper eq. (3.10) (robustness) |
| `sweep_online_{trunc,quad}.csv` | one-pass spherical SGD baseline over a grid of η=c/d (Claim 5) |
| `gd_trunc_r2_{traj,summary}.csv` | squared-loss full-batch GD, r₀=d⁻² (Claims 3/4) |
| `gd_trunc_r15_{traj,summary}.csv` | squared-loss full-batch GD, r₀=d⁻¹⁵ (exact Theorem 4.1 setting) |
| `gd_quad_r2_*`, `gdd_*` | untruncated-activation and δ-sweep controls |
| `gd_trunc_eta*_*` | learning-rate sweep for the O(log d / η) phase-1 length |
| `audit_{spectrum,uniform_bbp,indicator}.csv` | numerical audits of the spectral statements |
| `thm32_bound.csv` | audit of the Theorem 3.2 deficit bound 1 − C(e^{−M/2} + (d/n)^{1/5}) |
| `agg_*.csv`, `thresholds.csv`, `threshold_fits.csv` | aggregated curves and log-d fits |

Logbook: https://huggingface.co/spaces/vimarsh/repro-full-batch-gd-outperforms-one-pass-sgd-sample-complexity-separation