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