Reproduction — Why Self-Training Helps and Hurts: Denoising vs. Signal Forgetting
Independent reproduction of ICML 2026 paper VnA5q5jXVz (arXiv 2602.14029), Wu, Yang & Sun. No official code was released; everything here is written from the paper.
What is verified
| Claim | Content | Status | Evidence |
|---|---|---|---|
| 1 | Deterministic-equivalent recursion R*_t = B*_t (forgetting, up) + V*_t (noise, down exp) |
verified | claim1_decomposition.py, general_cov.py (spiked Thm 3.2 and general Thm 4.2) |
| 2 | U-shaped risk & optimal early stopping, strictly under anisotropy (s>1) | verified | claim2_ushape.py (Fig 1b, Fig 3a) |
| 3 | Direction-dependent spectral filter: survival (s/(s+tau))^{t+1}, noise (1+tau)^{-t} |
verified | claim3_spectral.py |
| 4 | iGCV consistently estimates risk & recovers t* with no validation set | verified | claim4_igcv.py |
| 5 | Trade-off persists for deep nets (ResNet-50 / CIFAR-10 self-distillation) | verified (GPU Job) | cifar_selfdistill.py (Fig 6a) |
Layout
src/linear_selftrain.py— Algorithm 1 (ridgeless/ridge self-training), spiked Thm 3.2, multi-spike Thm 3.6, general deterministic-equivalent recursion (Def 4.1 / eq 10), iGCV (eq 11-12), fast structured samplers.src/plotting.py— Plotly + CSV export helpers.claim{1,2,3,4}_*.py,general_cov.py— per-claim reproductions (linear theory, CPU).cifar_selfdistill.py— PEP-723 UV script for the ResNet-50/CIFAR-10 experiment (HF GPU Job).outputs/— generated figures (HTML) + raw data (CSV) per claim.
Reproduce
# linear-theory claims (CPU, ~1 min each). WSL2 note: single-thread BLAS is faster.
uv run --env-file .env python claim1_decomposition.py # .env pins OPENBLAS_NUM_THREADS=1
uv run --env-file .env python claim2_ushape.py
uv run --env-file .env python claim3_spectral.py
uv run --env-file .env python claim4_igcv.py
uv run --env-file .env python general_cov.py
# deep-net claim (GPU): run on Hugging Face Jobs
hf jobs uv run --flavor a10g-small --secrets HF_TOKEN cifar_selfdistill.py \
--n 10000 --K 4 --epochs 40 --etas 0.4,0.6,0.8