evalstate/synthetic-selftrain-denoising-forgetting

Synthetic self-training denoising-vs-forgetting trajectories

Reproduction of the U-shaped risk curve from Wu, Yang & Sun, Why Self-Training Helps and Hurts: Denoising vs. Signal Forgetting (arXiv:2602.14029; ICML 2026 submission, OpenReview VnA5q5jXVz).

This dataset contains all configs, per-iteration trajectories, theoretical predictions, and empirical risk measurements for the synthetic overparameterized-linear-regression self-training experiments. Every point on every curve traces back to an exact config + seed in configs.json.

Theory implemented (Theorem 3.2, single-spiked model)

Sigma = (s-1) u u^T + I_p, beta = r u, tau = rho - 1 (rho = p/n > 1):

• Systematic / signal-forgetting: B_t = r^2 s (1 - (s/(s+tau))^{t+1})^2 (grows)
• Stochastic / denoising: V_0 = sigma^2/tau + tau s r^2/(s+tau)^2, V_t = V_{t-1}/(1+tau) + tau r^2 s^{2t+1}/(s+tau)^{2(t+1)} (decays)
• Risk: R_t = B_t + V_t

This closed-form recursion was independently re-derived from the paper and verified to 0.000 relative error against the published reproduction logbook (Eishaan/repro-self-training-denoising-forgetting). Also implemented: the multi-spike superposition (Thm 3.6), the general covariance deterministic-equivalent (eq. 8-10, fixed-point tau + spectral filter phi(lambda)=lambda/(lambda+tau)), and the iterated-GCV early-stopping criterion (eq. 11-12, ridgeless continuity profile).

Files

File	Description
configs.json	Every run config (hyperparameters, seeds, covariance structure, p, n, rho, T) keyed by run_id
trajectories.csv	Long-format per-iteration: run_id, t, theory_R, theory_B, theory_V, sim_risk, sim_std
igcv.csv	iGCV estimate vs true risk per iteration (run_id, t, true_risk, igcv)
selection_summary.csv	Optimal stopping t* (true) vs t* (iGCV) per config
plots/*.png	Figures (U-shape, B/V decomposition, anisotropy, iGCV, power-law, multi-spike)
linear_selftrain.py	Theory + Monte-Carlo simulation + iGCV (source)
run_synthetic.py	Experiment runner (source)
validate_theory.py	Cross-check vs logbook/paper (source)

Key results

• U-shape reproduces in the spiked model (s=25): theory and simulation agree, t* = 5, 2, 1 for rho = 1.5, 2.0, 2.5 (larger overparameterization => earlier stop).
• B grows* (signal forgetting), V decays* (denoising); their sum is U-shaped.
• Anisotropy is required: s=1 (isotropic) is monotonic (no interior optimum); s>1 gives a U. This is the paper's rate-mismatch mechanism.
• iGCV recovers t exactly* using only the initial noisy dataset (no validation set): t*_iGCV = t*_true = 5, 2, 1, per-trial |delta t*|<=1 in 100% of trials.
• Universality: the U-shape persists for a power-law covariance Sigma_ii=1/i with sparse signal (the paper's Fig 5 setup), matching the general deterministic equivalent in Monte-Carlo simulation. (The eq. 8-10 deterministic-equivalent numerics have a residual t>=1 effective-noise discrepancy, documented in the report as a partial result; the spiked Theorem 3.2 closed-form is fully verified.)

CPU-only. NumPy/SciPy/Matplotlib. See the project report for the full analysis.