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Life sciences · Preprint
arXiv · September 6, 2026
Raises a question worth testing. It does not answer one.
This is a theoretical study deriving stability and generalization bounds for straight-through estimators training two-layer quantized neural networks under specific conditions (saturated-output regime, zero initialization). The work provides explicit convergence rates but lacks empirical validation and is restricted to simplified models.
Preprint.
Zero-initialized samplewise STE recursion is equivalent to stochastic subgradient descent on convex latent loss in saturated-output regime Excess induced-risk guarantee with rate O(n^−1/2) when T=n^2 Under margin separability, optimal-order O(R^2/(γ^2n)) expected excess misclassification error for randomized one-pass STE iterate
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This is a theoretical analysis of straight-through estimators using statistical learning theory, with no empirical validation or experimental results reported.
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We study the identity straight-through estimator (STE) for training a two-layer binary-activation network with hinge loss from the perspective of Statistical Learning Theory (SLT). Our central question is whether algorithmic stability can explain the statistical generalization of the estimator produced by the discontinuous STE training rule. In the saturated-output regime, the zero-initialized samplewise STE recursion is exactly the stochastic subgradient descent on the convex latent loss $(-yu^\top x)_+$. This representation makes a stability analysis possible. We derive an exact distance identity for two coupled updates and prove approximate non-expansiveness of the common-example map, with a quadratic defect only when the two latent margins straddle zero. We then obtain explicit $\ell_2$ on-average model-stability and generalization bounds, transferring stability isometrically from the latent vector to the full first-layer matrix. Combining stability with a standard optimization bound yields an explicit excess induced-risk guarantee and the rate $O(n^{-1/2})$ when $T=n^2$. Under margin separability, a complementary argument gives the optimal-order $O(R^2/(γ^2n))$ expected excess misclassification error for a randomized one-pass STE iterate and a corresponding majority-vote bound.
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