Property-Based Testing for Robust Softmax and Cross-Entropy
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The paper identifies two numerical bugs in standard softmax, log‑softmax, and cross‑entropy implementations: Softmax Collapse, where a dominant logit causes its gradient to be rounded to zero, and Softmax Cancellation, where student and teacher logits that are equal still produce non‑zero gradients. The authors provide straightforward implementations that correct both issues. Their fix removes the previously observed "Slingshot" phenomenon, accelerates grokking with weight decay, prevents accuracy collapse without weight decay, keeps student networks aligned with teachers during distillation, and demonstrates that post‑memorization logit growth is bounded by an equilibrium between weight decay and Adam’s epsilon hyperparameter.
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The paper addresses the challenge of creating machine learning learners that can guarantee provably correct predictions in difficult test-time scenarios, such as adversarial attacks and natural distribution shifts. It introduces a reliable learner with optimal theoretical guarantees for these settings and discusses practical implementations. The authors demonstrate strong performance on examples like linear separators under log-concave distributions and smooth boundary classifiers under smooth probability distributions.
The paper argues that empirical results in Machine Learning are often difficult to reproduce due to limited availability of code and supporting materials, which hampers research progress. It analyzes and quantifies these challenges and proposes concrete measures to enhance the verifiability of results, even if full reproducibility cannot be guaranteed. The authors provide their code and supporting resources on GitHub for reference.
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