Adversarial training improves PINNs by using the discriminator to mitigate spectral bias and stiffness, with a new NTK-based framework providing theoretical grounding and a practical algorithm.
Wasserstein generative adversarial networks
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Conditional optimal transport is used to turn raw PRM outputs into monotonic quantile functions that improve calibration and downstream Best-of-N performance on MATH-500 and AIME.
Span-level Wasserstein distances between hidden-state distributions of correct and incorrect rollouts provide a self-supervised signal to reweight advantages in GRPO, improving fine-grained credit assignment on math and code tasks.
A state distribution view of post-training shows that on-policy supervision from the learner itself can outperform fixed-dataset SFT and preserve retention better than aggressive supervised updates.
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Hidden States Know Where Reasoning Diverges: Credit Assignment via Span-Level Wasserstein Distance
Span-level Wasserstein distances between hidden-state distributions of correct and incorrect rollouts provide a self-supervised signal to reweight advantages in GRPO, improving fine-grained credit assignment on math and code tasks.