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Backpropagating Verifier Rewards Through Continuous Flow Language Models

Xu Han, Jiajing Hu, Li-Ping Liu

Trains a critic to score intermediate continuous token representations, enabling reward gradients through the denoising trajectory before final discrete decoding. Evaluates this post-training approach on four reasoning tasks.

First public: · Added to this list: October 18, 2026

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arXiv:2610.19080 · Initial submission: 2026-10-13

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Continuous-state reasoning — Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.

Alternative generation methods — Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.

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