# Countdown

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arXiv Oct 29, 2026
GRPO curricula stop following a fixed schedule: probe accuracy steers difficulty sampling, with the largest gains at intermediate levels
In GRPO reinforcement fine-tuning, a fixed easy-to-hard curriculum can drift from the model's actual progress. ClosedLoopGaussian keeps the Gaussian sampler's form but uses periodic probe accuracy to adjust how fast training advances and how widely it rehearses, leaving the reward, architecture and optimizer unchanged. On Countdown, mean exact-match accuracy over four seeds exceeds both the fixed curriculum and vanilla GRPO, with gains concentrated at intermediate difficulty, though seed dispersion is large and the comparison is read descriptively.
In GRPO reinforcement fine-tuning, a fixed easy-to-hard curriculum can drift from the model's actual progress. ClosedLoopGaussian keeps the Gaussian sampler's form but uses periodic probe accuracy to adjust how fast training advances and how widely it rehearses, leaving the reward, architecture and optimizer unchanged. On Countdown, mean exact-match accuracy over four seeds exceeds both the fixed curriculum and vanilla GRPO, with gains concentrated at intermediate difficulty, though seed dispersion is large and the comparison is read descriptively.
Texas Christian University
Yuv Raj Pant（First author）
ClosedLoopGaussian GRPO Curriculum Learning Reinforcement Fine-tuning Countdown
arXiv Oct 2, 2026
HC-DLM makes a continuous latent the only persistent generative state and beats both discrete and continuous diffusion baselines on Sudoku, Countdown and LM1B
The work proposes Hierarchical Continuous Diffusion Language Models (HC-DLM), in which a continuous latent is the only state persisting across steps while tokens are read out from it at every step and fed back as a scaffold conditioning the next latent update, with a training objective derived from a variational bound on the token likelihood; at matched model size it improves over discrete and continuous diffusion baselines in puzzle accuracy on Sudoku and Countdown and in generative perplexity on LM1B.
The work proposes Hierarchical Continuous Diffusion Language Models (HC-DLM), in which a continuous latent is the only state persisting across steps while tokens are read out from it at every step and fed back as a scaffold conditioning the next latent update, with a training objective derived from a variational bound on the token likelihood; at matched model size it improves over discrete and continuous diffusion baselines in puzzle accuracy on Sudoku and Countdown and in generative perplexity on LM1B.
University of Illinois Urbana-Champaign Amazon (United States)
Hui Ren（First author）
HC-DLM Diffusion Language Model Flow Matching Countdown Language modeling

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GRPO curricula stop following a fixed schedule: probe accuracy steers difficulty sampling, with the largest gains at intermediate levels

HC-DLM makes a continuous latent the only persistent generative state and beats both discrete and continuous diffusion baselines on Sudoku, Countdown and LM1B