{"ID":2870475,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.13136","arxiv_id":"2509.13136","title":"Discovering Mathematical Equations with Diffusion Language Model","abstract":"Discovering valid and meaningful mathematical equations from observed data plays a crucial role in scientific discovery. While this task, symbolic regression, remains challenging due to the vast search space and the trade-off between accuracy and complexity. In this paper, we introduce DiffuSR, a pre-training framework for symbolic regression built upon a continuous-state diffusion language model. DiffuSR employs a trainable embedding layer within the diffusion process to map discrete mathematical symbols into a continuous latent space, modeling equation distributions effectively. Through iterative denoising, DiffuSR converts an initial noisy sequence into a symbolic equation, guided by numerical data injected via a cross-attention mechanism. We also design an effective inference strategy to enhance the accuracy of the diffusion-based equation generator, which injects logit priors into genetic programming. Experimental results on standard symbolic regression benchmarks demonstrate that DiffuSR achieves competitive performance with state-of-the-art autoregressive methods and generates more interpretable and diverse mathematical expressions.","short_abstract":"Discovering valid and meaningful mathematical equations from observed data plays a crucial role in scientific discovery. While this task, symbolic regression, remains challenging due to the vast search space and the trade-off between accuracy and complexity. In this paper, we introduce DiffuSR, a pre-training framework...","url_abs":"https://arxiv.org/abs/2509.13136","url_pdf":"https://arxiv.org/pdf/2509.13136v1","authors":"[\"Xiaoxu Han\",\"Chengzhen Ning\",\"Jinghui Zhong\",\"Fubiao Yang\",\"Yu Wang\",\"Xin Mu\"]","published":"2025-09-16T14:53:44Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Diffusion Model\",\"Language Model\"]","has_code":false}