Discovering Mathematical Equations with Diffusion Language Model

• URL: http://arxiv.org/abs/2509.13136v1
• Date: Tue, 16 Sep 2025 14:53:44 GMT
• Title: Discovering Mathematical Equations with Diffusion Language Model
• Authors: Xiaoxu Han, Chengzhen Ning, Jinghui Zhong, Fubiao Yang, Yu Wang, Xin Mu,
• Abstract summary: We introduce DiffuSR, a pre-training framework for symbolic regression built upon a continuous-state diffusion language model.<n>DrouSR employs a trainable embedding layer within the diffusion process to map discrete mathematical symbols into a continuous latent space.<n>We also design an effective inference strategy to enhance the accuracy of the diffusion-based equation generator.
• Score: 6.384075523245284
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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