{"ID":2859045,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.07570","arxiv_id":"2510.07570","title":"Symbolic-Diffusion: Deep Learning Based Symbolic Regression with D3PM Discrete Token Diffusion","abstract":"Symbolic regression refers to the task of finding a closed-form mathematical expression to fit a set of data points. Genetic programming based techniques are the most common algorithms used to tackle this problem, but recently, neural-network based approaches have gained popularity. Most of the leading neural-network based models used for symbolic regression utilize transformer-based autoregressive models to generate an equation conditioned on encoded input points. However, autoregressive generation is limited to generating tokens left-to-right, and future generated tokens are conditioned only on previously generated tokens. Motivated by the desire to generate all tokens simultaneously to produce improved closed-form equations, we propose Symbolic Diffusion, a D3PM based discrete state-space diffusion model which simultaneously generates all tokens of the equation at once using discrete token diffusion. Using the bivariate dataset developed for SymbolicGPT, we compared our diffusion-based generation approach to an autoregressive model based on SymbolicGPT, using equivalent encoder and transformer architectures. We demonstrate that our novel approach of using diffusion-based generation for symbolic regression can offer comparable and, by some metrics, improved performance over autoregressive generation in models using similar underlying architectures, opening new research opportunities in neural-network based symbolic regression.","short_abstract":"Symbolic regression refers to the task of finding a closed-form mathematical expression to fit a set of data points. Genetic programming based techniques are the most common algorithms used to tackle this problem, but recently, neural-network based approaches have gained popularity. Most of the leading neural-network b...","url_abs":"https://arxiv.org/abs/2510.07570","url_pdf":"https://arxiv.org/pdf/2510.07570v1","authors":"[\"Ryan T. Tymkow\",\"Benjamin D. Schnapp\",\"Mojtaba Valipour\",\"Ali Ghodshi\"]","published":"2025-10-08T21:31:25Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Diffusion Model\",\"Transformer\"]","has_code":false}