SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training

• URL: http://arxiv.org/abs/2310.02227v3
• Date: Fri, 15 Mar 2024 06:00:29 GMT
• Title: SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training
• Authors: Kazem Meidani, Parshin Shojaee, Chandan K. Reddy, Amir Barati Farimani,
• Abstract summary: We introduce SNIP, a Symbolic-Numeric Integrated Pre-training model. By performing latent space analysis, we observe that SNIP provides cross-domain insights into the representations. Results show that SNIP effectively transfers to various tasks, consistently outperforming fully supervised baselines.
• Score: 17.623227360825258
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In an era where symbolic mathematical equations are indispensable for modeling complex natural phenomena, scientific inquiry often involves collecting observations and translating them into mathematical expressions. Recently, deep learning has emerged as a powerful tool for extracting insights from data. However, existing models typically specialize in either numeric or symbolic domains, and are usually trained in a supervised manner tailored to specific tasks. This approach neglects the substantial benefits that could arise from a task-agnostic multi-modal understanding between symbolic equations and their numeric counterparts. To bridge the gap, we introduce SNIP, a Symbolic-Numeric Integrated Pre-training model, which employs contrastive learning between symbolic and numeric domains, enhancing their mutual similarities in the embeddings. By performing latent space analysis, we observe that SNIP provides cross-domain insights into the representations, revealing that symbolic supervision enhances the embeddings of numeric data and vice versa. We evaluate SNIP across diverse tasks, including symbolic-to-numeric mathematical property prediction and numeric-to-symbolic equation discovery, commonly known as symbolic regression. Results show that SNIP effectively transfers to various tasks, consistently outperforming fully supervised baselines and competing strongly with established task-specific methods, especially in the low data regime scenarios where available data is limited. Code and model are available at: https://github.com/deep-symbolic-mathematics/Multimodal-Math-Pretraining

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