Multi-Modal Learning meets Genetic Programming: Analyzing Alignment in Latent Space Optimization

2026-04-09

AI Summary

This study investigates whether multimodal latent space optimization methods, such as SNIP, achieve fine-grained alignment between symbolic and numerical modalities to effectively guide genetic programming search in symbolic regression. We construct a CLIP-inspired multimodal framework that integrates contrastive pretraining, neural encoders, and continuous latent space optimization, enabling the first systematic evaluation of cross-modal alignment efficacy in this context. Experimental results demonstrate that SNIP attains only coarse-grained alignment, with no significant improvement in alignment quality throughout the optimization process, thereby failing to support efficient symbolic search. Our findings reveal that achieving fine-grained cross-modal alignment is a critical direction for advancing symbolic regression performance.

Abstract

Symbolic regression (SR) aims to discover mathematical expressions from data, a task traditionally tackled using Genetic Programming (GP) through combinatorial search over symbolic structures. Latent Space Optimization (LSO) methods use neural encoders to map symbolic expressions into continuous spaces, transforming the combinatorial search into continuous optimization. SNIP (Meidani et al., 2024), a contrastive pre-training model inspired by CLIP, advances LSO by introducing a multi-modal approach: aligning symbolic and numeric encoders in a shared latent space to learn the phenotype-genotype mapping, enabling optimization in the numeric space to implicitly guide symbolic search. However, this relies on fine-grained cross-modal alignment, whereas literature on similar models like CLIP reveals that such an alignment is typically coarse-grained. In this paper, we investigate whether SNIP delivers on its promise of effective bi-modal optimization for SR. Our experiments show that: (1) cross-modal alignment does not improve during optimization, even as fitness increases, and (2) the alignment learned by SNIP is too coarse to efficiently conduct principled search in the symbolic space. These findings reveal that while multi-modal LSO holds significant potential for SR, effective alignment-guided optimization remains unrealized in practice, highlighting fine-grained alignment as a critical direction for future work.

Problem

• Symbolic Regression
• Latent Space Optimization
• Multi-Modal Learning
• Cross-Modal Alignment
• Genetic Programming

Innovation

• Latent Space Optimization
• Symbolic Regression
• Multi-Modal Alignment
• Genetic Programming
• Contrastive Learning