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

TL;DR

This paper critically evaluates SNIP, a multi-modal latent space optimization approach for symbolic regression, revealing that its coarse alignment limits effective symbolic search despite promising potential.

Contribution

It provides an empirical analysis showing that SNIP's cross-modal alignment does not improve during optimization, questioning its effectiveness for symbolic search.

Findings

Cross-modal alignment does not improve with fitness increase.

SNIP's learned alignment is too coarse for effective symbolic search.

Effective fine-grained alignment is necessary for future improvements.

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.