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

arXiv: https://arxiv.org/abs/2604.08324 · HTML: https://mlsanity.com/paper/2604.08324/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 43 references that are in the map.
- First posted on arXiv 9 Apr 2026.

## Builds on (most cited first, 24 of 24)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Syntax-Directed Variational Autoencoder for Structured Data](https://mlsanity.com/paper/1802.08786/) (2018)
- [Does CLIP Bind Concepts? Probing Compositionality in Large Image Models](https://mlsanity.com/paper/2212.10537/) (2022)
- [SymFormer: End-to-end symbolic regression using transformer-based architecture](https://mlsanity.com/paper/2205.15764/) (2022)
- [Equivariant Similarity for Vision-Language Foundation Models](https://mlsanity.com/paper/2303.14465/) (2023)
- [SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training](https://mlsanity.com/paper/2310.02227/) (2023)
- [Mass-Producing Failures of Multimodal Systems with Language Models](https://mlsanity.com/paper/2306.12105/) (2023)
- [Symbolic regression via MDLformer-guided search: from minimizing prediction error to minimizing description length](https://mlsanity.com/paper/2411.03753/) (2024)
- [Efficient Generator of Mathematical Expressions for Symbolic Regression](https://mlsanity.com/paper/2302.09893/) (2023)
- [MMSR: Symbolic Regression is a Multi-Modal Information Fusion Task](https://mlsanity.com/paper/2402.18603/) (2024)
- [GENSR: Symbolic Regression Based in Equation Generative Space](https://mlsanity.com/paper/2602.20557/) (2026)
- [Transformer Semantic Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2501.18479/) (2025)
- [[RETRACTED]Evolving Form and Function: Dual-Objective Optimization in Neural Symbolic Regression Networks](https://mlsanity.com/paper/2502.17393/) (2025)
- [Analyzing Generalization in Pre-Trained Symbolic Regression](https://mlsanity.com/paper/2509.19849/) (2025)
- [Understanding Hardness of Vision-Language Compositionality from A Token-level Causal Lens](https://mlsanity.com/paper/2510.26302/) (2025)
- [Learning Semantics-aware Search Operators for Genetic Programming](https://mlsanity.com/paper/2502.04568/) (2025)
- [Discovering Mathematical Equations with Diffusion Language Model](https://mlsanity.com/paper/2509.13136/) (2025)
- [Symbolic-Diffusion: Deep Learning Based Symbolic Regression with D3PM Discrete Token Diffusion](https://mlsanity.com/paper/2510.07570/) (2025)

## Built on by (most cited first, 1 of 1)

- [SNIP++: Fine-Grained Symbolic-Numerical Alignment for Symbolic Regression](https://mlsanity.com/paper/2609.31965/) (2026)

## Abstract (arXiv)

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.