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Benjamin Léger

benjamin.leger@mila.quebec
Doctorat - Université Laval
Superviseur⋅e principal⋅e
Christian Gagné
Sujets de recherche
Apprentissage de la programmation
Apprentissage profond
Optimisation

Publications

SNIP++: Fine-Grained Symbolic-Numerical Alignment for Symbolic Regression
Benjamin Léger
Shubham Gupta
Samy Mammeri
Kazem Meidani
Cem Subakan
Christian Gagné
Mathematical expressions and the numerical behavior they produce are two views of the same underlying function, and connecting them is centr… (voir plus)al to scientific discovery. Symbolic Regression (SR) relies on this connection directly: it searches for an expression that reproduces a given behavior. Recent multi-modal models learn this connection by embedding symbolic expressions and their numerical behavior in a shared representation space. We show that this embedding space is only globally aligned: complete expressions correspond to complete behaviors, but the contribution of individual parts of an expression is not represented. This granularity gap leaves the model unable to tell how a local edit to an expression changes its behavior, the central operation in SR. We introduce a compositional alignment method that closes this gap: a structural positional encoding exposes the substructure of an expression to the encoder, and a multi-granularity contrastive objective grounds each subexpression in the behavior it produces before propagating this grounding to the full expression. The resulting representations close much of the modality gap between symbolic and numerical embeddings, reliably distinguish the effects of local edits that the original alignment cannot, and transfer to external SR corpora.
2026-09-24
arXiv (prépublication)
doi.org
arxiv.org
Multi-Modal Learning meets Genetic Programming: Analyzing Alignment in Latent Space Optimization
Benjamin Léger
Kazem Meidani
Christian Gagné
Symbolic regression (SR) aims to discover mathematical expressions from data, a task traditionally tackled using Genetic Programming (GP) th… (voir plus)rough 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.
2026-04-08
arXiv (prépublication)
doi.org
arxiv.org