Enumerating Chemical Structures, Stereoisomers, and Stereogenic Units with Analytic Combinatorics
arXiv:2609.02932
2026
Architecture
2 ideas extracted · analyzed Sep 4, 2026
What the math gives to ML
The paper's transferable asset is its symbolic-method view of recursively defined structured objects: a compact grammar is translated into generating functions whose coefficients count objects exactly, including quotienting by symmetries. For neural networks, this can become a principled generator of tree-, DAG-, or module-shaped architectures and training curricula with controlled size and structural diversity, rather than biased random mutation or ad hoc sampling. Multivariate generating functions also provide exact control over auxiliary architectural properties such as branching count, number of special modules, or symmetry markers. The payoff is most plausible for neural architecture search and synthetic graph-model generation, not for ordinary dense Transformers.
Ideas from this paper
Unverified
2026
Translate a recursive neural architecture grammar into a combinatorial specification and use its generating function to sample architectures uniformly conditional on size. This removes the severe shape and branching biases of naive random tree generation, producing a better-covered architecture-search population at the same evaluation budget.
Useful6/10
Difficulty5/10
Novelty7/10
Unverified
2026
Use a multivariate generating function to construct training examples or network variants with an exactly controlled amount of a structural attribute, such as graph branching, routing depth, skip connections, or the number of experts activated. Train by gradually changing the target coefficient slice instead of relying on an uncontrolled random curriculum.
Useful5/10
Difficulty5/10
Novelty8/10