Math: Generating functions

Machine-learning ideas tagged Generating functions in the Math taxonomy of the Math2NN corpus.

2 ideas found

Solves: Generalization Math: Generating functions Clear all

Unverified 2026

Exact nondecreasing-subsequence constrained decoder

Equip an autoregressive model with a hard constraint that generated token ranks cannot contain a nondecreasing subsequence of length k. Maintain a patience-sorting-style state representing the smallest ending token rank achievable by subsequences of lengths 1 through k-1, mask tokens that would create a length-k subsequence, and optionally sample uniformly among valid continuations using exact suffix counts. This provides a mathematically controlled data-augmentation or decoding regime for…

Useful6/10

Difficulty5/10

Novelty7/10

Sampling Accuracy Sample efficiency Generalization

Paper: Counting words without non-decreasing subwords of fixed length arXiv:2607.19410

Unverified 2026

Multivariate Structural Curriculum

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

Training Sample efficiency Generalization Accuracy

Paper: Enumerating Chemical Structures, Stereoisomers, and Stereogenic Units with Analytic Combinatorics arXiv:2609.02932