Math: Logic

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

Unverified 2026

Decision-Dependent Robustness Cutting Planes

Replace ordinary adversarial training over a fixed perturbation set with adaptive robust training in which the admissible perturbations depend on the current network state. Train on a small active set of hard scenarios, then search for a newly admissible scenario with larger loss or constraint violation and add it only when needed. This should reduce redundant adversarial examples while targeting worst-case regions induced by the current model.

Useful6/10
Difficulty5/10
Novelty6/10
Paper: Generalized Semi-Infinite Programming for Robust Optimal Control with Decision-Dependent Uncertainty arXiv:2609.01538
Unverified 2026

Automaton-Gated Objective Switching

Augment a neural policy with deterministic DFA states for the task objective and safety constraint, then select among objective-specific policy heads using those states. Before either target is reached, execute a mixed policy; after one target is reached, switch permanently to the policy specialized for the remaining target.

Useful6/10
Difficulty4/10
Novelty5/10
Paper: Optimal Constrained sc-LTL Planning in MDPs via Switching Policies arXiv:2608.05021
Unverified 2026

Prime-Gated Maximal-Length Binary Reservoir

Replace a learned recurrent transition with a sparse binary reservoir compiled from prime-count gates. Three permanently active control vertices implement copy and XNOR transitions, allowing the signal state to realize an affine feedback register over \(\mathbb F_2\) with period \(2^m-1\) using only \(O(m)\) edges and bounded in-degree. Train only an input projection and readout, or use straight-through estimators if end-to-end adaptation is required.

Useful5/10
Difficulty5/10
Novelty6/10
Paper: Pulse Graphs: Prime-Activated Boolean Dynamics on Directed Graphs arXiv:2607.10453