arXiv:2605. 26343v2 Announce Type: replace Abstract: Mechanistic interpretability seeks to explain a model's behaviour by finding its circuit: the sparse subgraph of the model's computation that is causally responsible for it.
By Barsat Khadka
The paper proposes treating the choice of monomial ordering for Gröbner basis computations as a reinforcement learning problem, using domain-informed reward signals that reflect actual computational cost. By training policies over the space of admissible orderings, the authors demonstrate that the learned strategies outperform traditional static heuristics such as GrevLex on benchmark problems from systems biology and computer vision. The resulting policies also resist simplification into interpretable models, suggesting that deep reinforcement learning captures complex geometric structure beyond conventional approaches.
By R. Caleb Bunch, Alperen A. Erg\"ur, Melika Golestani, Jessie Tong, Malia Walewski, Yunus E. Zeytuncu
The paper investigates how to obtain certificates of positivity and optimality for learning problems whose objectives and constraints are not necessarily polynomial. It isolates an axiomatic core of Fischer's constructive strict and weak Positivstellensätze and extends the resulting theorems to abstract function algebras over ordered fields. The framework distinguishes between objective/constraint functions built from broad classes of continuous or definable operations and auxiliary primitives that satisfy explicit scalar and closure axioms, providing instances over continuous and definable function algebras, including fields not closed under square roots, and analyzing lower-bound and global-optimality certificates as well as computational complexity.
arXiv:2608.30162v1 Announce Type: new
Abstract: We present a reinforcement-learning agent that solves symbolic equations step by step, covering both nonlinear closed equations (radicals, exponentials...
By Kevin P O Keeffe
arXiv:2608.30952v1 Announce Type: new
Abstract: Chemistry questions often demand exact computation and database lookups that a language model cannot supply from its parameters, so it must reach for e...
By Armin Dariani, Sifan Wu, Bang Liu, Entao Yang
arXiv:2609.08961v1 Announce Type: cross
Abstract: For a finite set $O$ of Boolean functions, we consider the class of propositional formulas built using the functions in $O$ as connectives. We determ...
By Balder ten Cate