arXiv:2606. 25394v1 Announce Type: new Abstract: Finding minimal arithmetic circuits for polynomials over finite fields is a combinatorially hard problem central to algebraic complexity theory.
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.
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.
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...
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...
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...
arXiv:2608.31067v1 Announce Type: new Abstract: Learning generalizable algorithmic computations remains a challenge for neural networks, as reflected in persistent failures on compositional and lengt...
arXiv:2609.00504v1 Announce Type: cross Abstract: In this work, we study radically uncoupled learning in discounted general-sum Markov games. Assuming ``$\mathsf{ETH}$ for $\mathsf{PPAD}$", we show t...
arXiv:2609.08736v1 Announce Type: new Abstract: We study certificates of positivity and optimality for learning problems whose objectives and constraints need not be polynomial. We isolate an axiomat...
arXiv:2606. 16077v1 Announce Type: cross Abstract: In this note, we introduce a polynomial-time version of the mistake-bounded language generation (MBLG) framework due to Kleinberg, Peale, and Reingold (2026).
arXiv:2512. 10903v2 Announce Type: replace Abstract: Circuit discovery aims to identify minimal subnetworks that are responsible for specific behaviors in large language models (LLMs).
Chemistry questions often demand exact computation and database lookups that a language model cannot supply from its parameters, so it must reach for external tools. Tool use here is a three-part prob...