automated reasoning engineers

Abstract: As agents take on longer and more complex problems, controlling the execution becomes a task in its own right. Each step in the run brings new control choices, like which partial work to build on, whether to start fresh, or when to stop. We introduce agentic meta-reasoning, an inference-time harness that makes these choices an explicit and structured reasoning process. Workers carry out the task-level computation, while a controller consolidates what the run has established, explores next options, assesses what each option is worth under the remaining budget, and dispatches the chosen work with context drawn from persistent memory. Between decisions the controller carries only a compact account of the run rather than replaying its full history. Our baselines span production coding agents and research harnesses, together with a Direct Control Agent using the same workers and compute budget allowance. On ProgramBench, which tests long-horizon agentic capability through program reconstruction, meta-reasoning achieves 71.5% with GPT-5.5 against 58.0% for Codex; with Opus 4.8 it achieves 67.2% against 65.5% for Claude Code. On the other benchmarks, spanning abstract reasoning, multi-domain long-horizon reasoning, and proof generation, it gains between 3.6 and 4.2 points over direct control, averaged across three frontier models. It keeps improving over the tested budget ranges where direct control plateaus, though its overhead can hurt at small budgets. Artifact-graph analysis reveals more reuse of earlier work, higher coverage of correct solutions in most settings, and nonuniform gains in final selection. These results indicate that spending computation on structured control becomes more important as agents scale to longer runs.

Abstract: Large language models (LLMs) are increasingly deployed for natural-language logical reasoning, where the final answer is easy to check but the proof behind it is not. In natural-language logical reasoning, an intermediate conclusion should follow from its premises, and the resulting derivation should support the final answer. Existing methods lack machine-checkable verification of intermediate conclusions and answer-supporting proof dependencies, so they may assign credit to invalid or answer-irrelevant steps. We propose Proof-R1, an RL framework from formal verification that trains LLMs to construct verifiable proofs for natural-language logical reasoning. Proof-R1 admits a generated conclusion into the verified proof state only when the corresponding reasoning action satisfies the proof obligations through UNSAT-based machine-checkable formal verification. Proof-R1 also recovers the answer-supporting dependency closure to trace the proof structure of the final answer and align outcome credit with the proof dependencies. Experiments demonstrate that Proof-R1 improves answer accuracy across three logical reasoning benchmarks and four backbone models and outperforms training-free agents and training-based methods in terms of reasoning-process verifiability.

Abstract: Existing agent memory frameworks mainly create memory through an agent's interaction with the factual world, e.g., remembering feedback from actions taken to improve performance on future tasks. However, these frameworks seldom ask the "what if" question during memory construction: what if a different action had been taken, would the feedback have changed, and how could this feedback become useful memory? Obtaining such feedback directly in an active environment can be expensive and can alter the state needed for comparison. In this work, we introduce COUNTERMEM, a reinforcement-learning framework for constructing and using verified counterfactual memory across tasks. After a failed action, COUNTERMEM evaluates local alternatives from a copy or reset of the original state using executable world models, such as tests, proof checkers, and solvers. It stores improvements with the original and corrected actions, checked outcomes, and conditions for reuse. A learned memory-use policy selects a retrieved record or skips memory to balance task success and interaction cost, while the base LLM remains fixed. Both memory and policy are frozen during held-out evaluation. We evaluate COUNTERMEM on 12 benchmark settings across six domains. With gpt-oss-120b, COUNTERMEM improves both ReAct and Reflexion on all 12 benchmarks across six domains, averaging a gain of 12.6 percentage points over their unaugmented versions. In the four-domain comparison across two backbones, task-run tokens decrease by 7.7-42.0%, excluding offline selector-training costs. Further analyses show that removing verification or persistent storage weakens the gains, while applying verified corrections to unsuitable decisions can reverse them. Code will be released upon acceptance.

Abstract: Resolution over parities, $\mathrm{Res}(\oplus)$, is the characteristic-two version of resolution over linear equations: clauses are disjunctions of affine equations over $\mathbb F_2$. Superpolynomial size lower bounds were previously known only for restricted refutations: tree-like, regular, or of bounded depth. We prove that every DAG-like $\mathrm{Res} (\oplus)$ refutation of the bit pigeonhole principle with $n+1$ pigeons and $n=2^\ell$ holes has more than $\exp(n/(32768\ell^2))=2^{Ω(n/\log^2 n)}$ clauses, for every $\ell\ge32$, with no restriction on regularity or depth. The proof translates an arbitrary refutation with $S$ clauses into a polynomial calculus refutation of degree $O(\log n)$ over $O(S+n^2)$ groups of extension variables in the style of Buss, Impagliazzo, Krajicek, Pudlak, Razborov, and Sgall. One substitution then removes all extension variables at once and leaves a nonzero low-degree polynomial derived from the pigeonhole axioms alone at degree at most $n/2$; a degree lower bound in the style of Razborov, proved through the homology of chessboard complexes, shows that no such derivation exists. The argument also yields a general sufficient condition for $\mathrm{Res}(\oplus)$ size lower bounds. The main theorem, this condition, and all their dependencies are formalized in Lean 4, and every statement links to its formal proof. The proof was developed with substantial AI assistance within an open research framework described in the final section.

Abstract: Automated theorem proving seeks to use computational systems to prove or disprove mathematical and logical statements [1, 2]. It underpins a wide range of applications, and enhancing theorem-proving capabilities remains a central objective in artificial intelligence [3]. Although recent neuro-symbolic systems have achieved remarkable progress [4-7], their operation is ultimately constrained by classical computational architectures. Quantum computing [8], by contrast, enables information encoding and coherent parallelism beyond classical limits [9-14], raising the possibility of accelerating structured symbolic deduction [15]. Here we report the experimental realization of automated geometry theorem proving on a fully programmable superconducting quantum processor. We develop two complementary quantum proving frameworks. The first implements Wu's algebraic elimination method using quantum pseudo-division, with multivariate polynomials represented in superposition states, enabling quantum algebraic theorem proving. The second implements the full-angle method as backward symbolic reasoning through a hybrid quantum strategy-guided architecture, demonstrating a general route toward quantum symbolic proof search. As illustrative examples, we prove two theorems on a superconducting quantum processor: the perpendicularity of the diagonals of a square and a 1978 International Mathematical Olympiad geometry problem. Our results establish, at the experimental level, automated logical reasoning as a viable task for near-term quantum processors and provide a concrete pathway toward quantum-enhanced symbolic intelligence.