SD-GPS: Solver-Driven Autoformalization and Theorem Proposing for Geometry Problem Solving
Researchers propose SD-GPS, a neuro-symbolic framework for geometry problem solving that treats a symbolic solver as an execution oracle during both formalization and deduction stages. The system combines solvability-guided reinforcement learning for autoformalization (built on QwenVL3-2B) with an impasse-aware agent that proposes and symbolically verifies auxiliary lemmas. Evaluations on Geometry3K and PGPS9K show SD-GPS outperforms existing multimodal, neural, and neuro-symbolic baselines across multiple task regimes. The work advances the line of research on grounding neural agents in formal systems for verifiable mathematical reasoning.
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Goedel-Architect achieves state-of-the-art formal theorem proving with blueprint-based agentic framework
Goedel-Architect is an agentic framework for formal theorem proving in Lean 4 that uses blueprint generation — a dependency graph of definitions and lemmas — rather than recursive decomposition, enabling parallel lemma closure and global refinement. Built on DeepSeek-V4-Flash (284B-A13B), it achieves 99.2% pass@1 on MiniF2F-test and 75.6% on PutnamBench, scaling to 100% on MiniF2F, 88.8% on PutnamBench, and 4/6 on IMO 2025 when seeded with natural-language proofs. The authors claim state-of-the-art performance for an open-source pipeline at up to 500x lower cost than comparable systems.
GamePad: A Learning Environment for Theorem Proving
OpenAI released GamePad, a learning environment designed to facilitate machine learning research on formal theorem proving. The tool provides an interface to the Coq proof assistant, enabling researchers to train models on proof states and tactics. This represents an early effort to apply ML techniques to automated mathematical reasoning and formal verification.
Large-Scale Evaluation of LLM-Driven Formal Proof Search on Open Mathematical Problems
Researchers present the first large-scale evaluation of LLM-based formal proof search on genuinely open mathematical problems, using Lean as a verification backend. Their most capable agent autonomously resolved 9 of 353 open Erdős problems and proved 44 of 492 OEIS conjectures, at a cost of a few hundred dollars per problem. The system is already being deployed in active research across combinatorics, optimization, graph theory, algebraic geometry, and quantum optics. The study also compares agent architectures, finding that more sophisticated designs outperform simple generate-and-verify loops on the hardest problems.
OpenAI Neural Theorem Prover Solves Formal Math Olympiad Problems in Lean
OpenAI developed a neural theorem prover integrated with the Lean proof assistant that can solve challenging high-school olympiad problems, including problems from AMC12, AIME, and two IMO-adapted problems. The system demonstrates automated formal mathematical reasoning at a level previously requiring human expertise. This represents a significant capability milestone in AI-assisted formal verification and mathematical problem-solving.
Skill-Conditioned Gated Self-Distillation (SGSD) for LLM Reasoning
SGSD is a new on-policy self-distillation method for LLM reasoning that replaces trusted privileged information (e.g., reference answers) with an experience-derived skill bank of skill-mistake pairs. It constructs a multi-teacher pool, validates each teacher's contribution via a verifier, and applies a gated objective to distill informative disagreements while suppressing noisy signals. On Qwen3-1.7B, SGSD outperforms GRPO by 6.2% and answer-conditioned OPSD by 1.7% on average across AIME24, AIME25, and HMMT25. The method relaxes the assumption of trusted privileged information, making self-distillation more practical under weaker supervision.
Geometric Action Model (GAM) repurposes geometric foundation models for 3D-aware robot manipulation
Researchers propose the Geometric Action Model (GAM), a language-conditioned robot manipulation policy that splits a pretrained geometric foundation model (GFM) to serve simultaneously as an observation encoder, causal future predictor, and action decoder. Unlike existing vision-language-action models that operate on 2D image frames, GAM explicitly incorporates 3D geometric priors for contact-rich manipulation. The approach claims improvements in accuracy, robustness, speed, and model size over foundation-model-scale baselines across simulation and real-robot benchmarks.
GRASP: Gradient-based Planning for World Models at Longer Horizons
Researchers from Berkeley, Meta, and collaborators introduce GRASP, a gradient-based planner designed to make long-horizon planning with learned world models more robust. The method addresses three core failure modes: ill-conditioned computation graphs from backpropagation through time, non-greedy loss landscapes with many local minima, and brittle gradients through high-dimensional vision models. GRASP lifts trajectory optimization into virtual states for parallel optimization across time, injects stochasticity into state iterates for exploration, and reshapes gradients to avoid problematic state-input gradient paths. The work is positioned in the context of scaling world models toward general-purpose simulators usable for control and planning.
Improving Mathematical Reasoning with Process Supervision
OpenAI trained a model achieving state-of-the-art mathematical problem solving by rewarding each correct reasoning step (process supervision) rather than only the final answer (outcome supervision). This approach improves performance on math benchmarks and carries an alignment benefit by training models to produce human-endorsed chain-of-thought reasoning. The work highlights a potential synergy between capability improvements and alignment techniques.