SPIRAL is a reinforcement learning framework that jointly optimizes sequential reasoning, parallel trace generation, and aggregation in language models for improved test-time performance.
Towards autonomous mathematics research.arXiv preprint arXiv:2602.10177, 2026
22 Pith papers cite this work, alongside 3 external citations. Polarity classification is still indexing.
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cs.AI 8 cs.LG 5 cs.CL 2 cs.CY 1 cs.DL 1 cs.IR 1 cs.MS 1 math.AG 1 math.RA 1 physics.comp-ph 1years
2026 22roles
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PhySciBench benchmark shows current AI models achieve at most 33.5% accuracy on physical science tasks; DelveAgent framework improves accuracy by up to 7.5 points and cuts costs to one-third.
A multi-agent framework called AutoformBot autoformalized 26 textbooks spanning analysis, algebra, topology, combinatorics and probability into a verified Lean 4 library of 45k declarations, demonstrating scalable formalization of graduate math.
An LLM-based agent with Lean verification autonomously solved multiple open Erdős problems and OEIS conjectures in the first large-scale test.
An interactive AI workbench for mathematicians achieves 48% on FrontierMath Tier 4 and helped solve open problems in early tests.
The minimal volume of stable surfaces of rank one is determined with uniqueness up to isomorphism, resolving a conjecture of Alexeev and the second author.
Stable tame isomorphism, quasi-isomorphism, and derived Morita equivalence are undecidable for semifree noncommutative DGAs.
Small 7B reasoning models were fine-tuned on synthetic and curated QFT problems using RL and SFT, yielding performance gains, error analysis, and public release of data and traces.
Matlas introduces a semantic retrieval system over 8.07 million mathematical statements from papers and textbooks, using dependency graphs and topological unfolding for self-contained search via natural language queries.
k-server-bench formulates potential-function discovery for the k-server conjecture as a code-based inequality-satisfaction task; current agents fully solve the resolved k=3 case and reduce violations on the open k=4 case.
Rethlas+Archon automatically construct and Lean-verify a counterexample showing weak quasi-completeness does not imply quasi-completeness for Noetherian local rings.
Danus uses a main planner, parallel workers, and a shared verified fact graph to construct long research-level mathematical proofs across six case studies.
LLM formal provers must shift from competition solvers to research agents that handle open-ended, under-specified frontier mathematics under machine-checked rigor.
A survey of 1,250 papers organizes AI self-improvement along two axes—what is improved and loop closure—finding that demonstrated self-improvement strength tracks a verification hierarchy from formal verifiers down to intrinsic self-assessment.
Self-trained verification trains verifiers to imitate informed versions of themselves using reference solutions, improving test-time V-R loops and training-time self-improvement with reported gains of 2x on hard math and 14x on scientific reasoning.
Introduces the Agentic Publication Protocol (APP) as a repository-based standard for publishing papers together with reproducibility artifacts and agent instructions.
Human-AI collaboration expanded a meta-idea on rational approximation into sign-embedding quantum algorithms for matrix problems, with humans retaining final judgment on routes and refinements.
AI for mathematics is best described as a supervision ladder — final answers, programs, process rewards, proof-assistant kernels — culminating in verified-discovery workflows.
Iteris, an agentic research system, produced evidence and drafts for two open computational math problems that were verified after human correction.
LLM agents produce outputs that meet basic functional criteria for creativity but lack the process-level, social, and personal elements required for ontological creativity.
Presents PAT, an agentic AI review tool using inference scaling that claims 34% better math error recall on SPOT benchmark and successful pilots at STOC and ICML conferences.
citing papers explorer
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SPIRAL: Learning to Search and Aggregate
SPIRAL is a reinforcement learning framework that jointly optimizes sequential reasoning, parallel trace generation, and aggregation in language models for improved test-time performance.
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Deep Research in Physical Sciences: A Multi-Agent Framework and Comprehensive Benchmark
PhySciBench benchmark shows current AI models achieve at most 33.5% accuracy on physical science tasks; DelveAgent framework improves accuracy by up to 7.5 points and cuts costs to one-third.
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Formalizing Mathematics at Scale
A multi-agent framework called AutoformBot autoformalized 26 textbooks spanning analysis, algebra, topology, combinatorics and probability into a verified Lean 4 library of 45k declarations, demonstrating scalable formalization of graduate math.
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Advancing Mathematics Research with AI-Driven Formal Proof Search
An LLM-based agent with Lean verification autonomously solved multiple open Erdős problems and OEIS conjectures in the first large-scale test.
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AI co-mathematician: Accelerating mathematicians with agentic AI
An interactive AI workbench for mathematicians achieves 48% on FrontierMath Tier 4 and helped solve open problems in early tests.
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The minimal volume of stable surfaces of rank one
The minimal volume of stable surfaces of rank one is determined with uniqueness up to isomorphism, resolving a conjecture of Alexeev and the second author.
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Undecidability problems for semifree DG algebras
Stable tame isomorphism, quasi-isomorphism, and derived Morita equivalence are undecidable for semifree noncommutative DGAs.
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Fine-Tuning Small Reasoning Models for Quantum Field Theory
Small 7B reasoning models were fine-tuned on synthetic and curated QFT problems using RL and SFT, yielding performance gains, error analysis, and public release of data and traces.
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Matlas: A Semantic Search Engine for Mathematics
Matlas introduces a semantic retrieval system over 8.07 million mathematical statements from papers and textbooks, using dependency graphs and topological unfolding for self-contained search via natural language queries.
-
$k$-server-bench: Automating Potential Discovery for the $k$-Server Conjecture
k-server-bench formulates potential-function discovery for the k-server conjecture as a code-based inequality-satisfaction task; current agents fully solve the resolved k=3 case and reduce violations on the open k=4 case.
-
Automated Conjecture Resolution with Formal Verification
Rethlas+Archon automatically construct and Lean-verify a counterexample showing weak quasi-completeness does not imply quasi-completeness for Noetherian local rings.
-
Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory
Danus uses a main planner, parallel workers, and a shared verified fact graph to construct long research-level mathematical proofs across six case studies.
-
From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier
LLM formal provers must shift from competition solvers to research agents that handle open-ended, under-specified frontier mathematics under machine-checked rigor.
-
Recursive Self-Improvement in AI: From Bounded Self-Refinement to Autonomous Research Loops
A survey of 1,250 papers organizes AI self-improvement along two axes—what is improved and loop closure—finding that demonstrated self-improvement strength tracks a verification hierarchy from formal verifiers down to intrinsic self-assessment.
-
Self-Trained Verification for Training- and Test-Time Self-Improvement
Self-trained verification trains verifiers to imitate informed versions of themselves using reference solutions, improving test-time V-R loops and training-time self-improvement with reported gains of 2x on hard math and 14x on scientific reasoning.
-
Agentic Publication Protocol: An Attempt to Modernize Scientific Publication
Introduces the Agentic Publication Protocol (APP) as a repository-based standard for publishing papers together with reproducibility artifacts and agent instructions.
-
From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms
Human-AI collaboration expanded a meta-idea on rational approximation into sign-embedding quantum algorithms for matrix problems, with humans retaining final judgment on routes and refinements.
-
Artificial Intelligence for Mathematical Reasoning: An Integrated Survey of Language Models, Neuro-symbolic Systems, and Verified Discovery
AI for mathematics is best described as a supervision ladder — final answers, programs, process rewards, proof-assistant kernels — culminating in verified-discovery workflows.
-
Iteris: Agentic Research Loops for Computational Mathematics
Iteris, an agentic research system, produced evidence and drafts for two open computational math problems that were verified after human correction.
-
On the Creativity of AI Agents
LLM agents produce outputs that meet basic functional criteria for creativity but lack the process-level, social, and personal elements required for ontological creativity.
-
Towards Automating Scientific Review with Google's Paper Assistant Tool
Presents PAT, an agentic AI review tool using inference scaling that claims 34% better math error recall on SPOT benchmark and successful pilots at STOC and ICML conferences.
- InfiniteScienceGym: An Unbounded, Procedurally-Generated Benchmark for Scientific Analysis