Graphs improve theorem proving in higher-order logic.
problem Challenges in converting higher-order logic formulas into graph-based representations.
method Used graph neural networks (GNNs) to represent and search higher-order logic.
result GNNs outperform state-of-the-art methods in higher-order theorem proving.
AI generates theorems and proofs for training theorem provers.
problem Limited human-written theorems and proofs for supervised learning.
method Proposes a neural generator to automatically synthesize theorems and proofs.
result Synthetic data improves automated theorem proving in Metamath.
Automated theorem prover proves non-orderability of groups.
problem Proving non-orderability of groups.
method Generic automated theorem prover with tools like positive cones, torsions, generalised torsions, and cofinal elements.
result Demonstrated automated proof of non-orderability of groups.
LeanDojo removes barriers to theorem proving with open-source tools and data.
problem Difficulty in reproducing and building on existing theorem proving methods.
method Introduces LeanDojo, an open-source Lean playground with toolkits, data, models, and benchmarks.
result ReProver, an LLM-based prover augmented with retrieval, outperforms non-retrieval baselines and GPT-4.
Study improves understanding of why agentic theorem provers succeed.
problem Understanding which components of agentic theorem provers improve proof success.
method Statistical provability theory and finite-horizon reachability MDP model.
result Bounds provability gap and explains components' effectiveness.
Formalizes vNM utility theorem using Lean 4, proving existence and uniqueness.
problem Formalizing and proving the von Neumann-Morgenstern utility theorem.
method Implement classical axioms in Lean 4, formalizing preference relations over lotteries.
result Machine-verified proofs of existence and uniqueness of utility representations.
New model shows hierarchical proof structure helps theorem provers.
problem How to efficiently learn proofs from teacher traces.
method Model proof search as MDP, analyze imitation learning from traces.
result Hierarchical proof structure leads to more efficient learning.
The problem-solving in automated theorem proving (ATP) can be interpreted as a search problem where the prover constructs a proof tree step by step. In this paper, we propose a deep reinforcement learning algorithm for proof search in intuitionistic propositional logic. The most significant challenge in the application…
In this paper, we introduce a system called GamePad that can be used to explore the application of machine learning methods to theorem proving in the Coq proof assistant. Interactive theorem provers such as Coq enable users to construct machine-checkable proofs in a step-by-step manner. Hence, they provide an opportuni…
Automated theorem proving without imitation, using tf-idf for premise selection.
problem Automated theorem proving in large knowledge bases without human guidance.
method Exploration mechanism mixing tf-idf selected premises in a deep reinforcement learning context.
result The prover trained with this approach outperforms provers trained only on human proofs.
Protocol assesses better model among two opaque models with minimal interaction.
problem Learning from two provers, one honest, the other potentially deceptive.
method Formulated and implemented a protocol for assessing better models among two opaque models.
result Protocol achieves near-optimal performance with minimal interaction and query access.
Formal methods verify continuous auctions at exchanges.
problem Ensuring fairness and correctness in continuous auctions.
method Formal specification, design, and verification of continuous double auctions.
result A verified algorithm satisfies natural properties of auctions.
GPT-f uses language models to find new proofs in formal math.
problem Generating original mathematical terms for automated theorem proving.
method Transformer-based language model for automated theorem proving and proof assistant.
result GPT-f contributed new proofs to the Metamath library.
Scalable verifier for recurrent neural networks using polyhedral abstractions.
problem Certifying the correctness of recurrent neural networks.
method Combining sampling, optimization, and Fermat's theorem for polyhedral abstractions; gradient descent for refinement.
result Successfully verified challenging recurrent models in various domains.
Transformed geometry into algebra to prove Pick's theorem efficiently.
problem Translating geometric Pick's theorem into formal algebraic proof.
method Formalized geometric Pick's theorem into algebraic proof using Lean.
result Efficient formal proof of Pick's theorem.
Benchmark for math reasoning models from human proofs.
problem Measuring and accelerating machine learning models in high-level mathematical reasoning.
method Built a non-synthetic dataset from theorem prover proofs, defined a task for model to fill in missing propositions, used hierarchical transformer to improve performance.
result Neural models can capture non-trivial mathematical reasoning, hierarchical transformer outperforms baseline.
This paper autoformalizes Euclidean geometry using LLMs and theorem provers.
problem Challenges in formalizing Euclidean geometry due to reliance on diagrams.
method Combines neuro-symbolic framework, SMT solvers, and LLMs to fill in diagrammatic gaps.
result Demonstrates the capability and limitations of LLMs on autoformalizing geometry problems.
In this article, we introduce rack invariants of oriented Legendrian knots in the 3-dimensional Euclidean space endowed with the standard contact structure, which we call Legendrian racks. These invariants form a generalization of the quandle invariants of knots. These rack invariants do not result in a complete invari…
Paper formalizes Simon's satisficing through FFSD, proving its equivalence to expected utility theory.
problem Formalizing Herbert Simon's bounded rationality concept in economic decision-making.
method Developed FFSD framework using Lean 4 theorem prover, proving equivalence to expected utility theory.
result Equivalence theorem linking FFSD to expected utility maximization for approximate indicator functions.
Paper formalizes multi-dimensional FSD using geometric methods.
problem Complex measure theory and calculus barriers to formalization in proof assistants.
method Geometric framework for first-order stochastic dominance in N dimensions.
result Geometric approach bypasses complex integration theory for direct comparison of survival probabilities.
Lean Copilot uses LLMs to assist theorem proving in Lean, improving efficiency and automation.
problem Challenges in using existing neural theorem provers to prove novel theorems autonomously.
method Introduces Lean Copilot, a framework for integrating LLMs into Lean's theorem proving process.
result Lean Copilot automates 74.2% of proof steps on average, significantly improving over existing methods.
Formalizes integral curves on Banach manifolds in Lean.
problem Existence and uniqueness of integral curves on Banach manifolds.
method Formalized differential equations on Banach spaces, then generalized to Banach manifolds.
result Established theorems for integral curves on Banach manifolds.
Neuro-symbolic system tackles conversational AI's need for natural, broad-ranging dialogue.
problem Understanding unstated presumptions in conversational AI commands.
method Neuro-symbolic theorem prover for multi-hop reasoning.
result Extracts multi-hop reasoning chains from natural language commands.
We explore the application of automated reasoning techniques to unknot detection, a classical problem of computational topology. We adopt a two-pronged experimental approach, using a theorem prover to try to establish a positive result (i.e. that a knot is the unknot), whilst simultaneously using a model finder to try …
This paper formalizes Q-learning and linear TD convergence using Lean 4.
problem Formalizing convergence properties of Q-learning and linear TD learning. method Formal verification using Lean 4 theorem prover and Mathlib library.
result Formalized almost sure convergence of Q-learning and linear TD learning. Classical clients can verify quantum learning tasks efficiently.
problem Making quantum learning accessible to classical clients.
method Developed a framework for classical verification of quantum learning.
result Quantum learning tasks can be efficiently verified by classical verifiers.
Formal framework verifies fairness, uniformity, and rationality in financial market trades.
problem Ensuring fairness, uniformity, and rationality in financial market trades.
method Formal definition and proof of properties in a theorem prover (Coq).
result Formal verification of double-sided auctions in financial markets.
NTP struggles to learn relationships without increased exploration.
problem NTP's performance in extracting true relationships among data is poor.
method Created synthetic logical datasets with injected relationships to test NTP's performance and identify algorithmic issues.
result Increasing exploration in NTP's algorithm improves its performance in recovering relationships.
Formally verifies fairness and uniformity in financial market trades.
problem Ensuring fairness and uniformity in automated trading systems.
method Formal definition and verification in Coq proof assistant.
result Properties of double-sided auction mechanisms verified.
Study generalizes non-interaction theorems for relativistic systems.
problem Understanding interactions in relativistic and non-relativistic systems.
method Generalizes non-interaction theorems for Lorentz violating systems and Galilei invariant systems.
result Extends analysis to very special relativity and anisotropic systems.
This research simplifies verification of machine learning systems using reparameterization.
problem Reduce or eliminate serious bugs in machine learning systems.
method Use proof assistants to construct machine-checked proofs of correctness, leveraging reparameterization to handle probabilistic claims.
result Demonstrates broad applicability of reparameterization to verify different types of machine learning systems.
Study optimal allocation in uncertain multi-armed bandits using Gittins' theorem.
problem Optimal allocation in uncertain multi-armed bandits.
method Theoretical analysis based on nonlinear expectations, with relaxation in optimality definition.
result Gittins' allocation index provides optimal choices under strong independence and relaxed optimality conditions.
Framework for systemic risk modeling using jointly exchangeable arrays.
problem Systemic risk in insurance portfolios with interactions.
method Jointly exchangeable arrays, central limit theorems, simulation-based validation.
result Asymptotic approximations for total portfolio losses in large portfolios over long time horizons.
Machine learning automates proof generation in Coq proof assistant.
problem Automating proof construction in proof assistants.
method Developed ASTactic, a deep learning model generating tactics as ASTs.
result ASTactic can generate effective tactics and prove new theorems.
Three theorems about arbitrage bubbles in financial equations.
problem Characterizing and solving generalized Black-Scholes equations with arbitrage bubbles.
method Analytical proofs of three theorems using the Feynman-Kac theorem.
result Exact solutions for Call contracts with arbitrage bubbles.
Derives fluctuation theorems and thermodynamic uncertainty relations for systems modeled as Bayes nets.
problem Entropy production in interacting systems modeled as Bayes nets.
method Derives fluctuation theorems and thermodynamic uncertainty relations for arbitrary sets and conditioned sets of systems in Bayes nets.
result Relates the entropy production of the overall system to the precisions of probability currents in individual systems.
This paper illustrates the themes of the title in terms of: van Kampen type theorems for the fundamental groupoid; holonomy and monodromy groupoids; and higher homotopy groupoids. Interaction with work of the writer is explored.
New method embeds time span into self-attention for better temporal pattern recognition.
problem Capturing temporal patterns in event sequences without recurrent networks.
method Functional time representation learning with Bochner's and Mercer's Theorems.
result Proposed methods outperform baseline models in various continuous-time event sequence prediction tasks.
A statistical physics model for the time evolutions of stock portfolios is proposed. In this model the time series of price changes are coded into the sequences of up and down spins. The Hamiltonian of the system is introduced and is expressed by spin-spin interactions as in spin glass models of disordered magnetic sys…
Study estimates long-term effects of online advertising mechanisms on user behavior and revenue.
problem Estimating long-term treatment effects in online advertising systems.
method Modeling treatment effects as a stopped random walk, using experimental design, and statistical methods.
result Confidence intervals for long-term treatment effects constructed using statistical techniques.
Develops 2-categorical methods for multi-parameter persistence.
problem Fundamental limitations of traditional persistence modules.
method 2-categorical structures to capture hierarchical interactions.
result New invariants effectively characterize multidimensional topological features.
Teaches Dirac operators for geometry and topology.
problem Interactions between geometry and topology.
method Families of Dirac operators and index theorems.
result Applications to metrics of positive scalar curvature and the three-dimensional Weinstein conjecture.
Neural interaction discoveries can be real or artifacts of model flexibility.
problem Identifying real neural interactions from data.
method Using a multiplicative-gating extension of neural additive vector autoregression.
result Effective rank of the joint lag-block covariance predicts interaction recoverability.
We show that the emerging field of discrete differential geometry can be usefully brought to bear on crystallization problems. In particular, we give a simplified proof of the Heitmann-Radin crystallization theorem (R. C. Heitmann, C. Radin, J. Stat. Phys. 22, 281-287, 1980), which concerns a system of N identical at…
New method for online learning in interacting particle systems.
problem Parameter estimation in stochastic interacting particle systems.
method Stochastic approximation of gradient of asymptotic log likelihood using continuous observations.
result Convergence to stationary points of asymptotic log-likelihood under suitable assumptions.
Random Intersection Chains selects important interactions from categorical features.
problem Heavy computational burden in considering all interactions for categorical features.
method Randomly generates chains of intersections, estimates and selects frequent patterns.
result Selected patterns are the most frequent in the data set.
Developed algebraic theory of bonded braids, proving Markov theorem.
problem Studied bonded knots and their algebraic properties.
method Introduced bonded braid monoid, proved Alexander and Markov theorems.
result Every bonded knot is the closure of a bonded braid, and equivalent knots have related braid representatives.
Upper bound found for systolic geometry on manifolds with positive scalar curvature.
problem Relationship between systolic geometry and positive scalar curvature.
method Spinorial methods combined with geometric measure theory and curvature estimates.
result Upper bound for the two-dimensional stable systole on certain manifolds.