Survey on automating geometry problem solving with large models.
problem Automating geometric problem solving with spatial understanding and logical reasoning.
method Synthesizes GPS advancements through benchmark construction, parsing, and reasoning paradigms.
result Unified analytical paradigm and emerging opportunities identified.
MathChat uses LLM agents to solve challenging math problems through conversational problem-solving.
problem Solving math problems expressed in natural language.
method MathChat is a conversational framework combining an LLM agent and a user proxy agent for collaborative problem-solving.
result MathChat improves tool-using prompting methods by 6% on difficult math problems.
AI aids in mathematics research and problem-solving.
problem Complex mathematical problems and discoveries.
method Explains AI principles and diverse applications in math.
result AI assists in discovering patterns, proving theorems, and challenging conjectures.
LATM framework uses LLMs to create and reuse tools for efficient problem-solving.
problem Improving problem-solving capabilities of LLMs with external tools.
method Closed-loop framework with two phases: tool making and tool using. LLMs act as both tool makers and users. Resource-intensive model for tool making, lightweight model for tool using.
result LATM framework achieves performance equivalent to using a powerful LLM for both roles but with significantly reduced costs.
This paper applies machine learning techniques to student modeling. It presents a method for discovering high-level student behaviors from a very large set of low-level traces corresponding to problem-solving actions in a learning environment. Basic actions are encoded into sets of domain-dependent attribute-value patt…
Problems for the graduate students who want to improve problem-solving skills in geometry. Every problem has a short elegant solution -- this gives a hint which was not available when the problem was discovered.
Enhances math problem-solving models with multi-turn preference learning.
problem Improving mathematical problem-solving capabilities of large language models.
method Introduces a multi-turn direct preference learning framework for tool-integrated mathematical reasoning tasks.
result Significant performance improvements in model accuracy on math datasets.
TIR expands LLM capabilities by enabling problem-solving strategies.
problem Lack of a principled theory explaining why LLMs with tools are more capable.
method Formal proof and Advantage Shaping Policy Optimization (ASPO) algorithm.
result TIR model decisively outperforms pure-text models on challenging benchmarks.
Abstractor enhances Transformers for relational reasoning, improving sample efficiency and performance.
problem Improving sample efficiency and performance in relational tasks.
method Introduces Abstractor module with relational cross-attention to enable explicit relational reasoning.
result Dramatic improvements in sample efficiency and performance on various relational tasks.
Current learning machines have successfully solved hard application problems, reaching high accuracy and displaying seemingly "intelligent" behavior. Here we apply recent techniques for explaining decisions of state-of-the-art learning machines and analyze various tasks from computer vision and arcade games. This showc…
As deep learning applications continue to become more diverse, an interesting question arises: Can general problem solving arise from jointly learning several such diverse tasks? To approach this question, deep multi-task learning is extended in this paper to the setting where there is no obvious overlap between task a…
Enhanced Transformer solves math problems better with explicit relation encoding.
problem Improving Transformer models for solving math word problems.
method Integrates Tensor-Product Representations and TP-Attention mechanism.
result Sets new state of the art on the Mathematics Dataset.
New method for tuning Graphical Lasso hyperparameters.
problem Tuning hyperparameters of Graphical Lasso.
method Bilevel optimization with first-order method.
result Derivation of Graphical Lasso Jacobian.
Classical knot recognition problem solved in NP with exponential time algorithm.
problem Determining if a virtual knot is classical.
method Proved NP membership and provided an exponential time algorithm.
result Classical knot recognition problem is in NP.
In this paper we present the first results of a pilot experiment in the capture and interpretation of multimodal signals of human experts engaged in solving challenging chess problems. Our goal is to investigate the extent to which observations of eye-gaze, posture, emotion and other physiological signals can be used t…
Rectangular peg problem solved for many curves.
problem Rectangular peg problem for continuous Jordan curves.
method Microlocal sheaf theory and recent work of Greene and Lobb.
result Affirmative answer for a large class of rectifiable curves.
For technology (like serious games) that aims to deliver interactive learning, it is important to address relevant mental experiences such as reflective thinking during problem solving. To facilitate research in this direction, we present the weDraw-1 Movement Dataset of body movement sensor data and reflective thinkin…
Knot genus problem solved for all 3-manifolds.
problem Determining if a knot bounds a surface of genus g in a fixed 3-manifold.
method Showing the problem is in co-NP for all 3-manifolds.
result The knot genus problem is now solved for all 3-manifolds, not just rational homology 3-spheres.
DPMC improves inverse problem solving with MCMC, reducing error in noisy conditions.
problem Inaccurate posterior approximation in inverse problems with high noise levels.
method DPMC uses Annealed MCMC to sample through a series of intermediate distributions, reducing accumulated error.
result DPMC outperforms DPS in various inverse problems, reducing error and evaluations.
Thurston's influence on French math traced and problems solved.
problem Major problems in French math traced back to Thurston.
method Overview and survey of Thurston's influence and results.
result French math problems rooted in Thurston's work.
This work investigates how multi-round reasoning improves LLM performance.
problem Improving problem-solving abilities in complex tasks with LLMs.
method Investigates approximation, learnability, and generalization properties of multi-round auto-regressive models.
result Transformers with finite context windows are universal approximators for Turing-computable functions and can approximate any Turing-computable sequence-to-sequence function through multi-round reasoning.
Fractional Laplacian inverse problem solved for connection Laplacians.
problem Determining structures from metric, bundle, and map knowledge.
method Local knowledge of metric, bundle, and map determines global structures.
result Global structures determined from local knowledge of metric, bundle, and map.
Study examines machine learning competitions' impact on AI development.
problem Fostering innovation and skill development in AI.
method Analysis of major competition platforms, workflows, and participant demographics.
result MLCs promote collaboration, reproducibility, and continuous innovation in AI.
Curve shortening problem solved via Schwarz function.
problem Solving the curve shortening problem in the z-plane. method Using the Schwarz function to solve the differential equation StSz=Szz. result Explicit solutions for known curve shortening flow shapes can be recovered.
Mathematical framework using Riemannian geometry for intelligence and consciousness.
problem Lack of a unified mathematical framework for intelligence and consciousness.
method Conceptualizes intelligence as tokens in a high-dimensional space, using Riemannian geometry to describe structure and dynamics.
result Integrates geometric concepts to offer a unified framework for intelligence and consciousness.
Sharp stability in Almgren problem solved in any dimension.
problem Quantitative stability in the radial isotropic Almgren problem.
method Developed a theory for estimating the sharp modulus under minimal assumptions.
result Sharp ε2 in any dimension, solving the critical mass problem. TRR detects stock portfolio crashes by simulating human reasoning.
problem Detecting stock portfolio crashes with limited historical data.
method Temporal Relational Reasoning (TRR) framework.
result TRR outperforms state-of-the-art techniques in detecting stock portfolio crashes.
The preceding three decades have seen the emergence, rise, and proliferation of machine learning (ML). From half-recognised beginnings in perceptrons, neural nets, and decision trees, algorithms that extract correlations (that is, patterns) from a set of data points have broken free from their origin in computational c…
3-manifold groups' word problem solved in nearly linear time.
problem Solving the word problem for 3-manifold groups efficiently.
method Proof for admissible graphs of groups, leveraging Croke and Kleiner's work.
result Word problem solved in O(nlogn) time for 3-manifold groups. State of the art methods in astronomical image reconstruction rely on the resolution of a regularized or constrained optimization problem. Solving this problem can be computationally intensive and usually leads to a quadratic or at least superlinear complexity w.r.t. the number of pixels in the image. We investigate in…
We present a method for the reconstruction of networks, based on the order of nodes visited by a stochastic branching process. Our algorithm reconstructs a network of minimal size that ensures consistency with the data. Crucially, we show that global consistency with the data can be achieved through purely local consid…
New capillary Christoffel-Minkowski problem solved for half-space.
problem Finding strictly convex capillary hypersurfaces from capillary functions.
method Established analogous result in capillary setting for half-space.
result Capillary functions lead to strictly convex capillary hypersurfaces.
Singular Yamabe problems involve changing sign solutions with interesting geometric properties.
problem Solving Yamabe problems with changing sign solutions and their geometric implications.
method Analyzing the behavior of conformal factors and zero loci in various dimensions.
result Zero loci of solutions are critical for conformal functionals and can be Willmore energy minimizers.
Hexagonal norm double bubble problem solved with minimal configurations.
problem Finding the optimal shapes for minimizing perimeter in hexagonal geometry.
method Elementary proof and geometric exclusions to simplify minimizer search.
result Existence of minimizing sets for volume ratio parameter α in (0,1].
This paper presents four different ways of looking at the well-known Least Squares Temporal Differences (LSTD) algorithm for computing the value function of a Markov Reward Process, each of them leading to different insights: the operator-theory approach via the Galerkin method, the statistical approach via instrumenta…
Independent component analysis (ICA), as an approach to the blind source-separation (BSS) problem, has become the de-facto standard in many medical imaging settings. Despite successes and a large ongoing research effort, the limitation of ICA to square linear transformations have not been overcome, so that general INFO…
Conditional diffusion models can approximate target distributions well with Gaussian-mixture reverse kernels.
problem Approximating target distributions in conditional diffusion models.
method Using finite Gaussian mixtures with ReLU-network logits as reverse kernels, reducing the problem to static conditional density approximation.
result The resulting neural reverse-kernel class is dense in conditional KL divergence under exact terminal matching.
Computer simulations have become a popular tool of assessing complex skills such as problem-solving skills. Log files of computer-based items record the entire human-computer interactive processes for each respondent. The response processes are very diverse, noisy, and of nonstandard formats. Few generic methods have b…
Bayesian inverse problems solved with Gaussian models for PDEs.
problem Solving inverse problems with limited data for PDEs.
method Constructing PDE-informed Gaussian priors for Bayesian inversion.
result PDE-informed Gaussian priors outperform traditional priors.
Improved bounds for proximal gradient algorithms with computational errors.
problem Analyzing convergence of proximal gradient algorithms with inaccuracies.
method Deriving new tighter deterministic and probabilistic bounds for convex composite problems.
result Probabilistic bounds are more robust and accurate for algorithm verification and performance guarantees.
Discrete Lagrange problems solved with Lie group constraints.
problem Solving discrete Lagrange problems with Lie group constraints.
method Proving critical sections are solutions of unconstrained variational problems, applying Noether theory and multisymplectic forms.
result Critical sections of discrete Lagrange problems are solutions of unconstrained variational problems.
The paper finds minimum Steklov eigenvalues on combinatorial graphs.
problem Finding the minimum Steklov eigenvalues on combinatorial graphs.
method Extending Friedman's nodal domain theory for Laplacian eigenfunctions to Steklov eigenfunctions.
result The minimum of the imth Steklov eigenvalue on a connected combinatorial graph is essentially attained by a star or a regular comb with minimal brooms. Neural Optimal Design of Experiments improves inverse problem solving efficiency.
problem Optimal experimental design in inverse problems.
method Jointly trains a reconstruction model and design variables in a single loop.
result Significantly reduces computational complexity and improves reconstruction accuracy.
MEP-Net uses MEP to generate solutions from limited data.
problem Generating solutions to scientific problems with incomplete information.
method Combines MEP with neural networks to learn complex distributions from moment constraints.
result Demonstrates MEP-Net's effectiveness in modeling biochemical reaction networks and generating complex distributions.
This article presents the use of Answer Set Programming (ASP) to mine sequential patterns. ASP is a high-level declarative logic programming paradigm for high level encoding combinatorial and optimization problem solving as well as knowledge representation and reasoning. Thus, ASP is a good candidate for implementing p…
Recently, crowdsourcing has emerged as an effective paradigm for human-powered large scale problem solving in various domains. However, task requester usually has a limited amount of budget, thus it is desirable to have a policy to wisely allocate the budget to achieve better quality. In this paper, we study the princi…
The classification of Willmore 2-spheres in the n-dimensional sphere Sn is a long-standing problem, solved only when n=3,4 by Bryant, Ejiri, Musso and Montiel independently. In this paper we give a classification when n=5. There are three types of such surfaces up to Möbius transformations: (1) super-conformal…
Paper identifies reductive MDPs, solving them in polynomial time.
problem Computational hardness of general MDPs and tractability of finite-horizon MDPs.
method Defines reductivity, a new class of SSPs, and develops a polynomial-time solution.
result Optimal policies can be found in polynomial time for reductive SSPs and MDPs.