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.
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.
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.
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.
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…
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.
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.
We incorporate Tensor-Product Representations within the Transformer in order to better support the explicit representation of relation structure. Our Tensor-Product Transformer (TP-Transformer) sets a new state of the art on the recently-introduced Mathematics Dataset containing 56 categories of free-form math word-pr…
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.
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.
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.
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 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…
The study uncovers latent capabilities of language models via causal representation learning.
problem Rigorous causal evaluations of language model capabilities are challenging due to confounding effects and computational costs.
method Proposes a causal representation learning framework to identify latent capability factors as causally interrelated after controlling for a common confounder (base model).
result Identifies a three-node linear causal structure explaining performance variations across 1500 models and six benchmarks.
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.
EDINET-Bench evaluates LLMs on complex financial tasks using Japanese financial statements.
problem Challenges in evaluating LLMs on financial tasks due to specialized expertise and scarce benchmarks.
method Developed EDINET-Bench, an open-source Japanese financial benchmark for LLMs on tasks like fraud detection and earnings forecasting.
result State-of-the-art LLMs perform only marginally better than logistic regression in financial tasks, highlighting the need for more realistic benchmarks.
New method samples from LLM posterior for coherent, useful responses.
problem Hallucinations in large language models.
method Posterior sampling for conditional generation, with calibration.
result Achieves statistical guarantees with higher downstream utility.
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…
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.
Quantum mechanics models human perception and decision-making, offering a new approach to understanding social dynamics.
problem Understanding the complex interactions between individuals and groups in social networks.
method Developed a simple computational code based on quantum mechanics principles to model human perception and decision-making.
result Quantum-inspired models can help explain differences in individual and group behavior.
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.
Auto-CEI improves LLM reasoning by balancing assertiveness and conservativeness.
problem Hallucinations and laziness in LLM reasoning tasks.
method Expert Iteration explores reasoning trajectories, guiding incorrect paths back on track and promoting appropriate 'I don't know' responses.
result Auto-CEI achieves superior alignment in logical reasoning, mathematics, and planning tasks.
Enhances large language models' reasoning through simpler off-policy reinforcement learning.
problem Improving large language models' ability to reason and solve problems.
method EM Policy Gradient, optimizing expected return over reasoning trajectories using Expectation-Maximization (EM) optimization.
result Achieves comparable or slightly superior performance to state-of-the-art methods on reasoning datasets, with additional cognitive behaviors.
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.
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.
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.