Self-supervised skip-tree training improves mathematical reasoning in language models.
problem Improving logical reasoning in language models for formal mathematics.
method Self-supervised language modeling on mathematical formulas, skip-tree task.
result Models trained on skip-tree task outperform standard models in mathematical reasoning tasks.
Mathematical general relativity reviewed.
problem Challenges in mathematical modeling of general relativity.
method Selected topics reviewed.
result Insights into mathematical models of general relativity.
Mathematical model predicts international trade and global economy dynamics.
problem Understanding complex international trade and economy interactions.
method Developed a mathematical model for non-equilibrium processes in open systems.
result Predicted model accurately reflects international trade and economy.
TopicEq model generates equations and text from scientific papers.
problem Communicating ideas in scientific texts using both mathematics and text.
method Joint topic and equation generation model using correlated topic model and RNN.
result Joint model outperforms existing topic and equation models for scientific texts.
Mathematical framework for language models processes text and predicts next tokens.
problem Understanding and optimizing the performance of large language models.
method Describes encoding, prediction models, learning from data, and deployment of LLMs.
result Demonstrates remarkable empirical successes and provides a platform for further research.
This paper evaluates neural models' mathematical reasoning abilities.
problem Evaluating neural models' capability in solving mathematical problems.
method Developed a task suite of mathematics problems, analyzed two sequence-to-sequence architecture classes.
result Notable differences in models' ability to solve and generalize mathematical problems.
Transformer models can solve complex math problems with less data.
problem Solving complex symbolic mathematics problems with limited data.
method Pretrain transformer models on language translation tasks and fine-tune for symbolic math.
result Pretrained transformer models achieve comparable accuracy to state-of-the-art models with less data.
Study of influenza A virus spread using mathematical equations.
problem Understanding the spread of influenza A virus infection.
method Mathematical model and analysis of dynamical system.
result Surface trajectories and asymptotic behavior of the system.
These notes grew out of a lecture course on mathematical methods of classical physics for students of mathematics and mathematical physics at the master's level. Also, physicists with a strong interest in mathematics may find this text useful as a resource complementary to existing textbooks on classical physics. Topic…
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.
Mathematical approach defines stability conditions for ML models.
problem Ensuring stability of machine learning models.
method Adopted topological and metric spaces theory to define stability.
result Stability of ML models depends on topological properties of classification sets.
Model for material elasticity and plasticity using networks.
problem Understanding the elasticity and plasticity of materials.
method Developed a mathematical model based on networks, defining tension tensor for periodic graphs.
result The model explains elasticity and plasticity through local moves on graphs.
These lecture notes provide a self-contained introduction to the mathematical methods required in a Bachelor degree programme in Business, Economics, or Management. In particular, the topics covered comprise real-valued vector and matrix algebra, systems of linear algebraic equations, Leontief's stationary input-output…
Advanced mathematical relativity course for math and physics students.
problem Mathematical foundations of general relativity.
method Comprehensive lecture notes covering advanced topics.
result Comprehensive coverage of mathematical relativity for advanced students.
This paper surveys and classifies attribute-aware CF models.
problem Rating prediction with user and item attributes.
method Mathematical classification of attribute-aware CF models into four categories.
result Comprehensive comparison of effectiveness among different categories.
The paper surveys mathematical results on filtration enlargement with financial examples.
problem Mathematical finance applications of filtration enlargement theory.
method Exhaustive survey and interpretation of key results from literature.
result Provides a compendium of known mathematical results for mathematical finance researchers.
Mathematical analysis improves SGMs, resolving memorization issues.
problem Improving performance and avoiding memorization in SGMs.
method Formulated SGMs using Wasserstein proximal operators and mean-field games.
result Improved SGM performance in terms of training samples and time.
Mathematical advances needed for Digital Twins, differing from traditional models.
problem Foundational mathematical advances required for Digital Twins.
method Multi-scale, multi-physics modeling and coupling, different reliability criteria and uncertainty assessments.
result AI/ML methods can perform well in biomedical problems but fail in simple engineering systems.
Golden age of mathematical finance in the late 20th century.
problem Foundations of mathematical finance during the late 20th century.
method Collaboration between economists and probabilists.
result Established two fundamental theorems of arbitrage theory and close formulas for options.
Paper proposes a math-inspired L2O model for better generalization.
problem Overfitting and poor generalization of generic L2O models.
method Derived mathematical conditions for successful update rules and proposed a novel L2O model.
result Proposed model outperforms generic L2O models in out-of-distribution settings.
Mathematical models reveal key factors for engaging Gen Z at work.
problem Understanding and improving engagement of Generation Z employees.
method Correlation and cluster analyses on engagement surveys.
result Clear responsibilities and challenging work are essential for Gen Z employees.
The aim of this paper is to discuss some applications of general topology in computer algorithms including modeling and simulation, and also in computer graphics and image processing. While the progress in these areas heavily depends on advances in computing hardware, the major intellectual achievements are the algorit…
Mathematical study shows post-hoc explanations are better than attention weights alone.
problem Understanding the internal behavior of attention-based models.
method Mathematical analysis of a simple attention-based architecture.
result Post-hoc explanations provide more useful insights than attention weights alone.
Develops a mathematical model for CLMM dynamics in DeFi.
problem Analyzing CLMMs in continuous time trading.
method Modeling CLMM dynamics as measure-valued processes, examining three arbitrage models.
result Trading fees limit admissible price processes, impacting CLMM design.
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.
Language models help text classification tasks by predicting next words.
problem Lack of theoretical understanding of why language models perform well on downstream tasks.
method Mathematical study of the connection between next word prediction and text classification, formalizing it and quantifying the benefit.
result Language models that are ε-optimal in cross-entropy learn features that can solve classification tasks with linear approximation.
Mathematical framework for differential machine learning in finance.
problem Theoretical assumptions in financial models and their impact on machine learning algorithms.
method Rigorous mathematical framework for differential machine learning in finance.
result Theoretical grounding enhances the predictive capabilities of neural networks in financial applications.
Extends Itô's formula for path-dependent functions in finance.
problem Modeling and hedging of path-dependent financial options.
method Functional extension of Itô's formula for C^{0,1}-functions of continuous weak Dirichlet processes.
result Validates the hedging or superhedging problems for path-dependent options.
BCF models estimate causal effects on multiple outcomes in TIMSS data.
problem Estimating causal effects on multiple outcomes in educational data.
method Bayesian Additive Regression Trees (BART) for multivariate causal inference.
result Positive and negative effects of home study conditions and school absence on student achievement.
Quantum computing promises new financial modeling.
problem Traditional financial modeling limitations.
method Overview of quantum computing applications in finance.
result Quantum computing can enhance financial modeling.
This is an introductory review of topological field theories (TFTs) called AKSZ sigma models. The AKSZ construction is a mathematical formulation for the construction and analyses of a large class of TFTs, inspired by the Batalin-Vilkovisky formalism of gauge theories. We begin by considering a simple two-dimensional t…
AI mirrors modern math's autonomous development, raising interpretive challenges.
problem AI's effectiveness in math mirrors historical autonomy of math.
method Analyzes historical evolution of modern mathematics and AI's role.
result AI's affinity with math's historical autonomy suggests interpretive limits.
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 article reviews mathematical insights into neural networks and machine learning.
problem Understanding the success and subtleties of neural network-based machine learning.
method Rigorous mathematical analysis, numerical experiments, and simplified models.
result Identification of open problems in the field.
Paper examines two methods for FX market volatility modeling.
problem FX market volatility modeling problem.
method Classical econometric GCH and mathematical approaches (SSA, dynamical systems stability analysis).
result Both mathematical tools show promising results in FX market volatility modeling.
Deep learning models are growing, posing new mathematical challenges.
problem Mathematical challenges in training, inference, generalization, and optimization of deep models.
method Formal mathematical analysis and communication with mathematicians, statisticians, and computer scientists.
result A set of new mathematical challenges in deep learning.
LLMs struggle with arithmetic tasks unless they use high numerical precision.
problem Improving arithmetical reasoning capabilities of LLMs.
method Theoretical analysis and empirical experiments on numerical precision.
result LLMs require high numerical precision to efficiently handle arithmetic tasks.
Develops a mathematical model for automatic differentiation in machine learning.
problem Current automatic differentiation lacks a simple mathematical model for machine learning.
method Articulates relationships between program differentiation and nonsmooth functions, provides a class of functions and nonsmooth calculus.
result Shows how nonsmooth calculus applies to stochastic approximation methods and evidence of artificial critical points.
In mathematical finance a popular approach for pricing options under some Levy model is to consider underlying that follows a Poisson jump diffusion process. As it is well known this results in a partial integro-differential equation (PIDE) that usually does not allow an analytical solution while numerical solution bri…
We propose a simple mathematical model for unemployment. Despite its simpleness, we claim that the model is more realistic and useful than recent models available in the literature. A case study with real data from Portugal supports our claim. An optimal control problem is formulated and solved, which provides some non…
RL methods applied to option pricing using modified QLBS and RLOP models.
problem Applying reinforcement learning to price options accurately.
method Developed modified QLBS and RLOP models, implemented RL learning algorithm with neural networks.
result Optimal hedging strategies learned by RL outperform baseline models.
Course on market microstructure models for students.
problem Market microstructure under asymmetric information.
method Introduction to Kyle model and related filtering, enlargement of filtrations, Markov bridges.
result Introduction and brief overview of advanced financial models.
Shapley values for feature importance lead to mathematical and practical issues.
problem Mathematical and practical issues with Shapley values for feature importance.
method Game-theoretic formulations of feature importance using Shapley values.
result Mathematical problems arise when using Shapley values for feature importance.
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.
Study evaluates different mathematical models for three case studies using statistical fitting.
problem Estimating outcomes in population dynamics, temperature variations, and market equilibrium.
method Applied various statistical equations (e.g., fractional exponential, sinusoidal) to three case studies.
result Optimal models differ by case study (fractional exponential for population dynamics, sinusoidal for temperature and market equilibrium).
Mathematical models with time dependent parameters are of great interest in financial Mathematics because they capture real life scenarios in the financial market. In this study, via the Lie group technique, we analyse evolution-type equations with time dependent parameters and give the general symmetry structure of th…
Mathematical framework for understanding attention in neural networks.
problem Lack of theoretical understanding of attention in neural networks.
method Proposes a measure-theoretic model of attention and interprets self-attention as a system of self-interacting particles.
result Shows that attention is Lipschitz-continuous under suitable assumptions.
Investigates the effects of nondominated sets of probability measures in robust models of finance.
problem Uncertainty in financial models due to multiple possible probability measures.
method Analyzes various results from mathematical finance literature under the assumption of nondominated sets of probability measures.
result Many classical results in robust models do not hold when the set of measures is nondominated.