This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension …
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48 results for “mathematical techniques”
This paper describes a new method for Symbolic Regression that allows to find mathematical expressions from a dataset. This method has a strong mathematical basis. As opposed to other methods such as Genetic Programming, this method is deterministic, and does not involve the creation of a population of initial solution…
t-SNE loses important features in data visualization.
problem t-SNE's loss of important features in data visualization.
method Established mathematical framework to understand t-SNE's loss in different scenarios.
result t-SNE loses important features of data in various scenarios.
This paper offers a mathematical introduction to GANs.
problem Understanding GANs from a mathematical perspective.
method Mathematical analysis of GANs.
result Provides clarity for math-oriented students.
An exploration of the mathematical structure and behavioural biases of 21st century financial crisesq-fin.ST
Study financial crises using mathematical techniques to compare equity performance.
problem Comparing financial crises to understand market dynamics and investor strategies.
method New mathematical techniques including portfolio diversification, linear operator method, and combinatorial portfolio optimisation.
result New methods to quantify and compare equity returns during different market crises.
This paper offers a mathematical framework to manage inventory risk in FX cash markets.
problem Inventory risk in FX cash markets due to flow uncertainty and volatility.
method Mathematical framework and approximation techniques for scalability.
result Maximizing expected profit while controlling inventory risk.
This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and mathematical programming for decision-making under uncertainty, and identifies potential r…
Survey on new Ricci flow techniques.
problem None explicitly stated.
method None explicitly stated.
result None explicitly stated.
Notes on generative modeling: flow matching, diffusion, optimal transport and Schr{ö}dinger bridgestat.ML
Abstract notes on generative modeling techniques.
problem Improving generative modeling techniques.
method Connections between optimal transport and Schrödinger bridge, flow matching.
result Showed connections between mathematical principles and generative modeling techniques.
Experimental life sciences like biology or chemistry have seen in the recent decades an explosion of the data available from experiments. Laboratory instruments become more and more complex and report hundreds or thousands measurements for a single experiment and therefore the statistical methods face challenging tasks…
Develops new techniques for learning from sequential data groups.
problem Learning from groups of inputs rather than individual inputs.
method Introduces feature-based and kernel-based learning techniques for sequential data.
result Achieves state-of-the-art performance on various real-world examples.
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…
Explains classic quantitative strategies and their workings.
problem Debunking the magic behind black-box quantitative strategies.
method Derives from simple intuitions and mathematics, addressing both formal and informal aspects.
result Provides a deeper understanding of quantitative strategies.
While it has become common to perform automated translations on natural language, performing translations between different representations of mathematical formulae has thus far not been possible. We implemented the first translator for mathematical formulae based on recursive neural networks. We chose recursive neural…
New framework explains deep learning using signal processing techniques.
problem Lack of a rigorous mathematical theory explaining deep learning performance.
method Transform-domain sparse regularization, Radon transform, and approximation theory.
result Explains neural network properties and performance.
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.
New mathematical framework proves the effectiveness of reducing neural network sizes.
problem Selecting optimal neural network sizes to avoid overfitting.
method Adaptive group Lasso applied to one-hidden-layer feedforward networks.
result Adaptive group Lasso is consistent and can accurately reconstruct network sizes.
The tetrahedral index connects to a q-Bessel function, revealing new mathematical techniques.
problem Exploring connections between the tetrahedral index and Hahn-Exton q-Bessel function.
method Establishing a correspondence between the tetrahedral index and the q-Bessel function.
result New techniques and conjectures in q-hypergeometric theory.
This article is written for the Proceedings of the Conference on Current Developments in Mathematics in Harvard University, November 16-17, 2007. It is an exposition of the analytic proof of the finite generation of the canonical ring for a compact complex algebraic manifold of general type. It lists and discusses the …
Study ablated data augmentation techniques and their mathematical equivalence to penalties.
problem Lack of mathematical understanding of differences between ablated data augmentation techniques.
method Formal model of mean ablated data augmentation and inverted dropout for linear regression; empirical validation for deep networks.
result Ablated data augmentation and inverted dropout are mathematically equivalent to penalties in optimization.
Exact Matrix Seriation through Mathematical Optimization: Stress and Effectiveness-Based Modelsmath.OC
Unified optimization framework for matrix seriation.
problem Discovering latent structure in relational data.
method Mathematical optimization models for seriation.
result Optimization models enhance solution quality and interpretability.
This study investigates porosity and topological properties of TPMS using machine learning.
problem Understanding the relationships between porosity and topological properties of TPMS.
method Application of machine learning techniques to analyze porosity and shape factor of TPMS.
result Conjectures suggesting polynomial relationships between porosity and shape factor of TPMS.
Unified view of SOMs and SNE from a common framework.
problem Comparing and understanding SOMs and SNE.
method Unified mathematical framework, quantitative comparison on datasets.
result SOMs and SNE can be derived from a common framework.
We consider an infinite dimensional optimization problem motivated by mathematical economics. Within the celebrated "Arbitrage Pricing Model", we use probabilistic and functional analytic techniques to show the existence of optimal strategies for investors who maximize their expected utility.
Geometric techniques reveal new insights into Gromov-Witten invariants.
problem Formulating Gromov-Witten invariants for complete intersections in projective space.
method Combining geometric group theory and geometric topology, focusing on geodesic laminations.
result Primitive cohomologies unify mathematical formulations of Gromov-Witten invariants.
In this paper we introduce a new technique based on high-dimensional Chebyshev Tensors that we call \emph{Orthogonal Chebyshev Sliding Technique}. We implemented this technique inside the systems of a tier-one bank, and used it to approximate Front Office pricing functions in order to reduce the substantial computation…
Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus, approximation theory, optimization and linear algebra. This article provides a very…
Adaptive Monte Carlo methods are recent variance reduction techniques. In this work, we propose a mathematical setting which greatly relaxes the assumptions needed by for the adaptive importance sampling techniques presented by Vazquez-Abad and Dufresne, Fu and Su, and Arouna. We establish the convergence and asymptoti…
Quantum GAN improves volatility modeling in finance.
problem Improving volatility modeling in finance using GANs.
method Developed a quantum GAN for volatility modeling.
result Quantum GAN provides exponential advantage over classical methods.
This paper studies how knots combine using Alexander Polynomials.
problem How knots combine and their determinants behave.
method Basic knot theory, Alexander Polynomials, and composition techniques.
result Generalized solution for knot determinants in compositions.
Calculation of an optimal tariff is a principal challenge for pricing actuaries. In this contribution we are concerned with the renewal insurance business discussing various mathematical aspects of calculation of an optimal renewal tariff. Our motivation comes from two important actuarial tasks, namely a) construction …
New method tackles inexact bilevel optimization for faster parameter learning.
problem Nested optimization problems in bilevel learning with computationally difficult exact solutions.
method Inexact derivative-free optimization algorithms for approximate lower-level solutions.
result Global convergence and worst-case complexity for the proposed approach.
The change of numeraire gives very important computational simplification in option pricing. This technique reduces the number of sources of risks that need to be accounted for and so it is useful in pricing complicated derivatives that have several sources of risks. In this article, we considered the underlying mathem…
Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain. Typical examples include undersampled magnetic resonance imaging, interior tomography, and sparse-view computed tomography, where deep lea…
MAD framework learns operators from physics-embedded data efficiently.
problem Data-driven methods require costly labeled datasets and model-driven techniques face efficiency-accuracy trade-offs.
method Integrates physical laws with data-driven learning to generate physics-embedded analytical solutions and synthetic data.
result Eliminates dependence on experimental or simulated training data, enabling efficient operator learning across multi-parameter systems.
Improves neural network search in combinatorial spaces of mathematical symbols.
problem Early commitment and initialization bias limit exploration in neural network search.
method Entropy regularization and distribution initialization methods.
result Improves performance, increases sample efficiency, lowers solution complexity.
The authors study the method of scaling in the context of the study of automorphism groups of complex domains in multiple dimensions. Various types of scaling techniques are compared and contrasted. Applications are given in a number of areas of complex geometric analysis. Relations with other parts of mathematics are …
Improved model predicts wildfire spread on slopes.
problem Accurate prediction of wildfire spread on slopes.
method Combines Rothermel model, Huygens' principle, and advanced techniques.
result More precise model of wildfire propagation.
Transformers learn functionals from distributions without losing information.
problem Lack of rigorous mathematical theory supporting Transformer performance.
method Proposed a Transformer learning framework, attention operator, and distribution regression.
result Transformers can compress distributions into function representations without loss of information.
Mathematical Reinforcement Learning faces a 'Two-Hump' problem due to sparse rewards and a scarcity of intermediate 'hard-but-solvable' instances.
problem Mathematical search problems in Reinforcement Learning
method Novel data generation techniques and algorithmic enhancements
result Substantial performance improvements over previous baselines
Turaev transformed knot theory and 3-manifold invariants.
problem Understanding knots and links invariants of 3-manifolds.
method Classical topology techniques and quantum topology.
result Introduced new ideas and tools in knot theory and 3-manifold invariants.
Analysis of different Mathematical Models for Different Case Studies Using Statistical Fittingmath.DG
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).
Chern-Weil and Chern-Simons theory extend to certain infinite-rank bundles that appear in mathematical physics. We discuss what is known of the invariant theory of the corresponding infinite-dimensional Lie groups. We use these techniques to detect cohomology classes for spaces of maps between manifolds and for diffeom…
Validation of the Replica Trick for Simple Modelscond-mat.dis-nn
We discuss replica analytic continuation using several simple models in order to prove mathematically the validity of replica analysis, which is used in a wide range of fields related to large scale complex systems. While replica analysis consists of two analytical techniques, the replica trick (or replica analytic con…
Finding the Sweet Spot: Trading Quality, Cost, and Speed During Inference-Time LLM Reflectionstat.ML
This paper compares self-reflection and budget tuning for LLMs, revealing domain-specific performance gains.
problem Improving inference-time performance of LLMs without retraining, balancing quality, cost, and latency.
method Systematic comparison of self-reflection and budget tuning across mathematical reasoning and translation tasks, evaluating various LLMs and model families.
result Substantial domain-dependent variation in self-reflection effectiveness, with up to 220% performance gains in mathematical reasoning.
Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five year…
Principal component analysis (PCA) is a mainstay of modern data analysis - a black box that is widely used but (sometimes) poorly understood. The goal of this paper is to dispel the magic behind this black box. This manuscript focuses on building a solid intuition for how and why principal component analysis works. Thi…
The challenge to fruitfully merge state-of-the-art techniques from mathematical finance and numerical analysis has inspired researchers to develop fast deterministic option pricing methods. As a result, highly efficient algorithms to compute option prices in Lévy models by solving partial integro differential equations…