Proves representability of complex semigroup systems.
problem Representability of systems of proportionally modular numerical semigroups.
method Canonical equivariant resolution of weighted homogeneous surface singularities.
result Every system of proportionally modular numerical semigroups is representable.
Custom narrow-precision representations boost DNN inference speed by 7.6x with minimal accuracy loss.
problem Improving computational efficiency of deep neural networks.
method Exploring and utilizing unconventional narrow-precision floating-point representations for DNN weights and activations.
result Average speedup of 7.6x with less than 1% accuracy loss.
We focus on mean-variance hedging problem for models whose asset price follows an exponential additive process. Some representations of mean-variance hedging strategies for jump type models have already been suggested, but none is suited to develop numerical methods of the values of strategies for any given time up to …
Flat semigroups can represent normal weighted homogeneous surface singularities.
problem Representability of flat semigroups in normal weighted homogeneous surface singularities.
method Study of numerical semigroups associated with surface singularities and prove representability conditions.
result A numerical semigroup is representable if and only if it can be written as a quotient of a flat semigroup.
EmbNum learns numerical attribute representations without distributional assumptions.
problem Semantic labeling of numerical values with unknown distributions.
method Neural numerical embedding model (EmbNum) for deep metric learning.
result EmbNum significantly outperforms state-of-the-art methods for numerical attribute semantic labeling.
The paper proposes efficient dictionary learning algorithms that avoid multiplications for sparse representations.
problem Sparse representation with reduced computational complexity.
method Factorizations of the dictionary into binary orthonormal, scaling, and shear transformations with closed-form solutions.
result The proposed methods are effective and can be compared to well-known transforms like FFT and DCT.
Visual design improves financial data classification accuracy.
problem Improving financial decision-making through better data representation.
method Comparing numeric vs visual data representations in supervised classification.
result Visual transformation of numeric data leads to higher predictability.
The forecasting and reconstruction of ocean and atmosphere dynamics from satellite observation time series are key challenges. While model-driven representations remain the classic approaches, data-driven representations become more and more appealing to benefit from available large-scale observation and simulation dat…
We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein-Stein, and Hull-White models, for which we provide numerical case studies. We find that our polynomial option price series expansion performs as efficiently and accura…
Reference metrics are used to define the differential structure on multicube representations of manifolds, i.e., they provide a simple and practical way to define what it means globally for tensor fields and their derivatives to be continuous. This paper introduces a general procedure for constructing reference metrics…
Deep networks don't improve on shallow ones for finding minima.
problem Improving representation of multidimensional mappings with deep neural networks.
method Numerical training methods to find minima in deep and shallow networks.
result Minima found with deep networks are worse than those found with shallow networks.
Datasets with a mixture of numerical and categorical attributes are routinely encountered in many application domains. In this work we examine an approach to clustering such datasets using homogeneity analysis. Homogeneity analysis determines a euclidean representation of the data. This can be analyzed by leveraging th…
A new method evaluates invariant performance of IRM-based representations.
problem Impact of data changes on machine learning model performance.
method Proposes a novel method to evaluate invariant performance of IRM-based representations.
result Establishes a robust criterion to assess invariant performance of various representation techniques.
Structural identity is a concept of symmetry in which network nodes are identified according to the network structure and their relationship to other nodes. Structural identity has been studied in theory and practice over the past decades, but only recently has it been addressed with representational learning technique…
Unified kernel framework extends to stochastic systems, improving numerical stability.
problem Extending kernel methods to stochastic dynamical systems with diffusion.
method Unified kernel framework, Feynman-Kac path-integral representations, collocation-based computational framework.
result Kernel equivalence under uniform ellipticity assumptions and improved numerical stability with moderate diffusion.
Two approaches to directly estimating Riesz representer are shown to be numerically equivalent under certain conditions.
problem Estimating Riesz representer in semiparametric statistics.
method Two distinct optimization problems solved by automatic debiased machine learning and sieve methods for conditional moment models.
result Numerical equivalence of estimators under specific regularization schemes, but not for others.
New method tightens variational representations of divergences for faster learning.
problem Improving tightness of variational representations of divergences for faster statistical estimation.
method Improved objective functionals constructed via an auxiliary optimization problem, leveraging neural network approximation.
result Tighter variational representations can result in significantly faster learning and more accurate estimation of divergences.
Language models can predict numeric values as strings.
problem Regression tasks with numeric predictions.
method Causal sequence decoding models trained for next-token prediction.
result Decoder-based heads perform as well as standard heads in numeric regression tasks.
Proposes a symmetric graph autoencoder for unsupervised learning.
problem Graph representation learning without labeled data.
method Symmetric graph convolutional autoencoder with Laplacian sharpening and signed graphs.
result Outperforms state-of-the-art algorithms in clustering, link prediction, and visualization tasks.
The paper proposes a method to learn representations from dendrograms.
problem Learning representations from dendrograms for machine learning applications.
method Develops a generalized framework for different distance measures and level functions, using embedding and aggregation techniques.
result Demonstrates the effectiveness of the method via numerical studies.
Study on CVA in volatility models, including rough volatility.
problem Calculating CVA in fractional and rough volatility models.
method General representation formula, specialized for volatility models, numerical and theoretical error analysis.
result Roughness influences the claim's price, and provides accurate approximations.
Paper shows strong convergence rates for fractional processes using Ornstein-Uhlenbeck representations.
problem Understanding and improving Monte Carlo schemes for fractional volatility models.
method Numerical discretizations of fractional processes using Ornstein-Uhlenbeck representations.
result Strong convergence rates of arbitrarily high polynomial order for fractional processes.
The paper provides VIX option pricing and hedging strategies for two stochastic volatility models.
problem Pricing and hedging of VIX options for specific stochastic volatility models.
method Develops representations of VIX call option prices and locally risk-minimizing strategies for Barndorff-Nielsen and Shephard models.
result Efficient representations and locally risk-minimizing strategies for numerical methods.
Researchers develop multi-utility representations for incomplete preferences linked to risk measures.
problem Handling incomplete preferences induced by set-valued risk measures.
method Established dual representations of set-valued risk measures to create parsimonious and well-behaved multi-utility representations.
result Unified dual representations of set-valued risk measures, linking them to scalar risk measures.
New method for manifold topological learning avoids remeshing issues.
problem Persistent homology on manifolds is numerically inconsistent.
method Persistent de Rham-Hodge Laplacians in Eulerian representation.
result Avoids numerical inconsistency over multiscale manifolds.
Let M be a once-punctured torus bundle over S1 with monodromy h. We show that, under certain hypotheses on h, "most" Dehn-fillings of M (in some cases all but finitely many) are virtually Z-representable. We apply our results to show that surgeries on the figure-eight knot with even numerator are …
A new method computes Greeks for multi-asset options using tensor trains and Fourier transforms.
problem Efficient computation of Greeks for multi-asset options with high accuracy and low sample complexity.
method Tensor train (TT) representations of Fourier-based pricing functions, combined with numerical differentiation or analytical approaches.
result Significant speed-ups of up to 105imes over Monte Carlo simulations while maintaining comparable accuracy. American options can be equivalent to European options under certain conditions.
problem Determining when American options can be simplified to European options.
method Using methods from Jourdain and Martini, Chrsitensen, and convex duality.
result A first step towards verifying representability of American options.
Researchers present and compare different representations of dissipative Hamiltonian DAE systems.
problem Understanding and transforming dissipative Hamiltonian DAE systems.
method Global geometric and algebraic points of view, translations between representations, characterizations, and numerical methods for computing structural information.
result A general DAE system can be transformed into a dissipative Hamiltonian or port-Hamiltonian DAE system.
MKA incorporates manifold geometry into kernel alignment for more robust representation comparison.
problem Inadequate accounting for manifold geometry in kernel alignment metrics.
method Derives a theoretical framework for Manifold Approximated Kernel Alignment (MKA).
result MKA provides a more robust foundation for measuring representations.
A new framework for graph representation learning.
problem Acquiring continuous representations of discrete objects like graphs.
method Nested SubSpace (NSS) arrangement and Disk-ANChor ARrangement (DANCAR).
result Successfully embedded WordNet in 20-dimensional space with high F1 score.
New PAC-Bayesian bounds improve CURL's representation learning.
problem Lack of theoretical understanding of CURL's performance.
method Extended Arora et al.'s PAC-Bayes framework to non-iid setting.
result Derived PAC-Bayesian generalisation bounds for CURL.
The paper associates knots to numerical semigroups and shows their Alexander polynomials coincide with semigroups' Poincaré series.
problem Understanding the algebraic structure of numerical semigroups through topological representations.
method Associaing iterated torus knots to free numerical semigroups and analyzing their knot complements and Alexander polynomials.
result Alexander polynomials of knots associated with free numerical semigroups coincide with the semigroup's Poincaré series.
New SRC algorithm for faster image recognition on graphs.
problem Image recognition on graphs with subspace assumptions.
method Sparse representation classifier with screening for graph classification.
result Consistent classification for random graphs, faster than original SRC.
Paper presents a hierarchical learning strategy for sparse data representation.
problem Sparse representation of multivariate datasets.
method Hierarchical approximation spaces at finer scales, stability and convergence analysis.
result Efficient data reconstruction and error minimization in prediction.
For a closed manifold equipped with a Riemannian metric, a triangulation, a representation of its fundamental group on an Hilbert module of finite type (over of finite von Neumann algebra), and a Hermitian structure on the flat bundle associated to the representation, one defines a numerical invariant, the relative tor…
Study Kähler-Ricci flow on rational homogeneous varieties using algebraic geometry and representation theory.
problem Analyzing the Kähler-Ricci flow on rational homogeneous varieties.
method Combining projective algebraic geometry and representation theory of semisimple Lie groups and Lie algebras.
result Explicit description and computation of solutions and geometric quantities along the flow.
Two-layer networks struggle with high frequencies due to numerical and computational limitations.
problem High frequency approximation and learning in shallow networks.
method Mathematical and computational analysis focusing on numerical error, computational cost, and stability.
result Explicit answers to fundamental computational issues in shallow networks' high frequency handling.
PCENet reduces uncertainty in high-dimensional data efficiently.
problem Uncertainty quantification in high-dimensional data is computationally expensive.
method Two-stage learning process: variational autoencoder for low-dimensional representation, polynomial chaos expansion for mapping.
result Model captures system dynamics, learns under uncertainty, estimates high-dimensional data uncertainty, matches output distribution moments.
This work improves sample efficiency in meta-learning for nonlinear tasks.
problem Learning complex tasks efficiently with limited data.
method Subspace-based representations for nonlinear tasks.
result Subspace-based representations can be learned efficiently and improve future task performance.
Deep model learns coupled representations from side information for sparse signal recovery.
problem Recovering signals from undersampled, incomplete or noisy linear measurements.
method Deep unfolding model incorporating side information from different modalities.
result Superior performance compared to single-modal and multimodal methods.
Model learns low-dimensional representation from heterogeneous data with missing values.
problem Handling high-dimensional, noisy, and missing data from clinical records.
method Latent Gaussian process with composite likelihoods and numerical quadrature.
result Improves upon existing GPLVM methods for heterogeneous data.
Pulling back the weight system associated with the spinor representation of the Lie algebra so(7) by the universal Vassiliev-Kontsevich invariant yields a numerical link invariant with values in formal power series. Computing some skein relations satisfied by this invariant, I derive a recursive algorithm for its evalu…
RandNLA uses randomness for matrix problems in machine learning.
problem Matrix problems in machine learning.
method Randomized Numerical Linear Algebra.
result New challenges in RandNLA due to hardware trends and advances in ML.
Proposes a deep learning method for effective data representation.
problem Constructing effective data representations for prediction.
method A deep dimension reduction approach to learning representations with sufficiency, low dimensionality, and disentanglement.
result The proposed deep nonparametric representation is consistent and performs better than existing methods.
Novel algorithm learns sparse signal representations over topological spaces.
problem Sparse representation of signals over combinatorial topological spaces.
method Leveraging Hodge theory, the paper embeds topology into a dictionary structure via concatenated sub-dictionaries, each as a polynomial of Hodge Laplacians, and optimizes the dictionary coefficients and sparse signal representation via iterative alternating algorithms.
result Efficiently learned sparse representations and underlying relational structure of topological signals.
A new method corrects weight values to improve treatment effect estimation.
problem Estimating heterogeneous treatment effects in high-dimensional data with sample selection bias.
method Differentiable Pareto-Smoothed Weighting (DPSW) framework.
result Our method outperforms existing methods in treatment effect estimation.
We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematical constraints linking the centerline's tangent to the orientation of …