Paper introduces normalized flat minima to address scale dependence in neural network optimization.
problem Scale dependence in existing flat minima definitions affects generalization studies.
method PAC-Bayesian analysis to introduce normalized flat minima, free from scale dependence.
result Normalized flat minima provides better hierarchy in hypothesis class and improved generalization.
Discussing issues in robust clustering, especially with Gaussian models.
problem Handling outliers and ambiguity in clustering groups.
method Focus on Gaussian mixture model, examining formal definitions, interactions, and tuning decisions.
result Outliers can confuse clustering groups and existing stability measures fail with them.
Paper interprets EMD for sets and proposes EMI, showing EMD's inferiority.
problem Definiteness issues in EMD for set comparisons.
method Set-theoretic interpretation of EMD, proposing EMI, analyzing definiteness, and comparing EMD to EMI.
result EMD is inferior to EMI in computer vision tasks.
New definition of interpretability makes model design more actionable.
problem Current definitions of interpretability are not actionable and inform users poorly.
method Proposes a new definition of interpretability that is general, simple, and actionable.
result New definition reveals necessary properties for designing interpretable models.
New definition shows no trade-off between adversarial and standard accuracy.
problem Inexact definition of adversarial perturbation causes confusion.
method Proposed a slight modification to adversarial perturbation definition.
result Existence of classifiers that are robust and achieve high standard accuracy.
New definition resolves ambiguity in non-stationary bandit classification.
problem Ambiguity in classifying non-stationary bandits using existing definitions.
method Introducing a formal definition that resolves ambiguity and provides a unified approach.
result Unified approach applicable to both Bayesian and frequentist formulations, resolves classification issues.
This paper derives radial fields on manifolds of symmetric positive definite matrices.
problem Lack of an expression for radial fields on manifolds of symmetric positive definite matrices.
method Derives an expression for radial fields on manifolds of symmetric positive definite matrices.
result Derives an expression for radial fields on manifolds of symmetric positive definite matrices.
Improved Bayesian learning rule handles positive-definite constraints efficiently.
problem Bayesian learning rule struggles with positive-definite constraints.
method Proposes an improved rule using Riemannian gradient methods for block-coordinate natural parameterization.
result Outperforms existing methods without increased computation.
New definition of interpretability for deep neural networks.
problem Vague definition of interpretability for deep neural networks.
method Proposed a new definition of human predictability for interpretability of DNNs.
result Our definition will help to the research of interpretability of DNNs.
New definitions of conserved quantities at null infinity resolve ambiguities in general relativity.
problem Ambiguities in defining conserved quantities like angular momentum at null infinity.
method New definitions based on Chen-Wang-Yau quasilocal conserved quantities and optimal isometric embedding theory.
result These new definitions are free of supertranslation ambiguity and limit to classical Bondi mass.
Completes proof of index theorem using rigorous path integrals for supersymmetric quantum mechanics.
problem Analytic difficulties in generalizing Feynman's path integral to non-quadratic potentials.
method Develops rigorous path integrals for a class of Lagrangians including spinors on Riemannian manifolds.
result Steepest-descent approximation to path integral for twisted N=1/2 supersymmetric quantum mechanics is provably correct. Solves the VAE learning issue by optimizing a more informative generator.
problem Learning issue in VAE where only one model can be optimal at a time.
method Introduces Variational InfoMax (VIM) learning objective to optimize both inference and generative models.
result Derives a learning objective that optimizes both inference and generative models.
Research resolves sign conventions in Floer theory for Morse-Bott case.
problem Sign conventions in filtered A∞-operations for Lagrangian Floer theory. method Defined filtered A∞-operations and verified formulae using de Rham model. result Resolved sign issues in Bott-Morse setting.
This work introduces oblivious fairness definitions for image generation.
problem Fairness in image generation with uncertain sensitive attributes.
method Introduces oblivious fairness definitions and uses Posterior Sampling.
result Conditional Proportional Representation can be achieved obliviously.
We provide a new proof for regularity of affine processes on general state spaces by methods from the theory of Markovian semimartingales. On the way to this result we also show that the definition of an affine process, namely as stochastically continuous time-homogeneous Markov process with exponential affine Fourier-…
Unified Morse-Bott-Smale chain complex, resolves well-definedness issue.
problem Well-definedness of Morse-Bott-Smale chain complex.
method Unified five degeneracy relations into a single condition.
result Quasi-isomorphic to Morse-Smale-Witten chain complex, alternative proof of Morse Homology Theorem.
We extend Sobolev transport to unbalanced measures on graphs.
problem Optimal transport struggles with measures of different total mass and high computational complexity.
method We propose a scalable unbalanced Sobolev transport (UST) for measures on graphs.
result UST admits a closed-form formula for fast computation and is negative definite.
Optimal transport for measures on noisy tree metrics is solved with robust approach.
problem Optimal transport problem for measures on noisy tree metrics.
method Max-min robust optimal transport approach considering uncertainty sets of tree metrics.
result Robust optimal transport admits a closed-form expression for fast computation.
New definitions of ESP for quantum reservoir computing handle non-stationary systems.
problem Traditional ESP does not apply to non-stationary systems.
method Introduce two new categories of ESP: non-stationary ESP and subset/subspace ESP.
result Demonstrates correspondence between non-stationary ESP and QRC with NARMA tasks.
New method estimates large covariance matrices using nonconvex penalties.
problem Estimating large covariance matrices in high-dimensional data.
method Developed a first-order algorithm using generalized nonconvex penalties.
result Positive-definite covariance estimators using nonconvex penalties.
Correlations between asset returns are important in many financial applications. In recent years, multivariate volatility models have been used to describe the time-varying feature of the correlations. However, the curse of dimensionality quickly becomes an issue as the number of correlations is k(k−1)/2 for k asse…
3D BF theory on certain 3-manifolds evaluated via residues and large k limits.
problem Singular and ill-defined partition function of 3D BF theory.
method Direct evaluation of path integral for specific 3-manifolds, using residues and large k limits of Chern-Simons matrix integrals.
result 3 definitions of the integral offer insights into the sum/integral over all flat connections.
Revises individual fairness by finding a fair metric for a model.
problem Difficulties in specifying a suitable fairness metric a priori.
method Introduces minimal metrics and applies randomized smoothing from adversarial robustness.
result Adapting minimal metrics to complex models yields interpretable fairness guarantees.
In this paper, we propose to (seamlessly) integrate b-bit minwise hashing with linear SVM to substantially improve the training (and testing) efficiency using much smaller memory, with essentially no loss of accuracy. Theoretically, we prove that the resemblance matrix, the minwise hashing matrix, and the b-bit minwise…
Paper defines the payback period for nonconventional cash flows using axioms.
problem Defining the payback period for nonconventional cash flows is challenging.
method Used axiomatic approach to define the payback period.
result The last break-even point of the project balance is the only definition consistent with axioms.
New measure of interference helps understand and mitigate learning issues in reinforcement learning.
problem Understanding and mitigating interference in reinforcement learning.
method Defined a new measure of interference, evaluated it, and identified key factors contributing to interference.
result Target network frequency and updates on the last layer are significant factors in interference.
Paper introduces robust methods for consensus ranking in AI systems.
problem Developing reliable ranking systems in AI despite contaminated data.
method Introduces robustness concepts and statistical methods for consensus ranking.
result Proposes extensions of breakdown point for consensus ranking.
Paper proposes a new algorithm for graph learning with covariance constraints.
problem Graphical models and factor analysis not jointly leveraged in graph learning processes.
method Penalized maximum likelihood estimation of an elliptical distribution with Riemannian optimization.
result Effectiveness of the proposed approach demonstrated on real-world data sets.
This post introduces model calibration and evaluation measures, highlighting issues with a common measure.
problem Ensuring model confidence accurately reflects true outcomes.
method Explains common calibration definition, ECE, and its drawbacks.
result New evaluation measures needed for comprehensive model calibration.
Paper proposes GEG to enhance fairness in binary and multi-class classification.
problem Fairness in multi-class classification tasks is under-explored.
method Formulates multi-objective problem between effectiveness and fairness constraints, proposes GEG algorithm.
result GEG improves fairness up to 92% and decreases accuracy up to 14%.
Survey on minimal penalty algorithms and slope heuristics.
problem Choosing optimal multiplicative constants from data.
method Minimal penalty and slope heuristics approach.
result Slope heuristics performs almost as well as residual-based estimators.
Fairness measures fail in predictive settings that intentionally shift outcomes.
problem Fairness measures fail in performative prediction settings.
method Formalized concept shift and counterfactual outcomes.
result Predictors that are fair during training become unfair during deployment.
We introduce a wrapped Gaussian for SPD matrices, enhancing data analysis.
problem Handling circular and non-flat data distributions on SPD manifolds.
method Introduced a non-isotropic wrapped Gaussian using the exponential map, derived theoretical properties, and proposed a maximum likelihood framework.
result Demonstrated the robustness and flexibility of the wrapped Gaussian model on synthetic and real-world datasets.
A new differentiable divergence for time series comparison.
problem Computing discrepancies between time series of varying lengths.
method Proposed a new divergence, soft-DTW divergence, addressing issues of differentiability and positivity.
result Showed that the new divergence is a valid divergence: non-negative and minimized when time series are equal.
In this paper we propose an overview of the recent academic literature devoted to the applications of Hawkes processes in finance. Hawkes processes constitute a particular class of multivariate point processes that has become very popular in empirical high frequency finance this last decade. After a reminder of the mai…
Improved DLG extracts accurate labels from gradients, overcoming DLG's convergence issues.
problem Private training data leakage from shared gradients in distributed learning systems.
method Proposes iDLG, a simple approach to synthesize accurate labels from gradients.
result iDLG reliably extracts ground-truth labels from gradients, unlike DLG.
We define relative Ruan invariants that count embedded connected symplectic submanifolds which contact a fixed stable symplectic hypersurface V in a symplectic 4-manifold (X,w) at prescribed points with prescribed contact orders (in addition to insertions on X\V) for stable V. We obtain invariants of the deformation cl…
QUACKIE creates a new benchmark for NLP interpretability.
problem Evaluating NLP interpretability methods is challenging due to biased ground truths.
method Formulated a custom classification task from question-answering datasets, generating unbiased ground truths.
result Demonstrated the effectiveness of current interpretability methods on the new benchmark.
This paper addresses Gaussian Process regression over probability measures, revealing a non-stationarity issue between Euclidean and Wasserstein kernels.
problem Non-stationarity issue between Euclidean and Wasserstein kernels in Gaussian Process regression over probability measures.
method Assuming Euclidean input space, applying algebraic transformation based on uncovered non-stationarity relationship to create a non-stationary and Wasserstein-based Gaussian Process model.
result An algebraic transformation simplifies learning a non-stationary Gaussian Process model over probability measures.
New method resolves ambiguity in measuring black hole merger angular momentum.
problem Ambiguity in measuring angular momentum during black hole mergers.
method Quasilocal mass and optimal isometric embedding theory.
result New definition of angular momentum free of supertranslation ambiguity.
Definite knots' quotients remain definite via Seifert surfaces.
problem Definiteness of knots and their quotients.
method Equivariant minimal genus Seifert surfaces.
result Quotients of definite periodic knots are definite.
The paper compares three hypoelliptic Laplacians on a specific 5D Cartan group.
problem Defining suitable hypoelliptic Laplacians for sharp estimates on Carnot groups.
method Introducing and comparing three hypoelliptic Laplacians on a specific Carnot group.
result Sharp div-curl type inequalities for the three hypoelliptic Laplacians.
META-DES.Oracle uses meta-learning and feature selection to improve ensemble selection accuracy.
problem Dynamic Ensemble Selection (DES) issues with classifier competence estimation.
method META-DES.Oracle integrates multiple criteria and an Oracle-based meta-feature selection scheme.
result META-DES.Oracle significantly improves classification accuracy compared to previous methods.
The clusters of a distribution are often defined by the connected components of a density level set. However, this definition depends on the user-specified level. We address this issue by proposing a simple, generic algorithm, which uses an almost arbitrary level set estimator to estimate the smallest level at which th…
We review the geometric setting of the field theory with locally anisotropic interactions. The concept of locally anisotropic space is introduced as a general one for various type of extensions of Lagrange and Finsler geometry and higher dimension (Kaluza--Klein type) spaces. The problem of definition of spinors on gen…
Transfer learning improves machine learning models for equipment diagnostics.
problem Limited model performance due to training data mismatch.
method Transfer learning to reuse knowledge from similar tasks.
result Transfer learning enhances model applicability in PHM.
New fairness concept extends minimax fairness to lexicographic fairness.
problem Fairness in supervised learning, especially lexicographic fairness.
method Introduced approximate lexifairness, derived algorithms for finding solutions, and proved generalization bounds.
result Proved that approximate lexifairness on training data implies approximate lexifairness on true distribution.
Positive definite operator-valued kernels generalize the well-known notion of reproducing kernels, and are naturally adapted to multi-output learning situations. This paper addresses the problem of learning a finite linear combination of infinite-dimensional operator-valued kernels which are suitable for extending func…