Unified deep metric learning approach using neural networks.
problem Learning embeddings of data and extending Euclidean distances.
method Deep Bregman divergences based on neural networks.
result Superior performance on benchmark datasets compared to existing methods.
Paper introduces a new method for learning Bregman divergence from data.
problem Suboptimal performance of classic distance metrics in deep metric learning.
method Learning empirical Bregman divergence from data using deep learning.
result Empirical Bregman divergence method outperforms other methods on public datasets.
Develops a new divergence framework that combines f-divergences and IPMs.
problem Comparing distributions that are not absolutely continuous.
method Introduces (f,Γ)-divergences as a two-stage mass-redistribution/mass-transport process. result Improves estimation, learning, and uncertainty quantification in GANs for heavy-tailed distributions.
Unified view of KL-divergence and IPMs via DRE, with new DRM metrics.
problem Unified understanding of KL-divergence and IPMs.
method Unified representation via maximum likelihood density-ratio estimation (DRE).
result Unified form of IPMs and novel DRM metrics.
Study odd generalized Einstein metrics on 3D Lie groups.
problem Classify odd generalized Einstein metrics on 3D Lie groups.
method Left-invariant generalized connections, divergence operators, and Ricci tensors.
result Describe all odd generalized Einstein metrics on all 3D Lie groups.
The paper explores statistical and topological properties of sliced probability divergences.
problem Understanding the topological, statistical, and computational consequences of slicing divergences.
method Deriving theoretical properties of sliced probability divergences, including metric axioms preservation and weak continuity.
result Sliced divergences share similar topological properties and have stable sample complexity.
New gauge condition fixes L2 metric divergence in hyperbolic monopole spaces.
problem Divergence of L2 metric on hyperbolic monopole moduli spaces. method Alternative gauge-fixing condition inspired by supersymmetry.
result Resulting geometry is hyperbolic hyperkähler, analogous to Euclidean monopole spaces.
Bregman divergences generalize measures such as the squared Euclidean distance and the KL divergence, and arise throughout many areas of machine learning. In this paper, we focus on the problem of approximating an arbitrary Bregman divergence from supervision, and we provide a well-principled approach to analyzing such…
New metrics defined on SPD matrices link to divergences and curvature.
problem Defining and characterizing metrics on SPD matrices.
method Developed a principle of deformed metrics and introduced balanced bilinear forms.
result Introduce Mixed-Euclidean metrics with negative sectional curvature.
Study on 3D Lie groups finds all generalized Einstein metrics.
problem Classifying generalized Einstein metrics on 3D Lie groups.
method Developed theory of left-invariant generalized pseudo-Riemannian metrics, computed Ricci tensor, determined all metrics.
result Determined all generalized Einstein metrics on three-dimensional Lie groups.
Paper explores how text generation quality and diversity metrics relate to distribution fitting.
problem Unclear relation between text generation quality and diversity metrics and distribution fitting.
method Theoretical approach to prove a linear combination of quality and diversity metrics can be a divergence metric.
result CR/NRR proposed as a better substitute for BLEU/Self-BLEU metrics.
We show that both Teichmuller space (with the Teichmuller metric) and the mapping class group (with a word metric) have geodesic divergence that is intermediate between the linear rate of flat spaces and the exponential rate of hyperbolic spaces. For every two geodesic rays in Teichmuller space, we find that their dive…
Paper introduces SDM for detecting LLM hallucinations, improving on entropy tests.
problem Challenges of Large Language Models (LLMs) with non-factual, nonsensical responses.
method Joint clustering on sentence embeddings to measure semantic divergence between prompts and responses.
result SDM framework detects deeper form of arbitrariness in LLM responses.
We extend the recently introduced theory of Lovasz-Bregman (LB) divergences (Iyer & Bilmes 2012) in several ways. We show that they represent a distortion between a "score" and an "ordering", thus providing a new view of rank aggregation and order based clustering with interesting connections to web ranking. We show ho…
We extend the recently introduced theory of Lovasz-Bregman (LB) divergences (Iyer & Bilmes, 2012) in several ways. We show that they represent a distortion between a 'score' and an 'ordering', thus providing a new view of rank aggregation and order based clustering with interesting connections to web ranking. We show h…
Separable Bregman divergences induce Riemannian metric spaces that are isometric to the Euclidean space after monotone embeddings. We investigate fixed rate quantization and its codebook Voronoi diagrams, and report on experimental performances of partition-based, hierarchical, and soft clustering algorithms with respe…
New method makes quality metrics scale-invariant for high-dimensional data.
problem Scale sensitivity in quality metrics affects the accuracy of data projections.
method Analytical and empirical investigation of stress and KL divergence; introduction of a scale-invariant technique.
result The proposed technique accurately captures expected behavior and makes metrics scale-invariant.
New rigidity results for quasi-Einstein metrics with non-zero divergence-free vector fields.
problem Classifying quasi-Einstein metrics with specific vector field properties.
method Analyzing quasi-Einstein metrics on closed manifolds and near-horizon geometries of extreme black holes.
result These metrics always admit a one-parameter group of isometries generated by the divergence-free vector field.
We propose a new metric to measure domain divergence and a new domain adaptation method for time-series classification. The metric belongs to the class of probability distributions-based metrics, is transductive, and does not assume the presence of source data samples. The 2-stage method utilizes an improved autoregres…
Recognizing subtle historical patterns is central to modeling and forecasting problems in time series analysis. Here we introduce and develop a new approach to quantify deviations in the underlying hidden generators of observed data streams, resulting in a new efficiently computable universal metric for time series. Th…
On a compact n-dimensional manifold M, it is well known that a critical metric of the total scalar curvature, restricted to the space of metrics with unit volume, is Einstein. It has been conjectured that a critical metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvat…
We introduce a new approximation of f-divergences for machine learning.
problem Variational representations of f-divergences for machine learning. method Definition and analysis of Moreau-Yosida approximation of f-divergences with the Wasserstein-1 metric. result Generalization and relaxation of hard Lipschitz constraints in f-divergences. The Wasserstein probability metric has received much attention from the machine learning community. Unlike the Kullback-Leibler divergence, which strictly measures change in probability, the Wasserstein metric reflects the underlying geometry between outcomes. The value of being sensitive to this geometry has been demo…
Proposes ATM method to improve domain adaptation.
problem Mitigating distribution divergence between source and target domains.
method Adversarial Tight Match (ATM) method using Maximum Density Divergence (MDD).
result New state-of-the-art performance on domain adaptation benchmarks.
New metrics quantify implementation risk in portfolio backtesting, revealing systematic differences in engine implementations.
problem Systematic divergence in backtested portfolio metrics due to differences in engine implementations.
method Formalized implementation risk, proposed four metrics, executed 15 strategies through five engines, analyzed source-code defects.
result Implementation risk introduces measurable ambiguity in performance attribution, but does not alter investment decisions.
New f-Betas for portfolio optimization using f-divergence risk measures.
problem Optimizing portfolio performance under varying market conditions.
method Derive f-Betas and Hellinger-Betas, using f-divergence risk measures.
result Demonstrated new Beta metrics provide better performance under stress.
This work presents a parametrized family of divergences, namely Alpha-Beta Log- Determinant (Log-Det) divergences, between positive definite unitized trace class operators on a Hilbert space. This is a generalization of the Alpha-Beta Log-Determinant divergences between symmetric, positive definite matrices to the infi…
The paper explores geometry of probability measures and barycenter maps.
problem Understanding the space of probability measures and their barycenter.
method Information geometry, Fisher metric, dualistic structures, divergences, geodesics.
result Recent developments in the geometry of probability measures and barycenter.
New formulations for comparing metric measure spaces with arbitrary positive measures.
problem Comparing metric measure spaces with arbitrary positive measures.
method Two novel formulations: a divergence and a conic lifting approach.
result Efficiently solvable formulations for comparing metric spaces with arbitrary positive measures.
The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegan…
New proof finds three divergence-free vector fields for any 3D manifold.
problem Proving the existence of divergence-free vector fields on 3D manifolds.
method Using geometric properties of eigenspinors in three dimensions.
result Found three divergence-free vector fields that are orthogonal and have the same length at every point.
Causal KL improves on existing metrics for evaluating causal models.
problem Insufficient discrimination between causal models using edit-distance and KL divergence.
method Introducing Causal KL, an augmented KL divergence that considers causal relationships.
result Causal KL variants effectively distinguish between observationally equivalent models.
On a compact n-dimensional manifold, it is well known that a critical metric of the total scalar curvature, restricted to the space of metrics with unit volume is Einstein. It has been conjectured that a critical metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature o…
LLM safety alignment explained as divergence estimation.
problem Aligning large language models to avoid harmful outputs.
method Presented a theoretical framework showing alignment methods as divergence estimators.
result KLDO method improves safety alignment using compliance-refusal datasets.
New separation concepts for Anosov representations help bound Thurston asymmetric metric.
problem Understanding diverging families of Anosov representations.
method Introducing separation concepts and analyzing combinatorial invariants.
result Critical exponent asymptotic to a graph invariant.
We study 1-parameter families in the space M1G of G-invariant, unit volume metrics on a given compact, connected, almost-effective homogeneous space M=G/H. In particular, we focus on diverging sequences, i.e. which are not contained in any compact subset of M1G, and we prove some structu…
New f-divergence measures improve robustness in noisy label learning.
problem Improving robustness in learning with noisy labels.
method Derived decoupling property of f-divergence measures under label noise. result Properly defined f-divergence measures are robust with label noise. In this paper, we study vacuum static spaces with the complete divergence of the Bach tensor and Weyl tensor. First, we prove that the vanishing of complete divergence of the Bach tensor and Weyl tensor implies the harmonicity of the metric, and we present examples in which these conditions do not imply Bach flatness. …
Introduces Cauchy-Schwarz divergence for domain adaptation.
problem Evaluating discrepancy between source and target domains in unsupervised domain adaptation.
method Introduces Cauchy-Schwarz divergence as a measure for evaluating discrepancy between marginal and conditional distributions.
result CS divergence offers a tighter generalization error bound than Kullback-Leibler divergence.
Study optimizes tree-based models for better alignment of predicted scores and actual probabilities.
problem Traditional calibration metrics fail to align predicted scores with actual probabilities when score distributions deviate from the underlying data.
method Optimizes tree-based models (Random Forest, XGBoost) using Kullback-Leibler (KL) divergence to minimize the difference between predicted and true probability distributions.
result Optimized tree-based models yield superior alignment between predicted scores and actual probabilities without significant performance loss.
Develops deep NMF models using β-divergences for feature extraction.
problem Inadequate evaluation metrics for deep NMF on diverse datasets.
method Introduces new deep NMF models using Kullback-Leibler divergence.
result Improves feature extraction quality across different types of data.
LMC algorithm converges to target in Chi-squared and Renyi divergence.
problem Sampling from target distribution using LMC with strong dissipativity and smoothness conditions.
method LMC algorithm with strong dissipativity and first-order smoothness, initialized with Gaussian.
result LMC reaches ε-neighborhood of target in Chi-squared and Renyi divergence in O(λ²dε⁻¹) steps.
Automates VI divergence selection for efficient few-shot learning.
problem Efficiently selecting divergence measures for VI to improve performance.
method Meta-learning algorithm to learn optimal divergence metric and variational parameter initialization.
result Meta-learning approach outperforms standard VI methods across various tasks.
Researchers found G2-structures with zero torsion on specific Lie groups.
problem Finding G2-structures with divergence-free torsion.
method Isometric flow to evolve G2-structures with divergence-free torsion as critical points.
result Three families of G2-structures on solvable Lie groups have zero torsion.
We study the geometry of probability distributions with respect to a generalized family of Csiszár f-divergences. A member of this family is the relative α-entropy which is also a Rényi analog of relative entropy in information theory and known as logarithmic or projective power divergence in statistics. We apply E…
New divergences improve estimation and GAN training performance.
problem Improving estimation and training in machine learning models.
method Function-space regularized Rényi divergences.
result New divergences reduce variance and improve training performance.
This paper introduces a new method to train normalizing flows using precision-recall divergences.
problem Training generative models with mode dropping and low-quality samples.
method Introduces PR-divergences and proposes a novel generative model to minimize precision-recall trade-offs.
result Normalizing flows can be trained to achieve specific precision-recall trade-offs using PR-divergences.
Paper calculates KL divergence for isotropic Gaussian-Markov fields.
problem Measuring divergence between isotropic Gaussian-Markov fields.
method Derives closed-form KL divergence expressions.
result Develops new similarity measures in image processing.