Optimizes CNNs by directing gradients along output channels.
problem Improving generalization error in CNNs.
method Output-channel directed re-weighted L2 or Sobolev metrics.
result Improves generalization error by optimizing gradients.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
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48 results for “direct metric optimization”
Paper tackles imbalanced binary classification by optimizing precision and recall directly.
problem Imbalanced binary classification where standard accuracy is misleading.
method Exact constrained reformulations for precision and recall optimization.
result ERO framework outperforms state-of-the-art methods on multiple datasets.
Paper proposes a new approach to optimal transport for vector and matrix densities.
problem Optimal transport for vector and matrix densities with positivity and action transitivity constraints.
method Gauge-theoretic approach using semi-direct product groups of diffeomorphisms and gauge transformations.
result Bures-type metrics on semi-direct product groups relate to Wasserstein-type metrics on vector and matrix densities via Riemannian submersions.
We construct normal forms for Lorentzian metrics on Engel distributions under the assumption that abnormal curves are timelike future directed Hamiltonian geodesics. Then we indicate some cases in which the abnormal timelike future directed curve initiating at the origin is geometrically optimal. We also give certain e…
Paper proves direct image sheaf positivity for certain Kähler fibrations.
problem Proving positivity of direct image sheaves for Kähler fibrations.
method Uses singular Hermitian line bundles and Narasimhan-Simha metric.
result Direct image sheaf is singular Nakano semi-positive.
Introduces MSW distances to improve SW metrics.
problem Redundant projections in SW distance.
method Imposes Markov structure on projecting directions.
result MSW distances improve SW metrics.
New approach optimizes decisions based on uncertainty in predictions.
problem Mismatch between prediction accuracy and decision loss in sequential design.
method Directional uncertainty-guided approach to sequential experimental design.
result Directional uncertainty-based design stops earlier and performs better.
Study uses outer metrics for PDE-constrained shape optimization over diffeomorphism group.
problem Optimizing shapes governed by PDEs over the diffeomorphism group.
method Outer metrics on diffeomorphism group, Riemannian steepest descent method.
result Riemannian approach outperforms other metrics in solving PDE-constrained shape optimization problems.
Rank-based metrics are some of the most widely used criteria for performance evaluation of computer vision models. Despite years of effort, direct optimization for these metrics remains a challenge due to their non-differentiable and non-decomposable nature. We present an efficient, theoretically sound, and general met…
StochasticRank optimizes ranking metrics efficiently and guarantees global convergence.
problem Optimizing discrete ranking metrics due to their ill-posed nature.
method Stochastic smoothing, gradient estimate, debiasing, and Stochastic Gradient Langevin Boosting.
result Global convergence and superior performance on ranking datasets.
Quantum Natural Gradientquant-ph
A quantum generalization of Natural Gradient Descent is presented as part of a general-purpose optimization framework for variational quantum circuits. The optimization dynamics is interpreted as moving in the steepest descent direction with respect to the Quantum Information Geometry, corresponding to the real part of…
We introduce a framework for Newton's flows in probability space with information metrics, named information Newton's flows. Here two information metrics are considered, including both the Fisher-Rao metric and the Wasserstein-2 metric. A known fact is that overdamped Langevin dynamics correspond to Wasserstein gradien…
A new method learns DAGs from data using permutation optimization.
problem Discovering latent DAGs from observational data.
method Optimizes over the Permutahedron to learn topological orderings and edges.
result Our method optimizes exact DAGs, is modular, and performs well on real-world data.
We prove existence of harmonic coordinates for the nonlinear Laplacian of a Finsler manifold and apply them in a proof of the Myers--Steenrod theorem for Finsler manifolds. Different from the Riemannian case, these coordinates are not suitable for studying optimal regularity of the fundamental tensor, nevertheless, we …
Introduces new metric for Riemannian metrics, extending unbalanced optimal transport.
problem Extending unbalanced optimal transport to Riemannian metrics.
method Dynamic and static formulations of unbalanced optimal transport on Riemannian metrics.
result Wasserstein--Ebin metric provides a new Riemannian structure on the space of Riemannian metrics.
In this paper, we propose a new metric to measure goodness-of-fit for classifiers, the Real World Cost function. This metric factors in information about a real world problem, such as financial impact, that other measures like accuracy or F1 do not. This metric is also more directly interpretable for users. To optimize…
A new metric based on hitting probabilities for directed graphs and Markov chains.
problem Lack of metrics specifically adapted to asymmetric structure of directed graphs and Markov chains.
method Metric based on hitting probabilities, insensitive to shortest and average walk distances.
result New structural theory of directed graphs and utility for various applications.
A new distance metric for vMF distributions simplifies spherical data analysis.
problem Intractability of normalization constants and lack of suitable geometric metrics for comparing vMF distributions.
method Proposes a Wasserstein-like distance that decomposes vMF distribution discrepancies into angular and concentration components.
result The proposed distance metric induces a latent geometric structure on the space of non-degenerate vMF distributions.
Optimizes Dirac eigenvalue bound using curvature and quasi-spherical metrics.
problem Optimizing the first Dirac eigenvalue of hypersurfaces.
method Combining positive mass theorem and quasi-spherical metrics.
result Proves optimal upper bound for first Dirac eigenvalue.
Introduces PCG for better counterfactual explanations in vision models.
problem Ambiguity in latent-space optimization methods for counterfactual explanations.
method Constructs counterfactuals by tracing geodesics under a perceptually Riemannian metric.
result PCG outperforms baselines and reveals hidden failure modes.
SELO model predicts link signs better than SDGNN using subgraph encoding and linear optimization.
problem Inferring the sign of links in signed networks with limited sign data.
method Subgraph Encoding via Linear Optimization (SELO) approach to learn edge embeddings.
result SELO model outperforms state-of-the-art methods on multiple real-world signed networks.
Paper studies metric ribbon graphs and provides a recursion for their volumes.
problem Calculating volumes of combinatorial moduli spaces of directed metric ribbon graphs.
method Decomposes directed ribbon graphs into simpler graphs with one vertex, proving a canonical recursion scheme for volumes.
result Explicit recursion for volumes of four-valent metric ribbon graphs provided.
Topolow embeds dissimilarity data into Euclidean space robustly against non-metricity and sparsity.
problem Embedding dissimilarity data into Euclidean space when dissimilarities are non-metric or sparse.
method Topolow uses a physics-inspired, gradient-free optimization framework to maximize likelihood under a Laplace error model.
result Topolow outperforms standard MDS methods in reconstructing sparse and non-Euclidean data.
Speech enhancement model is used to map a noisy speech to a clean speech. In the training stage, an objective function is often adopted to optimize the model parameters. However, in most studies, there is an inconsistency between the model optimization criterion and the evaluation criterion on the enhanced speech. For …
Study uses MTD model to optimize portfolios by capturing complex financial asset relationships.
problem Capturing nonlinear and directional relationships in financial markets.
method Directed and weighted financial networks using Mixture Transition Distribution (MTD) model.
result Portfolio optimization with network-based assortativity measures outperforms classical methods.
We consider the Zermelo navigation problem on the ellipsoid of revolution (spheroid) in the presence of a perturbation determined by a mild velocity vector field, , with application of Finsler metric of Randers type in the context of the corresponding optimal control represented by a time-efficient ship's he…
Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is suitably chosen. Selecting it adaptively and algorithmically from prior knowledge…
The paper predicts edge weights in weighted directed networks using metric geometry.
problem Predicting edge weights in weighted directed networks.
method Introducing new types of weighted directed networks (AWDNs), constructing metrics, and proposing modified kNN and SVM methods.
result The proposed methods outperform traditional approaches in predicting edge weights.
We develop some results on the positivity of direct image bundles in the particular case of a trivial fibration over a one-dimensional base. We also apply the results to study variations of Kahler metrics.
Riemannian optimal controlmath.OC
The aim of this paper is to adapt the general multitime maximum principle to a Riemannian setting. More precisely, we intend to study geometric optimal control problems constrained by the metric compatibility evolution PDE system; the evolution ("multitime") variables are the local coordinates on a Riemannian manifold,…
The paper is a study of geodesic in two-dimensional pseudo-Riemannian metrics. Firstly, the local properties of geodesics in a neighborhood of generic parabolic points are investigated. The equation of the geodesic flow has singularities at such points that leads to a curious phenomenon: geodesics cannot pass through s…
Information Theoretically Optimal Sample Complexity of Learning Dynamical Directed Acyclic Graphsstat.ML
Optimal sample complexity for learning DDAGs from noisy data.
problem Learning interactions in linear dynamical systems over DAGs.
method Proposed a metric and algorithm based on PSD matrix for reconstruction.
result Optimal sample complexity for learning DDAGs.
We study continuous groups of generalized Kerr-Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. We prove that all these vector fields can be intrinsically characterized and that they constitute a Lie algebra if the null deformation direction is fixe…
Optimal geodesics connect boundary points in Teichmüller space.
problem Finding optimal geodesics between boundary points of Teichmüller space.
method Analyzing horofunctions and Teichmüller geodesics.
result There is a unique optimal geodesic connecting boundary points.
PGD-trained models have a preferential direction in their gradients, which improves robustness.
problem Mathematical lack of clarity in the direction of preferential gradient alignment after adversarial training.
method Proposed a novel definition of preferential direction and evaluated it using a metric based on GANs.
result PGD-trained models have higher alignment with the proposed preferential direction than baseline models.
In this note we give a construction of a smooth Riemannian metric on R^n which is standard Euclidean outside a compact set K and such that it has N = n(n + 1)=2 invisible directions, meaning that all geodesics lines passing through the set K in these directions remain the same straight lines on exit. For example in the…
Optimizes Euclidean functions on Riemannian manifolds with warped metrics.
problem Optimizing functions in high-dimensional Euclidean spaces.
method Riemannian geometry, warped metric, geodesic curves, Taylor approximations, retraction maps.
result Efficient optimization of functions using third-order approximations of geodesics.
This note demonstrates how both the concept of distance and the concept of holonomy can be constructed from a suitable network with directed edges (and no lengths). The number of different edge types depends on the signature of the metric and the dimension of the holonomy group. If the holonomy group is of dimension on…
A brief survey on singularities of geodesic flows in smooth signature changing metrics on 2-surfacesmath.DG
We present a survey on generic singularities of geodesic flows in smooth signature changing metrics (often called pseudo-Riemannian) in dimension 2. Generically, a pseudo-Riemannian metric on a 2-manifold changes its signature (degenerates) along a curve , which locally separates into a Riemannian () an…
The study examines optimal synthesis in a radially symmetric Grushin space with conditions on the weight function.
problem Optimal synthesis in a radially symmetric Grushin space with a weight function.
method Analysis of the geometry of with a weighted Carnot-Carathéodory metric, providing conditions for Grushin-like structure, and describing optimal synthesis.
result Sufficient conditions on the weight function ensure a Grushin-like structure, and the candidate cut time coincides with the true cut time in the integrable case.
A key challenge in complex visuomotor control is learning abstract representations that are effective for specifying goals, planning, and generalization. To this end, we introduce universal planning networks (UPN). UPNs embed differentiable planning within a goal-directed policy. This planning computation unrolls a for…
For one-parameter degenerations of compact Kähler manifolds, we determine the asymptotic behavior of the first Chern form of the direct image of a Nakano semi-positive vector bundle twisted by the relative canonical bundle, when the direct image is equipped with the L2-metric.
Many machine learning problems can be expressed as the optimization of some cost functional over a parametric family of probability distributions. It is often beneficial to solve such optimization problems using natural gradient methods. These methods are invariant to the parametrization of the family, and thus can yie…
Constructs a convex Finsler metric on vector bundles under specific conditions.
problem Creating a convex Finsler metric on vector bundles with positive curvature.
method Uses the negativity of direct image bundles and Minkowski inequality for norms.
result Shows how to upgrade a Kobayashi positive Finsler metric to a convex one.
The study shows how many diameter directions in Besse manifolds relate to Blaschke manifolds.
problem Understanding the relationship between diameter directions and Blaschke manifolds in Besse manifolds.
method Analyzing the properties of Besse manifolds and pinched curvature metrics.
result Besse manifolds with many diameter directions are Blaschke manifolds.
Given a family of probability measures in P(X), the space of probability measures on a Hilbert space X, our goal in this paper is to highlight one ore more curves in P(X) that summarize efficiently that family. We propose to study this problem under the optimal transport (Wasserstein) geometry, using curves that are re…
We study the systolic area (defined as the ratio of the area over the square of the systole) of the 2-sphere endowed with a smooth riemannian metric as a function of this metric. This function, bounded from below by a positive constant over the space of metrics, have the standard metric for critic point, althoug…
We prove that constant scalar curvature Kähler metric "adjacent" to a fixed Kähler class is unique up to isomorphism. This extends the uniqueness theorem of Donaldson and Chen-Tian, and formally fits into the infinite dimensional G.I.T picture described by Donaldson. We prove that the Calabi flow near a cscK metric exi…