arXiv research

LoCo learns local representations without end-to-end synchronization, improving performance on complex tasks.

Develops transparent global models consistent with local explanations.

Proposes a new contrastive loss for semi-supervised medical image segmentation.

Study infers tree topology from customer data using contrastive learning.

A new model cleans vocal note event annotations in music.

This work improves medical image segmentation with limited annotations using contrastive learning.

Complex-valued neural networks avoid spurious local minima.

GraphCL learns node representations by maximizing similarity between perturbed node features.

Proposes a tool to contrast global vs personalized models in clinical prediction.

As the application of deep neural networks proliferates in numerous areas such as medical imaging, video surveillance, and self driving cars, the need for explaining the decisions of these models has become a hot research topic, both at the global and local level. Locally, most explanation methods have focused on ident…

Unified framework for SSL methods linking contrastive and non-contrastive approaches.

Explicitly constructed 3XOR instances hard for Sum-of-Squares hierarchy.

Contrastive learning properties studied, including feature suppression and hierarchical learning.

Recent advances in interpretable Machine Learning (iML) and eXplainable AI (XAI) construct explanations based on the importance of features in classification tasks. However, in a high-dimensional feature space this approach may become unfeasible without restraining the set of important features. We propose to utilize t…

FedMCC learns from distributed data to cluster and extract features.

Paper proposes G-CRD to improve GNNs by preserving global graph topology.

Study groups acting on trees with specific local actions, proving cohomology vanishing or infinite.

GraphACL learns graph representations without augmentation or homophily assumptions.

We study a minimalist kinetic model for economies. A system of agents with local trading rules display emergent demand behaviour. We examine the resulting wealth distribution to look for non-thermal behaviour. We compare and contrast this model with other similar models.

CNPs improve function approximation by contrastive learning.

An online algorithm improves cPCA for efficient, interpretable data analysis.

New stabilization found in planar elasticae with degenerate diffusion.

Optimizes contrastive learning with individualized temperatures for better performance on imbalanced datasets.

Flow preserves isoperimetric ratio for immersed surfaces.

We propose a special deformation of the Sasaki metric on tangent and unit tangent bundle of a Hermitian locally symmetric manifold. Geodesics of this deformed metric have different projections on a base manifold for tangent or unit tangent bundle cases in contrast to usual Sasaki metric. Nevertheless, the projections o…

Croke and Kleiner constructed two homeomorphic locally CAT(0) complexes whose universal covers have visual boundaries that are not homeomorphic. We construct two homeomorphic locally CAT(0) complexes so that the visual boundary of one universal cover contains a nonplanar graph, while the visual boundary of the other do…

Local smoothing of metrics with small curvature, removing Ricci curvature condition.

Central to robot exploration and mapping is the task of persistent localization in environmental fields characterized by spatially correlated measurements. This paper presents a Gaussian process localization (GP-Localize) algorithm that, in contrast to existing works, can exploit the spatially correlated field measurem…

We show that there exist non-trivial piecewise-linear (PL) knots with isolated singularities $S^{n-2}\subset S^n$, $n\geq 5$, whose complements have the homotopy type of a circle. This is in contrast to the case of smooth, PL locally-flat, and topological locally-flat knots, for which it is known that if the complement…

This paper analyzes the landscape of supervised contrastive loss in over-parameterized networks.

CIR method preserves relation for case-control studies.

A new method for multi-criteria recommender systems using graph attention networks.

End-to-end training of DBMs with improved gradient estimation.

We review recent work on the local geometry and optimal regularity of Lorentzian manifolds with bounded curvature. Our main results provide an estimate of the injectivity radius of an observer, and a local canonical foliations by CMC (Constant Mean Curvature) hypersurfaces, together with spatially harmonic coordinates.…

We show the local wellposedness of biharmonic wave maps with initial data of sufficiently high Sobolev regularity and a blow-up criterion in the sup-norm of the gradient of the solutions. In contrast to the wave maps equation we use a vanishing viscosity argument and an appropriate parabolic regularization in order to …

New compact ECS manifolds with rank 2 discovered, differing from previous rank 1 examples.

Perceptrons are neuronal devices capable of fully discriminating linearly separable classes. Although straightforward to implement and train, their applicability is usually hindered by non-trivial requirements imposed by real-world classification problems. Therefore, several approaches, such as kernel perceptrons, have…

We prove a new and general concentration inequality for the excess risk in least-squares regression with random design and heteroscedastic noise. No specific structure is required on the model, except the existence of a suitable function that controls the local suprema of the empirical process. So far, only the case of…

New rigidity theorem on static manifolds with boundary.

We provide a coordinate-free version of the local classification, due to A. G. Walker [Quart. J. Math. Oxford (2) 1, 69 (1950)], of null parallel distributions on pseudo-Riemannian manifolds. The underlying manifold is realized, locally, as the total space of a fibre bundle, each fibre of which is an affine principal b…

Optimizer memory affects learning rate sensitivity in shuffle order, impacting fine-tuning noise.

Biological and artificial neural systems are composed of many local processors, and their capabilities depend upon the transfer function that relates each local processor's outputs to its inputs. This paper uses a recent advance in the foundations of information theory to study the properties of local processors that u…

We perform an optimal localization of asymptotically flat initial data sets and construct data that have positive ADM mass but are exactly trivial outside a cone of arbitrarily small aperture. The gluing scheme that we develop allows to produce a new class of $N$-body solutions for the Einstein equation, which patently…

The paper explores conformal groups on plane waves and proves a conjecture in locally homogeneous settings.

The paper proposes an expanded version of the Local Variance Gamma model of Carr and Nadtochiy by adding drift to the governing underlying process. Still in this new model it is possible to derive an ordinary differential equation for the option price which plays a role of Dupire's equation for the standard local volat…

Letter analyzes training dynamics of a nonlinear contrastive learning model in high dimensions.

We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the existing optimization-based approach, we work from a purely matrix-algebraic perspective. Moreover, we prove that the algorithm converges locally and exhibits a linear…

Transformers with multiple layers learn to estimate bigram distributions, while single-layer models often get stuck in unigram local minima.