arXiv research

Projection-cost preservation is a low-rank approximation guarantee which ensures that the cost of any rank-$k$ projection can be preserved using a smaller sketch of the original data matrix. We present a general structural result outlining four sufficient conditions to achieve projection-cost preservation. These condit…

Let G be a connected semisimple Lie group without compact factors whose real rank is at least 2, and let Γ\subset G be an irreducible lattice. We provide a C^\infty classification for volume-preserving Cartan actions of Γand G. Also, if G has real rank at least 3, we provide a C^\infty classification for volume-preserv…

CoreFlow models matrix-valued distributions efficiently, preserving shared low-rank structure.

We prove that generalized mutation preserves several geometric invariants such as the volume and Goncharov invariant of Q-rank 1 locally symmetric spaces.

The paper introduces a framework to select efficient datasets for preserving model rankings.

Optimal privacy-preserving ranking from noisy comparisons.

Paper proposes a method to estimate counterfactual outcomes without a known SCM.

Let $D, Ω_1, ..., Ω_m$ be irreducible bounded symmetric domains. We study local holomorphic maps from $D$ into $Ω_1 \times... Ω_m$ preserving the invariant $(p, p)$-forms induced from the normalized Bergman metrics up to conformal constants. We show that the local holomorphic maps extends to algebraic maps in the rank …

A rank-n tensor on a Lorentzian manifold V whose contraction with n arbitrary causal future directed vectors is non-negative is said to have the dominant property. These tensors, up to sign, are called causal tensors, and we determine their general properties in dimension N. We prove that rank-2 tensors which map the n…

The paper establishes theoretical foundations for low-rank knowledge distillation in LLMs.

Maps preserving Carathéodory distance between symmetric domains are rigid.

Study on positivity properties of vector bundle Monge-Ampère equation.

GCML preserves geometric structure in manifold clustering for diverse data types.

Sign-RIP improves robust low-rank matrix recovery by preserving norms even with corrupted measurements.

New method uses causal thinking to make AI fairer decisions.

This method infers models from data with physical insights, minimizing model order.

First we investigate the evolutions of the radius function and its gradient along the volume-preserving mean curvature flow starting from a tube (of nonconstant radius) over a compact closed domain of a reflective submanifold in a symmetric space under certain condition for the radius function. Next, we prove that the …

New method improves tensor completion by selectively preserving important elements.

Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation methods, such as Tucker or CP decomposition, result in degraded model accuracy becau…

Multi-view spectral clustering, which aims at yielding an agreement or consensus data objects grouping across multi-views with their graph laplacian matrices, is a fundamental clustering problem. Among the existing methods, Low-Rank Representation (LRR) based method is quite superior in terms of its effectiveness, intu…

New saddle network architectures preserve convex-concave geometry in optimization problems.

This paper studies how key tensor properties are inherited in subtensors of tensor train decompositions.

This paper tackles fitting multilevel low rank matrices by addressing three problems.

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as positive-semidefiniteness, and they can produce approximations with a user-speci…

We study the model selection problem in conditional average treatment effect (CATE) prediction. Unlike previous works on this topic, we focus on preserving the rank order of the performance of candidate CATE predictors to enable accurate and stable model selection. To this end, we analyze the model performance ranking …

IMPACT optimizes LLM compression by focusing on activation importance, reducing model size up to 55.4%.

This paper solves aggregation of Pareto optimal models by using Bayesian priors and weighted averaging.

Global rigidity theorem for certain lattice actions on manifolds.

Due to the recent advances on Neural Architecture Search (NAS), it gains popularity in designing best networks for specific tasks. Although it shows promising results on many benchmarks and competitions, NAS still suffers from its demanding computation cost for searching high dimensional architectural design space, and…

Proposes MvLPE for better multi-view representation learning.

We describe a new method called t-ETE for finding a low-dimensional embedding of a set of objects in Euclidean space. We formulate the embedding problem as a joint ranking problem over a set of triplets, where each triplet captures the relative similarities between three objects in the set. By exploiting recent advance…

The paper addresses privacy in rank aggregation using randomized responses.

A generalized Clifford manifold is proposed in which there are coordinates not only for the basis vector generators, but for each element of the Clifford group, including the identity scalar. These new quantities are physically interpreted to represent internal structure of matter (e.g. classical or quantum spin). The …

Asynchronous federated modeling improves spatial data sharing without centralizing raw data.

We study higher rank Cartan actions on compact manifolds preserving an ergodic measure with full support. In particular, we classify actions by $\R ^k$ with $k \geq 3$ whose one-parameter groups act transitively as well as nondegenerate totally nonsymplectic $\Zk$-actions for $k \geq 3$.

We prove a theorem relating the automorphism group of a Cartan geometry to the group on which the geometry is modeled: a component of the adjoint representation of the first embeds in the adjoint representation of the second. Consequences of the theorem include general bounds on the rank and nilpotence degree of an aut…

In this paper, we investigate the ergodic and rigidity properties of weakly hyperbolic group actions. Motivated by classical theorems describing Anosov diffeomorphisms, we obtain two main results: First, all C^2 volume preserving weakly hyperbolic actions on closed manifolds are ergodic. This result generalizes Anosov'…

What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections. We examine the approach of first performing factorization in the compressed dom…

Proposes a method for ranking items across multiple aspects based on user feedback.

Let $D^2$ be the open unit disc in the Euclidean plane and let $G:= Diff(D2; area)$ be the group of smooth compactly supported area-preserving diffeomorphisms of $D^2$. We investigate the properties of G endowed with the autonomous metric. In particular, we construct a bi-Lipschitz homomorphism $Z^k \rightarrow G$ of a…

We examine the existence of one parameter groups of diffeomorphisms whose infinitesimal generators annihilate all scalar polynomial curvature invariants through the application of the Lie derivative, known as $\mathcal{I}$-preserving diffeomorphisms. Such mappings are a generalization of isometries and appear to be rel…

We simplify SSL by approximating redundant structural components with low-rank factorization.

The paper proves actions of lattices in higher rank groups have cost one.

New examples of isoparametric families on non-compact symmetric spaces.

Low-rank framework for task-specific LLM ranking from sparse comparisons.

We construct new homogeneous Einstein spaces with negative Ricci curvature in two ways: First, we give a method for classifying and constructing a class of rank one Einstein solvmanifolds whose derived algebras are two-step nilpotent. As an application, we describe an explicit continuous family of ten-dimensional Einst…

Efficient algorithm for Hadamard decomposition of matrices.

LR-EDNN reduces PDE solver complexity by limiting network weights to low-rank subspace.