Related papers: Pruning distance of upset-decomposable persistence…

This short note contains an elementary observation in response to the recent posting arXiv:1707.06593v1, which studies the Lipschitz extension modulus to $n$ additional points. We bound this modulus in terms of the well-studied Lipschitz…

Robustness of neural networks is commonly quantified via local or global Lipschitz constants. However, Lipschitz continuity can be overly coarse or overly restrictive as global robustness measure, failing to capture nuanced, data-dependent…

We consider symmetric (under the action of products of finite symmetric groups) real algebraic varieties and semi-algebraic sets, as well as symmetric complex varieties in affine and projective spaces, defined by polynomials of degrees…

Deep neural networks have made significant progress in the field of computer vision. Recent studies have shown that depth, width and shortcut connections of neural network architectures play a crucial role in their performance. One of the…

Let $R$ be a commutative Noetherian local ring. We prove a variety of new formulae for modules of finite quasi-projective or finite quasi-injective dimension. These include the Derived Depth Formula, itself an extension of Auslander famous…

This paper proposes to establish the distance between partial preference orderings based on two very different approaches. The first approach corresponds to the brute force method based on combinatorics. It generates all possible complete…

In this paper, we revisit the notion of length measures associated to planar closed curves. These are a special case of area measures of hypersurfaces which were introduced early on in the field of convex geometry. The length measure of a…

This paper introduces a coordinate descent version of the V\~u-Condat algorithm. By coordinate descent, we mean that only a subset of the coordinates of the primal and dual iterates is updated at each iteration, the other coordinates being…

A significant part of modern topological data analysis is concerned with the design and study of algebraic invariants of poset representations -- often referred to as multi-parameter persistence modules. One such invariant is the minimal…

Metric embeddings are a widely used method in algorithm design, where generally a ``complex'' metric is embedded into a simpler, lower-dimensional one. Historically, the theoretical computer science community has focused on bi-Lipschitz…

The property of preserving the convexity and concavity of the Bernstein polynomial and of the B\'{e}zier curves is used to generate a method of approximating the reliability polynomial of a hammock network. The mutual behaviour of the…

Lightweight and effective models are essential for devices with limited resources, such as intelligent vehicles. Structured pruning offers a promising approach to model compression and efficiency enhancement. However, existing methods often…

We study the sequential general online regression, known also as the sequential probability assignments, under logarithmic loss when compared against a broad class of experts. We focus on obtaining tight, often matching, lower and upper…

The pruning objective has recently extended beyond accuracy and sparsity to robustness in language models. Despite this, existing methods struggle to enhance robustness against adversarial attacks when continually increasing model sparsity…

The restricted strong convexity is an effective tool for deriving globally linear convergence rates of descent methods in convex minimization. Recently, the global error bound and quadratic growth properties appeared as new competitors. In…

The interleaving distance, although originally developed for persistent homology, has been generalized to measure the distance between functors modeled on many posets or even small categories. Existing theories require that such a poset…

Rademacher theorem states that every Lipschitz function on the Euclidean space is differentiable almost everywhere, where "almost everywhere" refers to the Lebesgue measure. In this paper we prove a differentiability result of similar type,…

We present the first dynamic algorithms for Dyck and tree edit distances with subpolynomial update times. Dyck edit distance measures how far a parenthesis string is from a well-parenthesized expression, while tree edit distance quantifies…

We demonstrate that for strongly log-convex densities whose potentials are discontinuous on manifolds, the ULA algorithm converges with stepsize bias of order $1/2$ in Wasserstein-p distance. Our resulting bound is then of the same order as…

Pruning is a standard technique for removing unnecessary structure from a neural network to reduce its storage footprint, computational demands, or energy consumption. Pruning can reduce the parameter-counts of many state-of-the-art neural…