arXiv research

Residual networks with block width max(d_x, d_y) approximate all functions.

The paper proves a theorem linking ball volume and Uryson width, with applications to 3-sphere metrics.

Deep ReLU nets with width d+1 can approximate any convex function on [0,1]^d.

Fisher width is a geometric measure of complexity on statistical manifolds.

Unified spectral framework for μP under joint width-depth scaling.

Joslim optimizes both width and weight configurations for slimmable neural networks, improving model efficiency.

New metric properties show volume constraints in collapsing spaces.

Random groups prove length constraints on product of conjugates.

Sharp dimension constraints for positive intermediate curvature metrics are established.

Paper develops DP algorithms for isotonic regression over posets.

Adversarial examples in deep ReLU networks with constant depth.

Improved sample complexity bounds for neural networks with depth independence.

Improves matrix multiplication throughput for asymmetric bit-width operands.

A remarkable characteristic of overparameterized deep neural networks (DNNs) is that their accuracy does not degrade when the network's width is increased. Recent evidence suggests that developing compressible representations is key for adjusting the complexity of large networks to the learning task at hand. However, t…

Study on predicting sequences with Gaussian constraints, linking to intrinsic volumes and metric complexity.

The width $w$ of a curve $γ$ in Euclidean space $R^n$ is the infimum of the distances between all pairs of parallel hyperplanes which bound $γ$, while its inradius $r$ is the supremum of the radii of all spheres which are contained in the convex hull of $γ$ and are disjoint from $γ$. We use a mixture of topological and…

Estimates generalization error for two-layer ReLU NNs through minimum norm solutions.

Study min-max theory for hypersurfaces with boundary constraints.

An algorithm calculates Gabai width for thousands of knots.

The study shows a 3D manifold's macroscopic dimension is 1 under specific curvature constraints.

Study extends knot width concept to higher dimensions, finding large widths possible.

Empirical study compares finite- and infinite-width BNNs, revealing performance differences under model mismatch.

Well-quasi-orders proved on embedded planar graphs.

2-width of 3-manifolds is bounded by 2 but embeddings can have infinite 2-width.

The isospectral problem for p-widths is solved using Zoll metrics on S^2.

VFlow enhances generative flows by augmenting data dimensions for better expressiveness.

Width trees link link invariants and bridge number.

New algorithms reduce dueling bandits' regret with neural networks and efficient exploration.

Lectures on deep learning properties in infinite and large-width networks.

A number of results for C$^2$-smooth surfaces of constant width in Euclidean 3-space ${\mathbb{E}}^3$ are obtained. In particular, an integral inequality for constant width surfaces is established. This is used to prove that the ratio of volume to cubed width of a constant width surface is reduced by shrinking it along…

Polygon $p$-widths are found via billiard trajectories.

Computed p-widths for hemisphere, first for manifolds with boundary.

Study bounds Urysohn width of manifolds under surgeries.

Computed p-widths for real projective plane.

Study shows width of Whitehead double knots is four times the original knot's width.

Gradient descent and SGD achieve low test error in specific network weight regimes.

While studying the existence of closed geodesics and minimal hypersurfaces in compact manifolds, the concept of width was introduced in different contexts. Generally, the width is realized by the energy of the closed geodesics or the volume of minimal hypersurfaces, which are found by the Minimax argument. Recently, Ma…

Study on Gaussian-width complexity on statistical manifolds and its applications in learning and recovery.

Proves conjecture about sphere widths under rotational symmetry.

New link invariants from diagram colorings match link widths.

Study infinite-depth limits of neural networks with fixed width.

Sparse logistic regression recovers any discrete pairwise graph model.

In "Width complexes for knots and 3-manifolds," Jennifer Schultens defines the width complex for a knot in order to understand the different positions a knot can occupy in the 3-sphere and the isotopies between these positions. She poses several questions about these width complexes; in particular, she asks whether the…

Characterizes the width of real projective spaces and computes Morse index.

In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix completion, and provide unified upper bounds on the sample complexity and the estimatio…

Sharp lower bound for first Neumann eigenvalue found in terms of diameter and width.

Wide neural networks can degrade performance, contrary to conventional wisdom.

We prove that among all constant width bodies of revolution, the minimum of the ratio of the volume to the cubed width is attained by the constant width body obtained by rotation of the Reuleaux triangle about an axis of symmetry.