arXiv research

New method trains shallow neural networks with subquadratic width scaling.

The paper proves Schauder estimates on cone products and characterizes harmonic functions.

Optimal private ERM and SCO with subquadratic gradient complexity.

A novel algorithm for unbiased graph kernel estimation with subquadratic time complexity.

On a complete Calabi-Yau manifold $M$ with maximal volume growth, a harmonic function with subquadratic polynomial growth is the real part of a holomorphic function. This generalizes a result of Conlon-Hein. We prove this result by proving a Liouville type theorem for harmonic $1$-forms, which follows from a new local …

When performing regression on a dataset with $p$ variables, it is often of interest to go beyond using main linear effects and include interactions as products between individual variables. For small-scale problems, these interactions can be computed explicitly but this leads to a computational complexity of at least $…

New algorithm reconstructs sparse networks in subquadratic time.

Improved efficient robust regression with near-linear time and subquadratic samples.

We study the number and the length of systoles on complete finite area orientable hyperbolic surfaces. In particular, we prove upper bounds on the number of systoles that a surface can have (the so-called kissing number for hyperbolic surfaces). Our main result is a bound which only depends on the topology of the surfa…

New algorithm solves unbalanced optimal transport on trees in quasi-linear time.

This work addresses dynamic KDE data structures with robustness to adversarial queries.

New algorithm reduces runtime for robust sparse mean estimation.

New findings show GD converges to a linear interpolator even with quadratic loss function under certain conditions.

We improve prediction risk estimation for large datasets using sketching and ridge regression.

Research shows quadratic growth in derivative maxima for certain interval diffeos with parabolic fixed points.

LoLCATs improves linearized LLM quality with less memory and compute.

Entity resolution seeks to merge databases as to remove duplicate entries where unique identifiers are typically unknown. We review modern blocking approaches for entity resolution, focusing on those based upon locality sensitive hashing (LSH). First, we introduce $k$-means locality sensitive hashing (KLSH), which is b…

New algorithms speed up attention computation for large models by limiting matrix entries.

This paper studies a Nyström type subsampling approach to large kernel learning methods in the misspecified case, where the target function is not assumed to belong to the reproducing kernel Hilbert space generated by the underlying kernel. This case is less understood, in spite of its practical importance. To model su…

We study the non Ricci flat gradient steady Kähler Ricci soliton with non-negative Ricci curvature and weak integrability condition of the scalar curvature $S$, namely $\underline{\lim}_{r\to \infty} r^{-1}\int_{B_r} S=0$, and show that it is a quotient of $Σ\times \mathbb{C}^{n-1-k}\times N^k$, where $Σ$ and $N$ denot…

In this paper we propose a Bayesian nonparametric approach to modelling sparse time-varying networks. A positive parameter is associated to each node of a network, which models the sociability of that node. Sociabilities are assumed to evolve over time, and are modelled via a dynamic point process model. The model is a…

The paper extends a Liouville theorem to biharmonic functions on manifolds with nonnegative Ricci curvature.

A general class of Lorentzian metrics, $M_0 x R^2$, $ds^2 = <.,.> + 2 du dv + H(x,u) du^2$, with $(M_0, <.,.>$ any Riemannian manifold, is introduced in order to generalize classical exact plane fronted waves. Here, we start a systematic study of their main geodesic properties: geodesic completeness, geodesic connected…

Adaptive dropout and regularization are shown to be dual in linear networks.

LaPSRL achieves optimal regret for isoperimetric RL distributions.

The study proves manifolds with positive scalar curvature can be decomposed into spherical and toroidal pieces.

The paper examines functional properties on manifolds with very negative curvature.

We consider the problem of performing linear regression over a stream of $d$-dimensional examples, and show that any algorithm that uses a subquadratic amount of memory exhibits a slower rate of convergence than can be achieved without memory constraints. Specifically, consider a sequence of labeled examples $(a_1,b_1)…

Fast linear transforms are ubiquitous in machine learning, including the discrete Fourier transform, discrete cosine transform, and other structured transformations such as convolutions. All of these transforms can be represented by dense matrix-vector multiplication, yet each has a specialized and highly efficient (su…

Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still poorly understood. This is in part because the heuristic is iterative and non-conve…

This paper examines how adversarial perturbations affect model performance and equilibrium learning.

Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including…

Nonparametric two sample testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. We refer to the most common settings as mean difference alternatives (MDA), for testing differences only in firs…

The paper explores efficient graph algorithms on geometric graphs and their computational limits.

Introduces bounded scale measure and generalizes property A.

Transformers can scale both context and task, but MLPs can only scale task.

New scaling framework for MoE architectures ensures stability and optimal performance at scale.

New principles needed for scaling large language models, challenging traditional regularization methods.

Improves U-Net for scale equivariance in semantic segmentation.

Introduces resemblance structure for large scale geometry.

New scaling laws optimize model size, training, and inference for better performance.

Derives a family of hyperparameter scaling strategies for neural networks.

To elucidate allometric scaling in complex systems, we investigated the underlying scaling relationships between typical three-scale indicators for approximately 500,000 Japanese firms; namely, annual sales, number of employees, and number of business partners. First, new scaling relations including the distributions o…

Study calculates tail risk for various mixture distributions.

A new robust scaling approach improves downstream metabolomics analysis.

Novel neural network solves PDEs with multi-scale resolution.

New pruning method breaks power law scaling, potentially reducing error to exponential.

CrossAD detects anomalies in time series data by considering cross-scale associations and cross-window modeling.