A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Optimal private ERM and SCO with subquadratic gradient complexity.
New method trains shallow neural networks with subquadratic width scaling.
New findings show GD converges to a linear interpolator even with quadratic loss function under certain conditions.
On a complete Calabi-Yau manifold 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 -forms, which follows from a new local …
We prove an interior Schauder estimate for the Laplacian on metric products of two dimensional cones with a Euclidean factor, generalizing the work of Donaldson and reproving the Schauder estimate of Guo-Song. We characterize the space of homogeneous subquadratic harmonic functions on products of cones, and identify sc…
A novel algorithm for unbiased graph kernel estimation with subquadratic time complexity.
LoLCATs improves linearized LLM quality with less memory and compute.
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…
When performing regression on a dataset with 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 $…
This work addresses dynamic KDE data structures with robustness to adversarial queries.
New algorithm reduces runtime for robust sparse mean estimation.
Research shows quadratic growth in derivative maxima for certain interval diffeos with parabolic fixed points.
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 -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 , namely , and show that it is a quotient of , where and 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, , , with 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…
New algorithm solves unbalanced optimal transport on trees in quasi-linear time.
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 improve prediction risk estimation for large datasets using sketching and ridge regression.
We consider the problem of performing linear regression over a stream of -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…
Implicit Q-learning and SARSA adjust step-sizes automatically, improving stability and performance.
Study distortion risk measures for step-weighted distributions.
Dance Dance Revolution (DDR) is a popular rhythm-based video game. Players perform steps on a dance platform in synchronization with music as directed by on-screen step charts. While many step charts are available in standardized packs, players may grow tired of existing charts, or wish to dance to a song for which no …
The CSA-ES is an Evolution Strategy with Cumulative Step size Adaptation, where the step size is adapted measuring the length of a so-called cumulative path. The cumulative path is a combination of the previous steps realized by the algorithm, where the importance of each step decreases with time. This article studies …
The paper explores efficient graph algorithms on geometric graphs and their computational limits.
Step decay schedules improve convergence in non-convex optimization.
The correspondence between residual networks and dynamical systems motivates researchers to unravel the physics of ResNets with well-developed tools in numeral methods of ODE systems. The Runge-Kutta-Fehlberg method is an adaptive time stepping that renders a good trade-off between the stability and efficiency. Can we …
We construct a deep portfolio theory. By building on Markowitz's classic risk-return trade-off, we develop a self-contained four-step routine of encode, calibrate, validate and verify to formulate an automated and general portfolio selection process. At the heart of our algorithm are deep hierarchical compositions of p…
In its simplest form, the traffic flow prediction problem is restricted to predicting a single time-step into the future. Multi-step traffic flow prediction extends this set-up to the case where predicting multiple time-steps into the future based on some finite history is of interest. This problem is significantly mor…
A Levi-Malcev type decomposition for -step solvable Lie algebras with a complex structure
The paper analyzes fixed step-size SA schemes on Riemannian manifolds.
Note on instabilities in super-time-stepping methods for Heston model.
Study on holonomy of Obata connection on specific nilmanifolds.
The study characterizes G₂-structures on 2-step nilpotent Lie groups.
For the efficient compensation of fiber nonlinearity, one of the guiding principles appears to be: fewer steps are better and more efficient. We challenge this assumption and show that carefully designed multi-step approaches can lead to better performance-complexity trade-offs than their few-step counterparts.