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.
Adaptive model selection for RL with unknown function classes.
We study the smooth structure of convex functions by generalizing a powerful concept so-called self-concordance introduced by Nesterov and Nemirovskii in the early 1990s to a broader class of convex functions, which we call generalized self-concordant functions. This notion allows us to develop a unified framework for …
This paper introduces new loss functions for balanced multi-class classification.
We demonstrate the usage of explicit form of the Thom class found by Mathai and Quillen for the definition of generating functional of a simple supersymmetric quantum mechanical model.
The vicinal risk minimization (VRM) principle, first proposed by \citet{vapnik1999nature}, is an empirical risk minimization (ERM) variant that replaces Dirac masses with vicinal functions. Although there is strong numerical evidence showing that VRM outperforms ERM if appropriate vicinal functions are chosen, a compre…
There has been a growing interest in expressivity of deep neural networks. However, most of the existing work about this topic focuses only on the specific activation function such as ReLU or sigmoid. In this paper, we investigate the approximation ability of deep neural networks with a broad class of activation functi…
We consider the problem of reinforcement learning over episodes of a finite-horizon deterministic system and as a solution propose optimistic constraint propagation (OCP), an algorithm designed to synthesize efficient exploration and value function generalization. We establish that when the true value function lies wit…
Study shows observability from a measurable set for Gevrey functions.
Paper develops efficient algorithms for zero-sum Markov games with general function classes.
On four-dimensional closed manifolds we introduce a class of canonical Riemannian metrics, that we call weak harmonic Weyl metrics, defined as critical points in the conformal class of a quadratic functional involving the norm of the divergence of the Weyl tensor. This class includes Einstein and, more in general, harm…
It is well known that quasi-isometric embeddings of Gromov hyperbolic spaces induce topological embeddings of their Gromov boundaries. A more general question is to detect classes of functions between Gromov hyperbolic spaces that induce continuous maps between their Gromov boundaries. In this paper we introduce the cl…
We consider a class of continuous functions on that is of interest from two different perspectives. First, it is closely related to sets of functions that have been studied as generalizations of the Takagi function. Second, each function in admits a linear pathwise quadratic variatio…
This research sets limits on how complex multi-class learning problems can be.
The paper analyzes risk bounds and Rademacher complexity in batch RL.
Study dynamic risk measures and performance indices using distortion functions.
The paper provides a new uniform tail bound for empirical processes.
We give a criterion for the coercivity of the Mabuchi functional for general Kähler classes on Fano manifolds in terms of Tian's alpha invariant. This generalises a result of Tian in the anti-canonical case implying the existence of a Kähler-Einstein metric. We also prove the alpha invariant is a continuous function on…
The paper proves neural networks' consistency and optimal convergence rates for various function classes.
A new loss function HUG decouples and generalizes neural collapse.
Study stabilizers of smooth functions on surfaces, focusing on Morse-Bott functions.
Develops uniform convergence guarantees for a broad class of risk functionals in supervised learning.
In deep neural network, the cross-entropy loss function is commonly used for classification. Minimizing cross-entropy is equivalent to maximizing likelihood under assumptions of uniform feature and class distributions. It belongs to generative training criteria which does not directly discriminate correct class from co…
Paper calculates eigenvalue decay rates for neural network kernels on general domains.
An elementary proof shows submodular functions can be represented as measure suprema.
Optimal algorithm for maximizing rewards in contextual bandits with resource constraints.
New particle-based VI algorithm expands function class and improves scalability.
The Chekanov theorem generalizes the classic Lyusternik-Shnirel'man and Morse theorems concerning critical points of a smooth function on a closed manifold. A Legendrian submanifold Λof space of 1-jets of the functions on a manifold M defines a multi-valued function whose graph is the projection of Λin J^0 M = M x R. T…
New algorithm reduces RL complexity with low switching costs.
We prove super-quadratic lower bounds for the growth of the filling area function of a certain class of Carnot groups. This class contains groups for which it is known that their Dehn function grows no faster than . We therefore obtain the existence of (finitely generated) nilpotent groups whose Dehn functio…
New insights on eluder dimension for function approximation in machine learning.
We discuss a special class of solutions to the minimal surface system. These are vector-valued functions that "decrease area" and are natural generalization of scalar functions. After defining area-decreasing maps, we show several classical results for the minimal surface equation can be generalized. We also conjecture…
We present a simple generative framework for learning to predict previously unseen classes, based on estimating class-attribute-gated class-conditional distributions. We model each class-conditional distribution as an exponential family distribution and the parameters of the distribution of each seen/unseen class are d…
Deep networks adapt to function regularity and data distribution.
We investigate classification results for general quadratic functions on torsion abelian groups. Unlike the previously studied situations, general quadratic functions are allowed to be inhomogeneous or degenerate. We study the discriminant construction which assigns, to an integral lattice with a distinguished characte…
The paper studies continuous submodular functions and their optimization.
This paper establishes minimax rates for online regression with arbitrary classes of functions and general losses. We show that below a certain threshold for the complexity of the function class, the minimax rates depend on both the curvature of the loss function and the sequential complexities of the class. Above this…
Smooth functions preserve Zygmund class on curves.
New Zap Q-learning accelerates reinforcement learning with neural networks.
Paper proposes anomaly detection using Eigentraces and one-class classification.
We consider the problem of finding critical points of functions that are non-convex and non-smooth. Studying a fairly broad class of such problems, we analyze the behavior of three gradient-based methods (gradient descent, proximal update, and Frank-Wolfe update). For each of these methods, we establish rates of conver…
Topological twists for 4d N=2 theories depend on spacetime type, gerbe connections, and generalized spin-c structures.
Improved generalization bounds for CNNs using Rademacher complexity.
Estimates fat-shattering dimension of aggregated function classes.
We derive bounds for a notion of adversarial risk, designed to characterize the robustness of linear and neural network classifiers to adversarial perturbations. Specifically, we introduce a new class of function transformations with the property that the risk of the transformed functions upper-bounds the adversarial r…
We start by studying the distribution of (cyclically reduced) elements of the free groups Fn with respect to their abelianization (or equivalently, their integer homology class. We derive an explicit generating function, and a limiting distribution, by means of certain results (of independent interest) on Chebyshev pol…
The Closest Point Method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys. 2008] and successfully applied to a variety of surface PDEs. In this paper we study the theoretical foundations of this method. The main idea is that surface diffe…
Locally maximizing orbits studied in twist maps and billiards.
Derives scalar reduction for generalized Kähler-Ricci solitons, proving uniqueness.