相关论文: Quadratic Upper Bound for Recursive Teaching Dimen…
A $d$-dimensional polycube is a facet-connected set of cells (cubes) on the $d$-dimensional cubical lattice $\mathbb{Z}^d$. Let $A_d(n)$ denote the number of $d$-dimensional polycubes (distinct up to translations) with $n$ cubes, and…
Using insight from numerical approximation of ODEs and the problem formulation and solution methodology of TD learning through a Galerkin relaxation, I propose a new class of TD learning algorithms. After applying the improved numerical…
The ability of artificial agents to increment their capabilities when confronted with new data is an open challenge in artificial intelligence. The main challenge faced in such cases is catastrophic forgetting, i.e., the tendency of neural…
Two recent approaches to computation in superposition reach different recursive capacity regimes: H\"anni et al. certify $\tilde{O}(d^{3/2})$ computable features in width $d$ via an approximate-linear recursive template, while Adler and…
Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random linear network coding. What the maximal cardinality of any constant-dimension code with finite dimension and minimum…
We study the gradient-based training of large-depth residual networks (ResNets) from standard random initializations. We show that infinite-depth ResNets behave as if they were infinitely wide, regardless of their actual width. More…
Resolving a linear combination of point sources from their band-limited Fourier data is a fundamental problem in imaging and signal processing. With the incomplete Fourier data and the inevitable noise in the measurement, there is a…
We study the complexity of computing the VC Dimension and Littlestone's Dimension. Given an explicit description of a finite universe and a concept class (a binary matrix whose $(x,C)$-th entry is $1$ iff element $x$ belongs to concept…
We consider the exploration-exploitation dilemma in finite-horizon reinforcement learning (RL). When the state space is large or continuous, traditional tabular approaches are unfeasible and some form of function approximation is mandatory.…
Matrix product operators allow efficient descriptions (or realizations) of states on a 1D lattice. We consider the task of learning a realization of minimal dimension from copies of an unknown state, such that the resulting operator is…
A decision tree recursively splits a feature space $\mathbb{R}^{d}$ and then assigns class labels based on the resulting partition. Decision trees have been part of the basic machine-learning toolkit for decades. A large body of work treats…
We study the classical and parameterized complexity of computing the positive non-clashing teaching dimension of a set of concepts, that is, the smallest number of examples per concept required to successfully teach an intelligent learner…
In response to a 1997 problem of M. Vidyasagar, we state a necessary and sufficient condition for distribution-free PAC learnability of a concept class $\mathscr C$ under the family of all non-atomic (diffuse) measures on the domain…
Block-coordinate descent (BCD) is a popular framework for large-scale regularized optimization problems with block-separable structure. Existing methods have several limitations. They often assume that subproblems can be solved exactly at…
We study the problem of adaptive control of a high dimensional linear quadratic (LQ) system. Previous work established the asymptotic convergence to an optimal controller for various adaptive control schemes. More recently, for the average…
Using a method we have utilized previously, namely through a finite power series expansion which also sometimes is known as the "radix polynomial" representation of an integer, we find an upper bound for a van der Waerden number that has a…
The PC algorithm learns maximally oriented causal Bayesian networks. However, there is no equivalent complete algorithm for learning the structure of relational models, a more expressive generalization of Bayesian networks. Recent…
Sequential learning problems are common in several fields of research and practical applications. Examples include dynamic pricing and assortment, design of auctions and incentives and permeate a large number of sequential treatment…
We study the generalization performance of gradient methods in the fundamental stochastic convex optimization setting, focusing on its dimension dependence. First, for full-batch gradient descent (GD) we give a construction of a learning…
We prove new upper and lower bounds on the VC-dimension of deep neural networks with the ReLU activation function. These bounds are tight for almost the entire range of parameters. Letting $W$ be the number of weights and $L$ be the number…