arXiv research

Study approximates unknown function levels with queries.

We approximate derivatives of functions on manifolds by embedding them and applying vector-valued operators.

Sharp bounds for approximating Sobolev functions by ridge functions and networks.

Improved neural network approximates analytic and L^p functions efficiently.

Study approximates nonlinear functionals using deep ReLU networks.

Method uses DNNs to approximate functions with specific asymptotic behavior.

Transformers struggle to approximate smooth functions, relying on piecewise constant approximations.

Smooth approximations for continuous functions on orbit spaces.

In this paper, we propose a generic framework for devising an adaptive approximation scheme for value function approximation in reinforcement learning, which introduces multiscale approximation. The two basic ingredients are multiresolution analysis as well as tree approximation. Starting from simple refinable function…

Due to the intractable partition function, the exact likelihood function for a Markov random field (MRF), in many situations, can only be approximated. Major approximation approaches include pseudolikelihood and Laplace approximation. In this paper, we propose a novel way of approximating the likelihood function throug…

Paper develops efficient RL algorithm for general value function approximation.

The paper shows neural networks can approximate functions over non-compact domains with non-polynomial activation.

Paper shows deep neural networks can approximate Korobov functions nearly optimally.

New RBF networks can approximate any continuous function.

ReLU is widely seen as the default choice for activation functions in neural networks. However, there are cases where more complicated functions are required. In particular, recurrent neural networks (such as LSTMs) make extensive use of both hyperbolic tangent and sigmoid functions. These functions are expensive to co…

Quantum neural networks approximate periodic functions more efficiently.

Deep networks with path norm regularization can approximate analytic functions.

Deep, wide ConvResNets can approximate functions and their smoothness.

Generalizes neural network approximation to infinite-dimensional manifolds and derivatives.

This work improves sample efficiency in neural function approximation for reinforcement learning.

2D CNNs approximate Korobov functions with near-optimal rates.

A new Kolmogorov-Arnold network improves function approximation and optimization.

In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within classical algorithms for low-rank approximation in order to exploit the possible sp…

Deep neural networks with piecewise-polynomial activations can approximate smooth functions and their derivatives.

Minimum width for ReLU networks to approximate L^p functions is max(d_x+1, d_y).

We propose fast approximations for the generalized sliced-Wasserstein distance.

Universal approximation theorem for differentiable maps on infinite-dimensional manifolds

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…

This work improves polynomial approximations for functions with asymmetric behavior.

Deep networks can learn functions approximated by shallow networks, but not all functions.

Let $U\subseteq\mathbb{R}^{n}$ be open and convex. We show that every (not necessarily Lipschitz or strongly) convex function $f:U\to\mathbb{R}$ can be approximated by real analytic convex functions, uniformly on all of $U$. In doing so we provide a technique which transfers results on uniform approximation on bounded …

Efficient offline reinforcement learning with neural networks using differentiable function approximation.

This paper develops fundamental limits of deep neural network learning by characterizing what is possible if no constraints are imposed on the learning algorithm and on the amount of training data. Concretely, we consider Kolmogorov-optimal approximation through deep neural networks with the guiding theme being a relat…

Efficiently approximates neural network function space distance.

New bounds on ReLU networks for low-regular functions.

Entropy-regularized NPG converges linearly with linear function approximation.

$Q$-learning with function approximation is one of the most popular methods in reinforcement learning. Though the idea of using function approximation was proposed at least 60 years ago, even in the simplest setup, i.e, approximating $Q$-functions with linear functions, it is still an open problem on how to design a pr…

In much of the literature on function approximation by deep networks, the function is assumed to be defined on some known domain, such as a cube or a sphere. In practice, the data might not be dense on these domains, and therefore, the approximation theory results are observed to be too conservative. In manifold learni…

The paper projects unknown manifolds onto hyperspheres for efficient function approximation.

TVS-FNNs can approximate any continuous function on expanded input spaces.

We show that finite-width deep ReLU neural networks yield rate-distortion optimal approximation (Bölcskei et al., 2018) of polynomials, windowed sinusoidal functions, one-dimensional oscillatory textures, and the Weierstrass function, a fractal function which is continuous but nowhere differentiable. Together with thei…

Study on RNNs' ability to approximate past-dependent Hölder functions and their application to regression.

Theory for deep neural network approximation of score function and its derivatives.

Functional input neural networks approximate continuous functions on weighted spaces.

Complex-valued neural networks can approximate any continuous function.

Efficiently plans large MDPs with weak function approximations.

Framework for universal graph function approximators outperforms existing methods.

Study shows how to approximate and estimate high-dimensional classification functions without the curse of dimensionality.