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Found 6 papers, 0 papers with code
Shallow neural network representation of polynomials
We show that $d$-variate polynomials of degree $R$ can be represented on $[0, 1]^d$ as shallow neural networks of width $2(R+d)^d$.
Nonparametric regression with modified ReLU networks
We consider regression estimation with modified ReLU neural networks in which network weight matrices are first modified by a function $\alpha$ before being multiplied by input vectors.
Expressive power of binary and ternary neural networks
We show that deep sparse ReLU networks with ternary weights and deep ReLU networks with binary weights can approximate $\beta$-H\"older functions on $[0, 1]^d$.
Neural networks with superexpressive activations and integer weights
An example of an activation function $\sigma$ is given such that networks with activations $\{\sigma, \lfloor\cdot\rfloor\}$, integer weights and a fixed architecture depending on $d$ approximate continuous functions on $[0, 1]^d$.
Analytic function approximation by path norm regularized deep networks
We show that neural networks with absolute value activation function and with the path norm, the depth, the width and the network weights having logarithmic dependence on $1/\varepsilon$ can $\varepsilon$-approximate functions that are analytic on certain regions of $\mathbb{C}^d$.
Function approximation by deep neural networks with parameters $\{0,\pm \frac{1}{2}, \pm 1, 2\}$
In this paper it is shown that $C_\beta$-smooth functions can be approximated by deep neural networks with ReLU activation function and with parameters $\{0,\pm \frac{1}{2}, \pm 1, 2\}$.
