Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Gradient Free Neural Network Framework Based on Universal
  Approximation Theorem   We present a numerical scheme for computation of Artificial Neural Networks
(ANN) weights, which stems from the Universal Approximation Theorem, avoiding
laborious iterations. The proposed algorithm adheres to the underlying theory,
is highly fast, and results in remarkably low errors when applied for
regression and classification of complex data-sets, such as the Griewank
function of multiple variables $\mathbf{x} \in \mathbb{R}^{100}$ with random
noise addition, and MNIST database for handwritten digits recognition, with
$7\times10^4$ images. The same mathematical formulation is found capable of
approximating highly nonlinear functions in multiple dimensions, with low
errors (e.g. $10^{-10}$) for the test-set of the unknown functions, their
higher-order partial derivatives, as well as numerically solving Partial
Differential Equations. The method is based on the calculation of the weights
of each neuron in small neighborhoods of the data, such that the corresponding
local approximation matrix is invertible. Accordingly, optimization of
hyperparameters is not necessary, as the number of neurons stems directly from
the dimensionality of the data, further improving the algorithmic speed. Under
this setting, overfitting is inherently avoided, and the results are
interpretable and reproducible. The complexity of the proposed algorithm is of
class P with
$\mathcal{O}(mn^2)+\mathcal{O}(\frac{m^3}{n^2})-\mathcal{O}(\log(n+1))$
computing time, with respect to the observations $m$ and features $n$, in
contrast with the NP-Complete class of standard algorithms for ANN training.
The performance of the method is high, irrespective of the size of the dataset,
and the test-set errors are similar or smaller than the training errors,
indicating the generalization efficiency of the algorithm.

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The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math