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Universal approximation with quadratic deep networks. [PDF]
Neural Netw, 2020 Recently, deep learning has achieved huge successes in many important applications. In our previous studies, we proposed quadratic/second-order neurons and deep quadratic neural networks. In a quadratic neuron, the inner product of a vector of data and the corresponding weights in a conventional neuron is replaced with a quadratic function.
Fan F, Xiong J, Wang G.
europepmc +6 more sources
Interval universal approximation for neural networks [PDF]
Proceedings of the ACM on Programming Languages, 2022 To verify safety and robustness of neural networks, researchers have successfully applied abstract interpretation , primarily using the interval abstract domain. In this paper, we study the theoretical power and limits of the interval domain for neural-network verification.
Somesh Jha
exaly +4 more sources
State Feedback Optimal L2-Induced Control of Nonlinear Systems Utilizing Universal Approximation [PDF]
EntropyThis paper presents an optimal L2-induced control problem for systems with multiple sector-bounded nonlinearities. Sufficient boundedness conditions for the L2-induced norm are derived in terms of a specific system of linear matrix inequalities (LMIs ...
Adrian-Mihail Stoica, Isaac Yaesh
doaj +2 more sources
Universal properties of approximation operators
Journal of Approximation Theory, 2012 The author studies the existence of universal functions with respect to some positive linear operators \(L_n:C[0,1]\to[0,1]\) that are closely related to the Popoviciu-Bohman-Korovkin theorem.
exaly +3 more sources
Universal approximation on the hypersphere [PDF]
Communications in Statistics - Theory and Methods, 2021 It is well known that any continuous probability density function on $\mathbb{R}^m$ can be approximated arbitrarily well by a finite mixture of normal distributions, provided that the number of mixture components is sufficiently large. The von-Mises-Fisher distribution, defined on the unit hypersphere $S^m$ in $\mathbb{R}^{m+1}$, has properties that ...
Ng, Tin Lok James, Kwong, Kwok-Kun
openaire +2 more sources
The Compact Support Neural Network
Sensors, 2021 Neural networks are popular and useful in many fields, but they have the problem of giving high confidence responses for examples that are away from the training data.
Adrian Barbu, Hongyu Mou
doaj +1 more source
Universal Approximation of Functions on Sets
CoRR, 2021 Modelling functions of sets, or equivalently, permutation-invariant functions, is a long-standing challenge in machine learning. Deep Sets is a popular method which is known to be a universal approximator for continuous set functions. We provide a theoretical analysis of Deep Sets which shows that this universal approximation property is only ...
Wagstaff, E +4 more
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A Theory of Cheap Control in Embodied Systems. [PDF]
PLoS Computational Biology, 2015 We present a framework for designing cheap control architectures of embodied agents. Our derivation is guided by the classical problem of universal approximation, whereby we explore the possibility of exploiting the agent's embodiment for a new and more ...
Guido Montúfar +2 more
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Novel Four-Layer Neural Network and Its Incremental Learning Based on Randomly Mapped Features
Jisuanji kexue yu tansuo, 2021 This paper proposes a four-layer neural network based on randomly feature mapping (FRMFNN) and its fast incremental learning algorithms. First, FRMFNN transforms the original input features into randomly mapped features by certain randomly mapping ...
YANG Yue, WANG Shitong
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One qubit as a universal approximant [PDF]
Physical Review A, 2021 10 pages + 6 (appendix); 7 figures + 4 (appendix) Changes made for publication. The text has been changed to improve clarity. A stronger relationship between the model in this paper and Machine Learning was stated. Some content has been moved to appendix.
Pérez-Salinas, Adrián +4 more
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