Threshold circuits of bounded depth
Andras Hajnal,Andras Hajnal,Wolfgang Maass,Wolfgang Maass,Pavel Pudlák,Pavel Pudlák,György Turán,György Turán,Mario Szegedy +8 more
TLDR
To what extent imprecise threshold gates (which behave unpredictably near the threshold value) can compute nontrivial functions in bounded depth and a bound is given for the permissible amount of imprecision.About:
This article is published in Journal of Computer and System Sciences.The article was published on 1993-04-01 and is currently open access. It has received 241 citations till now. The article focuses on the topics: Bounded function & Polynomial.read more
Citations
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Journal ArticleDOI
Neural network computation with DNA strand displacement cascades
TL;DR: It is suggested that DNA strand displacement cascades could be used to endow autonomous chemical systems with the capability of recognizing patterns of molecular events, making decisions and responding to the environment.
Proceedings Article
The Power of Depth for Feedforward Neural Networks
Ronen Eldan,Ohad Shamir +1 more
TL;DR: In this article, it was shown that a simple (approximately radial) function on R d, expressible by a small 3-layer feedforward neural networks, which cannot be approximated by any 2-layer network, unless its width is exponential in the dimension.
Posted Content
The Power of Depth for Feedforward Neural Networks
Ronen Eldan,Ohad Shamir +1 more
TL;DR: In this paper, it was shown that a simple (approximately radial) function expressible by a small 3-layer feed-forward neural network, which cannot be approximated by any 2-layer network, to more than a certain constant accuracy, unless its width is exponential in the dimension.
Journal ArticleDOI
Lower bounds for the computational power of networks of spiking neurons
TL;DR: It is shown that simple operations on phase differences between spike-trains provide a very powerful computational tool that can in principle be used to carry out highly complex computations on a small network of spiking neurons.
Proceedings ArticleDOI
On the power of the congested clique model
TL;DR: It is shown that the unicast congested clique can simulate powerful classes of bounded-depth circuits, implying that even slightly super-constant lower bounds for the congestedClique would give new lower bounds in circuit complexity.
References
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Book
Perceptrons: An Introduction to Computational Geometry
Marvin Minsky,Seymour A. Papert +1 more
TL;DR: The aim of this book is to seek general results from the close study of abstract version of devices known as perceptrons.
Proceedings ArticleDOI
Algebraic methods in the theory of lower bounds for Boolean circuit complexity
TL;DR: It is proved that depth k circuits with gates NOT, OR and MODp where p is a prime require Exp(&Ogr;(n1/2k)) gates to calculate MODr functions for any r ≠ pm.
Proceedings ArticleDOI
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
TL;DR: The method of proof is extended to investigate the complexity of the word problem for a fixed permutation group and show that polynomial size circuits of width 4 also recognize exactly nonuniform NC 1.