Log depth circuits for division and related problems
SIAM Journal on Computing
The complexity of Boolean functions
The complexity of Boolean functions
A geometric approach to threshold circuit complexity
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
On the circuit complexity of neural networks
NIPS-3 Proceedings of the 1990 conference on Advances in neural information processing systems 3
Bounds to Complexities of Networks for Sorting and for Switching
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Unbounded fan-in circuits and associative functions
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Two problems in concrete complexity: cycle detection and parallel prefix computation
Two problems in concrete complexity: cycle detection and parallel prefix computation
The complexity of computations by networks
IBM Journal of Research and Development - Mathematics and computing
Depth efficient neural networks for division and related problems
IEEE Transactions on Information Theory
2-1 Addition and Related Arithmetic Operations with Threshold Logic
IEEE Transactions on Computers
Deeper Sparsely Nets can be Optimal
Neural Processing Letters
A Constructive Approach to Calculating Lower Entropy Bounds
Neural Processing Letters
Two Operand Binary Adders with Threshold Logic
IEEE Transactions on Computers
Signed Digit Addition and Related Operations with Threshold Logic
IEEE Transactions on Computers
An Architecture for Computing Zech's Logarithms in GF(2m)
IEEE Transactions on Computers
Three-Dimensional Feedforward Neural Networks and Their Realization by Nano-Devices
Artificial Intelligence Review
On the Computational Power of Max-Min Propagation Neural Networks
Neural Processing Letters
Three-dimensional feedforward neural networks and their realization by nano-devices
Artificial intelligence in logic design
IEEE Transactions on Neural Networks
Constructive threshold logic addition: a synopsis of the last decade
ICANN/ICONIP'03 Proceedings of the 2003 joint international conference on Artificial neural networks and neural information processing
Neural network architecture selection: size depends on function complexity
ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part I
Optimal synthesis of boolean functions by threshold functions
ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part I
Role of function complexity and network size in the generalization ability of feedforward networks
IWANN'05 Proceedings of the 8th international conference on Artificial Neural Networks: computational Intelligence and Bioinspired Systems
Design tools for artificial nervous systems
Proceedings of the 49th Annual Design Automation Conference
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The tradeoffs between the depth (i.e., the time for parallel computation) and the size (i.e., the number of threshold gates) in neural networks are studied. The authors focus the study on the neural computations of symmetric Boolean functions and some arithmetic functions. It is shown that a significant reduction in the size is possible for symmetric functions and some arithmetic functions, at the expense of a small constant increase in depth. In the process, several neural networks which have the minimum size among all the known constructions have been developed. Results on implementing symmetric functions can be used to improve results about arbitrary Boolean functions. In particular, it is shown that any Boolean function can be computed in a depth-3 neural network with O(2/sup n/ /sup 2/) threshold gates; it is also proven that at least Omega (2/sup n/ /sup 3/) threshold gates are required.