Hopfield model applied to vowel and consonant discrimination
AIP Conference Proceedings 151 on Neural Networks for Computing
The complexity of Boolean functions
The complexity of Boolean functions
Bidirectional associative memories
IEEE Transactions on Systems, Man and Cybernetics
Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing
Circuit complexity and neural networks
Circuit complexity and neural networks
Analog computation via neural networks
Theoretical Computer Science
Discrete neural computation: a theoretical foundation
Discrete neural computation: a theoretical foundation
On the computational power of neural nets
Journal of Computer and System Sciences
Neural networks: a systematic introduction
Neural networks: a systematic introduction
Symmetric discrete universal neural networks
Theoretical Computer Science - Special issue on universal machines and computations
Approximability of the ground state problem for certain Ising spin glasses
Journal of Complexity
Journal of the ACM (JACM)
On the effect of analog noise in discrete-time analog computations
Neural Computation
Neural networks and analog computation: beyond the Turing limit
Neural networks and analog computation: beyond the Turing limit
A Recurrent Neural Network for N-Stage Optimal Control Problems
Neural Processing Letters
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
SOFSEM '95 Proceedings of the 22nd Seminar on Current Trends in Theory and Practice of Informatics
Some Afterthoughts on Hopfield Networks
SOFSEM '99 Proceedings of the 26th Conference on Current Trends in Theory and Practice of Informatics on Theory and Practice of Informatics
Derandomizing semidefinite programming based approximation algorithms
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
The computational power of discrete hopfield nets with hidden units
Neural Computation
Computational power of neural networks: a characterization in terms of Kolmogorov complexity
IEEE Transactions on Information Theory
Computing with continuous-time Liapunov systems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Exponential Transients in Continuous-Time Symmetric Hopfield Nets
ICANN '01 Proceedings of the International Conference on Artificial Neural Networks
Continuous-time symmetric Hopfield nets are computationally universal
Neural Computation
Exponential transients in continuous-time Liapunov systems
Theoretical Computer Science
A Discrete-Time Quantized-State Hopfield Neural Network
Annals of Mathematics and Artificial Intelligence
Evolutionary Bi-objective Learning with Lowest Complexity in Neural Networks: Empirical Comparisons
ICANNGA '07 Proceedings of the 8th international conference on Adaptive and Natural Computing Algorithms, Part I
Hi-index | 0.00 |
We investigate the computational properties of finite binary- and analog-state discrete-time symmetric Hopfield nets. For binary networks, we obtain a simulation of convergent asymmetric networks by symmetric networks with only a linear increase in network size and computation time. Then we analyze the convergence time of Hopfield nets in terms of the length of their bit representations. Here we construct an analog symmetric network whose convergence time exceeds the convergence time of any binary Hopfield net with the same representation length. Further, we prove that the MIN ENERGY problem for analog Hopfield nets is NP-hard and provide a polynomial time approximation algorithm for this problem in the case of binary nets. Finally, we show that symmetric analog nets with an external clock are computationally Turing universal.