# On the computational power of neural nets

@inproceedings{Siegelmann1992OnTC, title={On the computational power of neural nets}, author={Hava T. Siegelmann and Eduardo Sontag}, booktitle={COLT '92}, year={1992} }

This paper deals with finite networks which consist of interconnections of synchronously evolving processors. Each processor updates its state by applying a “sigmoidal” scalar nonlinearity to a linear combination of the previous states of all units. We prove that one may simulate all Turing Machines by rational nets. In particular, one can do this in linear time, and there is a net made up of about 1,000 processors which computes a universal partial-recursive function. Products (high order nets…

## 114 Citations

RECURRENT NEURAL NETWORKS AND FINITE AUTOMATA

- Computer ScienceComput. Intell.
- 1996

Finite size networks that consist of interconnections of synchronously evolving processors are studied to prove that any function for which the left and right limits exist can be applied to the neurons to yield a network which is at least as strong computationally as a finite automaton.

Analog computation via neural networks

- Computer Science[1993] The 2nd Israel Symposium on Theory and Computing Systems
- 1993

The authors pursue a particular approach to analog computation, based on dynamical systems of the type used in neural networks research, which exhibit at least some robustness with respect to noise and implementation errors.

Turing's analysis of computation and artificial neural networks

- Computer ScienceJ. Intell. Fuzzy Syst.
- 2002

The proposed simulation is in agreement with the correct interpretation of Turing's analysis of computation; compatible with the current approaches to analyze cognition as an interactive agent-environment process; and physically realizable since it does not use connection weights with unbounded precision.

Computational Power of Neuroidal Nets

- Computer ScienceSOFSEM
- 1999

It is shown that the computational power of neuroidal nets crucially depends on the size of allowable weights, and that the former nets are computationally equivalent to standard, non-programmable discrete neural nets, while, quite surprisingly, the latter nets are computation equivalent to a certain kind of analog neural nets.

Some structural complexity aspects of neural computation

- Computer Science[1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference
- 1993

Connections to space-bounded classes, simulation of parallel computational models such as Vector Machines, and a discussion of the characterizations of various nonuniform classes in terms of Kolmogorov complexity are presented.

The Power of Extra Analog Neuron

- Computer ScienceTPNC
- 2014

A finite automaton with a register is introduced which is shown to be computationally equivalent to a hybrid binary-state network with an extra analog unit and a sufficient condition for a language accepted by this automaton to be regular is found.

Neural networks between integer and rational weights

- Computer Science2017 International Joint Conference on Neural Networks (IJCNN)
- 2017

An intermediate model of binary-state neural networks with integer weights, corresponding to finite automata, is studied, which is extended with an extra analog unit with rational weights, as already two additional analog units allow for Turing universality.

Computational power of neural networks: a Kolmogorov complexity characterization

- Computer Science
- 1993

This work proves that the Kolmogorov complexity of the weights of neural networks is infinite, and shows that neural networks can be classified into an infinite hierarchy of different computing capabilities.

On the Computational Power of Recurrent Neural Networks for Structures

- Computer ScienceNeural Networks
- 1997

Foundations of recurrent neural networks

- Computer Science
- 1993

This dissertation focuses on the "recurrent network" model, in which the underlying graph is not subject to any constraints, and establishes a precise correspondence between the mathematical and computing choices.

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