On the Circuit Complexity of Sigmoid Feedforward Neural Networks

 BEIU Valeriu
 King's College London

 TAYLOR John G.
 King's College London
Search this Article
Author(s)

 BEIU Valeriu
 King's College London

 TAYLOR John G.
 King's College London
Journal

 Neural networks : the official journal of the International Neural Network Society

Neural networks : the official journal of the International Neural Network Society 9(7), 11551171, 19961001
References: 57

1
 Complexity in neural systems

ABUMOSTAFA Y.
Analog VLSI and neural systems, 353358, 1989
Cited by (1)

2
 On boundeddepth threshold circuits for pattern functions

ALBRECHT A.
Proceedings of the International Conference on Artificial Neural Networks ICANN'92, 135138, 1992
Cited by (1)

3
 <no title>

ALON N.
Explicit construction of depth2 majority circuits for comparison and addition, 1991
Cited by (1)

4
 Constant fanin digital neural networks are VLSIoptimal

BEIU V.
1st International Conference on Mathematics of Neural Networks and Applications MANNA '95, 1995
Cited by (1)

5
 <no title>

BEIU V.
VLSI complexity of discrete neural networks, 1996
Cited by (1)

6
 Efficient decomposition of comparison and its applications

BEIU V.
ESANN'93, Proceedings of the European Symposium on Artificial Neural Networks, 4550, 1993
Cited by (1)

7
 Comparison and threshold gate decomposition

BEIU V.
MicroNeuro'93 Microelectronics for Neural Networks, 8390, 1993
Cited by (1)

8
 Overview of some efficient threshold gate decomposition algorithms

BEIU V.
Proceedings of the 9th International Conference on Control System and Computer Science CSCS'9, 458469, 1993
Cited by (1)

9
 Areatime performances of some neural computations

BEIU V.
Proceedings of the IMACS International Symposium on Signal Processing Robotics and Neural Networks SPRANN'94, 664668, 1994
Cited by (1)

10
 On the circuit complexity of feedforward neural networks

BEIU V.
Proceedings of the International Conference on Artificial Neural Networks ICANN'94, 521524, 1994
Cited by (1)

11
 Optimal parallel ADDITION means constant fanin threshold gates

BEIU V.
Proceedings of the 1st International Conference on Technical Informatics ConTI'94 5, 166177, 1994
Cited by (1)

12
 <no title>

GOLDMANN J.
Simulating threshold circuits by majority circuits, 551560, 1994
Cited by (1)

13
 VLSI design of highspeed, lowarea addition circuitry

HAN T.
Proceedings of the International Conference on Circuit Design ICCD'87, 418422, 1987
Cited by (1)

14
 <no title>

HONG J.
On connectionist models, 1987
Cited by (2)

15
 <no title>

HU S.
Threshold logic, 1965
Cited by (2)

16
 Asymptotic estimation of addition time of a parallel adder

KRAPCHENKO V. M.
Problemy Kibernetiki 19, 107122, 1967
Cited by (1)

17
 <no title>

LEWIS P. M.
Threshold logic, 1967
Cited by (2)

18
 On a method of circuit synthesis

LUPANOV O. B.
Izvestia VUZ (Radiofizika) 1, 120140, 1958
Cited by (1)

19
 Implementing the algebra of logic functions in terms of bounded depth formulas in the basis +, , *

LUPANOV O. B.
Soviet Physics Doklady 6(2), 109122, 1961
Cited by (1)

20
 On the power of networks of majority functions. In Lecture Notes in Computer Science 540

MAYORAZ E.
Proceedings of the International Workshop on Artificial Neural Networks IWANN'91, 7885, 1991
Cited by (1)

21
 The synthesis of networks from threshold elements

NECIPORUK E. I.
Problemy Kibernetiki 11, 4962, 1964
Cited by (1)

22
 <no title>

PARBERRY I.
Circuit Complexity and Neural Networks, 1994
Cited by (5)

23
 Optimal carry save networks

PATERSON M. S.
Boolean Function Complexity, 174201, 1992
Cited by (1)

24
 <no title>

RAGHAVAN P.
Learning in threshold networks: a computational model and applications, 1988
Cited by (1)

25
 Probabilistic communication complexity of Boolean relations

RAZ R.
Proceedings of the 30th IEEE Foundations on Computer Science, 562567, 1989
Cited by (1)

26
 Monotone circuits for matching require linear depth

RAZ R.
Proceedings of the 22nd ACM Symposium on the Theory of Computing, 287292, 1990
Cited by (1)

27
 Application of matrix methods to the theory of lower bounds in computational complexity

RAZBOROV A. A.
Combinatorica 10(1), 8193, 1990
Cited by (1)

28
 On small depth threshold circuits. In Lecture Notes in Computer Science 621

RAZBOROV A. A.
Proceedings of the 3rd Scandinavian Workshop on Algorithm Theory, 4252, 1992
Cited by (1)

29
 On submodular complexity measures

RAZBOROV A. A.
Boolean function complexity, 7683, 1992
Cited by (1)

30
 On the circuit complexity of neural networks

ROYCHOWDHURY V. P.
Advances in Neural Information Processing Systems 3, Proceedings of NIPS'90, 953959, 1991
Cited by (1)

31
 On the complexity of neural networks with sigmoid units

SIU K. Y.
Neural Networks for Signal Processing IIProceedings of the IEEESP Workshop on Neural Networks and Signal Processing {NN}SP92, 2328, 1992
Cited by (1)

32
 <no title>

SIU K.Y.
Computing with almost optimal size threshold circuits, 1990
Cited by (2)

33
 Training a limitedinterconnect, synthetic neural IC

WALKER M. R.
Advances in Neural Information Processing Systems 1, Proceedings of NIPS'88, 777784, 1989
Cited by (1)

34
 <no title>

WEGENER I.
The Complexity of Boolean Functions, 1987
Cited by (10)

35
 <no title>

WEGENER I.
Advances in the theory of computation and computational mathematics, 1990
Cited by (1)

36
 εEntropy and the complexity of feedforward neural networks

WILLIAMSON R. C.
Advances in Neural Information Processing Systems 3, Proceedings of NIPS'90, 946952, 1991
Cited by (1)

37
 The Monotone Circuit Complexity of Boolean Functions

ALON N.
Combinatorica 7(1), 122, 1987
DOI Cited by (5)

38
 A comparison study of binary feedforward neural networks and digital circuits

ANDREE H. M.
Neural Networks 6(6), 758790, 1993
Cited by (1)

39
 A regular layout for parallel adders

BRENT R. P.
IEEE Trans. Comput. C31(3), 260264, 1982
DOI Cited by (43)

40
 Harmonic analysis of polynomial threshold functions

BRUCK J.
SIAM Journal on Discrete Mathematics 3(2), 168177, 1990
DOI Cited by (4)

41
 Polynomial threshold functions, ac^0 functions and spectral norms

BRUCK J.
SIAM Journal on Discrete Mathematics 21, 3342, 1992
Cited by (3)

42
 Constant depth reducibility

CHANDRA A. K.
SIAM Journal on Computing 13(2), 423539, 1984
Cited by (1)

43
 Delay optimization of carryskip adders and block carrylookahead adders using multidimensional programming

CHANG P. K.
IEEE Transactions on Computers 41(8), 920930, 1992
Cited by (1)

44
 Majority Gates vs. General Weighted Threshold Gates

GOLDMANN J.
Computational Complexity 2, 277300, 1992
DOI Cited by (3)

45
 Some notes on threshold circuits and multiplication in depth 4

HOFMEISTER T.
Information Processing Letters 39(4), 219226, 1991
Cited by (1)

46
 ELMa fast addition algorithm discovered by a program

KELLIHER T. P.
IEEE Trans. on Computers, 1992
Cited by (2)

47
 Parallel prefix computation

LADNER R. E.
J. ACM 27, 831838, 1975
DOI Cited by (21)

48
 Modelling the complexity of parallel and VLSI computations with Boolean circuits

PAPADOPOULOS C. V.
Microprocessors and Microsystems 19(1), 4350, 1995
Cited by (1)

49
 Lower bounds on threshold and related circuits via communication complexity

ROYCHOWDHURY V. P.
IEEE Transactions on Information Theory 40(2), 467474, 1994
Cited by (2)

50
 Classes of feedforward neural nets and their circuit complexity

SHAWETAYLOR J. S.
Neural Networks 5(6), 971977, 1992
Cited by (1)

51
 Neural computation of arithmetic functions

SIU K. Y.
Proceedings of the IEEE 78(10), 16691675, 1990
Cited by (2)

52
 On the Power of Threshold Circuits with Small Weights

SIU K. Y.
SIAM J. Disc. Math. 4(3), 423435, 1991
DOI Cited by (4)

53
 Depthsize tradeoffs for neural computations

SIU K. Y.
IEEE Transactions on Computers 40(12), 14021412, 1991
Cited by (1)

54
 Rational approximation techniques for analysis of neural networks

SIU K. Y.
IEEE Trans. Inf. Theory 40(2), 455466, 1994
Cited by (4)

55
 Algebraic methods in the theory of lower bounds for Boolean circuit complexity

SMOLENSKY R.
Proceedings of the 19th Annual ACM Symposium on Theory of Computing, 1987, 7782, 1987
Cited by (3)

56
 Optimal lower bounds on the depth of polynomialsize threshold circuits for some arithmetic function

WEGENER I.
Infor. Process. Lett. 46, 8587, 1993
Cited by (3)

57
 Areatime optimal adder design

WEI B. W. Y.
IEEE Transactions on Computers 39(5), 666675, 1990
Cited by (1)