On the capabilities of neural networks using limited precision weights

[1]  Valeriu Beiu,et al.  A Constructive Approach to Calculating Lower Entropy Bounds , 1999, Neural Processing Letters.

[2]  Valeriu Beiu,et al.  Deeper Sparsely Nets can be Optimal , 1998, Neural Processing Letters.

[3]  Valeriu Beiu,et al.  On VLSI-Optimal Neural Computations , 2002 .

[4]  Valeriu Beiu,et al.  On higher order noise immune perceptrons , 2001, IJCNN'01. International Joint Conference on Neural Networks. Proceedings (Cat. No.01CH37222).

[5]  Sorin Draghici,et al.  The constraint based decomposition (CBD) training architecture , 2001, Neural Networks.

[6]  Alan F. Murray,et al.  IEEE International Solid-State Circuits Conference , 2001 .

[7]  Valeriu Beiu,et al.  High-speed noise robust threshold gates , 2000, 2000 International Semiconductor Conference. 23rd Edition. CAS 2000 Proceedings (Cat. No.00TH8486).

[8]  V. Beiu,et al.  Ultra-fast noise immune CMOS threshold logic gates , 2000, Proceedings of the 43rd IEEE Midwest Symposium on Circuits and Systems (Cat.No.CH37144).

[9]  Sorin Draghici,et al.  Neural Networks in Analog Hardware - Design and Implementation Issues , 2000, Int. J. Neural Syst..

[10]  Aapo Hyvärinen,et al.  A Fast Fixed-Point Algorithm for Independent Component Analysis of Complex Valued Signals , 2000, Int. J. Neural Syst..

[11]  C. Yeh,et al.  Optimal-depth threshold circuits for multiplication and related problems , 1999, Conference Record of the Thirty-Third Asilomar Conference on Signals, Systems, and Computers (Cat. No.CH37020).

[12]  H. Suyari,et al.  Information theoretical approach to the storage capacity of neural networks with binary weights. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Taher Daud,et al.  Cascade Error Projection: A Learning Algorithm for Hardware Implementation , 1999, IWANN.

[14]  Tor Sverre Lande,et al.  Neuromorphic systems engineering: neural networks in silicon , 1998 .

[15]  Gert Cauwenberghs,et al.  Neuromorphic learning VLSI systems: a survey , 1998 .

[16]  Valeriu Beiu,et al.  On the circuit and VLSI complexity of threshold gate COMPARISON , 1998, Neurocomputing.

[17]  Indu Saxena,et al.  Discrete All-Positive Multilayer Perceptrons for Optical Implementation , 1998 .

[18]  Marek Karpinski,et al.  Simulating threshold circuits by majority circuits , 1993, SIAM J. Comput..

[19]  Tor Sverre Lande,et al.  Neuromorphic Systems Engineering , 1998 .

[20]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[21]  Valeriu Beiu,et al.  On limited fan-in optimal neural networks , 1997, Proceedings 4th Brazilian Symposium on Neural Networks.

[22]  Valeriu Beiu,et al.  A VLSI optimal constructive algorithm for classification problems , 1997 .

[23]  Michael E. Saks,et al.  Size-depth trade-offs for threshold circuits , 1993, SIAM J. Comput..

[24]  S. Drăghici,et al.  Limited weights neural networks: Very tight entropy based bounds , 1997 .

[25]  A. Engel,et al.  VAPNIK-CHERVONENKIS DIMENSION OF NEURAL NETWORKS WITH BINARY WEIGHTS , 1996, cond-mat/9608156.

[26]  David A. Sprecher,et al.  A Numerical Implementation of Kolmogorov's Superpositions II , 1996, Neural Networks.

[27]  Eduardo D. Sontag,et al.  Neural Networks with Quadratic VC Dimension , 1995, J. Comput. Syst. Sci..

[28]  Emile Fiesler,et al.  Neural Network Adaptations to Hardware Implementations , 1997 .

[29]  Valeriu Beiu,et al.  On the Circuit Complexity of Sigmoid Feedforward Neural Networks , 1996, Neural Networks.

[30]  Russell Beale,et al.  Handbook of Neural Computation , 1996 .

[31]  Taher Daud,et al.  Learning in neural networks: VLSI implementation strategies , 1996 .

[32]  M. A. Jabri,et al.  Adaptive Analog VLSI Neural Systems , 1995, Springer Netherlands.

[33]  David A. Sprecher,et al.  A Numerical Implementation of Kolmogorov's Superpositions , 1996, Neural Networks.

[34]  Emile Fiesler,et al.  Connectionist Quantization Functions , 1996 .

[35]  V. Beiu,et al.  Constant fan-in digital neural networks are VLSI-optimal , 1995 .

[36]  D. Signorini,et al.  Neural networks , 1995, The Lancet.

[37]  Günhan Dündar,et al.  The effects of quantization on multilayer neural networks , 1995, IEEE Trans. Neural Networks.

[38]  H T Siegelmann,et al.  Dating and Context of Three Middle Stone Age Sites with Bone Points in the Upper Semliki Valley, Zaire , 2007 .

[39]  Andreas Alexander Albrecht,et al.  On Lower Bounds for the Depth of Threshold Circuits with Weights from {-1, 0, +1} , 1995, GOSLER Final Report.

[40]  Don R. Hush,et al.  On the node complexity of neural networks , 1994, Neural Networks.

[41]  John J. Paulos,et al.  A neural network learning algorithm tailored for VLSI implementation , 1994, IEEE Trans. Neural Networks.

[42]  Joos Vandewalle,et al.  On the Circuit Complexity of Feedforward Neural Networks , 1994 .

[43]  Kai-Yeung Siu,et al.  On Optimal Depth Threshold Circuits for Multiplication and Related Problems , 1994, SIAM J. Discret. Math..

[44]  Noga Alon,et al.  Explicit Constructions of Depth-2 Majority Circuits for Comparison and Addition , 1994, SIAM J. Discret. Math..

[45]  Johan Håstad,et al.  Optimal Depth, Very Small Size Circuits for Symmetric Functions in AC0 , 1994, Inf. Comput..

[46]  Ian Parberry,et al.  Circuit complexity and neural networks , 1994 .

[47]  Manfred Glesner,et al.  Neurocomputers: an overview of neural networks in VLSI , 1994 .

[48]  Marwan A. Jabri,et al.  WATTLE: A Trainable Gain Analogue VLSI Neural Network , 1993, NIPS.

[49]  Patrice Y. Simard,et al.  Backpropagation without Multiplication , 1993, NIPS.

[50]  Hon Keung Kwan,et al.  Multilayer feedforward neural networks with single powers-of-two weights , 1993, IEEE Trans. Signal Process..

[51]  Hon Keung Kwan,et al.  Multiplierless multilayer feedforward neural network design suitable for continuous input-output mapping , 1993 .

[52]  Michael E. Saks,et al.  Size-depth trade-offs for threshold circuits , 1993, STOC.

[53]  Ingo Wegener,et al.  Optimal Lower Bounds on the Depth of Polynomial-Size Threshold Circuits for Some Arithmetic Functions , 1993, Inf. Process. Lett..

[54]  Yuzo Hirai,et al.  Hardware implementation of neural networks in Japan , 1993, Neurocomputing.

[55]  David A. Sprecher,et al.  A universal mapping for kolmogorov's superposition theorem , 1993, Neural Networks.

[56]  R. Meir,et al.  On the precision constraints of threshold elements , 1993 .

[57]  Francesco Piazza,et al.  Fast neural networks without multipliers , 1993, IEEE Trans. Neural Networks.

[58]  Hon Keung Kwan,et al.  Designing multilayer feedforward neural networks using simplified sigmoid activation functions and one-powers-of-two weights , 1992 .

[59]  Thomas Kailath,et al.  Computing with Almost Optimal Size Neural Networks , 1992, NIPS.

[60]  Kai-Yeung Siu,et al.  Optimal Depth Neural Networks for Multiplication and Related Problems , 1992, NIPS.

[61]  Marwan A. Jabri,et al.  Summed Weight Neuron Perturbation: An O(N) Improvement Over Weight Perturbation , 1992, NIPS.

[62]  Gert Cauwenberghs,et al.  A Fast Stochastic Error-Descent Algorithm for Supervised Learning and Optimization , 1992, NIPS.

[63]  Rudy Lauwereins,et al.  Simpler Neural Networks by Fan-In Reduction , 1992 .

[64]  Alexander A. Razborov,et al.  On Small Depth Threshold Circuits , 1992, SWAT.

[65]  Markus Höhfeld,et al.  Learning with limited numerical precision using the cascade-correlation algorithm , 1992, IEEE Trans. Neural Networks.

[66]  Alexander A. Razborov,et al.  Majority gates vs. general weighted threshold gates , 1992, [1992] Proceedings of the Seventh Annual Structure in Complexity Theory Conference.

[67]  Michael Kearns,et al.  Bounds on the sample complexity of Bayesian learning using information theory and the VC dimension , 1992, [Proceedings 1992] IJCNN International Joint Conference on Neural Networks.

[68]  John M. Zelle,et al.  Growing layers of perceptrons: introducing the Extentron algorithm , 1992, [Proceedings 1992] IJCNN International Joint Conference on Neural Networks.

[69]  Jehoshua Bruck,et al.  Polynomial Threshold Functions, AC^0 Functions, and Spectral Norms , 1992, SIAM J. Comput..

[70]  Vladimir Vapnik,et al.  Principles of Risk Minimization for Learning Theory , 1991, NIPS.

[71]  Thomas Kailath,et al.  Depth-Size Tradeoffs for Neural Computation , 1991, IEEE Trans. Computers.

[72]  Leonardo Maria Reyneri,et al.  An Analysis on the Performance of Silicon Implementations of Backpropagation Algorithms for Artificial Neural Networks , 1991, IEEE Trans. Computers.

[73]  Eddy Mayoraz,et al.  On the Power of Networks of Majority Functions , 1991, IWANN.

[74]  Christos H. Papadimitriou,et al.  Proceedings of the 32nd annual symposium on Foundations of computer science , 1991 .

[75]  Thomas Hofmeister,et al.  Some Notes on Threshold Circuits, and Multiplication in Depth 4 , 1991, Inf. Process. Lett..

[76]  Richard Beigel,et al.  On ACC (circuit complexity) , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[77]  T. Kailath,et al.  Computing With Almost Optimal Size Threshold Circuits , 1991, Proceedings. 1991 IEEE International Symposium on Information Theory.

[78]  Jehoshua Bruck,et al.  On The Power Of Threshold Circuits With Small Weights , 1991, Proceedings. 1991 IEEE International Symposium on Information Theory.

[79]  Kurt Hornik,et al.  Approximation capabilities of multilayer feedforward networks , 1991, Neural Networks.

[80]  Marwan A. Jabri,et al.  Weight perturbation: an optimal architecture and learning technique for analog VLSI feedforward and recurrent multilayer networks , 1992, IEEE Trans. Neural Networks.

[81]  Yun Xie Training Algorithms for Limited Precision Feedforward Neural Networks , 1991 .

[82]  Johan Håstad,et al.  On the power of small-depth threshold circuits , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[83]  Jehoshua Bruck,et al.  Neural computation of arithmetic functions , 1990 .

[84]  Kurt Hornik,et al.  Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks , 1990, Neural Networks.

[85]  Mark A. Holler,et al.  VLSI Implementations of Learning and Memory Systems: A Review , 1990, NIPS 1990.

[86]  Bernard Widrow,et al.  30 years of adaptive neural networks: perceptron, Madaline, and backpropagation , 1990, Proc. IEEE.

[87]  John J. Paulos,et al.  The Effects of Precision Constraints in a Backpropagation Learning Network , 1990, Neural Computation.

[88]  H. John Caulfield,et al.  Weight discretization paradigm for optical neural networks , 1990, Other Conferences.

[89]  H. Gutfreund,et al.  Capacity of neural networks with discrete synaptic couplings , 1990 .

[90]  Kenji Nakayama,et al.  A digital multilayer neural network with limited binary expressions , 1990, 1990 IJCNN International Joint Conference on Neural Networks.

[91]  Francesco Piazza,et al.  Multi-layer perceptrons with discrete weights , 1990, 1990 IJCNN International Joint Conference on Neural Networks.

[92]  J. J. Paulos,et al.  Artificial neural networks using MOS analog multipliers , 1990 .

[93]  Jehoshua Bruck,et al.  Harmonic Analysis of Polynomial Threshold Functions , 1990, SIAM J. Discret. Math..

[94]  Nelson Morgan,et al.  Artificial neural networks: electronic implementations—an introduction , 1990 .

[95]  Mark A. Holler,et al.  VLSI Implementations of Learning and Memory Systems , 1990, NIPS.

[96]  H.P. Graf,et al.  A reconfigurable CMOS neural network , 1990, 1990 37th IEEE International Conference on Solid-State Circuits.

[97]  S. Tam,et al.  An electrically trainable artificial neural network (ETANN) with 10240 'floating gate' synapses , 1990, International 1989 Joint Conference on Neural Networks.

[98]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1989, Math. Control. Signals Syst..

[99]  H. White,et al.  Universal approximation using feedforward networks with non-sigmoid hidden layer activation functions , 1989, International 1989 Joint Conference on Neural Networks.

[100]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[101]  Robert O. Grondin,et al.  Limited interconnectivity in synthetic neural systems , 1989 .

[102]  Carver Mead,et al.  Analog VLSI and neural systems , 1989 .

[103]  A. Thakoor,et al.  Design of parallel hardware neural network systems from custom analog VLSI 'building block' chips , 1989, International 1989 Joint Conference on Neural Networks.

[104]  R. Eckmiller,et al.  Neural Computers , 1989, Springer Study Edition.

[105]  David Haussler,et al.  What Size Net Gives Valid Generalization? , 1989, Neural Computation.

[106]  Robert B. Allen,et al.  Performance of a Stochastic Learning Microchip , 1990, NIPS.

[107]  Jia-Wei Hong On connectionist models , 1988 .

[108]  P. Raghavan,et al.  Learning in threshold networks , 1988, COLT '88.

[109]  Lawrence D. Jackel,et al.  VLSI implementation of a neural network model , 1988, Computer.

[110]  Tom Baker,et al.  Modifications to artificial neural networks models for Digital Hardware Implementation , 1988 .

[111]  Dan Hammerstrom,et al.  The Connectivity Analysis of Simple Association - or- How Many Connections Do You Need! , 1988 .

[112]  Joseph W. Goodman,et al.  On the power of neural networks for solving hard problems , 1990, J. Complex..

[113]  J. Yorke,et al.  Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics , 1987, Science.

[114]  Pavel Pudlák,et al.  Threshold circuits of bounded depth , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[115]  Lawrence D. Jackel,et al.  VLSI implementation of a neural network memory with several hundreds of neurons , 1987 .

[116]  R. Hecht-Nielsen Kolmogorov''s Mapping Neural Network Existence Theorem , 1987 .

[117]  Dan W. Hammerstrom,et al.  The Connectivity Analysis of Simple Association , 1987, NIPS.

[118]  Johan Håstad,et al.  Almost optimal lower bounds for small depth circuits , 1986, STOC '86.

[119]  Georg Schnitger,et al.  Parallel Computation with Threshold Functions , 1986, J. Comput. Syst. Sci..

[120]  Uzi Vishkin,et al.  Constant Depth Reducibility , 1984, SIAM J. Comput..

[121]  David J. Hand,et al.  Discrimination and Classification , 1982 .

[122]  Robert O. Winder,et al.  Threshold logic , 1971, IEEE Spectrum.

[123]  Saburo Muroga,et al.  Threshold logic and its applications , 1971 .

[124]  Vladimir Vapnik,et al.  Chervonenkis: On the uniform convergence of relative frequencies of events to their probabilities , 1971 .

[125]  N. P. Red’kin Synthesis of threshold circuits for certain classes of Boolean functions , 1970 .

[126]  Michael L. Dertouzos,et al.  Threshold Logic: A Synthesis Approach , 1965 .

[127]  D. Sprecher On the structure of continuous functions of several variables , 1965 .

[128]  Saburo Muroga,et al.  Lower Bounds of the Number of Threshold Functions and a Maximum Weight , 1962, IEEE Trans. Electron. Comput..

[129]  Robert O. Winder,et al.  Bounds on Threshold Gate Realizability , 1963, IEEE Transactions on Electronic Computers.

[130]  Robert C. Minnick,et al.  Linear-Input Logic , 1961, IRE Trans. Electron. Comput..