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Stochastic Analog Networks and Computational Complexity

Hava T. Siegelmann
1999 Journal of Complexity  
In the general case the computational class (PÂpoly) is associated with both deterministic and stochastic networks.  ...  The model of analog recurrent neural networks (ARNN) is typically perceived as based on either the practical powerful tool of automatic learning or on biological metaphors, yet it constitutes an appealing  ...  This work was funded by the Israeli Ministry of Art and Sciences, the Binational U.S.ÂIsrael Foundation, the fund for promotion of research at the Technion, and the VPR fund at the Technion.  ... 
doi:10.1006/jcom.1999.0505 fatcat:usi7n47xaja7xb52i3yikfvxhq

Noise optimizes super-Turing computation in recurrent neural networks

Emmett Redd, Steven Senger, Tayo Obafemi-Ajayi
2021 Physical Review Research  
This paper explores the benefit of added noise in increasing the computational complexity of digital recurrent neural networks (RNNs).  ...  The physically accepted model of the universe imposes rational number, stochastic limits on all calculations. An analog RNN with those limits calculates at the super-Turing complexity level BPP/log*.  ...  Nonetheless, the finite estimated advice is physically possible and the rational, stochastic neuron analog RNN can compute at a super-Turing complexity of BPP/log*.  ... 
doi:10.1103/physrevresearch.3.013120 fatcat:k7q2x4olgvafvkcvgtnhphrsre

XtokaxtikoX: A stochastic computing-based autonomous cyber-physical system

Rui Policarpo Duarte, Horacio Neto, Mario Vestias
2016 2016 IEEE International Conference on Rebooting Computing (ICRC)  
Conversely, the proposed work is able to directly translate analog signals into stochastic bitstreams, process the stochastic bitstreams and finally control analog actuators relying only on the information  ...  Traditional implementations of stochastic computing systems benefit from fast and compact implementation of arithmetic operators, and high tolerance to errors, but depend heavily on the conversion between  ...  INTRODUCTION Low resource consumption and complexity implementation of arithmetic operators, high resilience to errors, and high performance of Stochastic Computing has attracted a lot of interest from  ... 
doi:10.1109/icrc.2016.7738716 dblp:conf/icrc/DuarteNV16 fatcat:24h5cg7x65aoblgrkwh45f4o5y

Probabilistic computation by neuromine networks

R.D. Hangartner, P. Cull
2000 Biosystems (Amsterdam. Print)  
ON and which neuron will be OFF will be chosen at random (perhaps, it would be better to say that microscopic noise in the analog computation will be turned into a megascale random bit).  ...  Since we want to maintain a claim of plausibility and reasonableness we restrict ourselves to algorithmically easy to construct nets and we rule out infinite precision in parameters and in any analog parts  ...  The stochastic analog network model The model derived in Hangartner (1994) approximates the mean dynamics of a biological-inspired, homogeneous recurrent stochastic pulse neuromime network by a stochastic  ... 
doi:10.1016/s0303-2647(00)00120-9 pmid:11164644 fatcat:67yf54l63vanfgrwmxyf4o2kgi

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Hava T. Siegelmann
2012 Minds and Machines  
Our analog neural network allows for supra-Turing power while keeping track of computational constraints, and thus embeds a possible answer to the superiority of the biological intelligence within the  ...  In particular an analog of the Church-Turing thesis of digital computation is stated where the neural network takes place of the Turing machine.  ...  Comment on Stochastic Analog Neural Networks It is interesting to consider what happens to the analog networks when they exhibit stochastic and random behavior.  ... 
doi:10.1023/a:1021376718708 fatcat:zgqiws34c5danpy4tf3frjc5r4

Memory System Designed for Multiply-Accumulate (MAC) Engine Based on Stochastic Computing [article]

Xinyue Zhang, Yuan Wang, Yawen Zhang, Jiahao Song, Zuodong Zhang, Kaili Cheng, Runsheng Wang, Ru Huang
2019 arXiv   pre-print
Stochastic computing (SC) is an attractive paradigm implemented in low power applications which performs arithmetic operations with simple logic and low hardware cost.  ...  Convolutional neural network (CNN) achieves excellent performance on fascinating tasks such as image recognition and natural language processing at the cost of high power consumption.  ...  State-of-the-art performances are achieved on various tasks through CNN solutions but at the cost of high computational complexity and power consumption [2] .  ... 
arXiv:1904.10242v1 fatcat:4xkkdmpwynabtke5tufljc33o4

Emergence of direction- and orientation-selectivity and other complex structures from stochastic neuronal networks evolving under STDP

Nana Arizumi, Todd Coleman, Lee DeVille
2011 BMC Neuroscience  
Our computational model generates several interesting features; e.g. orientation-and direction-selectivity when the inputs are arranged in a manner analogous to a visual field.  ...  Our model is a discrete-time Markov chain which contains multiple excitatory and inhibitory input neurons, and has as outputs stochastic leaky integrate-and-fire neurons; the system evolves through the  ...  Our computational model generates several interesting features; e.g. orientation-and direction-selectivity when the inputs are arranged in a manner analogous to a visual field.  ... 
doi:10.1186/1471-2202-12-s1-p68 pmcid:PMC3240537 fatcat:x7hsq7uqeffdnhmaeqbm4wqnpa

R68-17 Synthesis of Resistive Digital-to-Analog Conversion Ladders for Arbitrary Codes with Fixed Positive Weights

C.F. Crocker
1968 IEEE transactions on computers  
also by a three-dimensional network of resistors.  ...  purpose of the investigation reported in this paper was to test the feasibility of solving Laplace's equation in a three-dimensional region having asymmetric boundaries by means of an electrolytic tank and  ...  The paper is instructive and of interest to those involved in the design of digital-to-analog converters or analog computers.  ... 
doi:10.1109/tc.1968.226900 fatcat:gndnuiluwjbyzn7mo6elqzdq44

Page 7438 of Mathematical Reviews Vol. , Issue 90M [page]

1990 Mathematical Reviews  
We discuss here the role of these analogies for constructing a qualitative mathematical background for studying complex queueing networks.”  ...  networks with unsymmetric stochastic capacity constraints.  ... 

Table of Contents

2020 IEEE Circuits and Systems Magazine  
Content also covers the areas represented by the Society technical committees: analog signal processing, cellular neural networks and array computing, circuits and systems for communications, computer-aided  ...  : analog, passive, switch capacitor, and digital filters; electronic circuits, networks, graph theory, and RF communication circuits; system theory; discrete, IC, and VLSI circuit design; multidimensional  ...  Introduction to Dynamic Stochastic Computing Siting Liu, Warren J.  ... 
doi:10.1109/mcas.2020.3005466 fatcat:bnf5w7kgxjhofavtlf7dbfmxku

A digital architecture employing stochasticism for the simulation of Hopfield neural nets

D.E. Van Den Bout, T.K. Miller
1989 IEEE Transactions on Circuits and Systems  
Results of simulations are given which show the stochastic architecture gives results similar to those found using standard analog neural networks or simulated annealing.  ...  expMdability (by cascading of multiple chips to host large networks), and practiculity (by building with very conservative MOS device technologies).  ...  The stochastic architecture offers a good compromise between the high speed of dedicated analog VLSI networks and the flexibility of a general-purpose computer.  ... 
doi:10.1109/31.31321 fatcat:xblswhcdg5gx7ngpbz4ijfrbxq

Page 3956 of Mathematical Reviews Vol. , Issue 92g [page]

1992 Mathematical Reviews  
Complex Systems 4 (1990), no. 5, 509-518. Summary: “Determining just what tasks are computable by neu- ral networks is of fundamental importance in neural computing.  ...  Complex Systems 3 (1989), no. 1, 29-36. 92g:68103b 68Q80 92B20 Franklin, Stan; Garzon, Max Erratum: “Global dynamics in neural networks”. Complex Systems 5 (1991), no. 1, 101.  ... 

Quantum stochasticity and neuronal computations

Peter Jedlicka, Peter Jedlicka
2009 Nature Precedings  
I am going to discuss recent theoretical proposals and experimental findings in quantum mechanics, complexity theory and computational neuroscience suggesting that biological evolution is able to take  ...  In this way stochastic quantum dynamics might sometimes alter the outcome of neuronal computations, not by generating classically impossible solutions, but by influencing the selection of many possible  ...  • The only intrinsically (objectively) stochastic (indeterministic) processes in physical world are quantum processes • Does quantum indeterminism affect the dynamics of neuronal networks?  ... 
doi:10.1038/npre.2009.3702 fatcat:wbungqsnzzfblntbw3liw7ggvu

Analog Computational Power

H. T. Siegelmann
1996 Science  
Shor questions the nature of the advice used in analog computation, or equivalently, the real weights in the neural networks model.  ...  METECHNICAL COMMENTS Analog Computational Power Response: Peter Shor (1) and Richard Y. Kain (2) recently commented on my report "Computation Beyond the Turing Limit" (3) .  ... 
doi:10.1126/science.271.5247.373 fatcat:axrjz52eibcaxbkmwih6qnox6e

Analog Signal Processing Using Stochastic Magnets [article]

Samiran Ganguly, Kerem Y. Camsari, Avik W. Ghosh
2018 arXiv   pre-print
We present a low barrier magnet based compact hardware unit for analog stochastic neurons and demonstrate its use as a building-block for neuromorphic hardware.  ...  By coupling circular magnetic tunnel junctions (MTJs) with a CMOS based analog buffer, we show that these units can act as leaky-integrate-and fire (LIF) neurons, a model of biological neural networks  ...  SIGNAL PROCESSING USING ANALOG STOCHASTIC NEURON (ASN) NETWORKS A.  ... 
arXiv:1812.08273v1 fatcat:vgzkgfmotrfjhiaajvpqjo4dui
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