Pulse-density modulation technique in VLSI implementations of neural network algorithms

Tomberg, J.; Kaski, Kimmo

doi:10.1109/4.62152

Cited by 73 publications

(12 citation statements)

References 11 publications

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“…This results in the minimum variance of the distribution. The required count interval for a desired precision ( ) is given in this case by (4). Theoretically all possible configurations of the multiplexer must be visited in this case.…”

Section: Discussionmentioning

confidence: 99%

“…The coefficient of variation (CV) is given by (3) We observe that the precision (the inverse of the CV) depends on the Bernoulli probability and improves with increasing signal integration period as . For a given CV the required integration period is given by (4) which increases as the square of the desired precision ( ). Also note that, for a given Bernoulli probability, the required signal integration period is directly proportional to the variance.…”

Section: Sequences Of Bernoulli Eventsmentioning

confidence: 99%

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Compound binomial processes in neural integration

Card

2001

IEEE Trans. Neural Netw.

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Explores some of the properties of stochastic digital signal processing in which the input signals are represented as sequences of Bernoulli events. The event statistics of the resulting stochastic process may be governed by compound binomial processes, depending upon how the individual input variables to a neural network are stochastically multiplexed. Similar doubly stochastic statistics can also result from datasets which are Bernoulli mixtures, depending upon the temporal persistence of the mixture components at the input terminals to the network. The principal contribution of these results is in determining the required integration period of the stochastic signals for a given precision in pulsed digital neural networks.

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Section: Discussionmentioning

confidence: 99%

Section: Sequences Of Bernoulli Eventsmentioning

confidence: 99%

Compound binomial processes in neural integration

Card

2001

IEEE Trans. Neural Netw.

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“…Comparisons of SSP with conventional deterministic implementations of neural networks, in particular those using serial binary radix arithmetic, were also made in [1]. Despite the statistical limitations, as a result of the hardware advantages SSP has been widely employed in the implementation of neural networks, for Manuscript example [5]- [15]. Analog versions of pulsed neural networks, for example those in [16] and [17], have many of the same properties but unlike SSP systems do not have all the advantages of standard digital integrated circuit designs.…”

Section: Introductionmentioning

confidence: 99%

Gaussian activation functions using Markov chains

Card

McNeill

2002

IEEE Trans. Neural Netw.

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We extend, in two major ways, earlier work in which sigmoidal neural nonlinearities were implemented using stochastic counters. 1) We define the signal to noise limitations of unipolar and bipolar stochastic arithmetic and signal processing. 2) We generalize the use of stochastic counters to include neural transfer functions employed in Gaussian mixture models. The hardware advantages of (nonlinear) stochastic signal processing (SSP) may be offset by increased processing time; we quantify these issues. The ability to realize accurate Gaussian activation functions for neurons in pulsed digital networks using simple hardware with stochastic signals is also analyzed quantitatively.

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“…Fig.1 shows the digital circuit realization of eq. (l) and (2). High and low levels of the signals in the circuit correspond to +I and -1 respectively.…”

Section: Arithmetic Circuits 21 Single-bit Addermentioning

confidence: 99%

“…In the filters every multi-bit multiplier is replaced by a AE modulator and a sign reverse circuit to perform the multiplication of single-bit signal and multi-bit coefficient. Digital neural networks using pulse density or pulse width modulated signals [2] are considered as another example of reduced signal processing circuits for pattern recognition or classification. These approaches are useful for their In this paper we propose arithmetic circuits adding and multiplying AX modulated signals directly and pave the way to single-bit general purpose signal processing without single-bit/multi-bit converters and large scale multi-bit arithmetic circuits.…”

Section: Introductionmentioning

confidence: 99%

Arithmetic circuits for single-bit digital signal processing

Fujisaka

Masuda

Sakamoto

et al.

ICECS'99. Proceedings of ICECS '99. 6th IEEE International Conference on Electronics, Circuits and Systems (Cat. No.99EX357)

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We propose simplc arithmetic circuits which directly add and multiply delta-sigma modulated single-bit signals without converting into multi-bit signals. Theoretical analysis and the circuit simulations show that the output noise is lower at low frequency. The ratio of maximum signal power to total noise power in the frequency band from DC to 1/32 ofsampling frequency is over 30dB.Any linear and nonlinear signal processing system will be practically built up using the arithmetic circuits and up/down counters integrating the singlebit signals. The application systems will be implemented in small LSI dice since both the simple arithmetic circuits and the single-bit signal routing require small physical areas. In this paper a synchronizaton loop is given as an application of the proposcd circuits.

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Pulse-density modulation technique in VLSI implementations of neural network algorithms

Cited by 73 publications

References 11 publications

Compound binomial processes in neural integration

Compound binomial processes in neural integration

Gaussian activation functions using Markov chains

Arithmetic circuits for single-bit digital signal processing

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