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Register a new userFundamental aspects of noise in analog-hardware neural networks
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Added by
Daniel Brunner
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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We study and analyze the fundamental aspects of noise propagation in recurrent as well as deep, multi-layer networks. The main focus of our study are neural networks in analogue hardware, yet the methodology provides insight for networks in general. The system under study consists of noisy linear nodes, and we investigate the signal-to-noise ratio at the networks outputs which is the upper limit to such a systems computing accuracy. We consider additive and multiplicative noise which can be purely local as well as correlated across populations of neurons. This covers the chief internal-perturbations of hardware networks and noise amplitudes were obtained from a physically implemented recurrent neural network and therefore correspond to a real-world system. Analytic solutions agree exceptionally well with numerical data, enabling clear identification of the most critical components and aspects for noise management. Focusing on linear nodes isolates the impact of network connections and allows us to derive strategies for mitigating noise. Our work is the starting point in addressing this aspect of analogue neural networks, and our results identify notoriously sensitive points while simultaneously highlighting the robustness of such computational systems.
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Deep neural networks unlocked a vast range of new applications by solving tasks of which many were previously deemed as reserved to higher human intelligence. One of the developments enabling this success was a boost in computing power provided by special purpose hardware. Further significant improvements in energy efficiency and speed require full parallelism and analog hardware, yet analogue neuron noise and its propagation, i.e. accumulation, threatens rendering such approaches inept. Here, we analyse for the first time the propagation of noise in parallel deep neural networks comprising noisy nonlinear neurons. We develop an analytical treatment for both, symmetric networks to highlight the underlying mechanisms, and networks trained with back propagation. We find that noise accumulation is generally bound, and adding additional network layers does not worsen the signal to noise ratio beyond this limit. Most importantly, noise accumulation can be suppressed entirely when neuron activation functions have a slope smaller than unity. We therefore developed the framework for noise of deep neural networks implemented in analog systems, and identify criteria allowing engineers to design noise-resilient novel neural network hardware.
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