When Neurons Fail

TL;DR

This paper analyzes neural network robustness by providing tight bounds on neuron failures without retraining, leveraging Lipschitz continuity, and distinguishing failure types, with implications for memory efficiency and cost-accuracy trade-offs.

Contribution

It introduces a novel bound on error propagation due to neuron failures, applicable to various failure models, and connects robustness with memory and learning costs.

Findings

Bound on neuron failure tolerance without harming computation

Extension of bounds to synapse failures and Byzantine neurons

Implications for memory cost reduction and robustness trade-offs

Abstract

We view a neural network as a distributed system of which neurons can fail independently, and we evaluate its robustness in the absence of any (recovery) learning phase. We give tight bounds on the number of neurons that can fail without harming the result of a computation. To determine our bounds, we leverage the fact that neural activation functions are Lipschitz-continuous. Our bound is on a quantity, we call the \textit{Forward Error Propagation}, capturing how much error is propagated by a neural network when a given number of components is failing, computing this quantity only requires looking at the topology of the network, while experimentally assessing the robustness of a network requires the costly experiment of looking at all the possible inputs and testing all the possible configurations of the network corresponding to different failure situations, facing a discouraging combinatorial explosion. We distinguish the case of neurons that can fail and stop their activity (crashed neurons) from the case of neurons that can fail by transmitting arbitrary values (Byzantine neurons). Interestingly, as we show in the paper, our bound can easily be extended to the case where synapses can fail. We show how our bound can be leveraged to quantify the effect of memory cost reduction on the accuracy of a neural network, to estimate the amount of information any neuron needs from its preceding layer, enabling thereby a boosting scheme that prevents neurons from waiting for unnecessary signals. We finally discuss the trade-off between neural networks robustness and learning cost.

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See pages 1-last of IPDPS_2017_IEEE_camera_ready.pdf