When Neurons Fail

By El Mahdi El Mhamdi, Rachid Guerraoui. 2017

37 citations recorded by the source corpus.

Neural networks have been traditionally considered robust in the sense that their precision degrades gracefully with the failure of neurons and can be compensated by additional learning phases. Nevertheless, critical applications for which neural networks are now appealing solutions, cannot afford any additional learning at run-time. In this paper, we view a multilayer 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 neuralactivation functions are Lipschitz-continuous. Our bound isgiven in the form of quantity, we call the Forward ErrorPropagation, computing this quantity only requires looking atthe topology of the network, while experimentally assessingthe robustness of a network requires the costly experiment oflooking at all the possible inputs and testing all the possibleconfigurations of the network corresponding to different failuresituations, 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). In the crash case, our bound involves the number of neuronsper layer, the Lipschitz constant of the neural activationfunction, the number of failing neurons, the synaptic weightsand the depth of the layer where the failure occurred. In thecase of Byzantine failures, our bound involves, in addition, thesynaptic transmission capacity. Interestingly, as we show inthe paper, our bound can easily be extended to the case wheresynapses can fail. We present three applications of our results. The first is aquantification of the effect of memory cost reduction on theaccuracy of a neural network. The second is a quantification ofthe amount of information any neuron needs from its precedinglayer, enabling thereby a boosting scheme that prevents neuronsfrom waiting for unnecessary signals. Our third applicationis a quantification of the trade-off between neural networksrobustness and learning cost.

Subfields: Cellular and Molecular Neuroscience, Electrical and Electronic Engineering

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Cellular and Molecular Neuroscience

In Electrical and Electronic Engineering

Citations in the corpus

The Hidden Vulnerability of Distributed Learning in Byzantium (2018, methodology): “In the mean time, theoretical evaluations of this propagated error were derived with a tight bound (El Mhamdi & Guerraoui, 2016; 2017; El Mhamdi et al., 2017) which relies on computing the Lipschitz coefﬁcient of the neural network and proving its exponential dependency with the depth.”
On the Robustness of a Neural Network (2017, methodology): “In this section, we extend the results of [34] to derive a bound on the average error made by the network, when neurons are crashed at random.”
When Neurons Fail - Technical Report (2016, background): “(The detailed derivation of the Lipschizness of φ is given in a companion technical report [33].”
Machine Learning with Adversaries: Byzantine Tolerant Gradient Descent (2017, methodology): “Robustness to adversarial input can be viewed through the ﬁne-grained lens we introduced in [8], for instance, one can see perturbations of pixels in the inputs as perturbations of neurons in layer zero.”