How Robust are Deep Neural Networks?

Convolutional and Recurrent, deep neural networks have been successful in machine learning systems for computer vision, reinforcement learning, and other allied fields. However, the robustness of such neural networks is seldom apprised, especially after high classification accuracy has been attained. In this paper, we evaluate the robustness of three recurrent neural networks to tiny perturbations, on three widely used datasets, to argue that high accuracy does not always mean a stable and a robust (to bounded perturbations, adversarial attacks, etc.) system. Especially, normalizing the spectrum of the discrete recurrent network to bound the spectrum (using power method, Rayleigh quotient, etc.) on a unit disk produces stable, albeit highly non-robust neural networks. Furthermore, using the $\epsilon$-pseudo-spectrum, we show that training of recurrent networks, say using gradient-based methods, often result in non-normal matrices that may or may not be diagonalizable. Therefore, the open problem lies in constructing methods that optimize not only for accuracy but also for the stability and the robustness of the underlying neural network, a criterion that is distinct from the other.

[1]  A. Tannenbaum Feedback stabilization of linear dynamical plants with uncertainty in the gain factor , 1980 .

[2]  Yoshua Bengio,et al.  Learning long-term dependencies with gradient descent is difficult , 1994, IEEE Trans. Neural Networks.

[3]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[4]  Jürgen Schmidhuber,et al.  Long Short-Term Memory , 1997, Neural Computation.

[5]  T. Başar Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms, and Approximate Inverses , 2001 .

[6]  Surya Ganguli,et al.  Memory traces in dynamical systems , 2008, Proceedings of the National Academy of Sciences.

[7]  K. Miller,et al.  Balanced Amplification: A New Mechanism of Selective Amplification of Neural Activity Patterns , 2009, Neuron.

[8]  Herbert Jaeger,et al.  Reservoir computing approaches to recurrent neural network training , 2009, Comput. Sci. Rev..

[9]  Karl J. Friston,et al.  Comparing Families of Dynamic Causal Models , 2010, PLoS Comput. Biol..

[10]  Karl J. Friston,et al.  Post hoc Bayesian model selection , 2011, NeuroImage.

[11]  Christopher Potts,et al.  Learning Word Vectors for Sentiment Analysis , 2011, ACL.

[12]  Karl J. Friston,et al.  Perception and self-organized instability , 2012, Front. Comput. Neurosci..

[13]  Klaus-Robert Müller,et al.  Efficient BackProp , 2012, Neural Networks: Tricks of the Trade.

[14]  Razvan Pascanu,et al.  On the difficulty of training recurrent neural networks , 2012, ICML.

[15]  Alex Graves,et al.  Neural Turing Machines , 2014, ArXiv.

[16]  Quoc V. Le,et al.  A Neural Conversational Model , 2015, ArXiv.

[17]  Geoffrey E. Hinton,et al.  A Simple Way to Initialize Recurrent Networks of Rectified Linear Units , 2015, ArXiv.

[18]  Karl J. Friston,et al.  Towards a Neuronal Gauge Theory , 2016, PLoS biology.

[19]  J. Rinn,et al.  DeCoN: Genome-wide Analysis of In Vivo Transcriptional Dynamics during Pyramidal Neuron Fate Selection in Neocortex , 2015, Neuron.

[20]  Guigang Zhang,et al.  Deep Learning , 2016, Int. J. Semantic Comput..

[21]  Les E. Atlas,et al.  Full-Capacity Unitary Recurrent Neural Networks , 2016, NIPS.

[22]  Yoshua Bengio,et al.  Unitary Evolution Recurrent Neural Networks , 2015, ICML.

[23]  Mark S. Goldman,et al.  Memory without Feedback in a Neural Network , 2009, Neuron.

[24]  James Bailey,et al.  Efficient Orthogonal Parametrisation of Recurrent Neural Networks Using Householder Reflections , 2016, ICML.

[25]  Christopher Joseph Pal,et al.  On orthogonality and learning recurrent networks with long term dependencies , 2017, ICML.

[26]  Karl J. Friston,et al.  Towards a Neuronal Gauge Theory , 2016, PLoS biology.

[27]  B. Sengupta,et al.  StackSeq2Seq: Dual Encoder Seq2Seq Recurrent Networks , 2017 .

[28]  Anil A. Bharath,et al.  LatentPoison - Adversarial Attacks On The Latent Space , 2017, ArXiv.

[29]  Alessandro Bay,et al.  Approximating meta-heuristics with homotopic recurrent neural networks , 2017, ArXiv.

[30]  Alessandro Bay,et al.  GeoSeq2Seq: Information Geometric Sequence-to-Sequence Networks , 2017, ICLR.

[31]  Qiang Ye,et al.  Orthogonal Recurrent Neural Networks with Scaled Cayley Transform , 2017, ICML.

[32]  Elliot Meyerson,et al.  Evolving Deep Neural Networks , 2017, Artificial Intelligence in the Age of Neural Networks and Brain Computing.