A Closer Look at Memorization in Deep Networks

We examine the role of memorization in deep learning, drawing connections to capacity, generalization, and adversarial robustness. While deep networks are capable of memorizing noise data, our results suggest that they tend to prioritize learning simple patterns first. In our experiments, we expose qualitative differences in gradient-based optimization of deep neural networks (DNNs) on noise vs. real data. We also demonstrate that for appropriately tuned explicit regularization (e.g., dropout) we can degrade DNN training performance on noise datasets without compromising generalization on real data. Our analysis suggests that the notions of effective capacity which are dataset independent are unlikely to explain the generalization performance of deep networks when trained with gradient based methods because training data itself plays an important role in determining the degree of memorization.

[1]  C. Gini Variabilita e Mutabilita. , 1913 .

[2]  J. L. Hodges,et al.  Discriminatory Analysis - Nonparametric Discrimination: Consistency Properties , 1989 .

[3]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1989, Math. Control. Signals Syst..

[4]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[5]  L. Ljung,et al.  Overtraining, regularization and searching for a minimum, with application to neural networks , 1995 .

[6]  Christopher M. Bishop,et al.  Current address: Microsoft Research, , 2022 .

[7]  Guozhong An,et al.  The Effects of Adding Noise During Backpropagation Training on a Generalization Performance , 1996, Neural Computation.

[8]  L. Eon Bottou Online Learning and Stochastic Approximations , 1998 .

[9]  Tony R. Martinez,et al.  The general inefficiency of batch training for gradient descent learning , 2003, Neural Networks.

[10]  P. Bartlett,et al.  Local Rademacher complexities , 2005, math/0508275.

[11]  Yann LeCun,et al.  The mnist database of handwritten digits , 2005 .

[12]  Yoshua. Bengio,et al.  Learning Deep Architectures for AI , 2007, Found. Trends Mach. Learn..

[13]  Y. Yao,et al.  On Early Stopping in Gradient Descent Learning , 2007 .

[14]  Klaus-Robert Müller,et al.  Kernel Analysis of Deep Networks , 2011, J. Mach. Learn. Res..

[15]  Yoshua Bengio,et al.  An Empirical Investigation of Catastrophic Forgeting in Gradient-Based Neural Networks , 2013, ICLR.

[16]  Surya Ganguli,et al.  Exact solutions to the nonlinear dynamics of learning in deep linear neural networks , 2013, ICLR.

[17]  Razvan Pascanu,et al.  On the Number of Linear Regions of Deep Neural Networks , 2014, NIPS.

[18]  Joan Bruna,et al.  Intriguing properties of neural networks , 2013, ICLR.

[19]  Ryota Tomioka,et al.  In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning , 2014, ICLR.

[20]  Jonathon Shlens,et al.  Explaining and Harnessing Adversarial Examples , 2014, ICLR.

[21]  Shin Ishii,et al.  Distributional Smoothing with Virtual Adversarial Training , 2015, ICLR 2016.

[22]  Ryan P. Adams,et al.  Gradient-based Hyperparameter Optimization through Reversible Learning , 2015, ICML.

[23]  Yoram Singer,et al.  Train faster, generalize better: Stability of stochastic gradient descent , 2015, ICML.

[24]  Jeff A. Bilmes,et al.  Analysis of Deep Neural Networks with Extended Data Jacobian Matrix , 2016, ICML.

[25]  Daniel Jiwoong Im,et al.  An empirical analysis of the optimization of deep network loss surfaces , 2016, 1612.04010.

[26]  Surya Ganguli,et al.  Exponential expressivity in deep neural networks through transient chaos , 2016, NIPS.

[27]  Daniel Jiwoong Im,et al.  An Empirical Analysis of Deep Network Loss Surfaces , 2016, ArXiv.

[28]  David J. Schwab,et al.  Comment on "Why does deep and cheap learning work so well?" [arXiv: 1608.08225] , 2016, ArXiv.

[29]  Max Tegmark,et al.  Why Does Deep and Cheap Learning Work So Well? , 2016, Journal of Statistical Physics.

[30]  Surya Ganguli,et al.  On the Expressive Power of Deep Neural Networks , 2016, ICML.

[31]  Percy Liang,et al.  Understanding Black-box Predictions via Influence Functions , 2017, ICML.

[32]  Samy Bengio,et al.  Understanding deep learning requires rethinking generalization , 2016, ICLR.

[33]  Armand Joulin,et al.  Unsupervised Learning by Predicting Noise , 2017, ICML.

[34]  Jorge Nocedal,et al.  On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima , 2016, ICLR.

[35]  Samy Bengio,et al.  Adversarial examples in the physical world , 2016, ICLR.

[36]  Stefano Soatto,et al.  Entropy-SGD: biasing gradient descent into wide valleys , 2016, ICLR.

[37]  Guillermo Sapiro,et al.  Robust Large Margin Deep Neural Networks , 2017, IEEE Transactions on Signal Processing.