A widespread folklore for explaining the success of Convolutional Neural Networks (CNNs) is that CNNs use a more compact representation than the Fully-connected Neural Network (FNN) and thus require fewer training samples to accurately estimate their parameters. We initiate the study of rigorously characterizing the sample complexity of estimating CNNs. We show that for an $m$-dimensional convolutional filter with linear activation acting on a $d$-dimensional input, the sample complexity of achieving population prediction error of $\epsilon$ is $\widetilde{O(m/\epsilon^2)$, whereas the sample-complexity for its FNN counterpart is lower bounded by $\Omega(d/\epsilon^2)$ samples. Since, in typical settings $m \ll d$, this result demonstrates the advantage of using a CNN. We further consider the sample complexity of estimating a one-hidden-layer CNN with linear activation where both the $m$-dimensional convolutional filter and the $r$-dimensional output weights are unknown. For this model, we show that the sample complexity is $\widetilde{O}\left((m+r)/\epsilon^2\right)$ when the ratio between the stride size and the filter size is a constant. For both models, we also present lower bounds showing our sample complexities are tight up to logarithmic factors. Our main tools for deriving these results are a localized empirical process analysis and a new lemma characterizing the convolutional structure. We believe that these tools may inspire further developments in understanding CNNs.

Real-world image recognition is often challenged by the variability of visual styles including object textures, lighting conditions, filter effects, etc. Although these variations have been deemed to be implicitly handled by more training data and deeper networks, recent advances in image style transfer suggest that it is also possible to explicitly manipulate the style information. Extending this idea to general visual recognition problems, we present Batch-Instance Normalization (BIN) to explicitly normalize unnecessary styles from images. Considering certain style features play an essential role in discriminative tasks, BIN learns to selectively normalize only disturbing styles while preserving useful styles. The proposed normalization module is easily incorporated into existing network architectures such as Residual Networks, and surprisingly improves the recognition performance in various scenarios. Furthermore, experiments verify that BIN effectively adapts to completely different tasks like object classification and style transfer, by controlling the trade-off between preserving and removing style variations. BIN can be implemented with only a few lines of code using popular deep learning frameworks.

Neural Information Processing Systems http://nips.cc/

DRAE and then generalize it to the CF setting. The synergy between denoising and CF enables CRAE to make accurate recommendations while learning to fill in the blanks in sequences.

Maximum mean discrepancy (MMD) has been successfully applied to learn deep generative models for characterizing a joint distribution of variables via kernel mean embedding. In this paper, we present conditional generative moment-matching networks (CGMMN), which learn a conditional distribution given some input variables based on a conditional maximum mean discrepancy (CMMD) criterion. The learning is performed by stochastic gradient descent with the gradient calculated by back-propagation. We evaluate CGMMN on a wide range of tasks, including predictive modeling, contextual generation, and Bayesian dark knowledge, which distills knowledge from a Bayesian model by learning a relatively small CGMMN student network. Our results demonstrate competitive performance in all the tasks.

We study the design of deep architectures for lossy image compression. We present two architectural recipes in the context of multi-stage progressive encoders and empirically demonstrate their importance on compression performance.

Neural Information Processing Systems http://nips.cc/

In this paper, we use a linear program to empirically decompose fitted neural networks into ensembles of low-bias sub-networks.

Data-driven approaches to solving robotic tasks have gained a lot of traction in recent years.

We study the implicit regularization imposed by gradient descent for learning multi-layer homogeneous functions including feed-forward fully connected and convolutional deep neural networks with linear, ReLU or Leaky ReLU activation. We rigorously prove that gradient flow (i.e.