Mechanism of feature learning in convolutional neural networks

Understanding the mechanism of how convolutional neural networks learn features from image data is a fundamental problem in machine learning and computer vision. In this work, we identify such a mechanism. We posit the Convolutional Neural Feature Ansatz, which states that covariances of filters in any convolutional layer are proportional to the average gradient outer product (AGOP) taken with respect to patches of the input to that layer. We present extensive empirical evidence for our ansatz, including identifying high correlation between covariances of filters and patch-based AGOPs for convolutional layers in standard neural architectures, such as AlexNet, VGG, and ResNets pre-trained on ImageNet. We also provide supporting theoretical evidence. We then demonstrate the generality of our result by using the patch-based AGOP to enable deep feature learning in convolutional kernel machines. We refer to the resulting algorithm as (Deep) ConvRFM and show that our algorithm recovers similar features to deep convolutional networks including the notable emergence of edge detectors. Moreover, we find that Deep ConvRFM overcomes previously identified limitations of convolutional kernels, such as their inability to adapt to local signals in images and, as a result, leads to sizable performance improvement over fixed convolutional kernels

Forecasting People Trajectories and Head Poses by Jointly Reasoning on Tracklets and Vislets

In this work, we explore the correlation between people trajectories and their head orientations. We argue that people trajectory and head pose forecasting can be modelled as a joint problem. Recent approaches on trajectory forecasting leverage short-term trajectories (aka tracklets) of pedestrians to predict their future paths. In addition, sociological cues, such as expected destination or pedestrian interaction, are often combined with tracklets. In this paper, we propose MiXing-LSTM (MX-LSTM) to capture the interplay between positions and head orientations (vislets) thanks to a joint unconstrained optimization of full covariance matrices during the LSTM backpropagation. We additionally exploit the head orientations as a proxy for the visual attention, when modeling social interactions. MX-LSTM predicts future pedestrians location and head pose, increasing the standard capabilities of the current approaches on long-term trajectory forecasting. Compared to the state-of-the-art, our approach shows better performances on an extensive set of public benchmarks. MX-LSTM is particularly effective when people move slowly, i.e. the most challenging scenario for all other models. The proposed approach also allows for accurate predictions on a longer time horizon.Comment: Accepted at IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2019. arXiv admin note: text overlap with arXiv:1805.0065

Stochastic Optimization for Deep CCA via Nonlinear Orthogonal Iterations

Deep CCA is a recently proposed deep neural network extension to the traditional canonical correlation analysis (CCA), and has been successful for multi-view representation learning in several domains. However, stochastic optimization of the deep CCA objective is not straightforward, because it does not decouple over training examples. Previous optimizers for deep CCA are either batch-based algorithms or stochastic optimization using large minibatches, which can have high memory consumption. In this paper, we tackle the problem of stochastic optimization for deep CCA with small minibatches, based on an iterative solution to the CCA objective, and show that we can achieve as good performance as previous optimizers and thus alleviate the memory requirement.Comment: in 2015 Annual Allerton Conference on Communication, Control and Computin