While deep feature learning has revolutionized techniques for static-image understanding, the same does not quite hold for video processing. Architectures and optimization techniques used for video are largely based off those for static images, potentially underutilizing rich video information. In this work, we rethink both the underlying network architecture and the stochastic learning paradigm for temporal data. To do so, we draw inspiration from classic theory on linear dynamic systems for modeling time series. By extending such models to include nonlinear mappings, we derive a series of novel recurrent neural networks that sequentially make top-down predictions about the future and then correct those predictions with bottom-up observations. Predictive-corrective networks have a number of desirable properties: (1) they can adaptively focus computation on surprising frames where predictions require large corrections, (2) they simplify learning in that only residual-like corrective terms need to be learned over time and (3) they naturally decorrelate an input data stream in a hierarchical fashion, producing a more reliable signal for learning at each layer of a network. We provide an extensive analysis of our lightweight and interpretable framework, and demonstrate that our model is competitive with the two-stream network on three challenging datasets without the need for computationally expensive optical flow.
Accelerating learning Recurrent neural nets are notoriously difficult to train because of the exploding gradients encountered during SGD @cite_26 . We refer the reader to @cite_25 for an excellent introduction to general SGD learning. Though naturally a sequential algorithm that processes one data example at a time, much recent work focuses on mini-batch methods that can exploit parallelism in GPU architectures or clusters @cite_10 . One general theme is efficient online approximation of second-order methods @cite_17 , which can model correlations between input features. Batch normalization @cite_56 computes correlation statistics between samples in a batch, speeding up convergence. Predictive-corrective networks naturally de-correlate batch statistics without needing expensive second-order computations (Fig. ).
@cite_26 @cite_56 @cite_10 @cite_25 @cite_17
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It is common practice to decay the learning rate. Here we show one can usually obtain the same learning curve on both training and test sets by instead increasing the batch size during training. This procedure is successful for stochastic gradient descent (SGD), SGD with momentum, Nesterov momentum, and Adam. It reaches equivalent test accuracies after the same number of training epochs, but with fewer parameter updates, leading to greater parallelism and shorter training times. We can further reduce the number of parameter updates by increasing the learning rate @math and scaling the batch size @math . Finally, one can increase the momentum coefficient @math and scale @math , although this tends to slightly reduce the test accuracy. Crucially, our techniques allow us to repurpose existing training schedules for large batch training with no hyper-parameter tuning. We train Inception-ResNet-V2 on ImageNet to @math validation accuracy in under 2500 parameter updates, efficiently utilizing training batches of 65536 images. It is common practice to decay the learning rate. Here we show one can usually obtain the same learning curve on both training and test sets by instead increasing the batch size during training. This procedure is successful for stochastic gradient descent (SGD), SGD with momentum, Nesterov momentum, and Adam. It reaches equivalent test accuracies after the same number of training epochs, but with fewer parameter updates, leading to greater parallelism and shorter training times. We can further reduce the number of parameter updates by increasing the learning rate @math and scaling the batch size @math . Finally, one can increase the momentum coefficient @math and scale @math , although this tends to slightly reduce the test accuracy. Crucially, our techniques allow us to repurpose existing training schedules for large batch training with no hyper-parameter tuning. We train ResNet-50 on ImageNet to @math validation accuracy in under 30 minutes. Training deep neural networks with Stochastic Gradient Descent, or its variants, requires careful choice of both learning rate and batch size. While smaller batch sizes generally converge in fewer training epochs, larger batch sizes offer more parallelism and hence better computational efficiency. We have developed a new training approach that, rather than statically choosing a single batch size for all epochs, adaptively increases the batch size during the training process. Our method delivers the convergence rate of small batch sizes while achieving performance similar to large batch sizes. We analyse our approach using the standard AlexNet, ResNet, and VGG networks operating on the popular CIFAR-10, CIFAR-100, and ImageNet datasets. Our results demonstrate that learning with adaptive batch sizes can improve performance by factors of up to 6.25 on 4 NVIDIA Tesla P100 GPUs while changing accuracy by less than 1 relative to training with fixed batch sizes. Several recent trends in machine learning theory and practice, from the design of state-of-the-art Gaussian Process to the convergence analysis of deep neural nets (DNNs) under stochastic gradient descent (SGD), have found it fruitful to study wide random neural networks. Central to these approaches are certain scaling limits of such networks. We unify these results by introducing a notion of a straightline that can express most neural network computations, and we characterize its scaling limit when its tensors are large and randomized. From our framework follows (1) the convergence of random neural networks to Gaussian processes for architectures such as recurrent neural networks, convolutional neural networks, residual networks, attention, and any combination thereof, with or without batch normalization; (2) conditions under which the -- that weights in backpropagation can be assumed to be independent from weights in the forward pass -- leads to correct computation of gradient dynamics, and corrections when it does not; (3) the convergence of the Neural Tangent Kernel, a recently proposed kernel used to predict training dynamics of neural networks under gradient descent, at initialization for all architectures in (1) without batch normalization. Mathematically, our framework is general enough to rederive classical random matrix results such as the semicircle and the Marchenko-Pastur laws, as well as recent results in neural network Jacobian singular values. We hope our work opens a way toward design of even stronger Gaussian Processes, initialization schemes to avoid gradient explosion vanishing, and deeper understanding of SGD dynamics in modern architectures.