The fully-connected layers of deep convolutional neural networks typically contain over 90% of the network parameters. Reducing the number of parameters while preserving predictive performance is critically important for training big models in distributed systems and for deployment in embedded devices.In this paper, we introduce a novel Adaptive Fastfood transform to reparameterize the matrix-vector multiplication of fully connected layers. Reparameterizing a fully connected layer with d inputs and n outputs with the Adaptive Fastfood transform reduces the storage and computational costs costs from O(nd) to O(n) and O(n log d) respectively. Using the Adaptive Fastfood transform in convolutional networks results in what we call a deep fried convnet. These convnets are end-to-end trainable, and enable us to attain substantial reductions in the number of parameters without affecting prediction accuracy on the MNIST and ImageNet datasets.

Abstract-Stochastic gradient algorithms are the main focus of large-scale optimization problems and led to important successes in the recent advancement of the deep learning algorithms. The convergence of SGD depends on the careful choice of learning rate and the amount of the noise in stochastic estimates of the gradients. In this paper, we propose an adaptive learning rate algorithm, which utilizes stochastic curvature information of the loss function for automatically tuning the learning rates. The information about the element-wise curvature of the loss function is estimated from the local statistics of the stochastic first order gradients. We further propose a new variance reduction technique to speed up the convergence. In our experiments with deep neural networks, we obtained better performance compared to the popular stochastic gradient algorithms.

The linear layer is one of the most pervasive modules in deep learning representations. However, it requires O(N 2 ) parameters and O(N 2 ) operations. These costs can be prohibitive in mobile applications or prevent scaling in many domains. Here, we introduce a deep, differentiable, fully-connected neural network module composed of diagonal matrices of parameters, A and D, and the discrete cosine transform C. The core module, structured as ACDC −1 , has O(N ) parameters and incurs O(N log N ) operations. We present theoretical results showing how deep cascades of ACDC layers approximate linear layers. ACDC is, however, a stand-alone module and can be used in combination with any other types of module. In our experiments, we show that it can indeed be successfully interleaved with ReLU modules in convolutional neural networks for image recognition. Our experiments also study critical factors in the training of these structured modules, including initialization and depth. Finally, this paper also points out avenues for implementing the complex version of ACDC using photonic devices.

The optimization of deep neural networks can be more challenging than traditional convex optimization problems due to the highly non-convex nature of the loss function, e.g. it can involve pathological landscapes such as saddle-surfaces that can be difficult to escape for algorithms based on simple gradient descent. In this paper, we attack the problem of optimization of highly non-convex neural networks by starting with a smoothed -or mollified -objective function which becomes more complex as the training proceeds. Our proposition is inspired by the recent studies in continuation methods: similar to curriculum methods, we begin learning an easier (possibly convex) objective function and let it evolve during the training, until it eventually goes back to being the original, difficult to optimize, objective function. The complexity of the mollified networks is controlled by a single hyperparameter which is annealed during the training. We show improvements on various difficult optimization tasks and establish a relationship between recent works on continuation methods for neural networks and mollifiers.

No abstract