The backpropagation algorithm has long been the canonical training method for neural networks. Modern paradigms are implicitly optimized for it, and numerous guidelines exist to ensure its proper use. Recently, synthetic gradients methods -where the error gradient is only roughly approximated - have garnered interest. These methods not only better portray how biological brains are learning, but also open new computational possibilities, such as updating layers asynchronously. Even so, they have failed to scale past simple tasks like MNIST or CIFAR-10. This is in part due to a lack of standards, leading to ill-suited models and practices forbidding such methods from performing to the best of their abilities. In this work, we focus on direct feedback alignment and present a set of best practices justified by observations of the alignment angles. We characterize a bottleneck effect that prevents alignment in narrow layers, and hypothesize it may explain why feedback alignment methods have yet to scale to large convolutional networks.
Direct Feedback Alignment (DFA) @cite_31 was introduced as a variant of FA with a direct feedback path from the error to each layer, allowing for layer-wise training (see Figure ). As this method presents both heightened biological realism and backward unlocking, it is the focus of this paper.
@cite_31
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Artificial neural networks are most commonly trained with the back-propagation algorithm, where the gradient for learning is provided by back-propagating the error, layer by layer, from the output layer to the hidden layers. A recently discovered method called feedback-alignment shows that the weights used for propagating the error backward don't have to be symmetric with the weights used for propagation the activation forward. In fact, random feedback weights work evenly well, because the network learns how to make the feedback useful. In this work, the feedback alignment principle is used for training hidden layers more independently from the rest of the network, and from a zero initial condition. The error is propagated through fixed random feedback connections directly from the output layer to each hidden layer. This simple method is able to achieve zero training error even in convolutional networks and very deep networks, completely without error back-propagation. The method is a step towards biologically plausible machine learning because the error signal is almost local, and no symmetric or reciprocal weights are required. Experiments show that the test performance on MNIST and CIFAR is almost as good as those obtained with back-propagation for fully connected networks. If combined with dropout, the method achieves 1.45 error on the permutation invariant MNIST task. This article proposes an enhanced differential fault analysis (DFA) method named as fault-propagation pattern-based DFA (FPP-DFA). The main idea of FPP-DFA is using the FPP of the ciphertext difference to predict the fault location and the fault-propagation path. It shows that FPP-DFA is very effective on SPN structure block ciphers using bitwise permutation, which is applied to two block ciphers. The first is PRESENT with the substitution-permutation sequence. With the fault model of injecting one nibble fault into the r-2nd round, on average 8 and 16 faults can reduce the key search space of PRESENT-80 128 to 214.7 and 221.1, respectively. The second is PRINTcipher with the permutation-substitution sequence. For the first time, it shows that although the permutation of PRINTcipher is secret key dependent, FPP-DFA still works well on it. With the fault model of injecting one nibble fault into the r-2nd round, 12 and 24 effective faults can reduce the key search space of PRINTcipher-48 96 to 213.7 and 222.8, respectively. This paper describes our submission to the 1st 3D Face Alignment in the Wild (3DFAW) Challenge. Our method builds upon the idea of convolutional part heatmap regression (Bulat and Tzimiropoulos, 2016), extending it for 3D face alignment. Our method decomposes the problem into two parts: (a) X,Y (2D) estimation and (b) Z (depth) estimation. At the first stage, our method estimates the X,Y coordinates of the facial landmarks by producing a set of 2D heatmaps, one for each landmark, using convolutional part heatmap regression. Then, these heatmaps, alongside the input RGB image, are used as input to a very deep subnetwork trained via residual learning for regressing the Z coordinate. Our method ranked 1st in the 3DFAW Challenge, surpassing the second best result by more than 22 . Code can be found at http: www.cs.nott.ac.uk psxab5 . We consider the 2 2 2 multiple-input multipleoutput interference channel where two source-destination pairs wish to communicate with the aid of two intermediate relays. In this paper, we propose a novel lattice strategy called Aligned Precoded Compute-and-Forward (PCoF). This scheme consists of two phases: 1) Using the CoF framework based on signal alignment we transform the Gaussian network into a deterministic finite field network. 2) Using linear precoding (over finite field) we eliminate the end-to-end interference in the finite field domain. Further, we exploit the algebraic structure of lattices to enhance the performance at finite SNR, such that beyond a degree of freedom result (also achievable by other means). We can also show that Aligned PCoF outperforms time sharing in a range of reasonably moderate SNR, with increasing gain as SNR increases.