**Kardam**

Asynchronous distributed machine learning solutions have proven very effective so far, but always assuming perfectly functioning workers. In practice, some of the workers can however exhibit Byzantine behavior, caused by hardware failures, software bugs, corrupt data, or even malicious attacks. We introduce \emph{Kardam}, the first distributed asynchronous stochastic gradient descent (SGD) algorithm that copes with Byzantine workers. Kardam consists of two complementary components: a filtering and a dampening component. The first is scalar-based and ensures resilience against $\frac{1}{3}$ Byzantine workers. Essentially, this filter leverages the Lipschitzness of cost functions and acts as a self-stabilizer against Byzantine workers that would attempt to corrupt the progress of SGD. The dampening component bounds the convergence rate by adjusting to stale information through a generic gradient weighting scheme. We prove that Kardam guarantees almost sure convergence in the presence of asynchrony and Byzantine behavior, and we derive its convergence rate. We evaluate Kardam on the CIFAR-100 and EMNIST datasets and measure its overhead with respect to non Byzantine-resilient solutions. We empirically show that Kardam does not introduce additional noise to the learning procedure but does induce a slowdown (the cost of Byzantine resilience) that we both theoretically and empirically show to be less than $f/n$, where $f$ is the number of Byzantine failures tolerated and $n$ the total number of workers. Interestingly, we also empirically observe that the dampening component is interesting in its own right for it enables to build an SGD algorithm that outperforms alternative staleness-aware asynchronous competitors in environments with honest workers. … **Progressive Spatial Recurrent Neural Network (PS-RNN)**

Intra prediction is an important component of modern video codecs, which is able to efficiently squeeze out the spatial redundancy in video frames. With preceding pixels as the context, traditional intra prediction schemes generate linear predictions based on several predefined directions (i.e. modes) for blocks to be encoded. However, these modes are relatively simple and their predictions may fail when facing blocks with complex textures, which leads to additional bits encoding the residue. In this paper, we design a Progressive Spatial Recurrent Neural Network (PS-RNN) that learns to conduct intra prediction. Specifically, our PS-RNN consists of three spatial recurrent units and progressively generates predictions by passing information along from preceding contents to blocks to be encoded. To make our network generate predictions considering both distortion and bit-rate, we propose to use Sum of Absolute Transformed Difference (SATD) as the loss function to train PS-RNN since SATD is able to measure rate-distortion cost of encoding a residue block. Moreover, our method supports variable-block-size for intra prediction, which is more practical in real coding conditions. The proposed intra prediction scheme achieves on average 2.4% bit-rate reduction on variable-block-size settings under the same reconstruction quality compared with HEVC. … **Higher Order Propagation Framework (HOPF)**

Given a graph wherein every node has certain attributes associated with it and some nodes have labels associated with them, Collective Classification (CC) is the task of assigning labels to every unlabeled node using information from the node as well as its neighbors. It is often the case that a node is not only influenced by its immediate neighbors but also by its higher order neighbors, multiple hops away. Recent state-of-the-art models for CC use differentiable variations of Weisfeiler-Lehman kernels to aggregate multi-hop neighborhood information. However, in this work, we show that these models suffer from the problem of Node Information Morphing wherein the information of the node is morphed or overwhelmed by the information of its neighbors when considering multiple hops. Further, existing models are not scalable as the memory and computation needs grow exponentially with the number of hops considered. To circumvent these problems, we propose a generic Higher Order Propagation Framework (HOPF) which includes (i) a differentiable Node Information Preserving (NIP) kernel and (ii) a scalable iterative learning and inferencing mechanism to aggregate information over larger hops. We do an extensive evaluation using 11 datasets from different domains and show that unlike existing CC models, our NIP model with iterative inference is robust across all the datasets and can handle much larger neighborhoods in a scalable manner. …

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**31**
*Tuesday*
Jul 2018

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