In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

[Q]: Weight pruning has proven to be an effective method in reducing the model size and computation cost while not sacrificing the model accuracy. Conventional sparse matrix formats, however, involve irregular index structures with large storage requirement and sequential reconstruction process, resulting in inefficient use of highly parallel computing resources. Hence, pruning is usually restricted to inference with a batch size of one, for which an efficient parallel matrix-vector multiplication method exists. In this paper, a new class of sparse matrix representation utilizing Viterbi algorithm that has a high, and more importantly, fixed index compression ratio regardless of the pruning rate, is proposed. In this approach, numerous sparse matrix candidates are first generated by the Viterbi encoder, and then the one that aims to minimize the model accuracy degradation is selected by the Viterbi algorithm. The model pruning process based on the proposed Viterbi encoder and Viterbi algorithm is highly parallelizable, and can be implemented efficiently in hardware to achieve low-energy, high-performance index decoding process. Compared with the existing magnitude-based pruning methods, index data storage requirement can be further compressed by 85.2% in MNIST and 83.9% in AlexNet while achieving similar pruning rate. Even compared with the relative index compression technique, our method can still reduce the index storage requirement by 52.7% in MNIST and 35.5% in AlexNet.
[A]: We present a new pruning method and sparse matrix format to enable high index compression ratio and parallel index decoding process.


[Q]: We introduce geomstats, a Python package for Riemannian modelization and optimization over manifolds such as hyperspheres, hyperbolic spaces, SPD matrices or Lie groups of transformations. Our contribution is threefold. First, geomstats allows the flexible modeling of many a machine learning problem through an efficient and extensively unit-tested implementations of these manifolds, as well as the set of useful Riemannian metrics, exponential and logarithm maps that we provide. Moreover, the wide choice of loss functions and our implementation of the corresponding gradients allow fast and easy optimization over manifolds. Finally, geomstats is the only package to provide a unified framework for Riemannian geometry, as the operations implemented in geomstats are available with different computing backends (numpy,tensorflow and keras), as well as with a GPU-enabled mode–-thus considerably facilitating the application of Riemannian geometry in machine learning. In this paper, we present geomstats through a review of the utility and advantages of manifolds in machine learning, using the concrete examples that they span to show the efficiency and practicality of their implementation using our package
[A]: We introduce geomstats, an efficient Python package for Riemannian modelization and optimization over manifolds compatible with both numpy and tensorflow .


[Q]: Stochastic gradient descent (SGD) with stochastic momentum is popular in nonconvex stochastic optimization and particularly for the training of deep neural networks. In standard SGD, parameters are updated by improving along the path of the gradient at the current iterate on a batch of examples, where the addition of a ``momentum'' term biases the update in the direction of the previous change in parameters. In non-stochastic convex optimization one can show that a momentum adjustment provably reduces convergence time in many settings, yet such results have been elusive in the stochastic and non-convex settings. At the same time, a widely-observed empirical phenomenon is that in training deep networks stochastic momentum appears to significantly improve convergence time, variants of it have flourished in the development of other popular update methods, e.g. ADAM, AMSGrad, etc. Yet theoretical justification for the use of stochastic momentum has remained a significant open question. In this paper we propose an answer: stochastic momentum improves deep network training because it modifies SGD to escape saddle points faster and, consequently, to more quickly find a second order stationary point. Our theoretical results also shed light on the related question of how to choose the ideal momentum parameter--our analysis suggests that $\beta \in [0,1)$ should be large (close to 1), which comports with empirical findings. We also provide experimental findings that further validate these conclusions.
[A]:
Higher momentum parameter $\beta$ helps for escaping saddle points faster