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.
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Question: Bitcoin is a virtual coinage system that enables users to trade virtually free of a central trusted authority. All transactions on the Bitcoin blockchain are publicly available for viewing, yet as Bitcoin is built mainly for security it's original structure does not allow for direct analysis of address transactions.
Existing analysis methods of the Bitcoin blockchain can be complicated, computationally expensive or inaccurate. We propose a computationally efficient model to analyze bitcoin blockchain addresses and allow for their use with existing machine learning algorithms. We compare our approach against Multi Level Sequence Learners (MLSLs), one of the best performing models on bitcoin address data.

Answer: a 2vec model for cryptocurrency transaction graphs

Question: 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

Answer: We introduce geomstats, an efficient Python package for Riemannian modelization and optimization over manifolds compatible with both numpy and tensorflow .

Question: The ability of overparameterized deep networks to generalize well has been linked to the fact that stochastic gradient descent (SGD) finds solutions that lie in flat, wide minima in the training loss -- minima where the output of the network is resilient to small random noise added to its parameters.
So far this observation has been used to provide generalization guarantees only for neural networks whose parameters are either extit{stochastic} or extit{compressed}. In this work, we present a general PAC-Bayesian framework that leverages this observation to provide a bound on the original network learned -- a network that is deterministic and uncompressed. What enables us to do this is a key novelty in our approach: our framework allows us to show that if on training data, the interactions between the weight matrices satisfy certain conditions that imply a wide training loss minimum, these conditions themselves {\em generalize} to the interactions between the matrices on test data, thereby implying a wide test loss minimum. We then apply our general framework in a setup where we assume that the pre-activation values of the network are not too small (although we assume this only on the training data). In this setup, we provide a generalization guarantee for the original (deterministic, uncompressed) network, that does not scale with product of the spectral norms of the weight matrices -- a guarantee that would not have been possible with prior approaches.

Answer:
We provide a PAC-Bayes based generalization guarantee for uncompressed, deterministic deep networks by generalizing noise-resilience of the network on the training data to the test data.