Siddhartha Satpathi

Siddhartha Satpathi, R Srikant

We consider the dynamics of gradient descent (GD) in overparameterized single hidden layer neural networks with a squared loss function. Recently, it has been shown that, under some conditions, the parameter values obtained using GD achieve zero training error and generalize well if the initial conditions are chosen appropriately. Here, through a Lyapunov analysis, we show that the dynamics of neural network weights under GD converge to a point which is close to the minimum norm solution subject to the condition that there is no training error when using the linear approximation to the neural network. To illustrate the application of this result, we show that the GD converges to a prediction function that generalizes well, thereby providing an alternative proof of the generalization results in Arora et al. (2019).

Semih Cayci, Siddhartha Satpathi, Niao He et al.

In this paper, we study the dynamics of temporal difference learning with neural network-based value function approximation over a general state space, namely, \emph{Neural TD learning}. We consider two practically used algorithms, projection-free and max-norm regularized Neural TD learning, and establish the first convergence bounds for these algorithms. An interesting observation from our results is that max-norm regularization can dramatically improve the performance of TD learning algorithms, both in terms of sample complexity and overparameterization. In particular, we prove that max-norm regularization improves state-of-the-art sample complexity and overparameterization bounds. The results in this work rely on a novel Lyapunov drift analysis of the network parameters as a stopped and controlled random process.

Siddhartha Satpathi, Supratim Deb, R Srikant et al.

We consider the problem of separating error messages generated in large distributed data center networks into error events. In such networks, each error event leads to a stream of messages generated by hardware and software components affected by the event. These messages are stored in a giant message log. We consider the unsupervised learning problem of identifying the signatures of events that generated these messages; here, the signature of an error event refers to the mixture of messages generated by the event. One of the main contributions of the paper is a novel mapping of our problem which transforms it into a problem of topic discovery in documents. Events in our problem correspond to topics and messages in our problem correspond to words in the topic discovery problem. However, there is no direct analog of documents. Therefore, we use a non-parametric change-point detection algorithm, which has linear computational complexity in the number of messages, to divide the message log into smaller subsets called episodes, which serve as the equivalents of documents. After this mapping has been done, we use a well-known algorithm for topic discovery, called LDA, to solve our problem. We theoretically analyze the change-point detection algorithm, and show that it is consistent and has low sample complexity. We also demonstrate the scalability of our algorithm on a real data set consisting of $97$ million messages collected over a period of $15$ days, from a distributed data center network which supports the operations of a large wireless service provider.

Luca Baldassarre, Nirav Bhan, Volkan Cevher et al.

Group-based sparsity models are proven instrumental in linear regression problems for recovering signals from much fewer measurements than standard compressive sensing. The main promise of these models is the recovery of "interpretable" signals through the identification of their constituent groups. In this paper, we establish a combinatorial framework for group-model selection problems and highlight the underlying tractability issues. In particular, we show that the group-model selection problem is equivalent to the well-known NP-hard weighted maximum coverage problem (WMC). Leveraging a graph-based understanding of group models, we describe group structures which enable correct model selection in polynomial time via dynamic programming. Furthermore, group structures that lead to totally unimodular constraints have tractable discrete as well as convex relaxations. We also present a generalization of the group-model that allows for within group sparsity, which can be used to model hierarchical sparsity. Finally, we study the Pareto frontier of group-sparse approximations for two tractable models, among which the tree sparsity model, and illustrate selection and computation trade-offs between our framework and the existing convex relaxations.