There has been a flurry of recent literature studying streaming algorithms for which the input stream is chosen adaptively by a blackbox adversary who observes the output of the streaming algorithm at each time step. However, these algorithms fail when the adversary has access to the internal state of the algorithm, rather than just the output of the algorithm. We study streaming algorithms in the whitebox adversarial model, where the stream is chosen adaptively by an adversary who observes the entire internal state of the algorithm at each time step. We show that nontrivial algorithms are still possible. We first give a randomized algorithm for the L1heavy hitters problem that outperforms the optimal deterministic MisraGries algorithm on long streams. If the whitebox adversary is computationally bounded, we use cryptographic techniques to reduce the memory of our L1heavy hitters algorithm even further and to design a number of additional algorithms for graph, string, and linear algebra problems. The existence of such algorithms is surprising, as the streaming algorithm does not even have a secret key in this model, i.e., its state is entirely known to the adversary. One algorithm we design is for estimating the number of distinct elements in amore »
Spiking Neural Networks Through the Lens of Streaming Algorithms
We initiate the study of biologicallyinspired spiking neural networks from the perspective of streaming algorithms. Like computers, human brains face memory limitations, which pose a significant obstacle when processing large scale and dynamically changing data. In computer science, these challenges are captured by the wellknown streaming model, which can be traced back to Munro and Paterson `78 and has had significant impact in theory and beyond. In the classical streaming setting, one must compute a function f of a stream of updates 𝒮 = {u₁,…,u_m}, given restricted singlepass access to the stream. The primary complexity measure is the space used by the algorithm. In contrast to the large body of work on streaming algorithms, relatively little is known about the computational aspects of data processing in spiking neural networks. In this work, we seek to connect these two models, leveraging techniques developed for streaming algorithms to better understand neural computation. Our primary goal is to design networks for various computational tasks using as few auxiliary (noninput or output) neurons as possible. The number of auxiliary neurons can be thought of as the "space" required by the network. Previous algorithmic work in spiking neural networks has many similarities with streaming algorithms. more »
 Publication Date:
 NSFPAR ID:
 10228808
 Journal Name:
 34th International Symposium on Distributed Computing (DISC)
 Sponsoring Org:
 National Science Foundation
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