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 a stream with insertions and deletions achieving a multiplicative approximation and sublinear space; such an algorithm is impossible for deterministic algorithms. We also give a general technique that translates any twoplayer deterministic communication lower bound to a lower bound for randomized algorithms robust to a whitebox adversary. In particular, our results show that for all p ≥ 0, there exists a constant Cp > 1 such that any
Cpapproximation algorithm for Fp moment estimation in insertiononly streams with a whitebox adversary requires Ω(n) space for a universe of size n. Similarly, there is a constant C > 1 such that any Capproximation algorithm in an insertiononly stream for matrix rank requires Ω(n) space with a whitebox adversary. These results do not contradict our upper bounds since they assume the adversary has unbounded computational power. Our algorithmic results based on cryptography thus show a separation between computationally bounded and unbounded adversaries. Finally, we prove a lower bound of Ω(log n) bits for the fundamental problem of deterministic approximate counting in a stream of 0’s and 1’s, which holds even if we know how many total stream updates we have seen so far at each point in the stream. Such a lower bound for approximate counting with additional information was previously unknown, and in our context, it shows a separation between multiplayer deterministic maximum communication and the whitebox space complexity of a streaming algorithm
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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. However, the connection between these two spacelimited models has not been formally addressed. We take the first steps towards understanding this connection. On the upper bound side, we design neural algorithms based on known streaming algorithms for fundamental tasks, including distinct elements, approximate median, and heavy hitters. The number of neurons in our solutions almost match the space bounds of the corresponding streaming algorithms. As a general algorithmic primitive, we show how to implement the important streaming technique of linear sketching efficiently in spiking neural networks. On the lower bound side, we give a generic reduction, showing that any spaceefficient spiking neural network can be simulated by a spaceefficient streaming algorithm. This reduction lets us translate streamingspace lower bounds into nearly matching neuralspace lower bounds, establishing a close connection between the two models.
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 NSFPAR ID:
 10228808
 Date Published:
 Journal Name:
 34th International Symposium on Distributed Computing (DISC)
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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