arXiv subjects

Yael Hitron

Publications and source records attributed to Yael Hitron.

3 recordsLinked to original sources

arXiv2020

Spiking Neural Networks Through the Lens of Streaming Algorithms

We initiate the study of biological neural networks from the perspective of streaming algorithms. Like computers, human brains suffer from memory limitations which pose a significant obstacle when processing large scale and dynamically changing data. In computer science, these challenges are captured by the well-known 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 some function $f$ of a stream of updates $\mathcal{S} = \{u_1,\ldots,u_m\}$, given restricted single-pass access to the stream. The primary complexity measure is the space used by the algorithm. We take the first steps towards understanding the connection between streaming and neural algorithms. On the upper bound side, we design neural algorithms based on known streaming algorithms for fundamental tasks, including distinct elements, approximate median, heavy hitters, and more. The number of neurons in our neural solutions almost matches 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 efficient in spiking neural networks. On the lower bound side, we give a generic reduction, showing that any space-efficient spiking neural network can be simulated by a space-efficiently streaming algorithm. This reduction lets us translate streaming-space lower bounds into nearly matching neural-space lower bounds, establishing a close connection between these two models.

cs.DC↗

arXiv2020

Broadcast CONGEST Algorithms against Adversarial Edges

We consider the corner-stone broadcast task with an adaptive adversary that controls a fixed number of $t$ edges in the input communication graph. In this model, the adversary sees the entire communication in the network and the random coins of the nodes, while maliciously manipulating the messages sent through a set of $t$ edges (unknown to the nodes). Since the influential work of [Pease, Shostak and Lamport, JACM'80], broadcast algorithms against plentiful adversarial models have been studied in both theory and practice for over more than four decades. Despite this extensive research, there is no round efficient broadcast algorithm for general graphs in the CONGEST model of distributed computing. We provide the first round-efficient broadcast algorithms against adaptive edge adversaries. Our two key results for $n$-node graphs of diameter $D$ are as follows: 1. For $t=1$, there is a deterministic algorithm that solves the problem within $\widetilde{O}(D^2)$ rounds, provided that the graph is 3 edge-connected. This round complexity beats the natural barrier of $O(D^3)$ rounds, the existential lower bound on the maximal length of $3$ edge-disjoint paths between a given pair of nodes in $G$. This algorithm can be extended to a $\widetilde{O}(D^{O(t)})$-round algorithm against $t$ adversarial edges in $(2t+1)$ edge-connected graphs. 2. For expander graphs with minimum degree of $\Omega(t^2\log n)$, there is an improved broadcast algorithm with $O(t \log ^2 n)$ rounds against $t$ adversarial edges. This algorithm exploits the connectivity and conductance properties of G-subgraphs obtained by employing the Karger's edge sampling technique. Our algorithms mark a new connection between the areas of fault-tolerant network design and reliable distributed communication.

cs.DS↗

arXiv2019

Counting to Ten with Two Fingers: Compressed Counting with Spiking Neurons

We consider the task of measuring time with probabilistic threshold gates implemented by bio-inspired spiking neurons. In the model of spiking neural networks, network evolves in discrete rounds, where in each round, neurons fire in pulses in response to a sufficiently high membrane potential. This potential is induced by spikes from neighboring neurons that fired in the previous round, which can have either an excitatory or inhibitory effect. We first consider a deterministic implementation of a neural timer and show that $\Theta(\log t)$ (deterministic) threshold gates are both sufficient and necessary. This raised the question of whether randomness can be leveraged to reduce the number of neurons. We answer this question in the affirmative by considering neural timers with spiking neurons where the neuron $y$ is required to fire for $t$ consecutive rounds with probability at least $1-\delta$, and should stop firing after at most $2t$ rounds with probability $1-\delta$ for some input parameter $\delta \in (0,1)$. Our key result is a construction of a neural timer with $O(\log\log 1/\delta)$ spiking neurons. Interestingly, this construction uses only one spiking neuron, while the remaining neurons can be deterministic threshold gates. We complement this construction with a matching lower bound of $\Omega(\min\{\log\log 1/\delta, \log t\})$ neurons. This provides the first separation between deterministic and randomized constructions in the setting of spiking neural networks. Finally, we demonstrate the usefulness of compressed counting networks for synchronizing neural networks.

cs.NE↗