More Like this

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

   Hitron, Yael; Parter, Merav (September 2019, European Symposium on Algorithms (ESA))

   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 Θ(logt) (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−δ, and should stop firing after at most 2t rounds with probability 1−δ for some input parameter δ∈(0,1). Our key result is a construction of a neural timer with O(loglog1/δ) 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 Ω(min{loglog1/δ,logt}) 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. 

   more » « less
2. The Computational Cost of Asynchronous Neural Communication

   Hitron, Yael; Parter, Merav; Perri, Gur (January 2020, 11th Innovations in Theoretical Computer Science Conference (ITCS))

   Biological neural computation is inherently asynchronous due to large variations in neuronal spike timing and transmission delays. So-far, most theoretical work on neural networks assumes the synchronous setting where neurons fire simultaneously in discrete rounds. In this work we aim at understanding the barriers of asynchronous neural computation from an algorithmic perspective. We consider an extension of the widely studied model of synchronized spiking neurons [Maass, Neural Networks 97] to the asynchronous setting by taking into account edge and node delays. - Edge Delays: We define an asynchronous model for spiking neurons in which the latency values (i.e., transmission delays) of non self-loop edges vary adversarially over time. This extends the recent work of [Hitron and Parter, ESA'19] in which the latency values are restricted to be fixed over time. Our first contribution is an impossibility result that implies that the assumption that self-loop edges have no delays (as assumed in Hitron and Parter) is indeed necessary. Interestingly, in real biological networks self-loop edges (a.k.a. autapse) are indeed free of delays, and the latter has been noted by neuroscientists to be crucial for network synchronization. To capture the computational challenges in this setting, we first consider the implementation of a single NOT gate. This simple function already captures the fundamental difficulties in the asynchronous setting. Our key technical results are space and time upper and lower bounds for the NOT function, our time bounds are tight. In the spirit of the distributed synchronizers [Awerbuch and Peleg, FOCS'90] and following [Hitron and Parter, ESA'19], we then provide a general synchronizer machinery. Our construction is very modular and it is based on efficient circuit implementation of threshold gates. The complexity of our scheme is measured by the overhead in the number of neurons and the computation time, both are shown to be polynomial in the largest latency value, and the largest incoming degree Δ of the original network. - Node Delays: We introduce the study of asynchronous communication due to variations in the response rates of the neurons in the network. In real brain networks, the round duration varies between different neurons in the network. Our key result is a simulation methodology that allows one to transform the above mentioned synchronized solution under edge delays into a synchronized under node delays while incurring a small overhead w.r.t space and time. 

   more » « less
3. The Computational Cost of Asynchronous Neural Communication

   Hitron, Y.; Parter, M.; Perri, G. (January 2020, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020))

   Biological neural computation is inherently asynchronous due to large variations in neuronal spike timing and transmission delays. So-far, most theoretical work on neural networks assumes the synchronous setting where neurons fire simultaneously in discrete rounds. In this work we aim at understanding the barriers of asynchronous neural computation from an algorithmic perspective. We consider an extension of the widely studied model of synchronized spiking neurons [Maass, Neural= Networks 97] to the asynchronous setting by taking into account edge and node delays. Edge Delays: We define an asynchronous model for spiking neurons in which the latency values (i.e., transmission delays) of non self-loop edges vary adversarially over time. This extends the recent work of [Hitron and Parter, ESA’19] in which the latency values are restricted to be fixed over time. Our first contribution is an impossibility result that implies that the assumption that self-loop edges have no delays (as assumed in Hitron and Parter) is indeed necessary. Interestingly, in real biological networks self-loop edges (a.k.a. autapse) are indeed free of delays, and the latter has been noted by neuroscientists to be crucial for network synchronization. To capture the computational challenges in this setting, we first consider the implementation of a single NOT gate. This simple function already captures the fundamental difficulties in the asynchronous setting. Our key technical results are space and time upper and lower bounds for the NOT function, our time bounds are tight. In the spirit of the distributed synchronizers [Awerbuch and Peleg, FOCS’90] and following [Hitron and Parter, ESA’19], we then provide a general synchronizer machinery. Our construction is very modular and it is based on efficient circuit implementation of threshold gates. The complexity of our scheme is measured by the overhead in the number of neurons and the computation time, both are shown to be polynomial in the largest latency value, and the largest incoming degree ∆ of the original network. Node Delays: We introduce the study of asynchronous communication due to variations in the response rates of the neurons in the network. In real brain networks, the round duration varies between different neurons in the network. Our key result is a simulation methodology that allows one to transform the above mentioned synchronized solution under edge delays into a synchronized under node delays while incurring a small overhead w.r.t space and time. 

   more » « less
4. Brief Announcement: Integrating Temporal Information to Spatial Information in a Neural Circuit

   Wang, Brabeeba; Lynch, Nancy (January 2019, 33rd International Symposium on Distributed Computing (DISC))

   null (Ed.)

   In this paper, we consider networks of deterministic spiking neurons, firing synchronously at discrete times. We consider the problem of translating temporal information into spatial information in such networks, an important task that is carried out by actual brains. Specifically, we define two problems: "First Consecutive Spikes Counting" and "Total Spikes Counting", which model temporal-coding and rate-coding aspects of temporal-to-spatial translation respectively. Assuming an upper bound of T on the length of the temporal input signal, we design two networks that solve two problems, each using O(log T) neurons and terminating in time T+1. We also prove that these bounds are tight. 

   more » « less
5. Integrating Temporal Information to Spatial Information in a Neural Circuit

   Wang, Mien Brabeea; Lynch, Nancy (January 2019, 7th Workshop on Biological Distributed Algorithms (BDA))

   In this paper, we consider a network of spiking neurons with a deterministic synchronous firing rule at discrete time. We propose three problems – “first consecutive spikes counting”,“total spikes counting” and “k-spikes temporal to spatial encoding” – to model how brains extract temporal information into spatial information from different neural codings. For a max input length T, we design three networks that solve these three problems with matching lower bounds in bothtime O(T) and number of neurons O(logT) in all three questions. 

   more » « less