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1. 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 singlemore »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.« less
2. Compressed Counting with Spiking Neurons (Extended Abstract)

   Hitron, Yael ; Parter, Merav ( January 2019 , 7th Workshop on Biological Distributed Algorithms (BDA))

   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. Discovering the underlying mechanisms by which the brain perceives the duration of time is one of the largest open enigma in computational neuroscience. To gain a better algorithmic understanding onto these processes, we introduce the neural timer problem. In this problem, one is given a time parameter t, an input neuron x, and an output neuron y. It is then required to design a minimum sized neural network (measured by the number of auxiliary neurons) in which every spike from x in a given round i, makes the output y fire for the subsequent t consecutive rounds.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 ofmore »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 2 t rounds with probability 1−δ for some input parameter δ∈(0,1). Our key result is a construction of a neural timer with O(log log 1/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{log log 1/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. In the spirit of distributed synchronizers [Awerbuch-Peleg, FOCS’90], we provide a general transformation (or simulation) that can take any synchronized network solution and simulate it in an asynchronous setting (where edges have arbitrary response latencies) while incurring a small overhead w.r.t the number of neurons and computation time.« less
3. Spiking Neural Networks Through the Lens of Streaming Algorithms

   Hitron, Y. ; Musco, C. ; Parter, M. ( January 2020 , 34th International Symposium on Distributed Computing (DISC))

   We initiate the study of biologically-inspired 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 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 a function f of a stream of updates 𝒮 = {u₁,…,u_m}, given restricted single-pass 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 (non-input 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 »However, the connection between these two space-limited 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 space-efficient spiking neural network can be simulated by a space-efficient streaming algorithm. This reduction lets us translate streaming-space lower bounds into nearly matching neural-space lower bounds, establishing a close connection between the two models.« less
4. Bio-mimetic high-speed target localization with fused frame and event vision for edge application

   https://doi.org/10.3389/fnins.2022.1010302  

   Lele, Ashwin Sanjay ; Fang, Yan ; Anwar, Aqeel ; Raychowdhury, Arijit ( November 2022 , Frontiers in Neuroscience)

   Evolution has honed predatory skills in the natural world where localizing and intercepting fast-moving prey is required. The current generation of robotic systems mimics these biological systems using deep learning. High-speed processing of the camera frames using convolutional neural networks (CNN) (frame pipeline) on such constrained aerial edge-robots gets resource-limited. Adding more compute resources also eventually limits the throughput at the frame rate of the camera as frame-only traditional systems fail to capture the detailed temporal dynamics of the environment. Bio-inspired event cameras and spiking neural networks (SNN) provide an asynchronous sensor-processor pair (event pipeline) capturing the continuous temporal details of the scene for high-speed but lag in terms of accuracy. In this work, we propose a target localization system combining event-camera and SNN-based high-speed target estimation and frame-based camera and CNN-driven reliable object detection by fusing complementary spatio-temporal prowess of event and frame pipelines. One of our main contributions involves the design of an SNN filter that borrows from the neural mechanism for ego-motion cancelation in houseflies. It fuses the vestibular sensors with the vision to cancel the activity corresponding to the predator's self-motion. We also integrate the neuro-inspired multi-pipeline processing with task-optimized multi-neuronal pathway structure in primates andmore »insects. The system is validated to outperform CNN-only processing using prey-predator drone simulations in realistic 3D virtual environments. The system is then demonstrated in a real-world multi-drone set-up with emulated event data. Subsequently, we use recorded actual sensory data from multi-camera and inertial measurement unit (IMU) assembly to show desired working while tolerating the realistic noise in vision and IMU sensors. We analyze the design space to identify optimal parameters for spiking neurons, CNN models, and for checking their effect on the performance metrics of the fused system. Finally, we map the throughput controlling SNN and fusion network on edge-compatible Zynq-7000 FPGA to show a potential 264 outputs per second even at constrained resource availability. This work may open new research directions by coupling multiple sensing and processing modalities inspired by discoveries in neuroscience to break fundamental trade-offs in frame-based computer vision 1 .« less
5. Optimizing state change detection in functional temporal networks through dynamic community detection

   https://doi.org/10.1093/comnet/cny030  

   Vaiana, Michael ; Goldberg, Ethan M. ; Muldoon, Sarah F. ; Porter, ed., Mason ( December 2018 , Journal of Complex Networks)

   Dynamic community detection provides a coherent description of network clusters over time, allowing one to track the growth and death of communities as the network evolves. However, modularity maximization, a popular method for performing multilayer community detection, requires the specification of an appropriate null network as well as resolution and interlayer coupling parameters. Importantly, the ability of the algorithm to accurately detect community evolution is dependent on the choice of these parameters. In functional temporal networks, where evolving communities reflect changing functional relationships between network nodes, it is especially important that the detected communities reflect any state changes of the system. Here, we present analytical work suggesting that a uniform null network provides improved sensitivity to the detection of small evolving communities in temporal networks with positive edge weights bounded above by 1, such as certain types of correlation networks. We then propose a method for increasing the sensitivity of modularity maximization to state changes in nodal dynamics by modelling self-identity links between layers based on the self-similarity of the network nodes between layers. This method is more appropriate for functional temporal networks from both a modelling and mathematical perspective, as it incorporates the dynamic nature of network nodes.more »We motivate our method based on applications in neuroscience where network nodes represent neurons and functional edges represent similarity of firing patterns in time. We show that in simulated data sets of neuronal spike trains, updating interlayer links based on the firing properties of the neurons provides superior community detection of evolving network structure when groups of neurons change their firing properties over time. Finally, we apply our method to experimental calcium imaging data that monitors the spiking activity of hundreds of neurons to track the evolution of neuronal communities during a state change from the awake to anaesthetized state.

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