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1. Robust computation with rhythmic spike patterns

   https://doi.org/10.1073/pnas.1902653116  

   Frady, E. Paxon; Sommer, Friedrich T. (August 2019, Proceedings of the National Academy of Sciences)

   Information coding by precise timing of spikes can be faster and more energy efficient than traditional rate coding. However, spike-timing codes are often brittle, which has limited their use in theoretical neuroscience and computing applications. Here, we propose a type of attractor neural network in complex state space and show how it can be leveraged to construct spiking neural networks with robust computational properties through a phase-to-timing mapping. Building on Hebbian neural associative memories, like Hopfield networks, we first propose threshold phasor associative memory (TPAM) networks. Complex phasor patterns whose components can assume continuous-valued phase angles and binary magnitudes can be stored and retrieved as stable fixed points in the network dynamics. TPAM achieves high memory capacity when storing sparse phasor patterns, and we derive the energy function that governs its fixed-point attractor dynamics. Second, we construct 2 spiking neural networks to approximate the complex algebraic computations in TPAM, a reductionist model with resonate-and-fire neurons and a biologically plausible network of integrate-and-fire neurons with synaptic delays and recurrently connected inhibitory interneurons. The fixed points of TPAM correspond to stable periodic states of precisely timed spiking activity that are robust to perturbation. The link established between rhythmic firing patterns and complex attractor dynamics has implications for the interpretation of spike patterns seen in neuroscience and can serve as a framework for computation in emerging neuromorphic devices. 

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2. 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. 

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3. 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. 

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4. A 22-pJ/spike 73-Mspikes/s 130k-compartment neural array transceiver with conductance-based synaptic and membrane dynamics

   https://doi.org/10.3389/fnins.2023.1198306  

   Park, Jongkil; Ha, Sohmyung; Yu, Theodore; Neftci, Emre; Cauwenberghs, Gert (August 2023, Frontiers in Neuroscience)

   Neuromorphic cognitive computing offers a bio-inspired means to approach the natural intelligence of biological neural systems in silicon integrated circuits. Typically, such circuits either reproduce biophysical neuronal dynamics in great detail as tools for computational neuroscience, or abstract away the biology by simplifying the functional forms of neural computation in large-scale systems for machine intelligence with high integration density and energy efficiency. Here we report a hybrid which offers biophysical realism in the emulation of multi-compartmental neuronal network dynamics at very large scale with high implementation efficiency, and yet with high flexibility in configuring the functional form and the network topology. The integrate-and-fire array transceiver (IFAT) chip emulates the continuous-time analog membrane dynamics of 65 k two-compartment neurons with conductance-based synapses. Fired action potentials are registered as address-event encoded output spikes, while the four types of synapses coupling to each neuron are activated by address-event decoded input spikes for fully reconfigurable synaptic connectivity, facilitating virtual wiring as implemented by routing address-event spikes externally through synaptic routing table. Peak conductance strength of synapse activation specified by the address-event input spans three decades of dynamic range, digitally controlled by pulse width and amplitude modulation (PWAM) of the drive voltage activating the log-domain linear synapse circuit. Two nested levels of micro-pipelining in the IFAT architecture improve both throughput and efficiency of synaptic input. This two-tier micro-pipelining results in a measured sustained peak throughput of 73 Mspikes/s and overall chip-level energy efficiency of 22 pJ/spike. Non-uniformity in digitally encoded synapse strength due to analog mismatch is mitigated through single-point digital offset calibration. Combined with the flexibly layered and recurrent synaptic connectivity provided by hierarchical address-event routing of registered spike events through external memory, the IFAT lends itself to efficient large-scale emulation of general biophysical spiking neural networks, as well as rate-based mapping of rectified linear unit (ReLU) neural activations. 

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5. Uncovering Neuronal Networks Defined by Consistent between-Neuron Spike Timing from Neuronal Spike Recordings

   https://doi.org/10.1523/ENEURO.0379-17.2018  

   van der Meij, Roemer; Voytek, Bradley (January 2018, eneuro)

   It is widely assumed that distributed neuronal networks are fundamental to the functioning of the brain. Consistent spike timing between neurons is thought to be one of the key principles for the formation of these networks. This can involve synchronous spiking or spiking with time delays, forming spike sequences when the order of spiking is consistent. Finding networks defined by their sequence of time-shifted spikes, denoted here as spike timing networks, is a tremendous challenge. As neurons can participate in multiple spike sequences at multiple between-spike time delays, the possible complexity of networks is prohibitively large. We present a novel approach that is capable of (1) extracting spike timing networks regardless of their sequence complexity, and (2) that describes their spiking sequences with high temporal precision. We achieve this by decomposing frequency-transformed neuronal spiking into separate networks, characterizing each network’s spike sequence by a time delay per neuron, forming a spike sequence timeline. These networks provide a detailed template for an investigation of the experimental relevance of their spike sequences. Using simulated spike timing networks, we show network extraction is robust to spiking noise, spike timing jitter, and partial occurrences of the involved spike sequences. Using rat multi-neuron recordings, we demonstrate the approach is capable of revealing real spike timing networks with sub-millisecond temporal precision. By uncovering spike timing networks, the prevalence, structure, and function of complex spike sequences can be investigated in greater detail, allowing us to gain a better understanding of their role in neuronal functioning. 

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