skip to main content


Title: Robust computation with rhythmic spike patterns
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.  more » « less
Award ID(s):
1718991
NSF-PAR ID:
10112746
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Proceedings of the National Academy of Sciences
ISSN:
0027-8424
Page Range / eLocation ID:
201902653
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. The recently discovered spatial-temporal information processing capability of bio-inspired Spiking neural networks (SNN) has enabled some interesting models and applications. However designing large-scale and high-performance model is yet a challenge due to the lack of robust training algorithms. A bio-plausible SNN model with spatial-temporal property is a complex dynamic system. Synapses and neurons behave as filters capable of preserving temporal information. As such neuron dynamics and filter effects are ignored in existing training algorithms, the SNN downgrades into a memoryless system and loses the ability of temporal signal processing. Furthermore, spike timing plays an important role in information representation, but conventional rate-based spike coding models only consider spike trains statistically, and discard information carried by its temporal structures. To address the above issues, and exploit the temporal dynamics of SNNs, we formulate SNN as a network of infinite impulse response (IIR) filters with neuron nonlinearity. We proposed a training algorithm that is capable to learn spatial-temporal patterns by searching for the optimal synapse filter kernels and weights. The proposed model and training algorithm are applied to construct associative memories and classifiers for synthetic and public datasets including MNIST, NMNIST, DVS 128 etc. Their accuracy outperforms state-of-the-art approaches.

     
    more » « less
  2. Abstract

    Spatio-temporal activity patterns have been observed in a variety of brain areas in spontaneous activity, prior to or during action, or in response to stimuli. Biological mechanisms endowing neurons with the ability to distinguish between different sequences remain largely unknown. Learning sequences of spikes raises multiple challenges, such as maintaining in memory spike history and discriminating partially overlapping sequences. Here, we show that anti-Hebbian spike-timing dependent plasticity (STDP), as observed at cortico-striatal synapses, can naturally lead to learning spike sequences. We design a spiking model of the striatal output neuron receiving spike patterns defined as sequential input from a fixed set of cortical neurons. We use a simple synaptic plasticity rule that combines anti-Hebbian STDP and non-associative potentiation for a subset of the presented patterns called rewarded patterns. We study the ability of striatal output neurons to discriminate rewarded from non-rewarded patterns by firing only after the presentation of a rewarded pattern. In particular, we show that two biological properties of striatal networks, spiking latency and collateral inhibition, contribute to an increase in accuracy, by allowing a better discrimination of partially overlapping sequences. These results suggest that anti-Hebbian STDP may serve as a biological substrate for learning sequences of spikes.

     
    more » « less
  3. 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. 
    more » « less
  4. The past decade has witnessed the great success of deep neural networks in various domains. However, deep neural networks are very resource-intensive in terms of energy consumption, data requirements, and high computational costs. With the recent increasing need for the autonomy of machines in the real world, e.g., self-driving vehicles, drones, and collaborative robots, exploitation of deep neural networks in those applications has been actively investigated. In those applications, energy and computational efficiencies are especially important because of the need for real-time responses and the limited energy supply. A promising solution to these previously infeasible applications has recently been given by biologically plausible spiking neural networks. Spiking neural networks aim to bridge the gap between neuroscience and machine learning, using biologically realistic models of neurons to carry out the computation. Due to their functional similarity to the biological neural network, spiking neural networks can embrace the sparsity found in biology and are highly compatible with temporal code. Our contributions in this work are: (i) we give a comprehensive review of theories of biological neurons; (ii) we present various existing spike-based neuron models, which have been studied in neuroscience; (iii) we detail synapse models; (iv) we provide a review of artificial neural networks; (v) we provide detailed guidance on how to train spike-based neuron models; (vi) we revise available spike-based neuron frameworks that have been developed to support implementing spiking neural networks; (vii) finally, we cover existing spiking neural network applications in computer vision and robotics domains. The paper concludes with discussions of future perspectives.

     
    more » « less
  5. Blohm, Gunnar (Ed.)

    Neural circuits consist of many noisy, slow components, with individual neurons subject to ion channel noise, axonal propagation delays, and unreliable and slow synaptic transmission. This raises a fundamental question: how can reliable computation emerge from such unreliable components? A classic strategy is to simply average over a population ofNweakly-coupled neurons to achieve errors that scale as1/N. But more interestingly, recent work has introduced networks of leaky integrate-and-fire (LIF) neurons that achieve coding errors that scalesuperclassicallyas 1/Nby combining the principles of predictive coding and fast and tight inhibitory-excitatory balance. However, spike transmission delays preclude such fast inhibition, and computational studies have observed that such delays can cause pathological synchronization that in turn destroys superclassical coding performance. Intriguingly, it has also been observed in simulations that noise can actuallyimprovecoding performance, and that there exists some optimal level of noise that minimizes coding error. However, we lack a quantitative theory that describes this fascinating interplay between delays, noise and neural coding performance in spiking networks. In this work, we elucidate the mechanisms underpinning this beneficial role of noise by derivinganalyticalexpressions for coding error as a function of spike propagation delay and noise levels in predictive coding tight-balance networks of LIF neurons. Furthermore, we compute the minimal coding error and the associated optimal noise level, finding that they grow as power-laws with the delay. Our analysis reveals quantitatively how optimal levels of noise can rescue neural coding performance in spiking neural networks with delays by preventing the build up of pathological synchrony without overwhelming the overall spiking dynamics. This analysis can serve as a foundation for the further study of precise computation in the presence of noise and delays in efficient spiking neural circuits.

     
    more » « less