The geometry of robustness in spiking neural networks

Internal sensory models allow for balance control using muscle spindle acceleration feedback

Motor control requires sensory feedback, and the nature of this feedback has implications for the tasks of the central nervous system (CNS): for an approximately linear mechanical system (e.g., a freely standing person, a rider on a bicycle), if the sensory feedback does not contain the state variables (i.e., joint position and velocity), then optimal control actions are based on an internal dynamical system that estimates these states from the available incomplete sensory feedback. Such a computational system can be implemented as a recurrent neural network (RNN), and it uses a sensory model to update the state estimates. This is highly relevant for muscle spindle primary afferents whose firing rates scale with acceleration: if fusimotor and skeletomotor control are perfectly coordinated, these firing rates scale with the exafferent joint acceleration component, and in the absence of fusimotor control, they scale with the total joint acceleration (exafferent plus reafferent). For both scenarios, a sensory model exists that expresses the exafferent joint acceleration as a function of the state variables, and for the second scenario, a sensory model exists that corrects for the reafferent joint acceleration. Simulations of standing and bicycle balance control under realistic conditions show that joint acceleration feedback is sufficient for balance control, but only if the reafferent acceleration component is either absent from the feedback or is corrected for in the computational system.

Efficient coding in biophysically realistic excitatory-inhibitory spiking networks

The principle of efficient coding posits that sensory cortical networks are designed to encode maximal sensory information with minimal metabolic cost. Despite the major influence of efficient coding in neuroscience, it has remained unclear whether fundamental empirical properties of neural network activity can be explained solely based on this normative principle. Here, we derive the structural, coding, and biophysical properties of excitatory-inhibitory recurrent networks of spiking neurons that emerge directly from imposing that the network minimizes an instantaneous loss function and a time-averaged performance measure enacting efficient coding. We assumed that the network encodes a number of independent stimulus features varying with a time scale equal to the membrane time constant of excitatory and inhibitory neurons. The optimal network has biologically plausible biophysical features, including realistic integrate-and-fire spiking dynamics, spike-triggered adaptation, and a non-specific excitatory external input. The excitatory-inhibitory recurrent connectivity between neurons with similar stimulus tuning implements feature-specific competition, similar to that recently found in visual cortex. Networks with unstructured connectivity cannot reach comparable levels of coding efficiency. The optimal ratio of excitatory vs inhibitory neurons and the ratio of mean inhibitory-to-inhibitory vs excitatory-to-inhibitory connectivity are comparable to those of cortical sensory networks. The efficient network solution exhibits an instantaneous balance between excitation and inhibition. The network can perform efficient coding even when external stimuli vary over multiple time scales. Together, these results suggest that key properties of biological neural networks may be accounted for by efficient coding.

Combining Sampling Methods with Attractor Dynamics in Spiking Models of Head-Direction Systems

Uncertainty is a fundamental aspect of the natural environment, requiring the brain to infer and integrate noisy signals to guide behavior effectively. Sampling-based inference has been proposed as a mechanism for dealing with uncertainty, particularly in early sensory processing. However, it is unclear how to reconcile sampling-based methods with operational principles of higher-order brain areas, such as attractor dynamics of persistent neural representations. In this study, we present a spiking neural network model for the head-direction (HD) system that combines sampling-based inference with attractor dynamics. To achieve this, we derive the required spiking neural network dynamics and interactions to perform sampling from a large family of probability distributions-including variables encoded with Poisson noise. We then propose a method that allows the network to update its estimate of the current head direction by integrating angular velocity samples-derived from noisy inputs-with a pull towards a circular manifold, thereby maintaining consistent attractor dynamics. This model makes specific, testable predictions about the HD system that can be examined in future neurophysiological experiments: it predicts correlated subthreshold voltage fluctuations; distinctive short- and long-term firing correlations among neurons; and characteristic statistics of the movement of the neural activity "bump" representing the head direction. Overall, our approach extends previous theories on probabilistic sampling with spiking neurons, offers a novel perspective on the computations responsible for orientation and navigation, and supports the hypothesis that sampling-based methods can be combined with attractor dynamics to provide a viable framework for studying neural dynamics across the brain.

Antifragile control systems in neuronal processing: a sensorimotor perspective

The stability-robustness-resilience-adaptiveness continuum in neuronal processing follows a hierarchical structure that explains interactions and information processing among the different time scales. Interestingly, using "canonical" neuronal computational circuits, such as Homeostatic Activity Regulation, Winner-Take-All, and Hebbian Temporal Correlation Learning, one can extend the behavior spectrum towards antifragility. Cast already in both probability theory and dynamical systems, antifragility can explain and define the interesting interplay among neural circuits, found, for instance, in sensorimotor control in the face of uncertainty and volatility. This perspective proposes a new framework to analyze and describe closed-loop neuronal processing using principles of antifragility, targeting sensorimotor control. Our objective is two-fold. First, we introduce antifragile control as a conceptual framework to quantify closed-loop neuronal network behaviors that gain from uncertainty and volatility. Second, we introduce neuronal network design principles, opening the path to neuromorphic implementations and transfer to technical systems.

The impact of spike timing precision and spike emission reliability on decoding accuracy

Precisely timed and reliably emitted spikes are hypothesized to serve multiple functions, including improving the accuracy and reproducibility of encoding stimuli, memories, or behaviours across trials. When these spikes occur as a repeating sequence, they can be used to encode and decode a potential time series. Here, we show both analytically and in simulations that the error incurred in approximating a time series with precisely timed and reliably emitted spikes decreases linearly with the number of neurons or spikes used in the decoding. This was verified numerically with synthetically generated patterns of spikes. Further, we found that if spikes were imprecise in their timing, or unreliable in their emission, the error incurred in decoding with these spikes would be sub-linear. However, if the spike precision or spike reliability increased with network size, the error incurred in decoding a time-series with sequences of spikes would maintain a linear decrease with network size. The spike precision had to increase linearly with network size, while the probability of spike failure had to decrease with the square-root of the network size. Finally, we identified a candidate circuit to test this scaling relationship: the repeating sequences of spikes with sub-millisecond precision in area HVC (proper name) of the zebra finch. This scaling relationship can be tested using both neural data and song-spectrogram-based recordings while taking advantage of the natural fluctuation in HVC network size due to neurogenesis.

Approximating Nonlinear Functions With Latent Boundaries in Low-Rank Excitatory-Inhibitory Spiking Networks

Deep feedforward and recurrent neural networks have become successful functional models of the brain, but they neglect obvious biological details such as spikes and Dale's law. Here we argue that these details are crucial in order to understand how real neural circuits operate. Towards this aim, we put forth a new framework for spike-based computation in low-rank excitatory-inhibitory spiking networks. By considering populations with rank-1 connectivity, we cast each neuron's spiking threshold as a boundary in a low-dimensional input-output space. We then show how the combined thresholds of a population of inhibitory neurons form a stable boundary in this space, and those of a population of excitatory neurons form an unstable boundary. Combining the two boundaries results in a rank-2 excitatory-inhibitory (EI) network with inhibition-stabilized dynamics at the intersection of the two boundaries. The computation of the resulting networks can be understood as the difference of two convex functions and is thereby capable of approximating arbitrary non-linear input-output mappings. We demonstrate several properties of these networks, including noise suppression and amplification, irregular activity and synaptic balance, as well as how they relate to rate network dynamics in the limit that the boundary becomes soft. Finally, while our work focuses on small networks (5-50 neurons), we discuss potential avenues for scaling up to much larger networks. Overall, our work proposes a new perspective on spiking networks that may serve as a starting point for a mechanistic understanding of biological spike-based computation.

From Brain Models to Robotic Embodied Cognition: How Does Biological Plausibility Inform Neuromorphic Systems?

We examine the challenging "marriage" between computational efficiency and biological plausibility-A crucial node in the domain of spiking neural networks at the intersection of neuroscience, artificial intelligence, and robotics. Through a transdisciplinary review, we retrace the historical and most recent constraining influences that these parallel fields have exerted on descriptive analysis of the brain, construction of predictive brain models, and ultimately, the embodiment of neural networks in an enacted robotic agent. We study models of Spiking Neural Networks (SNN) as the central means enabling autonomous and intelligent behaviors in biological systems. We then provide a critical comparison of the available hardware and software to emulate SNNs for investigating biological entities and their application on artificial systems. Neuromorphics is identified as a promising tool to embody SNNs in real physical systems and different neuromorphic chips are compared. The concepts required for describing SNNs are dissected and contextualized in the new no man's land between cognitive neuroscience and artificial intelligence. Although there are recent reviews on the application of neuromorphic computing in various modules of the guidance, navigation, and control of robotic systems, the focus of this paper is more on closing the cognition loop in SNN-embodied robotics. We argue that biologically viable spiking neuronal models used for electroencephalogram signals are excellent candidates for furthering our knowledge of the explainability of SNNs. We complete our survey by reviewing different robotic modules that can benefit from neuromorphic hardware, e.g., perception (with a focus on vision), localization, and cognition. We conclude that the tradeoff between symbolic computational power and biological plausibility of hardware can be best addressed by neuromorphics, whose presence in neurorobotics provides an accountable empirical testbench for investigating synthetic and natural embodied cognition. We argue this is where both theoretical and empirical future work should converge in multidisciplinary efforts involving neuroscience, artificial intelligence, and robotics.

Computational methods to study information processing in neural circuits

The brain is an information processing machine and thus naturally lends itself to be studied using computational tools based on the principles of information theory. For this reason, computational methods based on or inspired by information theory have been a cornerstone of practical and conceptual progress in neuroscience. In this Review, we address how concepts and computational tools related to information theory are spurring the development of principled theories of information processing in neural circuits and the development of influential mathematical methods for the analyses of neural population recordings. We review how these computational approaches reveal mechanisms of essential functions performed by neural circuits. These functions include efficiently encoding sensory information and facilitating the transmission of information to downstream brain areas to inform and guide behavior. Finally, we discuss how further progress and insights can be achieved, in particular by studying how competing requirements of neural encoding and readout may be optimally traded off to optimize neural information processing.

Natural gradient enables fast sampling in spiking neural networks

For animals to navigate an uncertain world, their brains need to estimate uncertainty at the timescales of sensations and actions. Sampling-based algorithms afford a theoretically-grounded framework for probabilistic inference in neural circuits, but it remains unknown how one can implement fast sampling algorithms in biologically-plausible spiking networks. Here, we propose to leverage the population geometry, controlled by the neural code and the neural dynamics, to implement fast samplers in spiking neural networks. We first show that two classes of spiking samplers-efficient balanced spiking networks that simulate Langevin sampling, and networks with probabilistic spike rules that implement Metropolis-Hastings sampling-can be unified within a common framework. We then show that careful choice of population geometry, corresponding to the natural space of parameters, enables rapid inference of parameters drawn from strongly-correlated high-dimensional distributions in both networks. Our results suggest design principles for algorithms for sampling-based probabilistic inference in spiking neural networks, yielding potential inspiration for neuromorphic computing and testable predictions for neurobiology.