Spectral cues are necessary to encode azimuthal auditory space in the mouse superior colliculus.

Sound localization plays a critical role in animal survival. Three cues can be used to compute sound direction: interaural timing differences (ITDs), interaural level differences (ILDs) and the direction-dependent spectral filtering by the head and pinnae (spectral cues). Little is known about how spectral cues contribute to the neural encoding of auditory space. Here we report on auditory space encoding in the mouse superior colliculus (SC). We show that the mouse SC contains neurons with spatially-restricted receptive fields (RFs) that form an azimuthal topographic map. We found that frontal RFs require spectral cues and lateral RFs require ILDs. The neurons with frontal RFs have frequency tunings that match the spectral structure of the specific head and pinna filter for sound coming from the front. These results demonstrate that patterned spectral cues in combination with ILDs give rise to the topographic map of azimuthal auditory space

Particle-filtering approaches for nonlinear Bayesian decoding of neuronal spike trains

The number of neurons that can be simultaneously recorded doubles every seven years. This ever increasing number of recorded neurons opens up the possibility to address new questions and extract higher dimensional stimuli from the recordings. Modeling neural spike trains as point processes, this task of extracting dynamical signals from spike trains is commonly set in the context of nonlinear filtering theory. Particle filter methods relying on importance weights are generic algorithms that solve the filtering task numerically, but exhibit a serious drawback when the problem dimensionality is high: they are known to suffer from the 'curse of dimensionality' (COD), i.e. the number of particles required for a certain performance scales exponentially with the observable dimensions. Here, we first briefly review the theory on filtering with point process observations in continuous time. Based on this theory, we investigate both analytically and numerically the reason for the COD of weighted particle filtering approaches: Similarly to particle filtering with continuous-time observations, the COD with point-process observations is due to the decay of effective number of particles, an effect that is stronger when the number of observable dimensions increases. Given the success of unweighted particle filtering approaches in overcoming the COD for continuous- time observations, we introduce an unweighted particle filter for point-process observations, the spike-based Neural Particle Filter (sNPF), and show that it exhibits a similar favorable scaling as the number of dimensions grows. Further, we derive rules for the parameters of the sNPF from a maximum likelihood approach learning. We finally employ a simple decoding task to illustrate the capabilities of the sNPF and to highlight one possible future application of our inference and learning algorithm

Ensemble Inhibition and Excitation in the Human Cortex: an Ising Model Analysis with Uncertainties

The pairwise maximum entropy model, also known as the Ising model, has been widely used to analyze the collective activity of neurons. However, controversy persists in the literature about seemingly inconsistent findings, whose significance is unclear due to lack of reliable error estimates. We therefore develop a method for accurately estimating parameter uncertainty based on random walks in parameter space using adaptive Markov Chain Monte Carlo after the convergence of the main optimization algorithm. We apply our method to the spiking patterns of excitatory and inhibitory neurons recorded with multielectrode arrays in the human temporal cortex during the wake-sleep cycle. Our analysis shows that the Ising model captures neuronal collective behavior much better than the independent model during wakefulness, light sleep, and deep sleep when both excitatory (E) and inhibitory (I) neurons are modeled; ignoring the inhibitory effects of I-neurons dramatically overestimates synchrony among E-neurons. Furthermore, information-theoretic measures reveal that the Ising model explains about 80%-95% of the correlations, depending on sleep state and neuron type. Thermodynamic measures show signatures of criticality, although we take this with a grain of salt as it may be merely a reflection of long-range neural correlations.Comment: 17 pages, 8 figure

Spiking Neural Networks for Inference and Learning: A Memristor-based Design Perspective

On metrics of density and power efficiency, neuromorphic technologies have the potential to surpass mainstream computing technologies in tasks where real-time functionality, adaptability, and autonomy are essential. While algorithmic advances in neuromorphic computing are proceeding successfully, the potential of memristors to improve neuromorphic computing have not yet born fruit, primarily because they are often used as a drop-in replacement to conventional memory. However, interdisciplinary approaches anchored in machine learning theory suggest that multifactor plasticity rules matching neural and synaptic dynamics to the device capabilities can take better advantage of memristor dynamics and its stochasticity. Furthermore, such plasticity rules generally show much higher performance than that of classical Spike Time Dependent Plasticity (STDP) rules. This chapter reviews the recent development in learning with spiking neural network models and their possible implementation with memristor-based hardware

Large-scale Spatiotemporal Spike Patterning Consistent with Wave Propagation in Motor Cortex

Aggregate signals in cortex are known to be spatiotemporally organized as propagating waves across the cortical surface, but it remains unclear whether the same is true for spiking activity in individual neurons. Furthermore, the functional interactions between cortical neurons are well documented but their spatial arrangement on the cortical surface has been largely ignored. Here we use a functional network analysis to demonstrate that a subset of motor cortical neurons in non-human primates spatially coordinate their spiking activity in a manner that closely matches wave propagation measured in the beta oscillatory band of the local field potential. We also demonstrate that sequential spiking of pairs of neuron contains task-relevant information that peaks when the neurons are spatially oriented along the wave axis. We hypothesize that the spatial anisotropy of spike patterning may reflect the underlying organization of motor cortex and may be a general property shared by other cortical areas

Event-Driven Contrastive Divergence for Spiking Neuromorphic Systems

Restricted Boltzmann Machines (RBMs) and Deep Belief Networks have been demonstrated to perform efficiently in a variety of applications, such as dimensionality reduction, feature learning, and classification. Their implementation on neuromorphic hardware platforms emulating large-scale networks of spiking neurons can have significant advantages from the perspectives of scalability, power dissipation and real-time interfacing with the environment. However the traditional RBM architecture and the commonly used training algorithm known as Contrastive Divergence (CD) are based on discrete updates and exact arithmetics which do not directly map onto a dynamical neural substrate. Here, we present an event-driven variation of CD to train a RBM constructed with Integrate & Fire (I&F) neurons, that is constrained by the limitations of existing and near future neuromorphic hardware platforms. Our strategy is based on neural sampling, which allows us to synthesize a spiking neural network that samples from a target Boltzmann distribution. The recurrent activity of the network replaces the discrete steps of the CD algorithm, while Spike Time Dependent Plasticity (STDP) carries out the weight updates in an online, asynchronous fashion. We demonstrate our approach by training an RBM composed of leaky I&F neurons with STDP synapses to learn a generative model of the MNIST hand-written digit dataset, and by testing it in recognition, generation and cue integration tasks. Our results contribute to a machine learning-driven approach for synthesizing networks of spiking neurons capable of carrying out practical, high-level functionality.Comment: (Under review