Multi-compartment Hodgkin-Huxley models are biophysical models of how electrical signals propagate throughout a neuron, and they form the basis of our knowledge of neural computation at the cellular level. However, these models have many free parameters that must be estimated for each cell, and existing fitting methods rely on intracellular voltage measurements that are highly challenging to obtain in vivo. Recent advances in neural recording technology with high-density probes and arrays enable dense sampling of extracellular voltage from many sites surrounding a neuron, allowing indirect measurement of many compartments of a cell simultaneously. Here, we propose a method for inferring the underlying membrane voltage, biophysical parameters, and the neuron's position relative to the probe, using extracellular measurements alone. We use an Extended Kalman Filter to infer membrane voltage and channel states using efficient, differentiable simulators. Then, we learn the model parameters by maximizing the marginal likelihood using gradient-based methods. We demonstrate the performance of this approach using simulated data and real neuron morphologies.

Dual Tree Single Clock (DTSC) Adiabatic Capacitive Neuron (ACN) circuits offer the potential for highly energy-efficient Artificial Neural Network (ANN) computation in full custom analog IC designs. The efficient mapping of Artificial Neuron (AN) abstract weights, extracted from the software-trained ANNs, onto physical ACN capacitance values has, however, yet to be fully researched. In this paper, we explore the unexpected hidden complexities, challenges and properties of the mapping, as well as, the ramifications for IC designers in terms accuracy, design and implementation. We propose an optimal, AN to ACN methodology, that promotes smaller chip sizes and improved overall classification accuracy, necessary for successful practical deployment. Using TensorFlow and Larq software frameworks, we train three different ANN networks and map their weights into the energy-efficient DTSC ACN capacitance value domain to demonstrate 100% functional equivalency. Finally, we delve into the impact of weight quantization on ACN performance using novel metrics related to practical IC considerations, such as IC floor space and comparator decision-making efficacy.

-- We present a novel framework for central pattern generator design that leverages the intrinsic rebound excitability of neurons in combination with winner-takes-all computation. Our approach unifies decision-making and rhythmic pattern generation within a simple yet powerful network architecture that employs all-to-all inhibitory connections enhanced by designable excitatory interactions. This design offers significant advantages regarding ease of implementation, adaptability, and robustness. We demonstrate its efficacy through a ring oscillator model, which exhibits adaptive phase and frequency modulation, making the framework particularly promising for applications in neuromorphic systems and robotics. Central pattern generators provide a bio-inspired framework for locomotion control in robotics and neuromorphic systems by autonomously generating robust, rhythmic motor patterns. In many robotic applications [1]-[6], these approaches enable smooth gait generation, rapid adaptation to disturbances and varying terrains, and reduced computational overhead.

With the help of special neuromorphic hardware, spiking neural networks (SNNs) are expected to realize artificial intelligence (AI) with less energy consumption. It provides a promising energy-efficient way for realistic control tasks by combining SNNs with deep reinforcement learning (DRL). In this paper, we focus on the task where the agent needs to learn multi-dimensional deterministic policies to control, which is very common in real scenarios. Recently, the surrogate gradient method has been utilized for training multi-layer SNNs, which allows SNNs to achieve comparable performance with the corresponding deep networks in this task. Most existing spike-based RL methods take the firing rate as the output of SNNs, and convert it to represent continuous action space (i.e., the deterministic policy) through a fully-connected (FC) layer. However, the decimal characteristic of the firing rate brings the floating-point matrix operations to the FC layer, making the whole SNN unable to deploy on the neuromorphic hardware directly. To develop a fully spiking actor network without any floating-point matrix operations, we draw inspiration from the non-spiking interneurons found in insects and employ the membrane voltage of the non-spiking neurons to represent the action. Before the non-spiking neurons, multiple population neurons are introduced to decode different dimensions of actions. Since each population is used to decode a dimension of action, we argue that the neurons in each population should be connected in time domain and space domain. Hence, the intra-layer connections are used in output populations to enhance the representation capacity. Finally, we propose a fully spiking actor network with intra-layer connections (ILC-SAN).

Mathematical models for the generation of the action potential can improve the understanding of physiological mechanisms that are consequence of the electrical activity in neurons. In such models, some equations involving empirically obtained functions of the membrane potential are usually defined. The best known of these models, the Hodgkin-Huxley model, is an example of this paradigm since it defines the conductances of ion channels in terms of the opening and closing rates of each type of gate present in the channels. These functions need to be derived from laboratory measurements that are often very expensive and produce little data because they involve a time-space-independent measurement of the voltage in a single channel of the cell membrane. In this work, we investigate the possibility of finding the Hodgkin-Huxley model's parametric functions using only two simple measurements (the membrane voltage as a function of time and the injected current that triggered that voltage) and applying Deep Learning methods to estimate these functions. This would result in an hybrid model of the action potential generation composed by the original Hodgkin-Huxley equations and an Artificial Neural Network that requires a small set of easy-to-perform measurements to be trained. Experiments were carried out using data generated from the original Hodgkin-Huxley model, and results show that a simple two-layer artificial neural network (ANN) architecture trained on a minimal amount of data can learn to model some of the fundamental proprieties of the action potential generation by estimating the model's rate functions.

The main computational task of Scientific Machine Learning (SciML) is function regression, required both for inputs as well as outputs of a simulation. Physics-Informed Neural Networks (PINNs) and neural operators (such as DeepONet) have been very effective in solving Partial Differential Equations (PDEs), but they tax computational resources heavily and cannot be readily adopted for edge computing. Here, we address this issue by considering Spiking Neural Networks (SNNs), which have shown promise in reducing energy consumption by two orders of magnitude or more. We present a SNN-based method to perform regression, which has been a challenge due to the inherent difficulty in representing a function's input domain and continuous output values as spikes. We first propose a new method for encoding continuous values into spikes based on a triangular matrix in space and time, and demonstrate its better performance compared to the existing methods. Next, we demonstrate that using a simple SNN architecture consisting of Leaky Integrate and Fire (LIF) activation and two dense layers, we can achieve relatively accurate function regression results. Moreover, we can replace the LIF with a trained Multi-Layer Perceptron (MLP) network and obtain comparable results but three times faster. Then, we introduce the DeepONet, consisting of a branch (typically a Fully-connected Neural Network, FNN) for inputs and a trunk (also a FNN) for outputs. We can build a spiking DeepONet by either replacing the branch or the trunk by a SNN. We demonstrate this new approach for classification using the SNN in the branch, achieving results comparable to the literature. Finally, we design a spiking DeepONet for regression by replacing its trunk with a SNN, and achieve good accuracy for approximating functions as well as inferring solutions of differential equations.

With the help of special neuromorphic hardware, spiking neural networks (SNNs) are expected to realize artificial intelligence with less energy consumption. It provides a promising energy-efficient way for realistic control tasks by combing SNNs and deep reinforcement learning (RL). There are only a few existing SNN-based RL methods at present. Most of them either lack generalization ability or employ Artificial Neural Networks (ANNs) to estimate value function in training. The former needs to tune numerous hyper-parameters for each scenario, and the latter limits the application of different types of RL algorithm and ignores the large energy consumption in training. To develop a robust spike-based RL method, we draw inspiration from non-spiking interneurons found in insects and propose the deep spiking Q-network (DSQN), using the membrane voltage of non-spiking neurons as the representation of Q-value, which can directly learn robust policies from high-dimensional sensory inputs using end-to-end RL. Experiments conducted on 17 Atari games demonstrate the effectiveness of DSQN by outperforming the ANN-based deep Q-network (DQN) in most games. Moreover, the experimental results show superior learning stability and robustness to adversarial attacks of DSQN.

Stochastic fluctuations of voltage-gated ion channels generate current and voltage noise in neuronal membranes. This noise may be a critical determinant of the efficacy of information processing within neural systems. Using Monte-Carlo simulations, we carry out a systematic investigation of the relationship between channel kinetics and the resulting membrane voltage noise using a stochastic Markov version of the Mainen-Sejnowski model of dendritic excitability in cortical neurons. Our simulations show that kinetic parameters which lead to an increase in membrane excitability (increasing channel densities, decreasing temperature) also lead to an increase in the magnitude of the sub-threshold voltage noise. Noise also increases as the membrane is depolarized from rest towards threshold. This suggests that channel fluctuations may interfere with a neuron's ability to function as an integrator of its synaptic inputs and may limit the reliability and precision of neural information processing.