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Networks of spiking neurons underpin the extraordinary information-processing capabilities of the brain and have emerged as pillar models in neuromorphic intelligence. Despite extensive research on spiking neural networks (SNNs), most are established on deterministic models. Integrating noise into SNNs leads to biophysically more realistic neural dynamics and may benefit model performance. This work presents the noisy spiking neural network (NSNN) and the noise-driven learning rule (NDL) by introducing a spiking neuron model incorporating noisy neuronal dynamics. Our approach shows how noise may act as a resource for computation and learning and theoretically provides a framework for general SNNs. Moreover, NDL provides an insightful biological rationale for surrogate gradients. By incorporating various SNN architectures and algorithms, we show that our approach exhibits competitive performance and improved robustness against challenging perturbations than deterministic SNNs. Additionally, we demonstrate the utility of the NSNN model for neural coding studies. Overall, NSNN offers a powerful, flexible, and easy-to-use tool for machine learning practitioners and computational neuroscience researchers.

In this work, we introduce a novel framework which combines physics and machine learning methods to analyse acoustic signals. Three methods are developed for this task: a Bayesian inference approach for inferring the spectral acoustics characteristics, a neural-physical model which equips a neural network with forward and backward physical losses, and the non-linear least squares approach which serves as benchmark. The inferred propagation coefficient leads to the room impulse response (RIR) quantity which can be used for relocalisation with uncertainty. The simplicity and efficiency of this framework is empirically validated on simulated data.

In recent years, learning-based control in robotics has gained significant attention due to its capability to address complex tasks in real-world environments. With the advances in machine learning algorithms and computational capabilities, this approach is becoming increasingly important for solving challenging control problems in robotics by learning unknown or partially known robot dynamics. Active exploration, in which a robot directs itself to states that yield the highest information gain, is essential for efficient data collection and minimizing human supervision. Similarly, uncertainty-aware deployment has been a growing concern in robotic control, as uncertain actions informed by the learned model can lead to unstable motions or failure. However, active exploration and uncertainty-aware deployment have been studied independently, and there is limited literature that seamlessly integrates them. This paper presents a unified model-based reinforcement learning framework that bridges these two tasks in the robotics control domain. Our framework uses a probabilistic ensemble neural network for dynamics learning, allowing the quantification of epistemic uncertainty via Jensen-Renyi Divergence. The two opposing tasks of exploration and deployment are optimized through state-of-the-art sampling-based MPC, resulting in efficient collection of training data and successful avoidance of uncertain state-action spaces. We conduct experiments on both autonomous vehicles and wheeled robots, showing promising results for both exploration and deployment.

We introduce an approach which allows inferring causal relationships between variables for which the time evolution is available. Our method builds on the ideas of Granger Causality and Transfer Entropy, but overcomes most of their limitations. Specifically, our approach tests whether the predictability of a putative driven system Y can be improved by incorporating information from a potential driver system X, without making assumptions on the underlying dynamics and without the need to compute probability densities of the dynamic variables. Causality is assessed by a rigorous variational scheme based on the Information Imbalance of distance ranks, a recently developed statistical test capable of inferring the relative information content of different distance measures. This framework makes causality detection possible even for high-dimensional systems where only few of the variables are known or measured. Benchmark tests on coupled dynamical systems demonstrate that our approach outperforms other model-free causality detection methods, successfully handling both unidirectional and bidirectional couplings, and it is capable of detecting the arrow of time when present. We also show that the method can be used to robustly detect causality in electroencephalography data in humans.

Spiking Neural Networks (SNNs) have recently attracted widespread research interest as an efficient alternative to traditional Artificial Neural Networks (ANNs) because of their capability to process sparse and binary spike information and avoid expensive multiplication operations. Although the efficiency of SNNs can be realized on the In-Memory Computing (IMC) architecture, we show that the energy cost and latency of SNNs scale linearly with the number of timesteps used on IMC hardware. Therefore, in order to maximize the efficiency of SNNs, we propose input-aware Dynamic Timestep SNN (DT-SNN), a novel algorithmic solution to dynamically determine the number of timesteps during inference on an input-dependent basis. By calculating the entropy of the accumulated output after each timestep, we can compare it to a predefined threshold and decide if the information processed at the current timestep is sufficient for a confident prediction. We deploy DT-SNN on an IMC architecture and show that it incurs negligible computational overhead. We demonstrate that our method only uses 1.46 average timesteps to achieve the accuracy of a 4-timestep static SNN while reducing the energy-delay-product by 80%.

Anycast messaging (i.e., sending a message to an unspecified receiver) has long been neglected by the anonymous communication community. An anonymous anycast prevents senders from learning who the receiver of their message is, allowing for greater privacy in areas such as political activism and whistleblowing. While there have been some protocol ideas proposed, formal treatment of the problem is absent. Formal definitions of what constitutes anonymous anycast and privacy in this context are however a requirement for constructing protocols with provable guarantees. In this work, we define the anycast functionality and use a game-based approach to formalize its privacy and security goals. We further propose Panini, the first anonymous anycast protocol that only requires readily available infrastructure. We show that Panini allows the actual receiver of the anycast message to remain anonymous, even in the presence of an honest but curious sender. In an empirical evaluation, we find that Panini adds only minimal overhead over regular unicast: Sending a message anonymously to one of eight possible receivers results in an end-to-end latency of 0.76s.

Recurrent neural networks are a powerful means to cope with time series. We show how autoregressive linear, i.e., linearly activated recurrent neural networks (LRNNs) can approximate any time-dependent function f(t) given by a number of function values. The approximation can effectively be learned by simply solving a linear equation system; no backpropagation or similar methods are needed. Furthermore, and this is probably the main contribution of this article, the size of an LRNN can be reduced significantly in one step after inspecting the spectrum of the network transition matrix, i.e., its eigenvalues, by taking only the most relevant components. Therefore, in contrast to other approaches, we do not only learn network weights but also the network architecture. LRNNs have interesting properties: They end up in ellipse trajectories in the long run and allow the prediction of further values and compact representations of functions. We demonstrate this by several experiments, among them multiple superimposed oscillators (MSO), robotic soccer, and predicting stock prices. LRNNs outperform the previous state-of-the-art for the MSO task with a minimal number of units.

We continue our investigation of finite deformation linear viscoelastodynamics by focusing on constructing accurate and reliable numerical schemes. The concrete thermomechanical foundation developed in the previous study paves the way for pursuing discrete formulations with critical physical and mathematical structures preserved. Energy stability, momentum conservation, and temporal accuracy constitute the primary factors in our algorithm design. For inelastic materials, the directionality condition, a property for the stress to be energy consistent, is extended with the dissipation effect taken into account. Moreover, the integration of the constitutive relations calls for an algorithm design of the internal state variables and their conjugate variables. A directionality condition for the conjugate variables is introduced as an indispensable ingredient for ensuring physically correct numerical dissipation. By leveraging the particular structure of the configurational free energy, a set of update formulas for the internal state variables is obtained. Detailed analysis reveals that the overall discrete schemes are energy-momentum consistent and achieve first- and second-order accuracy in time, respectively. Numerical examples are provided to justify the appealing features of the proposed methodology.

The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.

Dynamic neural network is an emerging research topic in deep learning. Compared to static models which have fixed computational graphs and parameters at the inference stage, dynamic networks can adapt their structures or parameters to different inputs, leading to notable advantages in terms of accuracy, computational efficiency, adaptiveness, etc. In this survey, we comprehensively review this rapidly developing area by dividing dynamic networks into three main categories: 1) instance-wise dynamic models that process each instance with data-dependent architectures or parameters; 2) spatial-wise dynamic networks that conduct adaptive computation with respect to different spatial locations of image data and 3) temporal-wise dynamic models that perform adaptive inference along the temporal dimension for sequential data such as videos and texts. The important research problems of dynamic networks, e.g., architecture design, decision making scheme, optimization technique and applications, are reviewed systematically. Finally, we discuss the open problems in this field together with interesting future research directions.