In recent years, legged robots based on deep reinforcement learning have made remarkable progress. Quadruped robots have demonstrated the ability to complete challenging tasks in complex environments and have been deployed in real-world scenarios to assist humans. Simultaneously, bipedal and humanoid robots have achieved breakthroughs in various demanding tasks. Current reinforcement learning methods can utilize diverse robot bodies and historical information to perform actions. However, prior research has not emphasized the speed and energy consumption of network inference, as well as the biological significance of the neural networks themselves. Most of the networks employed are traditional artificial neural networks that utilize multilayer perceptrons (MLP). In this paper, we successfully apply a novel Spiking Neural Network (SNN) to process legged robots, achieving outstanding results across a range of simulated terrains. SNN holds a natural advantage over traditional neural networks in terms of inference speed and energy consumption, and their pulse-form processing of body perception signals offers improved biological interpretability. To the best of our knowledge, this is the first work to implement SNN in legged robots.

Machine learning methods are progressively gaining acceptance in the electron microscopy community for de-noising, semantic segmentation, and dimensionality reduction of data post-acquisition. The introduction of the APIs by major instrument manufacturers now allows the deployment of ML workflows in microscopes, not only for data analytics but also for real-time decision-making and feedback for microscope operation. However, the number of use cases for real-time ML remains remarkably small. Here, we discuss some considerations in designing ML-based active experiments and pose that the likely strategy for the next several years will be human-in-the-loop automated experiments (hAE). In this paradigm, the ML learning agent directly controls beam position and image and spectroscopy acquisition functions, and human operator monitors experiment progression in real-and feature space of the system and tunes the policies of the ML agent to steer the experiment towards specific objectives. One of the hallmarks of the meeting was the large number of presentations on machine learning (ML) in microscopy, ranging from denoising, unsupervised data analysis via variational autoencoders, and supervised learning applications for semantic segmentations and feature identification. Remarkably, by now most manufacturers offer or have plans to offer Python application programming interfaces (APIs), allowing the deployment of the codes on operational microscopes. From this perspective, the technical barriers for the broad implementation of automated microscopy in which ML algorithms analyze the data streaming from instrument detectors and make decisions based on this data are lower than ever.

Over the past two decades, the availability of high-performance computing and the development of neural networks of larger capacity have conspired to fuel a revolution in the way we think at the optimisation of complex systems. When the dimensionality of the space of relevant design parameters exceeds a few units, and brute-force scans cease be a viable option for its exploration. We nowadays, have the option of letting automated systems find their way to configurations that correspond to advantageous extrema of carefully specified objective functions. The engine under the hood of these optimisation searches is automatic differentiation, which allows computer programs to keep track of the gradient of the objective function, through the chain rule of differential calculus, as computer code performs arbitrarily complex successions of operations to model the behaviour of the system. Crucial to a successful optimisation of the system is the inclusion in the model of all relevant effects that have an impact on the precision of the inference that the data generated by the system may produce. An incomplete description of the inference itself, or a mock up of the reconstruction techniques performing the dimensionality reduction step which translates raw data into high-level features informing the objective function, are likely to prevent the identification of designs that maximise the true objective, as they introduce a misalignment.

We present a general kernel-based framework for learning operators between Banach spaces along with a priori error analysis and comprehensive numerical comparisons with popular neural net (NN) approaches such as Deep Operator Net (DeepONet) [Lu et al.] and Fourier Neural Operator (FNO) [Li et al.]. We consider the setting where the input/output spaces of target operator $\mathcal{G}^\dagger\,:\, \mathcal{U}\to \mathcal{V}$ are reproducing kernel Hilbert spaces (RKHS), the data comes in the form of partial observations $\phi(u_i), \varphi(v_i)$ of input/output functions $v_i=\mathcal{G}^\dagger(u_i)$ ($i=1,\ldots,N$), and the measurement operators $\phi\,:\, \mathcal{U}\to \mathbb{R}^n$ and $\varphi\,:\, \mathcal{V} \to \mathbb{R}^m$ are linear. Writing $\psi\,:\, \mathbb{R}^n \to \mathcal{U}$ and $\chi\,:\, \mathbb{R}^m \to \mathcal{V}$ for the optimal recovery maps associated with $\phi$ and $\varphi$, we approximate $\mathcal{G}^\dagger$ with $\bar{\mathcal{G}}=\chi \circ \bar{f} \circ \phi$ where $\bar{f}$ is an optimal recovery approximation of $f^\dagger:=\varphi \circ \mathcal{G}^\dagger \circ \psi\,:\,\mathbb{R}^n \to \mathbb{R}^m$. We show that, even when using vanilla kernels (e.g., linear or Mat\'{e}rn), our approach is competitive in terms of cost-accuracy trade-off and either matches or beats the performance of NN methods on a majority of benchmarks. Additionally, our framework offers several advantages inherited from kernel methods: simplicity, interpretability, convergence guarantees, a priori error estimates, and Bayesian uncertainty quantification. As such, it can serve as a natural benchmark for operator learning.

Control techniques like MPC can realize contact-rich manipulation which exploits dynamic information, maintaining friction limits and safety constraints. However, contact geometry and dynamics are required to be known. This information is often extracted from CAD, limiting scalability and the ability to handle tasks with varying geometry. To reduce the need for a priori models, we propose a framework for estimating contact models online based on torque and position measurements. To do this, compliant contact models are used, connected in parallel to model multi-point contact and constraints such as a hinge. They are parameterized to be differentiable with respect to all of their parameters (rest position, stiffness, contact location), allowing the coupled robot/environment dynamics to be linearized or efficiently used in gradient-based optimization. These models are then applied for: offline gradient-based parameter fitting, online estimation via an extended Kalman filter, and online gradient-based MPC. The proposed approach is validated on two robots, showing the efficacy of sensorless contact estimation and the effects of online estimation on MPC performance.

Large language models have shown astonishing performance on a wide range of reasoning tasks. In this paper, we investigate whether they could reason about real-world events and help improve the prediction performance of event sequence models. We design LAMP, a framework that integrates a large language model in event prediction. Particularly, the language model performs abductive reasoning to assist an event sequence model: the event model proposes predictions on future events given the past; instructed by a few expert-annotated demonstrations, the language model learns to suggest possible causes for each proposal; a search module finds out the previous events that match the causes; a scoring function learns to examine whether the retrieved events could actually cause the proposal. Through extensive experiments on several challenging real-world datasets, we demonstrate that our framework -- thanks to the reasoning capabilities of large language models -- could significantly outperform the state-of-the-art event sequence models.

This paper presents a comprehensive review of the current state of the art in quantum navigation systems, with a specific focus on their application in maritime navigation. Quantum technologies have the potential to revolutionise navigation and positioning systems due to their ability to provide highly accurate and secure information. The review covers the principles of quantum navigation and highlights the latest developments in quantum-enhanced sensors, atomic clocks, and quantum communication protocols. The paper also discusses the challenges and opportunities of using quantum technologies in maritime navigation, including the effects that the maritime environment and the specificity of marine applications can have on the performance of quantum sensors. Finally, the paper concludes with a discussion on the future of quantum navigation systems and their potential impact on the maritime industry. This review aims at providing a valuable resource for researchers and engineers interested in the development and deployment of quantum navigation systems.

Trajectory adjustment decisions throughout the drilling process, called geosteering, affect subsequent choices and information gathering, thus resulting in a coupled sequential decision problem. Previous works on applying decision optimization methods in geosteering rely on greedy optimization or Approximate Dynamic Programming (ADP). Either decision optimization method requires explicit uncertainty and objective function models, making developing decision optimization methods for complex and realistic geosteering environments challenging to impossible. We use the Deep Q-Network (DQN) method, a model-free reinforcement learning (RL) method that learns directly from the decision environment, to optimize geosteering decisions. The expensive computations for RL are handled during the offline training stage. Evaluating DQN needed for real-time decision support takes milliseconds and is faster than the traditional alternatives. Moreover, for two previously published synthetic geosteering scenarios, our results show that RL achieves high-quality outcomes comparable to the quasi-optimal ADP. Yet, the model-free nature of RL means that by replacing the training environment, we can extend it to problems where the solution to ADP is prohibitively expensive to compute. This flexibility will allow applying it to more complex environments and make hybrid versions trained with real data in the future.

Neural network solvers represent an innovative and promising approach for tackling time-fractional partial differential equations by utilizing deep learning techniques. L1 interpolation approximation serves as the standard method for addressing time-fractional derivatives within neural network solvers. However, we have discovered that neural network solvers based on L1 interpolation approximation are unable to fully exploit the benefits of neural networks, and the accuracy of these models is constrained to interpolation errors. In this paper, we present the high-precision Hermite Neural Solver (HNS) for solving time-fractional partial differential equations. Specifically, we first construct a high-order explicit approximation scheme for fractional derivatives using Hermite interpolation techniques, and rigorously analyze its approximation accuracy. Afterward, taking into account the infinitely differentiable properties of deep neural networks, we integrate the high-order Hermite interpolation explicit approximation scheme with deep neural networks to propose the HNS. The experimental results show that HNS achieves higher accuracy than methods based on the L1 scheme for both forward and inverse problems, as well as in high-dimensional scenarios. This indicates that HNS has significantly improved accuracy and flexibility compared to existing L1-based methods, and has overcome the limitations of explicit finite difference approximation methods that are often constrained to function value interpolation. As a result, the HNS is not a simple combination of numerical computing methods and neural networks, but rather achieves a complementary and mutually reinforcing advantages of both approaches. The data and code can be found at \url{https://github.com/hsbhc/HNS}.

Transformers are widely used to extract complex semantic meanings from input tokens, yet they usually operate as black-box models. In this paper, we present a simple yet informative decomposition of hidden states (or embeddings) of trained transformers into interpretable components. For any layer, embedding vectors of input sequence samples are represented by a tensor $\boldsymbol{h} \in \mathbb{R}^{C \times T \times d}$. Given embedding vector $\boldsymbol{h}_{c,t} \in \mathbb{R}^d$ at sequence position $t \le T$ in a sequence (or context) $c \le C$, extracting the mean effects yields the decomposition \[ \boldsymbol{h}_{c,t} = \boldsymbol{\mu} + \mathbf{pos}_t + \mathbf{ctx}_c + \mathbf{resid}_{c,t} \] where $\boldsymbol{\mu}$ is the global mean vector, $\mathbf{pos}_t$ and $\mathbf{ctx}_c$ are the mean vectors across contexts and across positions respectively, and $\mathbf{resid}_{c,t}$ is the residual vector. For popular transformer architectures and diverse text datasets, empirically we find pervasive mathematical structure: (1) $(\mathbf{pos}_t)_{t}$ forms a low-dimensional, continuous, and often spiral shape across layers, (2) $(\mathbf{ctx}_c)_c$ shows clear cluster structure that falls into context topics, and (3) $(\mathbf{pos}_t)_{t}$ and $(\mathbf{ctx}_c)_c$ are mutually incoherent -- namely $\mathbf{pos}_t$ is almost orthogonal to $\mathbf{ctx}_c$ -- which is canonical in compressed sensing and dictionary learning. This decomposition offers structural insights about input formats in in-context learning (especially for induction heads) and in arithmetic tasks.