A formulation is developed for deterministically calculating the optimized paths for a multi-agent system consisting of heterogeneous vehicles. The essence of this formulation is the calculation of the shortest time for each agent to reach every grid point from its known initial position. Such arrival time map can be readily assessed using the Fast Marching Method (FMM), a computational algorithm originally designed for solving boundary value problems of the Eikonal equation. Leveraging the FMM method, we demonstrate that the minimal time rendezvous point and paths for all member vehicles can be uniquely determined with minimal computational concerns. To showcase the potential of our method, we use an example of a virtual rendezvous scenario that entails the coordination of a ship, an underwater vehicle, an aerial vehicle, and a ground vehicle to converge at the optimal location within the Tampa Bay area in minimal time. It illustrates the value of the developed framework in efficiently constructing continuous path planning, while accommodating different operational constraints of heterogeneous member vehicles.

Multi-head self-attention-based Transformers have shown promise in different learning tasks. Albeit these models exhibit significant improvement in understanding short-term and long-term contexts from sequences, encoders of Transformers and their variants fail to preserve layer-wise contextual information. Transformers usually project tokens onto sparse manifolds and fail to preserve mathematical equivalence among the token representations. In this work, we propose TransJect, an encoder model that guarantees a theoretical bound for layer-wise distance preservation between a pair of tokens. We propose a simple alternative to dot-product attention to ensure Lipschitz continuity. This allows TransJect to learn injective mappings to transform token representations to different manifolds with similar topology and preserve Euclidean distance between every pair of tokens in subsequent layers. Evaluations across multiple benchmark short- and long-sequence classification tasks show maximum improvements of 6.8% and 5.9%, respectively, over the variants of Transformers. Additionally, TransJect displays 79% better performance than Transformer on the language modeling task. We further highlight the shortcomings of multi-head self-attention from the statistical physics viewpoint. Although multi-head self-attention was incepted to learn different abstraction levels within the networks, our empirical analyses suggest that different attention heads learn randomly and unorderly. In contrast, TransJect adapts a mixture of experts for regularization; these experts are more orderly and balanced and learn different sparse representations from the input sequences. TransJect exhibits very low entropy and can be efficiently scaled to larger depths.

The Landsat program is the longest-running Earth observation program in history, with 50+ years of data acquisition by 8 satellites. The multispectral imagery captured by sensors onboard these satellites is critical for a wide range of scientific fields. Despite the increasing popularity of deep learning and remote sensing, the majority of researchers still use decision trees and random forests for Landsat image analysis due to the prevalence of small labeled datasets and lack of foundation models. In this paper, we introduce SSL4EO-L, the first ever dataset designed for Self-Supervised Learning for Earth Observation for the Landsat family of satellites (including 3 sensors and 2 product levels) and the largest Landsat dataset in history (5M image patches). Additionally, we modernize and re-release the L7 Irish and L8 Biome cloud detection datasets, and introduce the first ML benchmark datasets for Landsats 4-5 TM and Landsat 7 ETM+ SR. Finally, we pre-train the first foundation models for Landsat imagery using SSL4EO-L and evaluate their performance on multiple semantic segmentation tasks.

We introduce Clifford Group Equivariant Neural Networks: a novel approach for constructing $\mathrm{O}(n)$- and $\mathrm{E}(n)$-equivariant models. We identify and study the $\textit{Clifford group}$, a subgroup inside the Clifford algebra tailored to achieve several favorable properties. Primarily, the group's action forms an orthogonal automorphism that extends beyond the typical vector space to the entire Clifford algebra while respecting the multivector grading. This leads to several non-equivalent subrepresentations corresponding to the multivector decomposition. Furthermore, we prove that the action respects not just the vector space structure of the Clifford algebra but also its multiplicative structure, i.e., the geometric product. These findings imply that every polynomial in multivectors, An advantage worth mentioning is that we obtain expressive layers that can elegantly generalize to inner-product spaces of any dimension. We demonstrate, notably from a single core implementation, state-of-the-art performance on several distinct tasks, including a three-dimensional $n$-body experiment, a four-dimensional Lorentz-equivariant high-energy physics experiment, and a five-dimensional convex hull experiment.

Large language models (LLMs) demonstrate impressive multilingual capability, but their performance varies substantially across different languages. In this work, we introduce a simple yet effective method, called cross-lingual-thought prompting (XLT), to systematically improve the multilingual capability of LLMs. Specifically, XLT is a generic template prompt that stimulates cross-lingual and logical reasoning skills to enhance task performance across languages. We conduct comprehensive evaluations on 7 typical benchmarks related to reasoning, understanding, and generation tasks, covering both high-resource and low-resource languages. Experimental results show that XLT not only remarkably enhances the performance of various multilingual tasks but also significantly reduces the gap between the average performance and the best performance of each task in different languages. Notably, XLT brings over 10 points of average improvement in arithmetic reasoning and open-domain question-answering tasks.

The field of safe multi-agent reinforcement learning, despite its potential applications in various domains such as drone delivery and vehicle automation, remains relatively unexplored. Training agents to learn optimal policies that maximize rewards while considering specific constraints can be challenging, particularly in scenarios where having a central controller to coordinate the agents during the training process is not feasible. In this paper, we address the problem of multi-agent policy optimization in a decentralized setting, where agents communicate with their neighbors to maximize the sum of their cumulative rewards while also satisfying each agent's safety constraints. We consider both peak and average constraints. In this scenario, there is no central controller coordinating the agents and both the rewards and constraints are only known to each agent locally/privately. We formulate the problem as a decentralized constrained multi-agent Markov Decision Problem and propose a momentum-based decentralized policy gradient method, DePAint, to solve it. To the best of our knowledge, this is the first privacy-preserving fully decentralized multi-agent reinforcement learning algorithm that considers both peak and average constraints. We also provide theoretical analysis and empirical evaluation of our algorithm in various scenarios and compare its performance to centralized algorithms that consider similar constraints.

Parametric reduced-order modelling often serves as a surrogate method for hemodynamics simulations to improve the computational efficiency in many-query scenarios or to perform real-time simulations. However, the snapshots of the method require to be collected from the same discretisation, which is a straightforward process for physical parameters, but becomes challenging for geometrical problems, especially for those domains featuring unparameterised and unique shapes, e.g. patient-specific geometries. In this work, a data-driven surrogate model is proposed for the efficient prediction of blood flow simulations on similar but distinct domains. The proposed surrogate model leverages group surface registration to parameterise those shapes and formulates corresponding hemodynamics information into geometry-informed snapshots by the diffeomorphisms constructed between a reference domain and original domains. A non-intrusive reduced-order model for geometrical parameters is subsequently constructed using proper orthogonal decomposition, and a radial basis function interpolator is trained for predicting the reduced coefficients of the reduced-order model based on compressed geometrical parameters of the shape. Two examples of blood flowing through a stenosis and a bifurcation are presented and analysed. The proposed surrogate model demonstrates its accuracy and efficiency in hemodynamics prediction and shows its potential application toward real-time simulation or uncertainty quantification for complex patient-specific scenarios.

Automated visual inspection of on-and offshore wind turbines using aerial robots provides several benefits, namely, a safe working environment by circumventing the need for workers to be suspended high above the ground, reduced inspection time, preventive maintenance, and access to hard-to-reach areas. A novel nonlinear model predictive control (NMPC) framework alongside a global wind turbine path planner is proposed to achieve distance-optimal coverage for wind turbine inspection. Unlike traditional MPC formulations, visual tracking NMPC (VT-NMPC) is designed to track an inspection surface, instead of a position and heading trajectory, thereby circumventing the need to provide an accurate predefined trajectory for the drone. An additional capability of the proposed VT-NMPC method is that by incorporating inspection requirements as visual tracking costs to minimize, it naturally achieves the inspection task successfully while respecting the physical constraints of the drone. Multiple simulation runs and real-world tests demonstrate the efficiency and efficacy of the proposed automated inspection framework, which outperforms the traditional MPC designs, by providing full coverage of the target wind turbine blades as well as its robustness to changing wind conditions. The implementation codes are open-sourced.

In the realm of maritime transportation, autonomous vessel navigation in natural inland waterways faces persistent challenges due to unpredictable natural factors. Existing scheduling algorithms fall short in handling these uncertainties, compromising both safety and efficiency. Moreover, these algorithms are primarily designed for non-autonomous vessels, leading to labor-intensive operations vulnerable to human error. To address these issues, this study proposes a risk-aware motion control approach for vessels that accounts for the dynamic and uncertain nature of tide islands in a distributionally robust manner. Specifically, a model predictive control method is employed to follow the reference trajectory in the time-space map while incorporating a risk constraint to prevent grounding accidents. To address uncertainties in tide islands, a novel modeling technique represents them as stochastic polytopes. Additionally, potential inaccuracies in waterway depth are addressed through a risk constraint that considers the worst-case uncertainty distribution within a Wasserstein ambiguity set around the empirical distribution. Using sensor data collected in the Guadalquivir River, we empirically demonstrate the performance of the proposed method through simulations on a vessel. As a result, the vessel successfully navigates the waterway while avoiding grounding accidents, even with a limited dataset of observations. This stands in contrast to existing non-robust controllers, highlighting the robustness and practical applicability of the proposed approach.

Diffusion models have shown promising results for a wide range of generative tasks with continuous data, such as image and audio synthesis. However, little progress has been made on using diffusion models to generate discrete symbolic music because this new class of generative models are not well suited for discrete data while its iterative sampling process is computationally expensive. In this work, we propose a diffusion model combined with a Generative Adversarial Network, aiming to (i) alleviate one of the remaining challenges in algorithmic music generation which is the control of generation towards a target emotion, and (ii) mitigate the slow sampling drawback of diffusion models applied to symbolic music generation. We first used a trained Variational Autoencoder to obtain embeddings of a symbolic music dataset with emotion labels and then used those to train a diffusion model. Our results demonstrate the successful control of our diffusion model to generate symbolic music with a desired emotion. Our model achieves several orders of magnitude improvement in computational cost, requiring merely four time steps to denoise while the steps required by current state-of-the-art diffusion models for symbolic music generation is in the order of thousands.