Real-world data distributions often shift continuously across multiple latent factors such as time, geography, and socioeconomic contexts. However, existing domain generalization approaches typically treat domains as discrete or as evolving along a single axis (e.g., time). This oversimplification fails to capture the complex, multidimensional nature of real-world variation. This paper introduces the task of Continuous Domain Generalization (CDG), which aims to generalize predictive models to unseen domains defined by arbitrary combinations of continuous variations. We present a principled framework grounded in geometric and algebraic theories, showing that optimal model parameters across domains lie on a low-dimensional manifold. To model this structure, we propose a Neural Lie Transport Operator (NeuralLio), which enables structure-preserving parameter transitions by enforcing geometric continuity and algebraic consistency. To handle noisy or incomplete domain variation descriptors, we introduce a gating mechanism to suppress irrelevant dimensions and a local chart-based strategy for robust generalization. Extensive experiments on synthetic and real-world datasets, including remote sensing, scientific documents, and traffic forecasting, demonstrate that our method significantly outperforms existing baselines in both generalization accuracy and robustness.

The formation control of multi-agent systems has increasingly drawn attention for fulfilling numerous emerging applications and services. To achieve high-accuracy formation, the location awareness of all agents becomes an essential requirement. In this paper, we address the problem of network localization and formation control in a cooperative system with asynchronous agents. In particular, we formulate the joint localization and synchronization of agents as a statistical inference problem. The underlying probabilistic model is represented by a factor graph from which a message-passing algorithm is designed that computes approximations of the marginals of unknown variables, i.e. agents’ locations and clock offsets. Due to the Euclidean-norm operator involved in their computation no parametric closed-form expressions of the messages exist. As a compromise, implemented message-passing methods therefore resort to approximations of these messages. Conventional methods rely either on a first-order Taylor expansion of the norm operation or on non-parametric representations, e.g. by means particle filters (PFs), to compute such approximations. However, the former approach suffers from poor performance while the latter one experiences high complexity. The proposed message-passing algorithm in this paper is parametric. Specifically, it passes Gaussian messages that can be essentially obtained by suitably augmenting the factor graph and applying on it a hybrid method for combining belief propagation and variational message passing. Subsequently, the agents can exploit the estimated locations for determining the control policy. Two types of control policy are designed based on the optimization of a generalized cost function. We show that the proposed scheme enjoys a reduced complexity for multi-agent localization while achieving the desired formation with excellent accuracy.

Hyper-parameter tuning (HPT) for deep learning (DL) models is prohibitively expensive. Sequential model-based optimization (SMBO) emerges as the state-of-the-art (SOTA) approach to automatically optimize HPT performance due to its heuristic advantages. Unfortunately, focusing on algorithm optimization rather than a large-scale parallel HPT system, existing SMBO-based approaches still cannot effectively remove their strong sequential nature, posing two performance problems: (1)extremely low tuning speedand (2)sub-optimal model quality. In this paper, we propose FastTuning, a fast, scalable, and generic system aiming at parallelly accelerating SMBO-based HPT for large DL/ML models. The key is to partition the highly complex search space into multiple smaller sub-spaces, each of which is assigned to and optimized by a different tuning worker in parallel. However, determining the right level of resource allocation to strike a balance between quality and cost remains a challenge. To address this, we further propose NIMBLE, a dynamic scheduling strategy that is specially designed for FastTuning, including (1) Dynamic Elimination Algorithm, (2) Sub-space Re-division, and (3) Posterior Information Sharing. Finally, we incorporate 6 SOTAs (i.e., 3 tuning algorithms and 3 parallel tuning tools) into FastTuning. Experimental results, on ResNet18, VGG19, ResNet50, and ResNet152, show that FastTuning can consistently offer much faster tuning speed (up to$80\times$) with better accuracy (up to 4.7% improvement), thereby enabling the application of automatic HPT to real-life DL models.