Heterogeneous federated learning without assuming any structure is challenging due to the conflicts among non-identical data distributions of clients.

ABSTRACT We develop a Markov decision process (MDP) framework to autonomously make guidance decisions for satellite collision avoidance maneuver (CAM) and a reinforcement learning policy gradient (RL-PG) algorithm to enable direct optimization of guidance policy using historic CAM data. In addition to maintaining acceptable collision risks, this approach seeks to minimize the average propellant consumption of CAMs by making early maneuver decisions. We model CAM as a continuous state, discrete action and finite horizon MDP, where the critical decision is determining when to initiate the maneuver. By deciding to maneuver earlier than conventional methods, the Markov policy effectively favors CAMs that achieve comparable rates of collision risk reduction while consuming less propellant. Using historical data of tracked conjunction events, we verify this framework and conduct an extensive parameter-sensitivity study. When evaluated on synthetic conjunction events, the trained policy consumes significantly less propellant overall and per maneuver in comparison to a conventional cut-off policy that initiates maneuvers 24 hours before the time of closest approach (TCA). On historical conjunction events, the trained policy consumes more propellant overall but consumes less propellant per maneuver. For both historical and synthetic conjunction events, the trained policy is slightly more conservative in identifying conjunctions events that warrant CAMs in comparison to cutoff policies.

The field has seen many efforts to measure 3D and motion understanding from videos, each contributing a part of the overall goal.

While training models and labeling data are resource-intensive, a wealth of pre-trained models and unlabeled data exists.

In the first phase, we individually train both 2D and 3D classifiers with the classification loss of each domain. After that, we jointly train them using the proposed 2D-to-3D and 3D-to-2D losses, in addition to the classification loss. Here, in the second phase, please note that we first train our framework without the 3D-to-2D loss for the first few epochs. As we explained in Section 4.1 of the main paper, we augment the images and point clouds before we In this subsection, we provide our augmentation methods in detail. On the other hand, when we use a smaller patch size, fine details of the image could not be preserved.

In this work, we propose a novel Cross Attention Network to address the challenging problems in few-shot classification.

The fact that DAG learning can be reduced to learning a topological sort is well-known. Theorem 3.1 is an immediate corollary of Lemma B.1. For completeness, we include a proof below. In this appendix, we illustrate how Theorem 3.1 can be extended to the case where residual variances Then the order π is identifiable. Before proving this result, we illustrate it with an example.

Large Language Models (LLMs) hallucinate, generating factually incorrect yet confident assertions. We argue this stems from the Transformer's Softmax function, which creates "Artificial Certainty" by collapsing ambiguous attention scores into a single probability distribution, discarding uncertainty information at each layer. To fix this, we introduce the Credal Transformer, which replaces standard attention with a Credal Attention Mechanism (CAM) based on evidential theory. CAM produces a "credal set" (a set of distributions) instead of a single attention vector, with the set's size directly measuring model uncertainty. We implement this by re-conceptualizing attention scores as evidence masses for a Dirichlet distribution: sufficient evidence recovers standard attention, while insufficient evidence yields a diffuse distribution, representing ambiguity. Empirically, the Credal Transformer identifies out-of-distribution inputs, quantifies ambiguity, and significantly reduces confident errors on unanswerable questions by abstaining. Our contribution is a new architecture to mitigate hallucinations and a design paradigm that integrates uncertainty quantification directly into the model, providing a foundation for more reliable AI.

The effectiveness of Multimodal Chain-of-Thought (MCoT) prompting is often limited by the use of randomly or manually selected examples. These examples fail to account for both model-specific knowledge distributions and the intrinsic complexity of the tasks, resulting in suboptimal and unstable model performance. To address this, we propose a novel framework inspired by the pedagogical principle of "tailored teaching with balanced difficulty". We reframe prompt selection as a prompt curriculum design problem: constructing a well ordered set of training examples that align with the model's current capabilities. Our approach integrates two complementary signals: (1) model-perceived difficulty, quantified through prediction disagreement in an active learning setup, capturing what the model itself finds challenging; and (2) intrinsic sample complexity, which measures the inherent difficulty of each question-image pair independently of any model. By jointly analyzing these signals, we develop a difficulty-balanced sampling strategy that ensures the selected prompt examples are diverse across both dimensions. Extensive experiments conducted on five challenging benchmarks and multiple popular Multimodal Large Language Models (MLLMs) demonstrate that our method yields substantial and consistent improvements and greatly reduces performance discrepancies caused by random sampling, providing a principled and robust approach for enhancing multimodal reasoning.