Mainstream approaches for unsupervised domain adaptation (UDA) learn domaininvariant representations to narrow the domain shift, which are empirically effective but theoretically challenged by the hardness or impossibility theorems. Recently, self-training has been gaining momentum in UDA, which exploits unlabeled target data by training with target pseudo-labels. However, as corroborated in this work, under distributional shift, the pseudo-labels can be unreliable in terms of their large discrepancy from target ground truth. In this paper, we propose Cycle Self-Training (CST), a principled self-training algorithm that explicitly enforces pseudo-labels to generalize across domains.

Inthe forward step, CST generates target pseudo-labels with asource-trained classifier.

We thank the reviewers for their insightful feedback; we address each review below. R1: "...it is known how to solve the BFE optimisation problem by double loop algorithms" "...what is meant by'they are run once..."' "...meaningless for pairwise marginals..." Agreed. We included the pairwise marginals just for completeness. "Ising model...expect that the estimation quality will degrade with the (average) interaction strength." "The experiments have in my view a preliminary character" We agree our experiments are on small datasets.

We thank the reviewers for their insightful feedback; we address each review below. R1: "...it is known how to solve the BFE optimisation problem by double loop algorithms" "...what is meant by'they are run once..."' "...meaningless for pairwise marginals..." Agreed. We included the pairwise marginals just for completeness. "Ising model...expect that the estimation quality will degrade with the (average) interaction strength." "The experiments have in my view a preliminary character" We agree our experiments are on small datasets.

The Markov Chain Monte Carlo (MCMC) algorithm is one of the most widely used methods for sampling from intractable distributions (Robert & Casella, 2013).

--Feature engineering continues to play a critical role in image classification, particularly when interpretability and computational efficiency are prioritized over deep learning models with millions of parameters. In this study, we revisit classical machine learning based image classification through a novel approach centered on Permutation Entropy (PE), a robust and computationally lightweight measure traditionally used in time series analysis but rarely applied to image data. We extend PE to two-dimensional images and propose a multiscale, multi-orientation entropy-based feature extraction approach that characterizes spatial order and complexity along rows, columns, diagonals, anti-diagonals, and local patches of the image. T o enhance the discriminatory power of the entropy features, we integrate two classic image descriptors: the Histogram of Oriented Gradients (HOG) to capture shape and edge structure, and Local Binary Patterns (LBP) to encode micro-texture of an image. The resulting hand-crafted feature set, comprising of 780 dimensions, is used to train Support V ector Machine (SVM) classifiers optimized through grid search. The proposed approach is evaluated on multiple benchmark datasets, including Fashion-MNIST, KMNIST, EMNIST, and CIF AR-10, where it delivers competitive classification performance without relying on deep architectures. Our results demonstrate that the fusion of PE with HOG and LBP provides a compact, interpretable, and effective alternative to computationally expensive and limited interpretable deep learning models. This shows a potential of entropy-based descriptors in image classification and contributes a lightweight and generalizable solution to interpretable machine learning in image classification and computer vision. A Sen, B.K. Parida and D.I. Bondar are with Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA.

Line-breaking passes (LBPs) are crucial tactical actions in football, allowing teams to penetrate defensive lines and access high-value spaces. In this study, we present an unsupervised, clustering-based framework for detecting and analysing LBPs using synchronised event and tracking data from elite matches. Our approach models opponent team shape through vertical spatial segmentation and identifies passes that disrupt defensive lines within open play. Beyond detection, we introduce several tactical metrics, including the space build-up ratio (SBR) and two chain-based variants, LBPCh$^1$ and LBPCh$^2$, which quantify the effectiveness of LBPs in generating immediate or sustained attacking threats. We evaluate these metrics across teams and players in the 2022 FIFA World Cup, revealing stylistic differences in vertical progression and structural disruption. The proposed methodology is explainable, scalable, and directly applicable to modern performance analysis and scouting workflows.

Current robotic planning methods often rely on predicting multi-frame images with full pixel details. While this fine-grained approach can serve as a generic world model, it introduces two significant challenges for downstream policy learning: substantial computational costs that hinder real-time deployment, and accumulated inaccuracies that can mislead action extraction. Planning with coarse-grained subgoals partially alleviates efficiency issues. However, their forward planning schemes can still result in off-task predictions due to accumulation errors, leading to misalignment with long-term goals. This raises a critical question: Can robotic planning be both efficient and accurate enough for real-time control in long-horizon, multi-stage tasks? To address this, we propose a Latent Space Backward Planning scheme (LBP), which begins by grounding the task into final latent goals, followed by recursively predicting intermediate subgoals closer to the current state. The grounded final goal enables backward subgoal planning to always remain aware of task completion, facilitating on-task prediction along the entire planning horizon. The subgoal-conditioned policy incorporates a learnable token to summarize the subgoal sequences and determines how each subgoal guides action extraction. Through extensive simulation and real-robot long-horizon experiments, we show that LBP outperforms existing fine-grained and forward planning methods, achieving SOTA performance. Project Page: https://lbp-authors.github.io