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).

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

Deepfake technology utilizes deep learning based face manipulation techniques to seamlessly replace faces in videos creating highly realistic but artificially generated content. Although this technology has beneficial applications in media and entertainment misuse of its capabilities may lead to serious risks including identity theft cyberbullying and false information. The integration of DL with visual cognition has resulted in important technological improvements particularly in addressing privacy risks caused by artificially generated deepfake images on digital media platforms. In this study we propose an efficient and lightweight method for detecting deepfake images and videos making it suitable for devices with limited computational resources. In order to reduce the computational burden usually associated with DL models our method integrates machine learning classifiers in combination with keyframing approaches and texture analysis. Moreover the features extracted with a histogram of oriented gradients (HOG) local binary pattern (LBP) and KAZE bands were integrated to evaluate using random forest extreme gradient boosting extra trees and support vector classifier algorithms. Our findings show a feature-level fusion of HOG LBP and KAZE features improves accuracy to 92% and 96% on FaceForensics++ and Celeb-DFv2 respectively.

We develop convergent minimization algorithms for Bethe variational approximations which explicitly constrain marginal estimates to families of valid distributions. While existing message passing algorithms define fixed point iterations corresponding to stationary points of the Bethe free energy, their greedy dynamics do not distinguish between local minima and maxima, and can fail to converge. For continuous estimation problems, this instability is linked to the creation of invalid marginal estimates, such as Gaussians with negative variance. Conversely, our approach leverages multiplier methods with well-understood convergence properties, and uses bound projection methods to ensure that marginal approximations are valid at all iterations. We derive general algorithms for discrete and Gaussian pairwise Markov random fields, showing improvements over standard loopy belief propagation. We also apply our method to a hybrid model with both discrete and continuous variables, showing improvements over expectation propagation.

This paper introduces a robust approach for automated defect detection in tire X-ray images by harnessing traditional feature extraction methods such as Local Binary Pattern (LBP) and Gray Level Co-Occurrence Matrix (GLCM) features, as well as Fourier and Wavelet-based features, complemented by advanced machine learning techniques. Recognizing the challenges inherent in the complex patterns and textures of tire X-ray images, the study emphasizes the significance of feature engineering to enhance the performance of defect detection systems. By meticulously integrating combinations of these features with a Random Forest (RF) classifier and comparing them against advanced models like YOLOv8, the research not only benchmarks the performance of traditional features in defect detection but also explores the synergy between classical and modern approaches. The experimental results demonstrate that these traditional features, when fine-tuned and combined with machine learning models, can significantly improve the accuracy and reliability of tire defect detection, aiming to set a new standard in automated quality assurance in tire manufacturing.