Point cloud processing has become a cornerstone technology in many 3D vision tasks. However, arbitrary rotations introduce variations in point cloud orientations, posing a long-standing challenge for effective representation learning. The core of this issue is the disruption of the point cloud's intrinsic directional characteristics caused by rotational perturbations. Recent methods attempt to implicitly model rotational equivariance and invariance, preserving directional information and propagating it into deep semantic spaces. Yet, they often fall short of fully exploiting the multiscale directional nature of point clouds to enhance feature representations. To address this, we propose the Direction-Perceptive Vector Network (DiPVNet). At its core is an atomic dot-product operator that simultaneously encodes directional selectivity and rotation invariance--endowing the network with both rotational symmetry modeling and adaptive directional perception. At the local level, we introduce a Learnable Local Dot-Product (L2DP) Operator, which enables interactions between a center point and its neighbors to adaptively capture the non-uniform local structures of point clouds. At the global level, we leverage generalized harmonic analysis to prove that the dot-product between point clouds and spherical sampling vectors is equivalent to a direction-aware spherical Fourier transform (DASFT). This leads to the construction of a global directional response spectrum for modeling holistic directional structures. We rigorously prove the rotation invariance of both operators. Extensive experiments on challenging scenarios involving noise and large-angle rotations demonstrate that DiPVNet achieves state-of-the-art performance on point cloud classification and segmentation tasks. Our code is available at https://github.com/wxszreal0/DiPVNet.

Hypergraphs provide a natural way to represent higher-order interactions among multiple entities. While undirected hypergraphs have been extensively studied, the case of directed hypergraphs, which can model oriented group interactions, remains largely under-explored despite its relevance for many applications. Recent approaches in this direction often exhibit an implicit bias toward homophily, which limits their effectiveness in heterophilic settings. Rooted in the algebraic topology notion of Cellular Sheaves, Sheaf Neural Networks (SNNs) were introduced as an effective solution to circumvent such a drawback. While a generalization to hypergraphs is known, it is only suitable for undirected hypergraphs, failing to tackle the directed case. In this work, we introduce Directional Sheaf Hypergraph Networks (DSHN), a framework integrating sheaf theory with a principled treatment of asymmetric relations within a hypergraph. From it, we construct the Directed Sheaf Hypergraph Laplacian, a complex-valued operator by which we unify and generalize many existing Laplacian matrices proposed in the graph- and hypergraph-learning literature. Across 7 real-world datasets and against 13 baselines, DSHN achieves relative accuracy gains from 2% up to 20%, showing how a principled treatment of directionality in hypergraphs, combined with the expressive power of sheaves, can substantially improve performance.

Feature selection is crucial for fuzzy decision systems (FDSs), as it identifies informative features and eliminates rule redundancy, thereby enhancing predictive performance and interpretability. Most existing methods either fail to directly align evaluation criteria with learning performance or rely solely on non-directional Euclidean distances to capture relationships among decision classes, which limits their ability to clarify decision boundaries. However, the spatial distribution of instances has a potential impact on the clarity of such boundaries. Motivated by this, we propose Spatially-aware Separability-driven Feature Selection (S$^2$FS), a novel framework for FDSs guided by a spatially-aware separability criterion. This criterion jointly considers within-class compactness and between-class separation by integrating scalar-distances with spatial directional information, providing a more comprehensive characterization of class structures. S$^2$FS employs a forward greedy strategy to iteratively select the most discriminative features. Extensive experiments on ten real-world datasets demonstrate that S$^2$FS consistently outperforms eight state-of-the-art feature selection algorithms in both classification accuracy and clustering performance, while feature visualizations further confirm the interpretability of the selected features.

These relations often possess a natural notion of direction.

Image goal navigation requires two different skills: firstly, core navigation skills, including the detection of free space and obstacles, and taking decisions based on an internal representation; and secondly, computing directional information by comparing visual observations to the goal image. Current state-of-the-art methods either rely on dedicated image-matching, or pre-training of computer vision modules on relative pose estimation. In this paper, we study whether this task can be efficiently solved with end-to-end training of full agents with RL, as has been claimed by recent work. A positive answer would have impact beyond Embodied AI and allow training of relative pose estimation from reward for navigation alone. In this large experimental study we investigate the effect of architectural choices like late fusion, channel stacking, space-to-depth projections and cross-attention, and their role in the emergence of relative pose estimators from navigation training. W e show that the success of recent methods is influenced up to a certain extent by simulator settings, leading to shortcuts in simulation. However, we also show that these capabilities can be transferred to more realistic setting, up to some extent. W e also find evidence for correlations between navigation performance and probed (emerging) relative pose estimation performance, an important sub skill.

Graph Neural Networks (GNNs) have emerged as a powerful tool for modeling relational data in applications such as financial fraud detection [1], [2] and social network analysis [3]. As GNNs are increasingly deployed in safety-critical domains where their decisions impact human lives and societal well-being [4], [5], ensuring their trustworthiness has become essential. Unlike traditional software systems, where correctness can often be ensured through formal verification [6], [7], deep learning models--including GNNs--function as black boxes, making it difficult to validate their decisions. To address this, explainability has become essential for deploying GNNs in real-world decision-making pipelines. Recently, post-hoc explanation methods such as GNNExplainer [8] and PGExplainer [9] are widely used to enhance user trust, facilitate model debugging for developers, and provide external validation for regulatory compliance in these black-box GNN models. A useful analogy can be drawn between explaining con-volutional neural networks (CNNs) and GNNs. As shown in Figure 1, CNN explainability method Grad-CAM [10], highlight key image regions influencing a prediction--e.g., focusing on a dog's face to classify it as "dog." Similarly, GNN explainers identify critical subgraph structures affecting predictions.

Originality: The paper proposes a novel model for the recently introduced VCR task. The main novelty of the proposed model lies in the component GraphVLAD and directional GCN modules. The paper describes that one of the closest works to this work is that of Narsimhan et al., NeurIPS 2018 that used GCN to infer answers in VQA, however that work constructs an undirected graph, ignoring the directional information between the graph nodes. This paper uses directed graph instead and shows the usefulness of incorporating directional information. It would be good for this paper to include more related work on GraphVLAD front. Quality: The paper evaluates the proposed approach on the VCR dataset and compares with the baselines and previous state-of-the-art, demonstrating how the proposed work improves the previous best performance significantly.

In recent years, machine learning (ML) models have shown great success in materials science by accurately predicting quantum properties of atomistic systems several orders of magnitude faster than ab initio simulations [1]. These ML models have practically assisted researchers in developing novel materials across various fields, such as fluorescent molecules [2], electret polymers [3] and so on. Graph neural networks (GNNs) [4, 5] are particularly notable among ML models for atomic systems because molecules are especially suitable for 3D graph representations where each atom is characterized by its 3D Cartesian coordinate. The 3D molecular information, such as bond lengths and angles, is crucial for model learning [6, 7, 8]. However, these rotationally invariant representations may lack directional information, causing the model to view distinct structures as identical [9, 10].

Anatomical consistency in biomarker segmentation is crucial for many medical image analysis tasks. A promising paradigm for achieving anatomically consistent segmentation via deep networks is incorporating pixel connectivity, a basic concept in digital topology, to model inter-pixel relationships. However, previous works on connectivity modeling have ignored the rich channel-wise directional information in the latent space. In this work, we demonstrate that effective disentanglement of directional sub-space from the shared latent space can significantly enhance the feature representation in the connectivity-based network. To this end, we propose a directional connectivity modeling scheme for segmentation that decouples, tracks, and utilizes the directional information across the network. Experiments on various public medical image segmentation benchmarks show the effectiveness of our model as compared to the state-of-the-art methods. Code is available at https://github.com/Zyun-Y/DconnNet.