429 research outputs found

    Hyperbolic Geometry in Computer Vision: A Novel Framework for Convolutional Neural Networks

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    Real-world visual data exhibit intrinsic hierarchical structures that can be represented effectively in hyperbolic spaces. Hyperbolic neural networks (HNNs) are a promising approach for learning feature representations in such spaces. However, current methods in computer vision rely on Euclidean backbones and only project features to the hyperbolic space in the task heads, limiting their ability to fully leverage the benefits of hyperbolic geometry. To address this, we present HCNN, the first fully hyperbolic convolutional neural network (CNN) designed for computer vision tasks. Based on the Lorentz model, we generalize fundamental components of CNNs and propose novel formulations of the convolutional layer, batch normalization, and multinomial logistic regression (MLR). Experimentation on standard vision tasks demonstrates the effectiveness of our HCNN framework and the Lorentz model in both hybrid and fully hyperbolic settings. Overall, we aim to pave the way for future research in hyperbolic computer vision by offering a new paradigm for interpreting and analyzing visual data. Our code is publicly available at https://github.com/kschwethelm/HyperbolicCV

    Learning Weakly Supervised Audio-Visual Violence Detection in Hyperbolic Space

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    In recent years, the task of weakly supervised audio-visual violence detection has gained considerable attention. The goal of this task is to identify violent segments within multimodal data based on video-level labels. Despite advances in this field, traditional Euclidean neural networks, which have been used in prior research, encounter difficulties in capturing highly discriminative representations due to limitations of the feature space. To overcome this, we propose HyperVD, a novel framework that learns snippet embeddings in hyperbolic space to improve model discrimination. Our framework comprises a detour fusion module for multimodal fusion, effectively alleviating modality inconsistency between audio and visual signals. Additionally, we contribute two branches of fully hyperbolic graph convolutional networks that excavate feature similarities and temporal relationships among snippets in hyperbolic space. By learning snippet representations in this space, the framework effectively learns semantic discrepancies between violent and normal events. Extensive experiments on the XD-Violence benchmark demonstrate that our method outperforms state-of-the-art methods by a sizable margin.Comment: 8 pages, 5 figure

    Federated Learning with Manifold Regularization and Normalized Update Reaggregation

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    Federated Learning (FL) is an emerging collaborative machine learning framework where multiple clients train the global model without sharing their own datasets. In FL, the model inconsistency caused by the local data heterogeneity across clients results in the near-orthogonality of client updates, which leads to the global update norm reduction and slows down the convergence. Most previous works focus on eliminating the difference of parameters (or gradients) between the local and global models, which may fail to reflect the model inconsistency due to the complex structure of the machine learning model and the Euclidean space's limitation in meaningful geometric representations. In this paper, we propose FedMRUR by adopting the manifold model fusion scheme and a new global optimizer to alleviate the negative impacts. Concretely, FedMRUR adopts a hyperbolic graph manifold regularizer enforcing the representations of the data in the local and global models are close to each other in a low-dimensional subspace. Because the machine learning model has the graph structure, the distance in hyperbolic space can reflect the model bias better than the Euclidean distance. In this way, FedMRUR exploits the manifold structures of the representations to significantly reduce the model inconsistency. FedMRUR also aggregates the client updates norms as the global update norm, which can appropriately enlarge each client's contribution to the global update, thereby mitigating the norm reduction introduced by the near-orthogonality of client updates. Furthermore, we theoretically prove that our algorithm can achieve a linear speedup property for non-convex setting under partial client participation.Experiments demonstrate that FedMRUR can achieve a new state-of-the-art (SOTA) accuracy with less communication

    Hyperbolic Image-Text Representations

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    Visual and linguistic concepts naturally organize themselves in a hierarchy, where a textual concept ``dog'' entails all images that contain dogs. Despite being intuitive, current large-scale vision and language models such as CLIP do not explicitly capture such hierarchy. We propose MERU, a contrastive model that yields hyperbolic representations of images and text. Hyperbolic spaces have suitable geometric properties to embed tree-like data, so MERU can better capture the underlying hierarchy in image-text data. Our results show that MERU learns a highly interpretable representation space while being competitive with CLIP's performance on multi-modal tasks like image classification and image-text retrieval.Comment: Technical repor

    Geometric Interaction Augmented Graph Collaborative Filtering

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    Graph-based collaborative filtering is capable of capturing the essential and abundant collaborative signals from the high-order interactions, and thus received increasingly research interests. Conventionally, the embeddings of users and items are defined in the Euclidean spaces, along with the propagation on the interaction graphs. Meanwhile, recent works point out that the high-order interactions naturally form up the tree-likeness structures, which the hyperbolic models thrive on. However, the interaction graphs inherently exhibit the hybrid and nested geometric characteristics, while the existing single geometry-based models are inadequate to fully capture such sophisticated topological patterns. In this paper, we propose to model the user-item interactions in a hybrid geometric space, in which the merits of Euclidean and hyperbolic spaces are simultaneously enjoyed to learn expressive representations. Experimental results on public datasets validate the effectiveness of our proposal

    Inferring Concept Hierarchies from Text Corpora via Hyperbolic Embeddings

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    We consider the task of inferring is-a relationships from large text corpora. For this purpose, we propose a new method combining hyperbolic embeddings and Hearst patterns. This approach allows us to set appropriate constraints for inferring concept hierarchies from distributional contexts while also being able to predict missing is-a relationships and to correct wrong extractions. Moreover -- and in contrast with other methods -- the hierarchical nature of hyperbolic space allows us to learn highly efficient representations and to improve the taxonomic consistency of the inferred hierarchies. Experimentally, we show that our approach achieves state-of-the-art performance on several commonly-used benchmarks
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