Hyperbolic Vision Transformers: Combining Improvements in Metric Learning (2203.10833v2)

Abstract: Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings and a distance-based loss function to match the representations -- usually, the Euclidean distance is utilized. An emerging interest in learning hyperbolic data embeddings suggests that hyperbolic geometry can be beneficial for natural data. Following this line of work, we propose a new hyperbolic-based model for metric learning. At the core of our method is a vision transformer with output embeddings mapped to hyperbolic space. These embeddings are directly optimized using modified pairwise cross-entropy loss. We evaluate the proposed model with six different formulations on four datasets achieving the new state-of-the-art performance. The source code is available at https://github.com/htdt/hyp_metric.

• The paper introduces hyperbolic embedding spaces that capture hierarchical data structures more effectively than traditional Euclidean methods.
• It integrates Vision Transformers with a modified pairwise cross-entropy loss, enhancing metric learning performance in image retrieval tasks.
• Empirical evaluations on multiple datasets demonstrate state-of-the-art results, underscoring the method's potential for complex data representations.

An Expert Review of "Hyperbolic Vision Transformers: Combining Improvements in Metric Learning"

The paper "Hyperbolic Vision Transformers: Combining Improvements in Metric Learning" integrates recent advancements in metric learning to propose a novel approach to image retrieval and similar tasks. By leveraging the capabilities of hyperbolic geometry, this research addresses the challenge of constructing discriminative and accurate embeddings for metric learning.

Core Contributions

Two principal innovations are introduced in the paper:

1. Hyperbolic Embedding Space: The authors propose leveraging hyperbolic space to address challenges in metric learning. Hyperbolic geometry, characterized by its exponential growth properties, is particularly adept at representing naturally hierarchical data, which is a prevalent attribute of real-world datasets. Hyperbolic embeddings were shown to outperform traditional Euclidean embeddings in capturing latent hierarchical structures, owing to their ability to efficiently represent complex data distributions in lower dimensions.
2. Integration with Vision Transformers: Vision transformers (ViTs) have emerged as a formidable alternative to convolutional neural networks (CNNs) for various computer vision tasks, with their lack of inductive biases allowing them to extrapolate more generalized features given adequate training data. This paper integrates ViTs with hyperbolic embeddings using a modified pairwise cross-entropy loss, capitalizing on the strengths of both architectures.

Methodology

• Vision Transformer Architecture: The ViT model processes images by dividing them into patches, translating these into embeddings, and mapping these embeddings into hyperbolic space. This setup purportedly benefits from the ViT's capacity to generalize from unseen classes due to its architecture and training regimen.
• Hyperbolic Mapping and Optimization: Embeddings derived from the ViT are mapped onto a hyperbolic space (specifically the Poincaré ball). The network utilizes a pairwise cross-entropy loss function adapted for hyperbolic distances to optimize these embeddings, focusing on differentiating representations by minimizing inter-class and maximizing intra-class distances.
• Empirical Strategy: The authors validated their methodology over four datasets, achieving new state-of-the-art performance results. They further quantified the delta-hyperbolicity of different datasets and assessed the effectiveness of the method across a range of hyperparameters, including embedding dimensionality and batch size.

Empirical Findings

• The paper demonstrated enhanced performance compared to traditional Euclidean-based methods, highlighting the value of hyperbolic embeddings in natural and complex hierarchical datasets.
• ViT-based approaches using hyperbolic embeddings outperformed alternatives employing CNN architectures.
• Experimental results underscored the advantage of hyperbolic space for encoding rich structural relationships without necessitating higher dimensional spaces.

Implications and Future Directions

The paper provides a compelling case for the integration of hyperbolic geometrical techniques within vision transformer frameworks, setting a precedent for future research in multi-modal embedding spaces and hierarchical data representation. While the current investigation primarily focuses on vision tasks, similar applications are conceivable in fields like natural language processing, where hierarchical structures are also prevalent.

Conclusion

The research introduces a methodologically sound synthesis of hyperbolic space embeddings and vision transformers for metric learning, elucidating promising pathways for future explorations in artificial intelligence. The paper suggests a significant potential for the development of more capable algorithms for various recognition and retrieval tasks, as evidenced by its empirical evaluations. This foundational work lays the groundwork for future investigations into the confluence of geometric paradigms and deep learning architectures.