Hyperbolic Deep Neural Networks: A Survey

Peng, Wei; Varanka, Tuomas; Mostafa, Abdelrahman; Shi, Henglin; Zhao, Guoying

doi:10.48550/arxiv.2101.04562

Cited by 11 publications

(12 citation statements)

References 85 publications

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“…It has been repeatedly shown that the hyperbolic space is able to embed hierarchical structures with minimal distortion [33,36,38]. To that end, we investigate the potential of incorporating hierarchical relations between classes for image segmentation on hyperbolic manifolds.…”

Section: Hierarchical Hyperbolic Class Embeddingmentioning

confidence: 99%

Hyperbolic Image Segmentation

GhadimiAtigh¹,

Schoep²,

Acar³

et al. 2022

Preprint

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Figure 1. Two examples of insights that come for free with Hyperbolic Image Segmentation. For both examples, each black dot denotes a pixel embedding in hyperbolic space. Left (Pascal VOC): next to per-pixel classification, the distance to the origin in hyperbolic space provides a free measure of uncertainty. Right (COCO-Stuff-10k): the hyperbolic positioning of pixels even allows us to pinpoint interiors and edges of objects, as indicated by the colored boxes and their corresponding pixels in the segmentation map. Other benefits of hyperbolic embeddings for segmentation include zero-label generalization and better performance in low-dimensional embedding spaces.

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Section: Hierarchical Hyperbolic Class Embeddingmentioning

confidence: 99%

Hyperbolic Image Segmentation

GhadimiAtigh¹,

Schoep²,

Acar³

et al. 2022

Preprint

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“…For this paper, we primarily study embedding into the two-dimensional Poincaré disks. It is well known that tree-like structure embeds well into the Poincaré disk since the distance gets stretched close to the boundary of Poincaré disks [37,[64][65][66]. Thus it is interesting to view jets as tree structures and embed them into Poincaré disks.…”

Section: Hyperbolic Embedding Of Jetsmentioning

confidence: 99%

Neural Embedding: Learning the Embedding of the Manifold of Physics Data

Park¹,

Harris²,

Ostdiek³

2022

Preprint

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In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in the data analysis pipeline for many applications. Using progressively more realistic simulated collisions at the Large Hadron Collider, we show that this embedding approach learns the underlying latent structure. With the notion of volume in Euclidean spaces, we provide for the first time a viable solution to quantifying the true search capability of model agnostic search algorithms in collider physics (i.e. anomaly detection). Finally, we discuss how the ideas presented in this paper can be employed to solve many practical challenges that require the extraction of physically meaningful representations from information in complex high dimensional datasets.

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“…The computational complexity for N strings of size M is reduced from O(N 2 M 2 / log M ) for the centre string and O(N 2 M ) for the greedy baselines to O(N M ) for the proposed method. Future work could employ models that directly operate in the hyperbolic space [52] to further improve the performance.…”

Section: Steiner String Approach To Multiple Sequence Alignmentmentioning

confidence: 99%

“…[24,12] provide some initial work in this direction with respect to the edit distance. Moreover, the capacity of the hyperbolic space could be further exploited using models that directly operate in the space [52,55,56].…”

Section: Type Of Labelsmentioning

confidence: 99%

Neural Distance Embeddings for Biological Sequences

Corso¹,

Ying²,

Pándy³

et al. 2021

Preprint

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The development of data-dependent heuristics and representations for biological sequences that reflect their evolutionary distance is critical for large-scale biological research. However, popular machine learning approaches, based on continuous Euclidean spaces, have struggled with the discrete combinatorial formulation of the edit distance that models evolution and the hierarchical relationship that characterises real-world datasets. We present Neural Distance Embeddings (NeuroSEED), a general framework to embed sequences in geometric vector spaces, and illustrate the effectiveness of the hyperbolic space that captures the hierarchical structure and provides an average 22% reduction in embedding RMSE against the best competing geometry. The capacity of the framework and the significance of these improvements are then demonstrated devising supervised and unsupervised NeuroSEED approaches to multiple core tasks in bioinformatics. Benchmarked with common baselines, the proposed approaches display significant accuracy and/or runtime improvements on real-world datasets. As an example for hierarchical clustering, the proposed pretrained and from-scratch methods match the quality of competing baselines with 30x and 15x runtime reduction, respectively.

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Hyperbolic Deep Neural Networks: A Survey

Cited by 11 publications

References 85 publications

Hyperbolic Image Segmentation

Hyperbolic Image Segmentation

Neural Embedding: Learning the Embedding of the Manifold of Physics Data

Neural Distance Embeddings for Biological Sequences

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