Hyperbolic Deep Neural Networks: A Survey

Modeling Tree-like Heterophily on Symmetric Matrix Manifolds

Tree-like structures, characterized by hierarchical relationships and power-law distributions, are prevalent in a multitude of real-world networks, ranging from social networks to citation networks and protein-protein interaction networks. Recently, there has been significant interest in utilizing hyperbolic space to model these structures, owing to its capability to represent them with diminished distortions compared to flat Euclidean space. However, real-world networks often display a blend of flat, tree-like, and circular substructures, resulting in heterophily. To address this diversity of substructures, this study aims to investigate the reconstruction of graph neural networks on the symmetric manifold, which offers a comprehensive geometric space for more effective modeling of tree-like heterophily. To achieve this objective, we propose a graph convolutional neural network operating on the symmetric positive-definite matrix manifold, leveraging Riemannian metrics to facilitate the scheme of information propagation. Extensive experiments conducted on semi-supervised node classification tasks validate the superiority of the proposed approach, demonstrating that it outperforms comparative models based on Euclidean and hyperbolic geometries.

Exploring Hierarchical Information in Hyperbolic Space for Self-Supervised Image Hashing

In real-world datasets, visually related images often form clusters, and these clusters can be further grouped into larger categories with more general semantics. These inherent hierarchical structures can help capture the underlying distribution of data, making it easier to learn robust hash codes that lead to better retrieval performance. However, existing methods fail to make use of this hierarchical information, which in turn prevents the accurate preservation of relationships between data points in the learned hash codes, resulting in suboptimal performance. In this paper, our focus is on applying visual hierarchical information to self-supervised hash learning and addressing three key challenges, including the construction, embedding, and exploitation of visual hierarchies. We propose a new self-supervised hashing method named Hierarchical Hyperbolic Contrastive Hashing (HHCH), making breakthroughs in three aspects. First, we propose to embed continuous hash codes into hyperbolic space for accurate semantic expression since embedding hierarchies in the hyperbolic space generates less distortion than in the hyper-sphere or Euclidean space. Second, we update the K-Means algorithm to make it run in the hyperbolic space. The proposed hierarchical hyperbolic K-Means algorithm can achieve the adaptive construction of hierarchical semantic structures. Last but not least, to exploit the hierarchical semantic structures in hyperbolic space, we propose the hierarchical contrastive learning algorithm, including hierarchical instance-wise and hierarchical prototype-wise contrastive learning. Extensive experiments on four benchmark datasets demonstrate that the proposed method outperforms state-of-the-art self-supervised hashing methods. Our codes are released at https://github.com/HUST-IDSM-AI/HHCH.git.

Analysis and review of techniques and tools based on machine learning and deep learning for prediction of lysine malonylation sites in protein sequences

The post-translational modifications occur as crucial molecular regulatory mechanisms utilized to regulate diverse cellular processes. Malonylation of proteins, a reversible post-translational modification of lysine/k residues, is linked to a variety of biological functions, such as cellular regulation and pathogenesis. This modification plays a crucial role in metabolic pathways, mitochondrial functions, fatty acid oxidation and other life processes. However, accurately identifying malonylation sites is crucial to understand the molecular mechanism of malonylation, and the experimental identification can be a challenging and costly task. Recently, approaches based on machine learning (ML) have been suggested to address this issue. It has been demonstrated that these procedures improve accuracy while lowering costs and time constraints. However, these approaches also have specific shortcomings, including inappropriate feature extraction out of protein sequences, high-dimensional features and inefficient underlying classifiers. As a result, there is an urgent need for effective predictors and calculation methods. In this study, we provide a comprehensive analysis and review of existing prediction models, tools and benchmark datasets for predicting malonylation sites in protein sequences followed by a comparison study. The review consists of the specifications of benchmark datasets, explanation of features and encoding methods, descriptions of the predictions approaches and their embedding ML or deep learning models and the description and comparison of the existing tools in this domain. To evaluate and compare the prediction capability of the tools, a new bunch of data has been extracted based on the most updated database and the tools have been assessed based on the extracted data. Finally, a hybrid architecture consisting of several classifiers including classical ML models and a deep learning model has been proposed to ensemble the prediction results. This approach demonstrates the better performance in comparison with all prediction tools included in this study (the source codes of the models presented in this manuscript are available in https://github.com/Malonylation). Database URL: https://github.com/A-Golshan/Malonylation.

The principle "like begets like" in algebra-matrix genetics and code biology

The article is devoted to analysis of emergent properties of the system of binary oppositions in the genetic code ensemble. The epochal model of the double helix of DNA by Watson and Crick showed that the multiple reproduction of genetic information on DNA strands uses the ancient principle "like begets like" based on the simple complementarity in pairs of nucleobases. Each of these pairs is built on the binary opposition "purine-pyrimidine". But the system of DNA n-plet alphabets and genetic coding is much richer in types of binary oppositions, which also have some coding meanings related to this principle. The article contains the results of the application of the author's "method of hierarchy binary stochastics" (HBS-method) to the analysis of the quasi-stochastic organization of binary sequences of hydrogen bonds in genomic single-stranded DNAs. This analysis revealed hidden probability rules related to dichotomous fractal-like probability trees. The relationship between inherited bodily dichotomies in living organisms and the discovered probability dichotomies in information sequences of genomic DNAs is discussed. The encoding properties of molecular binary oppositions in the DNA nucleotide system allows the algorithmic construction of (2n∗2n)-matrices of probabilities of n-plets in these binary sequences, which are matrix representations of 2n-dimensional hyperbolic numbers. Connections of these multidimensional numbers with some inherited physiological phenomena and deep neural networks are noted. A unified algebra-numeric certification of the DNAs of genomes and genes - based on these multidimensional numerical systems - is proposed.

Vison transformer adapter-based hyperbolic embeddings for multi-lesion segmentation in diabetic retinopathy

Diabetic Retinopathy (DR) is a major cause of blindness worldwide. Early detection and treatment are crucial to prevent vision loss, making accurate and timely diagnosis critical. Deep learning technology has shown promise in the automated diagnosis of DR, and in particular, multi-lesion segmentation tasks. In this paper, we propose a novel Transformer-based model for DR segmentation that incorporates hyperbolic embeddings and a spatial prior module. The proposed model is primarily built on a traditional Vision Transformer encoder and further enhanced by incorporating a spatial prior module for image convolution and feature continuity, followed by feature interaction processing using the spatial feature injector and extractor. Hyperbolic embeddings are used to classify feature matrices from the model at the pixel level. We evaluated the proposed model's performance on the publicly available datasets and compared it with other widely used DR segmentation models. The results show that our model outperforms these widely used DR segmentation models. The incorporation of hyperbolic embeddings and a spatial prior module into the Vision Transformer-based model significantly improves the accuracy of DR segmentation. The hyperbolic embeddings enable us to better capture the underlying geometric structure of the feature matrices, which is important for accurate segmentation. The spatial prior module improves the continuity of the features and helps to better distinguish between lesions and normal tissues. Overall, our proposed model has potential for clinical use in automated DR diagnosis, improving accuracy and speed of diagnosis. Our study shows that the integration of hyperbolic embeddings and a spatial prior module with a Vision Transformer-based model improves the performance of DR segmentation models. Future research can explore the application of our model to other medical imaging tasks, as well as further optimization and validation in real-world clinical settings.

Structure-preserving visualization for single-cell RNA-Seq profiles using deep manifold transformation with batch-correction

Dimensionality reduction and visualization play an important role in biological data analysis, such as data interpretation of single-cell RNA sequences (scRNA-seq). It is desired to have a visualization method that can not only be applicable to various application scenarios, including cell clustering and trajectory inference, but also satisfy a variety of technical requirements, especially the ability to preserve inherent structure of data and handle with batch effects. However, no existing methods can accommodate these requirements in a unified framework. In this paper, we propose a general visualization method, deep visualization (DV), that possesses the ability to preserve inherent structure of data and handle batch effects and is applicable to a variety of datasets from different application domains and dataset scales. The method embeds a given dataset into a 2- or 3-dimensional visualization space, with either a Euclidean or hyperbolic metric depending on a specified task type with type static (at a time point) or dynamic (at a sequence of time points) scRNA-seq data, respectively. Specifically, DV learns a structure graph to describe the relationships between data samples, transforms the data into visualization space while preserving the geometric structure of the data and correcting batch effects in an end-to-end manner. The experimental results on nine datasets in complex tissue from human patients or animal development demonstrate the competitiveness of DV in discovering complex cellular relations, uncovering temporal trajectories, and addressing complex batch factors. We also provide a preliminary attempt to pre-train a DV model for visualization of new incoming data.

Curvature-Adaptive Meta-Learning for Fast Adaptation to Manifold Data

Meta-learning methods are shown to be effective in quickly adapting a model to novel tasks. Most existing meta-learning methods represent data and carry out fast adaptation in euclidean space. In fact, data of real-world applications usually resides in complex and various Riemannian manifolds. In this paper, we propose a curvature-adaptive meta-learning method that achieves fast adaptation to manifold data by producing suitable curvature. Specifically, we represent data in the product manifold of multiple constant curvature spaces and build a product manifold neural network as the base-learner. In this way, our method is capable of encoding complex manifold data into discriminative and generic representations. Then, we introduce curvature generation and curvature updating schemes, through which suitable product manifolds for various forms of data manifolds are constructed via few optimization steps. The curvature generation scheme identifies task-specific curvature initialization, leading to a shorter optimization trajectory. The curvature updating scheme automatically produces appropriate learning rate and search direction for curvature, making a faster and more adaptive optimization paradigm compared to hand-designed optimization schemes. We evaluate our method on a broad set of problems including few-shot classification, few-shot regression, and reinforcement learning tasks. Experimental results show that our method achieves substantial improvements as compared to meta-learning methods ignoring the geometry of the underlying space.