相关论文: Topological Neural Tangent Kernel

Most real-world networks are embedded in latent geometries. If a node in a network is found in the vicinity of another node in the latent geometry, the two nodes have a disproportionately high probability of being connected by a link. The…

Data with low-dimensional nonlinear structure are ubiquitous in engineering and scientific problems. We study a model problem with such structure -- a binary classification task that uses a deep fully-connected neural network to classify…

Topological Deep Learning (TDL) has emerged as a paradigm to process and learn from signals defined on higher-order combinatorial topological spaces, such as simplicial or cell complexes. Although many complex systems have an asymmetric…

We propose a spherical kernel for efficient graph convolution of 3D point clouds. Our metric-based kernels systematically quantize the local 3D space to identify distinctive geometric relationships in the data. Similar to the regular grid…

Graph contrastive learning (GCL) has recently emerged as a new concept which allows for capitalizing on the strengths of graph neural networks (GNNs) to learn rich representations in a wide variety of applications which involve abundant…

Knots are deeply entangled with every branch of science. One of the biggest open challenges in knot theory is to formalise a knot invariant that can unambiguously and efficiently distinguish any two knotted curves. Additionally, the…

Recent work by Jacot et al. (2018) has shown that training a neural network using gradient descent in parameter space is related to kernel gradient descent in function space with respect to the Neural Tangent Kernel (NTK). Lee et al. (2019)…

We propose the Tikhonov layer, a graph neural network layer that is interpretable by design: once trained, its learned parameters directly reveal which node features and which aspects of the graph topology were leveraged for prediction. In…

Transformers have revolutionized performance in Natural Language Processing and Vision, paving the way for their integration with Graph Neural Networks (GNNs). One key challenge in enhancing graph transformers is strengthening the…

Graph neural networks (GNNs) are increasingly used to model biological systems, yet the reliability of post-hoc explanation methods for recovering meaningful molecular mechanisms remains unclear. Here, we systematically evaluate four widely…

In this work, we investigate the generalization properties of random feature methods. Our analysis extends prior results for Tikhonov regularization to a broad class of spectral regularization techniques and further generalizes the setting…

Many computer vision and machine learning problems are modelled as learning tasks on graphs where graph neural networks GNNs have emerged as a dominant tool for learning representations of graph structured data A key feature of GNNs is…

Rich feature learning in tasks that unfold over time often requires the model to pass through bifurcations, constituting qualitative changes in the underlying model dynamics. We develop a local theory of gradient descent near these…

Graph Neural Networks (GNNs) excel at learning from pairwise interactions but often overlook multi-way and hierarchical relationships. Topological Deep Learning (TDL) addresses this limitation by leveraging combinatorial topological spaces.…

This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient…

Hypergraphs and simplical complexes both capture the higher-order interactions of complex systems, ranging from higher-order collaboration networks to brain networks. One open problem in the field is what should drive the choice of the…

Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…

Graph neural networks (GNNs) have proven effective in capturing relationships among nodes in a graph. This study introduces a novel perspective by considering a graph as a simplicial complex, encompassing nodes, edges, triangles, and…

Understanding how brain structure and function interact is key to explaining intelligence yet modeling them jointly is challenging as the structural and functional connectome capture complementary aspects of organization. We introduced…

Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its…