Related papers: Higher-Order Regularization Learning on Hypergraph…
In this work, we address the solution of both linear and nonlinear ill-posed inverse problems by developing a novel graph-based regularization framework, where the regularization term is formulated through an iteratively updated graph…
Hypergraphs are useful mathematical models for describing complex relationships among members of a structured graph, while hyperdigraphs serve as a generalization that can encode asymmetric relationships in the data. However, obtaining…
Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…
Hierarchical goal-conditioned reinforcement learning (H-GCRL) provides a powerful framework for tackling complex, long-horizon tasks by decomposing them into structured subgoals. However, its practical adoption is hindered by poor data…
In recent literature there are plenty of works that combine handcrafted and learnable regularizers to solve inverse imaging problems. While this hybrid approach has demonstrated promising results, the motivation for combining handcrafted…
How to obtain the desirable representation of a 3D shape is a key challenge in 3D shape retrieval task. Most existing 3D shape retrieval methods focus on capturing shape representation with different neural network architectures, while the…
Higher-order networks have so far been considered primarily in the context of studying the structure of complex systems, i.e., the higher-order or multi-way relations connecting the constituent entities. More recently, a number of studies…
We establish a family of subspace-based learning method for multi-view learning using the least squares as the fundamental basis. Specifically, we investigate orthonormalized partial least squares (OPLS) and study its important properties…
Over the recent years, Graph Neural Networks have become increasingly popular in network analytic and beyond. With that, their architecture noticeable diverges from the classical multi-layered hierarchical organization of the traditional…
The graph Laplacian plays key roles in information processing of relational data, and has analogies with the Laplacian in differential geometry. In this paper, we generalize the analogy between graph Laplacian and differential geometry to…
Unsupervised heterogeneous graph representation learning (UHGRL) has gained increasing attention due to its significance in handling practical graphs without labels. However, heterophily has been largely ignored, despite its ubiquitous…
In this paper, we investigate the empirical impact of orthogonality regularization (OR) in deep learning, either solo or collaboratively. Recent works on OR showed some promising results on the accuracy. In our ablation study, however, we…
In recent years, the attention mechanism contributes significantly to hypergraph based neural networks. However, these methods update the attention weights with the network propagating. That is to say, this type of attention mechanism is…
Hierarchical Reinforcement Learning (HRL) has made notable progress in complex control tasks by leveraging temporal abstraction. However, previous HRL algorithms often suffer from serious data inefficiency as environments get large. The…
Many scientific datasets are of high dimension, and the analysis usually requires visual manipulation by retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing…
Regularization techniques are crucial to improving the generalization performance and training efficiency of deep neural networks. Many deep learning algorithms rely on weight decay, dropout, batch/layer normalization to converge faster and…
Goal-conditioned hierarchical reinforcement learning (GCHRL) provides a promising approach to solving long-horizon tasks. Recently, its success has been extended to more general settings by concurrently learning hierarchical policies and…
In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective. We reveal that Hodge orthogonality fundamentally resolves spectral interference by isolating unlearnable…
Hierarchical reinforcement learning (HRL) is a promising approach to extend traditional reinforcement learning (RL) methods to solve more complex tasks. Yet, the majority of current HRL methods require careful task-specific design and…
Motivated by the need to address the degeneracy of canonical Laplace learning algorithms in low label rates, we propose to reformulate graph-based semi-supervised learning as a nonconvex generalization of a \emph{Trust-Region Subproblem}…