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Given the complex geometry of white matter streamlines, Autoencoders have been proposed as a dimension-reduction tool to simplify the analysis streamlines in a low-dimensional latent spaces. However, despite these recent successes, the majority of encoder architectures only perform dimension reduction on single streamlines as opposed to a full bundle of streamlines. This is a severe limitation of the encoder architecture that completely disregards the global geometric structure of streamlines at the expense of individual fibers. Moreover, the latent space may not be well structured which leads to doubt into their interpretability. In this paper we propose a novel Differentiable Vector Quantized Variational Autoencoder, which are engineered to ingest entire bundles of streamlines as single data-point and provides reliable trustworthy encodings that can then be later used to analyze streamlines in the latent space. Comparisons with several state of the art Autoencoders demonstrate superior performance in both encoding and synthesis.

We present a method for fitting monotone curves using cubic B-splines, which is equivalent to putting a monotonicity constraint on the coefficients. We explore different ways of enforcing this constraint and analyze their theoretical and empirical properties. We propose two algorithms for solving the spline fitting problem: one that uses standard optimization techniques and one that trains a Multi-Layer Perceptrons (MLP) generator to approximate the solutions under various settings and perturbations. The generator approach can speed up the fitting process when we need to solve the problem repeatedly, such as when constructing confidence bands using bootstrap. We evaluate our method against several existing methods, some of which do not use the monotonicity constraint, on some monotone curves with varying noise levels. We demonstrate that our method outperforms the other methods, especially in high-noise scenarios. We also apply our method to analyze the polarization-hole phenomenon during star formation in astrophysics. The source code is accessible at \texttt{\url{//github.com/szcf-weiya/MonotoneSplines.jl}}.

The pseudo-inverse of a graph Laplacian matrix, denoted as $L^\dagger$, finds extensive application in various graph analysis tasks. Notable examples include the calculation of electrical closeness centrality, determination of Kemeny's constant, and evaluation of resistance distance. However, existing algorithms for computing $L^\dagger$ are often computationally expensive when dealing with large graphs. To overcome this challenge, we propose novel solutions for approximating $L^\dagger$ by establishing a connection with the inverse of a Laplacian submatrix $L_v$. This submatrix is obtained by removing the $v$-th row and column from the original Laplacian matrix $L$. The key advantage of this connection is that $L_v^{-1}$ exhibits various interesting combinatorial interpretations. We present two innovative interpretations of $L_v^{-1}$ based on spanning trees and loop-erased random walks, which allow us to develop efficient sampling algorithms. Building upon these new theoretical insights, we propose two novel algorithms for efficiently approximating both electrical closeness centrality and Kemeny's constant. We extensively evaluate the performance of our algorithms on five real-life datasets. The results demonstrate that our novel approaches significantly outperform the state-of-the-art methods by several orders of magnitude in terms of both running time and estimation errors for these two graph analysis tasks. To further illustrate the effectiveness of electrical closeness centrality and Kemeny's constant, we present two case studies that showcase the practical applications of these metrics.

Cross-modal MRI segmentation is of great value for computer-aided medical diagnosis, enabling flexible data acquisition and model generalization. However, most existing methods have difficulty in handling local variations in domain shift and typically require a significant amount of data for training, which hinders their usage in practice. To address these problems, we propose a novel adaptive domain generalization framework, which integrates a learning-free cross-domain representation based on image gradient maps and a class prior-informed test-time adaptation strategy for mitigating local domain shift. We validate our approach on two multi-modal MRI datasets with six cross-modal segmentation tasks. Across all the task settings, our method consistently outperforms competing approaches and shows a stable performance even with limited training data.

This work focuses on developing methods for approximating the solution operators of a class of parametric partial differential equations via neural operators. Neural operators have several challenges, including the issue of generating appropriate training data, cost-accuracy trade-offs, and nontrivial hyperparameter tuning. The unpredictability of the accuracy of neural operators impacts their applications in downstream problems of inference, optimization, and control. A framework based on the linear variational problem that gives the correction to the prediction furnished by neural operators is considered based on earlier work in JCP 486 (2023) 112104. The operator, called Residual-based Error Corrector Operator or simply Corrector Operator, associated with the corrector problem is analyzed further. Numerical results involving a nonlinear reaction-diffusion model in two dimensions with PCANet-type neural operators show almost two orders of increase in the accuracy of approximations when neural operators are corrected using the correction scheme. Further, topology optimization involving a nonlinear reaction-diffusion model is considered to highlight the limitations of neural operators and the efficacy of the correction scheme. Optimizers with neural operator surrogates are seen to make significant errors (as high as 80 percent). However, the errors are much lower (below 7 percent) when neural operators are corrected.

A significant bottleneck in applying current reinforcement learning algorithms to real-world scenarios is the need to reset the environment between every episode. This reset process demands substantial human intervention, making it difficult for the agent to learn continuously and autonomously. Several recent works have introduced autonomous reinforcement learning (ARL) algorithms that generate curricula for jointly training reset and forward policies. While their curricula can reduce the number of required manual resets by taking into account the agent's learning progress, they rely on task-specific knowledge, such as predefined initial states or reset reward functions. In this paper, we propose a novel ARL algorithm that can generate a curriculum adaptive to the agent's learning progress without task-specific knowledge. Our curriculum empowers the agent to autonomously reset to diverse and informative initial states. To achieve this, we introduce a success discriminator that estimates the success probability from each initial state when the agent follows the forward policy. The success discriminator is trained with relabeled transitions in a self-supervised manner. Our experimental results demonstrate that our ARL algorithm can generate an adaptive curriculum and enable the agent to efficiently bootstrap to solve sparse-reward maze navigation tasks, outperforming baselines with significantly fewer manual resets.

Exploring the application of powerful large language models (LLMs) on the fundamental named entity recognition (NER) task has drawn much attention recently. This work aims to investigate the possibilities of pushing the boundary of zero-shot NER with LLM via a training-free self-improving strategy. We propose a self-improving framework, which utilize an unlabeled corpus to stimulate the self-learning ability of LLMs on NER. First, we use LLM to make predictions on the unlabeled corpus and obtain the self-annotated data. Second, we explore various strategies to select reliable samples from the self-annotated dataset as demonstrations, considering the similarity, diversity and reliability of demonstrations. Finally, we conduct inference for the test query via in-context learning with the selected self-annotated demonstrations. Through comprehensive experimental analysis, our study yielded the following findings: (1) The self-improving framework further pushes the boundary of zero-shot NER with LLMs, and achieves an obvious performance improvement; (2) Iterative self-improving or naively increasing the size of unlabeled corpus does not guarantee improvements; (3) There might still be space for improvement via more advanced strategy for reliable entity selection.

Finite element models of electrical machines allow insights in electrothermal stresses which endanger the insulation system of the machine. This paper presents a thermal finite element model of a 3.7 kW squirrel-cage induction machine. The model resolves the conductors and the surrounding insulation materials in the stator slots. A set of transient thermal scenarios is defined and measured in the machine laboratory. These data are used to assess the finite element model.

Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.

Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism which has been demonstrated effective is the most fundamental part of GNNs. Although most of GNNs basically follow a message passing manner, litter effort has been made to discover and analyze their essential relations. In this paper, we establish a surprising connection between different propagation mechanisms with a unified optimization problem, showing that despite the proliferation of various GNNs, in fact, their proposed propagation mechanisms are the optimal solution optimizing a feature fitting function over a wide class of graph kernels with a graph regularization term. Our proposed unified optimization framework, summarizing the commonalities between several of the most representative GNNs, not only provides a macroscopic view on surveying the relations between different GNNs, but also further opens up new opportunities for flexibly designing new GNNs. With the proposed framework, we discover that existing works usually utilize naive graph convolutional kernels for feature fitting function, and we further develop two novel objective functions considering adjustable graph kernels showing low-pass or high-pass filtering capabilities respectively. Moreover, we provide the convergence proofs and expressive power comparisons for the proposed models. Extensive experiments on benchmark datasets clearly show that the proposed GNNs not only outperform the state-of-the-art methods but also have good ability to alleviate over-smoothing, and further verify the feasibility for designing GNNs with our unified optimization framework.