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We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods, which only work with one entry at a time, resulting in a significantly better convergence rate than the original approach. To assess the applicability of our method, we compute the subgraph centrality and total communicability of several large networks. In all benchmarks analyzed so far, the performance of our method was significantly superior to the competition, being able to scale up to 64 CPU cores with remarkable efficiency.

Time-series anomaly detection deals with the problem of detecting anomalous timesteps by learning normality from the sequence of observations. However, the concept of normality evolves over time, leading to a "new normal problem", where the distribution of normality can be changed due to the distribution shifts between training and test data. This paper highlights the prevalence of the new normal problem in unsupervised time-series anomaly detection studies. To tackle this issue, we propose a simple yet effective test-time adaptation strategy based on trend estimation and a self-supervised approach to learning new normalities during inference. Extensive experiments on real-world benchmarks demonstrate that incorporating the proposed strategy into the anomaly detector consistently improves the model's performance compared to the baselines, leading to robustness to the distribution shifts.

Numerous self-supervised learning paradigms, such as contrastive learning and masked image modeling, have been proposed to acquire powerful and general representations from unlabeled data. However, these models are commonly pretrained within their specific framework alone, failing to consider the complementary nature of visual representations. To tackle this issue, we introduce Comprehensive Distillation with Multiple Self-supervised Teachers (DMT) for pretrained model compression, which leverages the strengths of multiple off-the-shelf self-supervised models. Our experimental results on prominent benchmark datasets exhibit that the proposed method significantly surpasses state-of-the-art competitors while retaining favorable efficiency metrics. On classification tasks, our DMT framework utilizing three different self-supervised ViT-Base teachers enhances the performance of both small/tiny models and the base model itself. For dense tasks, DMT elevates the AP/mIoU of standard SSL models on MS-COCO and ADE20K datasets by 4.0%.

With the development of deep learning and natural language processing techniques, pre-trained language models have been widely used to solve information retrieval (IR) problems. Benefiting from the pre-training and fine-tuning paradigm, these models achieve state-of-the-art performance. In previous works, plain texts in Wikipedia have been widely used in the pre-training stage. However, the rich structured information in Wikipedia, such as the titles, abstracts, hierarchical heading (multi-level title) structure, relationship between articles, references, hyperlink structures, and the writing organizations, has not been fully explored. In this paper, we devise four pre-training objectives tailored for IR tasks based on the structured knowledge of Wikipedia. Compared to existing pre-training methods, our approach can better capture the semantic knowledge in the training corpus by leveraging the human-edited structured data from Wikipedia. Experimental results on multiple IR benchmark datasets show the superior performance of our model in both zero-shot and fine-tuning settings compared to existing strong retrieval baselines. Besides, experimental results in biomedical and legal domains demonstrate that our approach achieves better performance in vertical domains compared to previous models, especially in scenarios where long text similarity matching is needed.

Although neural networks have made remarkable advancements in various applications, they require substantial computational and memory resources. Network quantization is a powerful technique to compress neural networks, allowing for more efficient and scalable AI deployments. Recently, Re-parameterization has emerged as a promising technique to enhance model performance while simultaneously alleviating the computational burden in various computer vision tasks. However, the accuracy drops significantly when applying quantization on the re-parameterized networks. We identify that the primary challenge arises from the large variation in weight distribution across the original branches. To address this issue, we propose a coarse & fine weight splitting (CFWS) method to reduce quantization error of weight, and develop an improved KL metric to determine optimal quantization scales for activation. To the best of our knowledge, our approach is the first work that enables post-training quantization applicable on re-parameterized networks. For example, the quantized RepVGG-A1 model exhibits a mere 0.3% accuracy loss. The code is in //github.com/NeonHo/Coarse-Fine-Weight-Split.git

We study hypothesis testing under communication constraints, where each sample is quantized before being revealed to a statistician. Without communication constraints, it is well known that the sample complexity of simple binary hypothesis testing is characterized by the Hellinger distance between the distributions. We show that the sample complexity of simple binary hypothesis testing under communication constraints is at most a logarithmic factor larger than in the unconstrained setting and this bound is tight. We develop a polynomial-time algorithm that achieves the aforementioned sample complexity. Our framework extends to robust hypothesis testing, where the distributions are corrupted in the total variation distance. Our proofs rely on a new reverse data processing inequality and a reverse Markov inequality, which may be of independent interest. For simple $M$-ary hypothesis testing, the sample complexity in the absence of communication constraints has a logarithmic dependence on $M$. We show that communication constraints can cause an exponential blow-up leading to $\Omega(M)$ sample complexity even for adaptive algorithms.

Physics-Informed Neural Networks (PINNs) are a class of deep learning neural networks that learn the response of a physical system without any simulation data, and only by incorporating the governing partial differential equations (PDEs) in their loss function. While PINNs are successfully used for solving forward and inverse problems, their accuracy decreases significantly for parameterized systems. PINNs also have a soft implementation of boundary conditions resulting in boundary conditions not being exactly imposed everywhere on the boundary. With these challenges at hand, we present first-order physics-informed neural networks (FO-PINNs). These are PINNs that are trained using a first-order formulation of the PDE loss function. We show that, compared to standard PINNs, FO-PINNs offer significantly higher accuracy in solving parameterized systems, and reduce time-per-iteration by removing the extra backpropagations needed to compute the second or higher-order derivatives. Additionally, FO-PINNs can enable exact imposition of boundary conditions using approximate distance functions, which pose challenges when applied on high-order PDEs. Through three examples, we demonstrate the advantages of FO-PINNs over standard PINNs in terms of accuracy and training speedup.

The generalization of neural networks is a central challenge in machine learning, especially concerning the performance under distributions that differ from training ones. Current methods, mainly based on the data-driven paradigm such as data augmentation, adversarial training, and noise injection, may encounter limited generalization due to model non-smoothness. In this paper, we propose to investigate generalization from a Partial Differential Equation (PDE) perspective, aiming to enhance it directly through the underlying function of neural networks, rather than focusing on adjusting input data. Specifically, we first establish the connection between neural network generalization and the smoothness of the solution to a specific PDE, namely "transport equation". Building upon this, we propose a general framework that introduces adaptive distributional diffusion into transport equation to enhance the smoothness of its solution, thereby improving generalization. In the context of neural networks, we put this theoretical framework into practice as $\textbf{PDE+}$ ($\textbf{PDE}$ with $\textbf{A}$daptive $\textbf{D}$istributional $\textbf{D}$iffusion) which diffuses each sample into a distribution covering semantically similar inputs. This enables better coverage of potentially unobserved distributions in training, thus improving generalization beyond merely data-driven methods. The effectiveness of PDE+ is validated through extensive experimental settings, demonstrating its superior performance compared to SOTA methods.

We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.

Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.