We study nonparametric regression by an over-parameterized two-layer neural network trained by gradient descent (GD) in this paper. We show that, if the neural network is trained by GD with early stopping, then the trained network renders a sharp rate of the nonparametric regression risk of $\cO(\eps_n^2)$, which is the same rate as that for the classical kernel regression trained by GD with early stopping, where $\eps_n$ is the critical population rate of the Neural Tangent Kernel (NTK) associated with the network and $n$ is the size of the training data. It is remarked that our result does not require distributional assumptions on the training data, in a strong contrast with many existing results which rely on specific distributions such as the spherical uniform data distribution or distributions satisfying certain restrictive conditions. The rate $\cO(\eps_n^2)$ is known to be minimax optimal for specific cases, such as the case that the NTK has a polynomial eigenvalue decay rate which happens under certain distributional assumptions. Our result formally fills the gap between training a classical kernel regression model and training an over-parameterized but finite-width neural network by GD for nonparametric regression without distributional assumptions. We also provide confirmative answers to certain open questions or address particular concerns in the literature of training over-parameterized neural networks by GD with early stopping for nonparametric regression, including the characterization of the stopping time, the lower bound for the network width, and the constant learning rate used in GD.
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Networking：IFIP International Conferences on Networking。
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We study the problem of statically optimizing select-project-join (SPJ) plans where unary key constraints are allowed. A natural measure of a plan, which we call the output degree and which has been studied previously, is the minimum degree of a polynomial bounding the plan's output relation, as a function of the input database's maximum relation size. This measure is, by definition, invariant under passing from a plan to another plan that is semantically equivalent to the first. In this article, we consider a plan measure which we call the intermediate degree; this measure is defined to be the minimum degree bounding the size of all intermediate relations computed during a plan's execution -- again, as a function of the input database's maximum relation size. We present an algorithm that, given an SPJ plan $q$ and a set $\Sigma$ of unary keys, computes an SPJ plan $q'$ that is semantically equivalent to $q$ (over databases satisfying $\Sigma$) and that has the minimum intermediate degree over all such semantically equivalent plans. For the types of plans considered, we thus obtain a complete and effective understanding of intermediate degree.
This work introduces ClustEm4Ano, an anonymization pipeline that can be used for generalization and suppression-based anonymization of nominal textual tabular data. It automatically generates value generalization hierarchies (VGHs) that, in turn, can be used to generalize attributes in quasi-identifiers. The pipeline leverages embeddings to generate semantically close value generalizations through iterative clustering. We applied KMeans and Hierarchical Agglomerative Clustering on $13$ different predefined text embeddings (both open and closed-source (via APIs)). Our approach is experimentally tested on a well-known benchmark dataset for anonymization: The UCI Machine Learning Repository's Adult dataset. ClustEm4Ano supports anonymization procedures by offering more possibilities compared to using arbitrarily chosen VGHs. Experiments demonstrate that these VGHs can outperform manually constructed ones in terms of downstream efficacy (especially for small $k$-anonymity ($2 \leq k \leq 30$)) and therefore can foster the quality of anonymized datasets. Our implementation is made public.
Learning-based methods have demonstrated remarkable performance in solving inverse problems, particularly in image reconstruction tasks. Despite their success, these approaches often lack theoretical guarantees, which are crucial in sensitive applications such as medical imaging. Recent works by Arndt et al (2023 Inverse Problems 39 125018, 2024 Inverse Problems 40 045021) addressed this gap by analyzing a data-driven reconstruction method based on invertible residual networks (iResNets). They revealed that, under reasonable assumptions, this approach constitutes a convergent regularization scheme. However, the performance of the reconstruction method was only validated on academic toy problems and small-scale iResNet architectures. In this work, we address this gap by evaluating the performance of iResNets on two real-world imaging tasks: a linear blurring operator and a nonlinear diffusion operator. To do so, we extend some of the theoretical results from Arndt et al to encompass nonlinear inverse problems and offer insights for the design of large-scale performant iResNet architectures. Through numerical experiments, we compare the performance of our iResNet models against state-of-the-art neural networks, confirming their efficacy. Additionally, we numerically investigate the theoretical guarantees of this approach and demonstrate how the invertibility of the network enables a deeper analysis of the learned forward operator and its learned regularization.
Despite recent advancements in deep learning, its application in real-world medical settings, such as phonocardiogram (PCG) classification, remains limited. A significant barrier is the lack of high-quality annotated datasets, which hampers the development of robust, generalizable models that can perform well on newly collected, out-of-distribution (OOD) data. Self-Supervised Learning (SSL) contrastive learning, has shown promise in mitigating the issue of data scarcity by using unlabeled data to enhance model robustness. Even though SSL methods have been proposed and researched in other domains, works focusing on the impact of data augmentations on model robustness for PCG classification are limited. In particular, while augmentations are a key component in SSL, selecting the most suitable policy during training is highly challenging. Improper augmentations can lead to substantial performance degradation and even hinder a network's ability to learn meaningful representations. Addressing this gap, our research aims to explore and evaluate a wide range of audio-based augmentations and uncover combinations that enhance SSL model performance in PCG classification. We conduct a comprehensive comparative analysis across multiple datasets, assessing the impact of various augmentations on model performance. Our findings reveal that depending on the training distribution, augmentation choice significantly influences model robustness, with fully-supervised models experiencing up to a 32\% drop in effectiveness when evaluated on unseen data, while SSL models demonstrate greater resilience, losing only 10\% or even improving in some cases. This study also highlights the most promising and appropriate augmentations for PCG signal processing, by calculating their effect size on training. These insights equip researchers with valuable guidelines for developing reliable models in PCG signal processing.
Several photonic microring resonators (MRRs) based analog accelerators have been proposed to accelerate the inference of integer-quantized CNNs with remarkably higher throughput and energy efficiency compared to their electronic counterparts. However, the existing analog photonic accelerators suffer from three shortcomings: (i) severe hampering of wavelength parallelism due to various crosstalk effects, (ii) inflexibility of supporting various dataflows other than the weight-stationary dataflow, and (iii) failure in fully leveraging the ability of photodetectors to perform in-situ accumulations. These shortcomings collectively hamper the performance and energy efficiency of prior accelerators. To tackle these shortcomings, we present a novel Hybrid timE Amplitude aNalog optical Accelerator, called HEANA. HEANA employs hybrid time-amplitude analog optical multipliers (TAOMs) that increase the flexibility of HEANA to support multiple dataflows. A spectrally hitless arrangement of TAOMs significantly reduces the crosstalk effects, thereby increasing the wavelength parallelism in HEANA. Moreover, HEANA employs our invented balanced photo-charge accumulators (BPCAs) that enable buffer-less, in-situ, temporal accumulations to eliminate the need to use reduction networks in HEANA, relieving it from related latency and energy overheads. Our evaluation for the inference of four modern CNNs indicates that HEANA provides improvements of atleast 66x and 84x in frames-per-second (FPS) and FPS/W (energy-efficiency), respectively, for equal-area comparisons, on gmean over two MRR-based analog CNN accelerators from prior work.
Graph representation learning methods are highly effective in handling complex non-Euclidean data by capturing intricate relationships and features within graph structures. However, traditional methods face challenges when dealing with heterogeneous graphs that contain various types of nodes and edges due to the diverse sources and complex nature of the data. Existing Heterogeneous Graph Neural Networks (HGNNs) have shown promising results but require prior knowledge of node and edge types and unified node feature formats, which limits their applicability. Recent advancements in graph representation learning using Large Language Models (LLMs) offer new solutions by integrating LLMs' data processing capabilities, enabling the alignment of various graph representations. Nevertheless, these methods often overlook heterogeneous graph data and require extensive preprocessing. To address these limitations, we propose a novel method that leverages the strengths of both LLM and GNN, allowing for the processing of graph data with any format and type of nodes and edges without the need for type information or special preprocessing. Our method employs LLM to automatically summarize and classify different data formats and types, aligns node features, and uses a specialized GNN for targeted learning, thus obtaining effective graph representations for downstream tasks. Theoretical analysis and experimental validation have demonstrated the effectiveness of our method.
In the post-deep learning era, the Transformer architecture has demonstrated its powerful performance across pre-trained big models and various downstream tasks. However, the enormous computational demands of this architecture have deterred many researchers. To further reduce the complexity of attention models, numerous efforts have been made to design more efficient methods. Among them, the State Space Model (SSM), as a possible replacement for the self-attention based Transformer model, has drawn more and more attention in recent years. In this paper, we give the first comprehensive review of these works and also provide experimental comparisons and analysis to better demonstrate the features and advantages of SSM. Specifically, we first give a detailed description of principles to help the readers quickly capture the key ideas of SSM. After that, we dive into the reviews of existing SSMs and their various applications, including natural language processing, computer vision, graph, multi-modal and multi-media, point cloud/event stream, time series data, and other domains. In addition, we give statistical comparisons and analysis of these models and hope it helps the readers to understand the effectiveness of different structures on various tasks. Then, we propose possible research points in this direction to better promote the development of the theoretical model and application of SSM. More related works will be continuously updated on the following GitHub: //github.com/Event-AHU/Mamba_State_Space_Model_Paper_List.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
One principal approach for illuminating a black-box neural network is feature attribution, i.e. identifying the importance of input features for the network's prediction. The predictive information of features is recently proposed as a proxy for the measure of their importance. So far, the predictive information is only identified for latent features by placing an information bottleneck within the network. We propose a method to identify features with predictive information in the input domain. The method results in fine-grained identification of input features' information and is agnostic to network architecture. The core idea of our method is leveraging a bottleneck on the input that only lets input features associated with predictive latent features pass through. We compare our method with several feature attribution methods using mainstream feature attribution evaluation experiments. The code is publicly available.
Translational distance-based knowledge graph embedding has shown progressive improvements on the link prediction task, from TransE to the latest state-of-the-art RotatE. However, N-1, 1-N and N-N predictions still remain challenging. In this work, we propose a novel translational distance-based approach for knowledge graph link prediction. The proposed method includes two-folds, first we extend the RotatE from 2D complex domain to high dimension space with orthogonal transforms to model relations for better modeling capacity. Second, the graph context is explicitly modeled via two directed context representations. These context representations are used as part of the distance scoring function to measure the plausibility of the triples during training and inference. The proposed approach effectively improves prediction accuracy on the difficult N-1, 1-N and N-N cases for knowledge graph link prediction task. The experimental results show that it achieves better performance on two benchmark data sets compared to the baseline RotatE, especially on data set (FB15k-237) with many high in-degree connection nodes.
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