Convergence Theory of Learning Over-parameterized ResNet: A Full Characterization

ResNet structure has achieved great empirical success since its debut. Recent work established the convergence of learning over-parameterized ResNet with a scaling factor $\tau=1/L$ on the residual branch where $L$ is the network depth. However, it is not clear how learning ResNet behaves for other values of $\tau$. In this paper, we fully characterize the convergence theory of gradient descent for learning over-parameterized ResNet with different values of $\tau$. Specifically, with hiding logarithmic factor and constant coefficients, we show that for $\tau\le 1/\sqrt{L}$ gradient descent is guaranteed to converge to the global minma, and especially when $\tau\le 1/L$ the convergence is irrelevant of the network depth. Conversely, we show that for $\tau>L^{-\frac{1}{2}+c}$, the forward output grows at least with rate $L^c$ in expectation and then the learning fails because of gradient explosion for large $L$. This means the bound $\tau\le 1/\sqrt{L}$ is sharp for learning ResNet with arbitrary depth. To the best of our knowledge, this is the first work that studies learning ResNet with full range of $\tau$.Comment: 31 page

The Davis-Gut law for independent and identically distributed Banach space valued random elements

An analog of the Davis-Gut law for a sequence of independent and identically distributed Banach space valued random elements is obtained, which extends the result of Li and Rosalsky (A supplement to the Davis-Gut law. J. Math. Anal. Appl. 330 (2007), 1488-1493)

Sorption hysteresis in wood and its coupling to swelling: a new modelling approach

Sorption hysteresis of amorphous cellulose is studied. Cellulose, as a renewable organic biopolymer, is an essential component of various natural composites such as wood. A coupling process between sorption and deformation leads to the hysteresis as observed in sorption and swelling, both experimental and simulated for cellulose and wood in general

EDGE++: Improved Training and Sampling of EDGE

Recently developed deep neural models like NetGAN, CELL, and Variational Graph Autoencoders have made progress but face limitations in replicating key graph statistics on generating large graphs. Diffusion-based methods have emerged as promising alternatives, however, most of them present challenges in computational efficiency and generative performance. EDGE is effective at modeling large networks, but its current denoising approach can be inefficient, often leading to wasted computational resources and potential mismatches in its generation process. In this paper, we propose enhancements to the EDGE model to address these issues. Specifically, we introduce a degree-specific noise schedule that optimizes the number of active nodes at each timestep, significantly reducing memory consumption. Additionally, we present an improved sampling scheme that fine-tunes the generative process, allowing for better control over the similarity between the synthesized and the true network. Our experimental results demonstrate that the proposed modifications not only improve the efficiency but also enhance the accuracy of the generated graphs, offering a robust and scalable solution for graph generation tasks

A Comprehensive Study on Knowledge Graph Embedding over Relational Patterns Based on Rule Learning

Knowledge Graph Embedding (KGE) has proven to be an effective approach to solving the Knowledge Graph Completion (KGC) task. Relational patterns which refer to relations with specific semantics exhibiting graph patterns are an important factor in the performance of KGE models. Though KGE models' capabilities are analyzed over different relational patterns in theory and a rough connection between better relational patterns modeling and better performance of KGC has been built, a comprehensive quantitative analysis on KGE models over relational patterns remains absent so it is uncertain how the theoretical support of KGE to a relational pattern contributes to the performance of triples associated to such a relational pattern. To address this challenge, we evaluate the performance of 7 KGE models over 4 common relational patterns on 2 benchmarks, then conduct an analysis in theory, entity frequency, and part-to-whole three aspects and get some counterintuitive conclusions. Finally, we introduce a training-free method Score-based Patterns Adaptation (SPA) to enhance KGE models' performance over various relational patterns. This approach is simple yet effective and can be applied to KGE models without additional training. Our experimental results demonstrate that our method generally enhances performance over specific relational patterns. Our source code is available from GitHub at https://github.com/zjukg/Comprehensive-Study-over-Relational-Patterns.Comment: This paper is accepted by ISWC 202

Influence of Source Credibility on Consumer Acceptance of Genetically Modified Foods in China

This paper examines the reasoning mechanism behind the consumer acceptance of genetically modified foods (GMFs) in China, and investigates influence of source credibility on consumer acceptance of GMFs. Based on the original Persuasion Model—which was developed by Carl Hovland, an American psychologist and pioneer in the study of communication and its effect on attitudes and beliefs—we conducted a survey using multistage sampling from 1167 urban residents, which were proportionally selected from six cities in three economic regions (south, central, and north) in the Jiangsu province through face to face interviews. Mixed-process regression that could correct endogeneity and ordered probit model were used to test the impact of source credibility on consumers’ acceptance of GMFs. Our major finding was that consumer acceptance of GMFs is affected by such factors as information source credibility, general attitudes, gender, and education levels. The reliability of biotechnology research institutes, government offices devoted to management of GM organisms (GMOs), and GMO technological experts have expedited urban consumer acceptance of GM soybean oil. However, public acceptance can also decrease as faith in the environmental organization. We also found that ignorance of the endogeneity of above mentioned source significantly undervalued its effect on consumers’ acceptance. Moreover, the remaining three sources (non-GMO experts, food companies, and anonymous information found on the Internet) had almost no effect on consumer acceptance. Surprisingly, the more educated people in our survey were more skeptical towards GMFs. Our results contribute to the behavioral literature on consumer attitudes toward GMFs by developing a reasoning mechanism determining consumer acceptance of GMFs. Particularly, this paper quantitatively studied the influence of different source credibility on consumer acceptance of GMFs by using mixed-process regression to correct endogeneity in information sources, while taking into consideration of information asymmetry and specific preference in the use of information sources