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In this paper, we advance the understanding of neural network training dynamics by examining the intricate interplay of various factors introduced by weight parameters in the initialization process. Motivated by the foundational work of Luo et al. (J. Mach. Learn. Res., Vol. 22, Iss. 1, No. 71, pp 3327-3373), we explore the gradient descent dynamics of neural networks through the lens of macroscopic limits, where we analyze its behavior as width $m$ tends to infinity. Our study presents a unified approach with refined techniques designed for multi-layer fully connected neural networks, which can be readily extended to other neural network architectures. Our investigation reveals that gradient descent can rapidly drive deep neural networks to zero training loss, irrespective of the specific initialization schemes employed by weight parameters, provided that the initial scale of the output function $\kappa$ surpasses a certain threshold. This regime, characterized as the theta-lazy area, accentuates the predominant influence of the initial scale $\kappa$ over other factors on the training behavior of neural networks. Furthermore, our approach draws inspiration from the Neural Tangent Kernel (NTK) paradigm, and we expand its applicability. While NTK typically assumes that $\lim_{m\to\infty}\frac{\log \kappa}{\log m}=\frac{1}{2}$, and imposes each weight parameters to scale by the factor $\frac{1}{\sqrt{m}}$, in our theta-lazy regime, we discard the factor and relax the conditions to $\lim_{m\to\infty}\frac{\log \kappa}{\log m}>0$. Similar to NTK, the behavior of overparameterized neural networks within the theta-lazy regime trained by gradient descent can be effectively described by a specific kernel. Through rigorous analysis, our investigation illuminates the pivotal role of $\kappa$ in governing the training dynamics of neural networks.

Conversational Aspect-Based Sentiment Analysis (DiaASQ) aims to detect quadruples \{target, aspect, opinion, sentiment polarity\} from given dialogues. In DiaASQ, elements constituting these quadruples are not necessarily confined to individual sentences but may span across multiple utterances within a dialogue. This necessitates a dual focus on both the syntactic information of individual utterances and the semantic interaction among them. However, previous studies have primarily focused on coarse-grained relationships between utterances, thus overlooking the potential benefits of detailed intra-utterance syntactic information and the granularity of inter-utterance relationships. This paper introduces the Triple GNNs network to enhance DiaAsQ. It employs a Graph Convolutional Network (GCN) for modeling syntactic dependencies within utterances and a Dual Graph Attention Network (DualGATs) to construct interactions between utterances. Experiments on two standard datasets reveal that our model significantly outperforms state-of-the-art baselines. The code is available at \url{https://github.com/nlperi2b/Triple-GNNs-}., Comment: Accepted by CSCWD2024

While quantum computing has strong potential in data-driven fields, the privacy issue of sensitive or valuable information involved in the quantum algorithm should be considered. Differential privacy (DP), which is a fundamental privacy tool widely used in the classical scenario, has been extended to the quantum domain, i.e., quantum differential privacy (QDP). QDP may become one of the most promising approaches toward privacy-preserving quantum computing since it is not only compatible with classical DP mechanisms but also achieves privacy protection by exploiting unavoidable quantum noise in noisy intermediate-scale quantum (NISQ) devices. This paper provides an overview of the various implementations of QDP and their performance in terms of privacy parameters under the DP setting. Specifically, we propose a taxonomy of QDP techniques, categorizing the literature on whether internal or external randomization is used as a source to achieve QDP and how these implementations are applied to each phase of the quantum algorithm. We also discuss challenges and future directions for QDP. By summarizing recent advancements, we hope to provide a comprehensive, up-to-date review for researchers venturing into this field., Comment: To be published in QCE24 (IEEE Quantum Week 2024)

Given the importance of ancient Chinese in capturing the essence of rich historical and cultural heritage, the rapid advancements in Large Language Models (LLMs) necessitate benchmarks that can effectively evaluate their understanding of ancient contexts. To meet this need, we present AC-EVAL, an innovative benchmark designed to assess the advanced knowledge and reasoning capabilities of LLMs within the context of ancient Chinese. AC-EVAL is structured across three levels of difficulty reflecting different facets of language comprehension: general historical knowledge, short text understanding, and long text comprehension. The benchmark comprises 13 tasks, spanning historical facts, geography, social customs, art, philosophy, classical poetry and prose, providing a comprehensive assessment framework. Our extensive evaluation of top-performing LLMs, tailored for both English and Chinese, reveals a substantial potential for enhancing ancient text comprehension. By highlighting the strengths and weaknesses of LLMs, AC-EVAL aims to promote their development and application forward in the realms of ancient Chinese language education and scholarly research. The AC-EVAL data and evaluation code are available at https://github.com/yuting-wei/AC-EVAL.

Quantum computing has been widely applied in various fields, such as quantum physics simulations, quantum machine learning, and big data analysis. However, in the domains of data-driven paradigm, how to ensure the privacy of the database is becoming a vital problem. For classical computing, we can incorporate the concept of differential privacy (DP) to meet the standard of privacy preservation by manually adding the noise. In the quantum computing scenario, researchers have extended classic DP to quantum differential privacy (QDP) by considering the quantum noise. In this paper, we propose a novel approach to satisfy the QDP definition by considering the errors generated by the projection operator measurement, which is denoted as shot noises. Then, we discuss the amount of privacy budget that can be achieved with shot noises, which serves as a metric for the level of privacy protection. Furthermore, we provide the QDP of shot noise in quantum circuits with depolarizing noise. Through numerical simulations, we show that shot noise can effectively provide privacy protection in quantum computing.

Conversational aspect-based sentiment quadruple analysis (DiaASQ) aims to extract the quadruple of target-aspect-opinion-sentiment within a dialogue. In DiaASQ, a quadruple's elements often cross multiple utterances. This situation complicates the extraction process, emphasizing the need for an adequate understanding of conversational context and interactions. However, existing work independently encodes each utterance, thereby struggling to capture long-range conversational context and overlooking the deep inter-utterance dependencies. In this work, we propose a novel Dynamic Multi-scale Context Aggregation network (DMCA) to address the challenges. Specifically, we first utilize dialogue structure to generate multi-scale utterance windows for capturing rich contextual information. After that, we design a Dynamic Hierarchical Aggregation module (DHA) to integrate progressive cues between them. In addition, we form a multi-stage loss strategy to improve model performance and generalization ability. Extensive experimental results show that the DMCA model outperforms baselines significantly and achieves state-of-the-art performance.

Dropout is a widely utilized regularization technique in the training of neural networks, nevertheless, its underlying mechanism and its impact on achieving good generalization abilities remain poorly understood. In this work, we derive the stochastic modified equations for analyzing the dynamics of dropout, where its discrete iteration process is approximated by a class of stochastic differential equations. In order to investigate the underlying mechanism by which dropout facilitates the identification of flatter minima, we study the noise structure of the derived stochastic modified equation for dropout. By drawing upon the structural resemblance between the Hessian and covariance through several intuitive approximations, we empirically demonstrate the universal presence of the inverse variance-flatness relation and the Hessian-variance relation, throughout the training process of dropout. These theoretical and empirical findings make a substantial contribution to our understanding of the inherent tendency of dropout to locate flatter minima.

Previous research has shown that fully-connected networks with small initialization and gradient-based training methods exhibit a phenomenon known as condensation during training. This phenomenon refers to the input weights of hidden neurons condensing into isolated orientations during training, revealing an implicit bias towards simple solutions in the parameter space. However, the impact of neural network structure on condensation has not been investigated yet. In this study, we focus on the investigation of convolutional neural networks (CNNs). Our experiments suggest that when subjected to small initialization and gradient-based training methods, kernel weights within the same CNN layer also cluster together during training, demonstrating a significant degree of condensation. Theoretically, we demonstrate that in a finite training period, kernels of a two-layer CNN with small initialization will converge to one or a few directions. This work represents a step towards a better understanding of the non-linear training behavior exhibited by neural networks with specialized structures.

In this work, we systematically investigate linear multi-step methods for differential equations with memory. In particular, we focus on the numerical stability for multi-step methods. According to this investigation, we give some sufficient conditions for the stability and convergence of some common multi-step methods, and accordingly, a notion of A-stability for differential equations with memory. Finally, we carry out the computational performance of our theory through numerical examples.

The phenomenon of distinct behaviors exhibited by neural networks under varying scales of initialization remains an enigma in deep learning research. In this paper, based on the earlier work by Luo et al.~\cite{luo2021phase}, we present a phase diagram of initial condensation for two-layer neural networks. Condensation is a phenomenon wherein the weight vectors of neural networks concentrate on isolated orientations during the training process, and it is a feature in non-linear learning process that enables neural networks to possess better generalization abilities. Our phase diagram serves to provide a comprehensive understanding of the dynamical regimes of neural networks and their dependence on the choice of hyperparameters related to initialization. Furthermore, we demonstrate in detail the underlying mechanisms by which small initialization leads to condensation at the initial training stage.

Mobility edge, a critical energy separating localized and extended excitations, is a key concept for understanding quantum localization. Aubry-Andr\'{e} (AA) model, a paradigm for exploring quantum localization, does not naturally allow mobility edges due to self-duality. Using the momentum-state lattice of quantum gas of Cs atoms to synthesize a nonlinear AA model, we provide experimental evidence for mobility edge induced by interactions. By identifying the extended-to-localized transition of different energy eigenstates, we construct a mobility-edge phase diagram. The location of mobility edge in the low- or high-energy region is tunable via repulsive or attractive interactions. Our observation is in good agreement with the theory, and supports an interpretation of such interaction-induced mobility edge via a generalized AA model. Our work also offers new possibilities to engineer quantum transport and phase transitions in disordered systems., Comment: 7+4 pages, 8 figures