Implicit regularization is an important way to interpret neural networks. Recent theory starts to explain implicit regularization with the model of deep matrix factorization (DMF) and analyze the trajectory of discrete gradient dynamics in the optimization process. These discrete gradient dynamics are relatively small but not infinitesimal, thus fitting well with the practical implementation of neural networks. Currently, discrete gradient dynamics analysis has been successfully applied to shallow networks but encounters the difficulty of complex computation for deep networks. In this work, we introduce another discrete gradient dynamics approach to explain implicit regularization, i.e. landscape analysis. It mainly focuses on gradient regions, such as saddle points and local minima. We theoretically establish the connection between saddle point escaping (SPE) stages and the matrix rank in DMF. We prove that, for a rank-R matrix reconstruction, DMF will converge to a second-order critical point after R stages of SPE. This conclusion is further experimentally verified on a low-rank matrix reconstruction problem. This work provides a new theory to analyze implicit regularization in deep learning.

Existing Multiple Object Tracking (MOT) methods design complex architectures for better tracking performance. However, without a proper organization of input information, they still fail to perform tracking robustly and suffer from frequent identity switches. In this paper, we propose two novel methods together with a simple online Message Passing Network (MPN) to address these limitations. First, we explore different integration methods for the graph node and edge embeddings and put forward a new IoU (Intersection over Union) guided function, which improves long term tracking and handles identity switches. Second, we introduce a hierarchical sampling strategy to construct sparser graphs which allows to focus the training on more difficult samples. Experimental results demonstrate that a simple online MPN with these two contributions can perform better than many state-of-the-art methods. In addition, our association method generalizes well and can also improve the results of private detection based methods.

In this paper, we propose a novel primal-dual proximal splitting algorithm (PD-PSA), named BALPA, for the composite optimization problem with equality constraints, where the loss function consists of a smooth term and a nonsmooth term composed with a linear mapping. In BALPA, the dual update is designed as a proximal point for a time-varying quadratic function, which balances the implementation of primal and dual update and retains the proximity-induced feature of classic PD-PSAs. In addition, by this balance, BALPA eliminates the inefficiency of classic PD-PSAs for composite optimization problems in which the Euclidean norm of the linear mapping or the equality constraint mapping is large. Therefore, BALPA not only inherits the advantages of simple structure and easy implementation of classic PD-PSAs but also ensures a fast convergence when these norms are large. Moreover, we propose a stochastic version of BALPA (S-BALPA) and apply the developed BALPA to distributed optimization to devise a new distributed optimization algorithm. Furthermore, a comprehensive convergence analysis for BALPA and S-BALPA is conducted, respectively. Finally, numerical experiments demonstrate the efficiency of the proposed algorithms.

The main challenge for fine-grained few-shot image classification is to learn feature representations with higher inter-class and lower intra-class variations, with a mere few labelled samples. Conventional few-shot learning methods however cannot be naively adopted for this fine-grained setting -- a quick pilot study reveals that they in fact push for the opposite (i.e., lower inter-class variations and higher intra-class variations). To alleviate this problem, prior works predominately use a support set to reconstruct the query image and then utilize metric learning to determine its category. Upon careful inspection, we further reveal that such unidirectional reconstruction methods only help to increase inter-class variations and are not effective in tackling intra-class variations. In this paper, we for the first time introduce a bi-reconstruction mechanism that can simultaneously accommodate for inter-class and intra-class variations. In addition to using the support set to reconstruct the query set for increasing inter-class variations, we further use the query set to reconstruct the support set for reducing intra-class variations. This design effectively helps the model to explore more subtle and discriminative features which is key for the fine-grained problem in hand. Furthermore, we also construct a self-reconstruction module to work alongside the bi-directional module to make the features even more discriminative. Experimental results on three widely used fine-grained image classification datasets consistently show considerable improvements compared with other methods. Codes are available at: https://github.com/PRIS-CV/Bi-FRN.

This paper introduced key aspects of applying Machine Learning (ML) models, improved trading strategies, and the Quasi-Reversibility Method (QRM) to optimize stock option forecasting and trading results. It presented the findings of the follow-up project of the research "Application of Convolutional Neural Networks with Quasi-Reversibility Method Results for Option Forecasting". First, the project included an application of Recurrent Neural Networks (RNN) and Long Short-Term Memory (LSTM) networks to provide a novel way of predicting stock option trends. Additionally, it examined the dependence of the ML models by evaluating the experimental method of combining multiple ML models to improve prediction results and decision-making. Lastly, two improved trading strategies and simulated investing results were presented. The Binomial Asset Pricing Model with discrete time stochastic process analysis and portfolio hedging was applied and suggested an optimized investment expectation. These results can be utilized in real-life trading strategies to optimize stock option investment results based on historical data.

This paper presents a methodology for combining programming and mathematics to optimize elevator wait times. Based on simulated user data generated according to the canonical three-peak model of elevator traffic, we first develop a naive model from an intuitive understanding of the logic behind elevators. We take into consideration a general array of features including capacity, acceleration, and maximum wait time thresholds to adequately model realistic circumstances. Using the same evaluation framework, we proceed to develop a Deep Q Learning model in an attempt to match the hard-coded naive approach for elevator control. Throughout the majority of the paper, we work under a Markov Decision Process (MDP) schema, but later explore how the assumption fails to characterize the highly stochastic overall Elevator Group Control System (EGCS).

A Transformer-based deep direct sampling method is proposed for a class of boundary value inverse problems. A real-time reconstruction is achieved by evaluating the learned inverse operator between carefully designed data and the reconstructed images. An effort is made to give a specific example to a fundamental question: whether and how one can benefit from the theoretical structure of a mathematical problem to develop task-oriented and structure-conforming deep neural networks? Specifically, inspired by direct sampling methods for inverse problems, the 1D boundary data in different frequencies are preprocessed by a partial differential equation-based feature map to yield 2D harmonic extensions as different input channels. Then, by introducing learnable non-local kernels, the direct sampling is recast to a modified attention mechanism. The proposed method is then applied to electrical impedance tomography, a well-known severely ill-posed nonlinear inverse problem. The new method achieves superior accuracy over its predecessors and contemporary operator learners, as well as shows robustness with respect to noise. This research shall strengthen the insights that the attention mechanism, despite being invented for natural language processing tasks, offers great flexibility to be modified in conformity with the a priori mathematical knowledge, which ultimately leads to the design of more physics-compatible neural architectures.

我们介绍了第一个机器学习引力波搜索模拟数据挑战（MLGWSC-1）的结果。在这一挑战中，参与的小组必须从二进制黑洞合并中识别出复杂性和持续时间逐渐嵌入在逐渐更现实的噪声中的引力波信号。 4个提供的数据集中的决赛包含O3A观察的真实噪声，并发出了20秒的持续时间，其中包含进动效应和高阶模式。我们介绍了在提交前从参与者未知的1个月的测试数据中得出的6个输入算法的平均灵敏度距离和运行时。其中4个是机器学习算法。我们发现，最好的基于机器学习的算法能够以每月1个的错误警报率（FAR）的速度（FAR）实现基于匹配过滤的生产分析的敏感距离的95％。相反，对于真实的噪音，领先的机器学习搜索获得了70％。为了更高的范围，敏感距离缩小的差异缩小到某些数据集上选择机器学习提交的范围$ \ geq 200 $以优于传统搜索算法的程度。我们的结果表明，当前的机器学习搜索算法可能已经在有限的参数区域中对某些生产设置有用。为了改善最新的技术，机器学习算法需要降低他们能够检测信号并将其有效性扩展到参数空间区域的虚假警报率，在这些区域中，建模的搜索在计算上很昂贵。根据我们的发现，我们汇编了我们认为，将机器学习搜索提升到重力波信号检测中的宝贵工具，我们认为这是最重要的研究领域。

激活函数是元素的数学函数，在深神经网络（DNN）中起着至关重要的作用。已经提出了许多新颖和复杂的激活功能来提高DNN的准确性，但在训练过程中还可以通过反向传播消耗大量记忆。在这项研究中，我们提出了嵌套的正向自动分化（正向AD），专门针对用于记忆效率的DNN训练的元素激活函数。我们在两个广泛使用的深度学习框架（Tensorflow和Pytorch）中部署了嵌套的AD，分别支持静态和动态计算图。我们的评估表明，在相同的记忆降低率下，嵌套的前AD嵌套将记忆足迹降低到1.97倍，比基线模型降低了20％。

近年来，在应用预训练的语言模型（例如Bert）上，取得了巨大进展，以获取信息检索（IR）任务。在网页中通常使用的超链接已被利用用于设计预训练目标。例如，超链接的锚文本已用于模拟查询，从而构建了巨大的查询文档对以进行预训练。但是，作为跨越两个网页的桥梁，尚未完全探索超链接的潜力。在这项工作中，我们专注于建模通过超链接连接的两个文档之间的关系，并为临时检索设计一个新的预训练目标。具体而言，我们将文档之间的关系分为四组：无链接，单向链接，对称链接和最相关的对称链接。通过比较从相邻组采样的两个文档，该模型可以逐渐提高其捕获匹配信号的能力。我们提出了一个渐进的超链接预测（{php}）框架，以探索预训练中超链接的利用。对两个大规模临时检索数据集和六个提问数据集的实验结果证明了其优于现有的预训练方法。