The extragradient method has recently gained increasing attention, due to its convergence behavior on smooth games. In $n$-player differentiable games, the eigenvalues of the Jacobian of the vector field are distributed on the complex plane, exhibiting more convoluted dynamics compared to classical (i.e., single player) minimization. In this work, we take a polynomial-based analysis of the extragradient with momentum for optimizing games with \emph{cross-shaped} Jacobian spectrum on the complex plane. We show two results. First, based on the hyperparameter setup, the extragradient with momentum exhibits three different modes of convergence: when the eigenvalues are distributed $i)$ on the real line, $ii)$ both on the real line along with complex conjugates, and $iii)$ only as complex conjugates. Then, we focus on the case $ii)$, i.e., when the eigenvalues of the Jacobian have \emph{cross-shaped} structure, as observed in training generative adversarial networks. For this problem class, we derive the optimal hyperparameters of the momentum extragradient method, and show that it achieves an accelerated convergence rate.

随机梯度下降血液（SGDM）是许多优化方案中的主要算法，包括凸优化实例和非凸神经网络训练。然而，在随机设置中，动量会干扰梯度噪声，通常导致特定的台阶尺寸和动量选择，以便保证收敛，留出加速。另一方面，近端点方法由于其数值稳定性和针对不完美调谐的弹性而产生了很多关注。他们随机加速的变体虽然已接受有限的注意：动量与（随机）近端点的稳定性相互作用仍然在很大程度上是不孤立的。为了解决这个问题，我们专注于随机近端点算法的动量（SPPAM）的收敛性和稳定性，并显示SPPAM与随机近端点算法（SPPA）相比具有更好的收缩因子的更快的线性收敛速度，如适当的HyperParameter调整。在稳定性方面，我们表明SPPAM取决于问题常数比SGDM更有利，允许更广泛的步长和导致收敛的动量。

神经网络修剪对于在预训练的密集网络架构中发现有效，高性能的子网有用。然而，更常见的是，它涉及三步过程 - 预先训练，修剪和重新训练 - 这是计算昂贵的，因为必须完全预先训练的密集模型。幸运的是，已经经过了多种作品，证明可以通过修剪发现高性能的子网，而无需完全预先训练密集网络。旨在理论上分析修剪网络表现良好的密集网络预培训量，我们发现在两层全连接网络上的SGD预训练迭代数量中发现了一个理论界限，超出了由此进行修剪贪婪的前瞻性选择产生了一个达到良好训练错误的子网。该阈值显示在对数上依赖于数据集的大小，这意味着具有较大数据集的实验需要更好地训练通过修剪以执行良好执行的子网。我们经验展示了我们在各种架构和数据集中的理论结果的有效性，包括在Mnist上培训的全连接网络以及在CIFAR10和ImageNet上培训的几个深度卷积神经网络（CNN）架构。

Most scanning LiDAR sensors generate a sequence of point clouds in real-time. While conventional 3D object detectors use a set of unordered LiDAR points acquired over a fixed time interval, recent studies have revealed that substantial performance improvement can be achieved by exploiting the spatio-temporal context present in a sequence of LiDAR point sets. In this paper, we propose a novel 3D object detection architecture, which can encode LiDAR point cloud sequences acquired by multiple successive scans. The encoding process of the point cloud sequence is performed on two different time scales. We first design a short-term motion-aware voxel encoding that captures the short-term temporal changes of point clouds driven by the motion of objects in each voxel. We also propose long-term motion-guided bird's eye view (BEV) feature enhancement that adaptively aligns and aggregates the BEV feature maps obtained by the short-term voxel encoding by utilizing the dynamic motion context inferred from the sequence of the feature maps. The experiments conducted on the public nuScenes benchmark demonstrate that the proposed 3D object detector offers significant improvements in performance compared to the baseline methods and that it sets a state-of-the-art performance for certain 3D object detection categories. Code is available at https://github.com/HYjhkoh/MGTANet.git

A machine learning (ML) system must learn not only to match the output of a target function on a training set, but also to generalize to novel situations in order to yield accurate predictions at deployment. In most practical applications, the user cannot exhaustively enumerate every possible input to the model; strong generalization performance is therefore crucial to the development of ML systems which are performant and reliable enough to be deployed in the real world. While generalization is well-understood theoretically in a number of hypothesis classes, the impressive generalization performance of deep neural networks has stymied theoreticians. In deep reinforcement learning (RL), our understanding of generalization is further complicated by the conflict between generalization and stability in widely-used RL algorithms. This thesis will provide insight into generalization by studying the learning dynamics of deep neural networks in both supervised and reinforcement learning tasks.

We study the learning dynamics of self-predictive learning for reinforcement learning, a family of algorithms that learn representations by minimizing the prediction error of their own future latent representations. Despite its recent empirical success, such algorithms have an apparent defect: trivial representations (such as constants) minimize the prediction error, yet it is obviously undesirable to converge to such solutions. Our central insight is that careful designs of the optimization dynamics are critical to learning meaningful representations. We identify that a faster paced optimization of the predictor and semi-gradient updates on the representation, are crucial to preventing the representation collapse. Then in an idealized setup, we show self-predictive learning dynamics carries out spectral decomposition on the state transition matrix, effectively capturing information of the transition dynamics. Building on the theoretical insights, we propose bidirectional self-predictive learning, a novel self-predictive algorithm that learns two representations simultaneously. We examine the robustness of our theoretical insights with a number of small-scale experiments and showcase the promise of the novel representation learning algorithm with large-scale experiments.

由于其学习能力和模仿复杂的数据分布的能力，深层生成机器学习模型（DGM）在整个设计社区的流行一直在越来越受欢迎。 DGM经过常规培训，以最大程度地减少分布与生成数据的分布与对其训练的数据集的分布之间的统计差异。尽管足以生成“现实”的假数据的任务，但该目标通常不足以设计综合任务。相反，设计问题通常要求遵守设计要求，例如性能目标和约束。在工程设计中推进DGM需要新的培训目标，以促进工程设计目标。在本文中，我们介绍了第一个同时优化性能，可行性，多样性和目标成就的深层生成模型。我们在八个评估指标上针对几个深层生成模型的拟议方法的性能进行了基准性能，这些模型着重于设计性能目标的可行性，多样性和满意度。在具有挑战性的多目标自行车框架设计问题上测试了方法，并具有偏斜的不同数据类型的多模式数据。在八个指标中的六个指标中，提出的框架被发现胜过所有深层生成模型。

This paper demonstrates how Automated Machine Learning (AutoML) methods can be used as effective surrogate models in engineering design problems. To do so, we consider the challenging problem of structurally-performant bicycle frame design and demonstrate across-the-board dominance by AutoML in regression and classification surrogate modeling tasks. We also introduce FRAMED -- a parametric dataset of 4500 bicycle frames based on bicycles designed by practitioners and enthusiasts worldwide. Accompanying these frame designs, we provide ten structural performance values such as weight, displacements under load, and safety factors computed using finite element simulations for all the bicycle frame designs. We formulate two challenging test problems: a performance-prediction regression problem and a feasibility-prediction classification problem. We then systematically search for optimal surrogate models using Bayesian hyperparameter tuning and neural architecture search. Finally, we show how a state-of-the-art AutoML method can be effective for both regression and classification problems. We demonstrate that the proposed AutoML models outperform the strongest gradient boosting and neural network surrogates identified through Bayesian optimization by an improved F1 score of 24\% for classification and reduced mean absolute error by 12.5\% for regression. Our work introduces a dataset for bicycle design practitioners, provides two benchmark problems for surrogate modeling researchers, and demonstrates the advantages of AutoML in machine learning tasks. The dataset and code are provided at \url{http://decode.mit.edu/projects/framed/}.

我们考虑一个矩阵完成问题，用于将社交或项目相似性图形作为侧面信息。我们开发了一种普遍的，无参数和计算的有效算法，该算法以分层图形聚类开始，然后迭代地改进图形聚类和矩阵额定值。在一个层次的随机块模型，尊重实际相关的社交图和低秩评级矩阵模型（要详细），我们证明了我们的算法实现了观察到的矩阵条目数量的信息 - 理论限制（即，最佳通过与较低的不可能结果一起导出的样本复杂性）通过最大似然估计。该结果的一个结果是利用社交图的层次结构，相对于简单地识别不同组的情况，在不诉诸于它们的情况下，可以产生相对于不同组的样本复杂性的大量增益。我们对合成和现实世界数据集进行了广泛的实验，以证实我们的理论结果，并展示了利用图形侧信息的其他矩阵完成算法的显着性能改进。

神经结构搜索（NAS）的成功受到过度计算要求的限制。虽然现代重量共享NAS方法，例如飞镖在单位数GPU天中可以完成搜索，但从共享权重中提取最终的最佳架构是众所周知的不可靠性。培训 - 速度估计（TSE），最近开发的普遍开发的普遍估计，以贝叶斯边缘似然解释的用来代替飞镖基于梯度优化的验证损失。这可以防止飞镖跳过连接崩溃，这显着提高了NASBench-201和原始飞镖搜索空间的性能。我们通过应用各种飞镖诊断来扩展这些结果，并显示不使用验证集产生的几种不寻常的行为。此外，我们的实验产生了在与操作选择相比，尽管通常在文献中受到有限的关注，但仍会产生对搜索性能的强烈影响的深度间隙和拓扑选择的具体示例。