我们解决了从单个观测轨迹估算马尔可夫链的混合时间的基本问题。与以前考虑了希尔伯特空间方法来估计光谱差距的作品相反，我们选择了基于收缩的总变异的方法。具体而言，我们根据Dobrushin定义并估算了广义收缩系数。我们表明，与光谱差距不同，该数量可以控制到强烈通用常数的混合时间，并且对于非可逆链仍然有效。我们在系数周围设计了完全依赖数据的置信区间，该系数既比其光谱对应物更易于计算和更薄。此外，我们通过展示如何利用有关过渡矩阵的其他信息来启动超越最坏情况的分析，以便获得有关其相对于诱导统一规范的实例依赖性速率以及其某些混合属性。

我们解决了估计混合时间的问题$ t _ {\ mathsf {mix}} $从单个长度$ m $的单个轨迹中的任意Ergodic有限状态马尔可夫链的$。 Hsu等人解决了可逆情况。 [2019]，他将一般案件作为一个空旷的问题。在可逆情况下，马尔可夫操作员是自我伴侣的事实，极大地促进了分析，而魏尔的不平等允许对经验特征值进行无维度的扰动分析。如Hsu等。指出，在没有可逆性（引起不对称的对概率矩阵）的情况下，现有的扰动分析对$ D $ $ d $的状态数量的指数依赖性最差。此外，即使可以更好地依赖$ d $的特征值扰动分析，在不可逆的情况下，光谱间隙和混合时间之间的连接也不像可逆情况下那么简单。我们的关键见解是估计伪柔性差距$ \ gamma _ {\ mathsf {ps}}} $，这使我们能够克服对称性的损失并实现对最小的平稳概率$ \ pi_ \ pi_ \ star $ \ star $和$ \ gamma _ {\ mathsf {ps}} $。此外，在可逆情况下，我们在$ t _ {\ Mathsf {mix}} $和precision $ \ varepsilon $中获得几乎同时获得的（取决于对数因素）的最小值，并在HSU等人中缩小了差距，他的差距是$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ varepsilon $在下限中为常数。最后，我们为$ \ gamma _ {\ mathsf {ps}} $构建完全的经验置信区间，它以大约$ 1/\ sqrt {m} $的速度收缩至零案子。

The aim of this paper is to introduce a new learning procedure for neural networks and to demonstrate that it works well enough on a few small problems to be worth further investigation. The Forward-Forward algorithm replaces the forward and backward passes of backpropagation by two forward passes, one with positive (i.e. real) data and the other with negative data which could be generated by the network itself. Each layer has its own objective function which is simply to have high goodness for positive data and low goodness for negative data. The sum of the squared activities in a layer can be used as the goodness but there are many other possibilities, including minus the sum of the squared activities. If the positive and negative passes could be separated in time, the negative passes could be done offline, which would make the learning much simpler in the positive pass and allow video to be pipelined through the network without ever storing activities or stopping to propagate derivatives.

In heterogeneous networks (HetNets), the overlap of small cells and the macro cell causes severe cross-tier interference. Although there exist some approaches to address this problem, they usually require global channel state information, which is hard to obtain in practice, and get the sub-optimal power allocation policy with high computational complexity. To overcome these limitations, we propose a multi-agent deep reinforcement learning (MADRL) based power control scheme for the HetNet, where each access point makes power control decisions independently based on local information. To promote cooperation among agents, we develop a penalty-based Q learning (PQL) algorithm for MADRL systems. By introducing regularization terms in the loss function, each agent tends to choose an experienced action with high reward when revisiting a state, and thus the policy updating speed slows down. In this way, an agent's policy can be learned by other agents more easily, resulting in a more efficient collaboration process. We then implement the proposed PQL in the considered HetNet and compare it with other distributed-training-and-execution (DTE) algorithms. Simulation results show that our proposed PQL can learn the desired power control policy from a dynamic environment where the locations of users change episodically and outperform existing DTE MADRL algorithms.

Cell-free massive MIMO is emerging as a promising technology for future wireless communication systems, which is expected to offer uniform coverage and high spectral efficiency compared to classical cellular systems. We study in this paper how cell-free massive MIMO can support federated edge learning. Taking advantage of the additive nature of the wireless multiple access channel, over-the-air computation is exploited, where the clients send their local updates simultaneously over the same communication resource. This approach, known as over-the-air federated learning (OTA-FL), is proven to alleviate the communication overhead of federated learning over wireless networks. Considering channel correlation and only imperfect channel state information available at the central server, we propose a practical implementation of OTA-FL over cell-free massive MIMO. The convergence of the proposed implementation is studied analytically and experimentally, confirming the benefits of cell-free massive MIMO for OTA-FL.

As an efficient graph analytical tool, graph neural networks (GNNs) have special properties that are particularly fit for the characteristics and requirements of wireless communications, exhibiting good potential for the advancement of next-generation wireless communications. This article aims to provide a comprehensive overview of the interplay between GNNs and wireless communications, including GNNs for wireless communications (GNN4Com) and wireless communications for GNNs (Com4GNN). In particular, we discuss GNN4Com based on how graphical models are constructed and introduce Com4GNN with corresponding incentives. We also highlight potential research directions to promote future research endeavors for GNNs in wireless communications.

Dynamic evaluation of language models (LMs) adapts model parameters at test time using gradient information from previous tokens and substantially improves LM performance. However, it requires over 3x more compute than standard inference. We present Fast Weight Layers (FWLs), a neural component that provides the benefits of dynamic evaluation much more efficiently by expressing gradient updates as linear attention. A key improvement over dynamic evaluation is that FWLs can also be applied at training time so the model learns to make good use of gradient updates. FWLs can easily be added on top of existing transformer models, require relatively little extra compute or memory to run, and significantly improve language modeling perplexity.

The GLOM architecture proposed by Hinton [2021] is a recurrent neural network for parsing an image into a hierarchy of wholes and parts. When a part is ambiguous, GLOM assumes that the ambiguity can be resolved by allowing the part to make multi-modal predictions for the pose and identity of the whole to which it belongs and then using attention to similar predictions coming from other possibly ambiguous parts to settle on a common mode that is predicted by several different parts. In this study, we describe a highly simplified version of GLOM that allows us to assess the effectiveness of this way of dealing with ambiguity. Our results show that, with supervised training, GLOM is able to successfully form islands of very similar embedding vectors for all of the locations occupied by the same object and it is also robust to strong noise injections in the input and to out-of-distribution input transformations.

Time series anomaly detection has applications in a wide range of research fields and applications, including manufacturing and healthcare. The presence of anomalies can indicate novel or unexpected events, such as production faults, system defects, or heart fluttering, and is therefore of particular interest. The large size and complex patterns of time series have led researchers to develop specialised deep learning models for detecting anomalous patterns. This survey focuses on providing structured and comprehensive state-of-the-art time series anomaly detection models through the use of deep learning. It providing a taxonomy based on the factors that divide anomaly detection models into different categories. Aside from describing the basic anomaly detection technique for each category, the advantages and limitations are also discussed. Furthermore, this study includes examples of deep anomaly detection in time series across various application domains in recent years. It finally summarises open issues in research and challenges faced while adopting deep anomaly detection models.

Panoptic segmentation assigns semantic and instance ID labels to every pixel of an image. As permutations of instance IDs are also valid solutions, the task requires learning of high-dimensional one-to-many mapping. As a result, state-of-the-art approaches use customized architectures and task-specific loss functions. We formulate panoptic segmentation as a discrete data generation problem, without relying on inductive bias of the task. A diffusion model based on analog bits is used to model panoptic masks, with a simple, generic architecture and loss function. By simply adding past predictions as a conditioning signal, our method is capable of modeling video (in a streaming setting) and thereby learns to track object instances automatically. With extensive experiments, we demonstrate that our generalist approach can perform competitively to state-of-the-art specialist methods in similar settings.