Quantization summarizes continuous distributions by calculating a discrete
approximation. Among the widely adopted methods for data quantization is
Lloyd's algorithm, which partitions the space into Vorono\"i cells, that can be
seen as clusters, and constructs a discrete distribution based on their
centroids and probabilistic masses. Lloyd's algorithm estimates the optimal
centroids in a minimal expected distance sense, but this approach poses
significant challenges in scenarios where data evaluation is costly, and
relates to rare events. Then, the single cluster associated to no event takes
the majority of the probability mass. In this context, a metamodel is required
and adapted sampling methods are necessary to increase the precision of the
computations on the rare clusters.

该研究论文介绍了离散化对连续分布进行概括的方法，重点讨论了 Lloyd 算法在数据离散化中的应用以及相关挑战和解决方案。

FunQuant：在罕见事件和耗时模拟环境中执行量子化的 R 软件包

FunQuant: A R package to perform quantization in the context of rare  events and time-consuming simulations

We seek to semantically describe a set of images, capturing both the
attributes of single images and the variations within the set. Our procedure is
analogous to Principle Component Analysis, in which the role of projection
vectors is replaced with generated phrases. First, a centroid phrase that has
the largest average semantic similarity to the images in the set is generated,
where both the computation of the similarity and the generation are based on
pretrained vision-language models. Then, the phrase that generates the highest
variation among the similarity scores is generated, using the same models. The
next phrase maximizes the variance subject to being orthogonal, in the latent
space, to the highest-variance phrase, and the process continues. Our
experiments show that our method is able to convincingly capture the essence of
image sets and describe the individual elements in a semantically meaningful
way within the context of the entire set. Our code is available at:
this https URL.

该研究旨在运用预先训练的视觉 - 语言模型，通过生成短语来语义上描述一组图像，从而捕捉到单个图像的属性和整个集合内部的变化，并通过对不同短语之间的相似度进行计算和比较，从而将图像集合的关键特征有效地捕捉和说明。

用文本 - PCA 描述图像集

Describing Sets of Images with Textual-PCA

Federated learning is a paradigm that enables local devices to jointly train
a server model while keeping the data decentralized and private. In federated
learning, since local data are collected by clients, it is hardly guaranteed
that the data are correctly annotated. Although a lot of studies have been
conducted to train the networks robust to these noisy data in a centralized
setting, these algorithms still suffer from noisy labels in federated learning.
Compared to the centralized setting, clients' data can have different noise
distributions due to variations in their labeling systems or background
knowledge of users. As a result, local models form inconsistent decision
boundaries and their weights severely diverge from each other, which are
serious problems in federated learning. To solve these problems, we introduce a
novel federated learning scheme that the server cooperates with local models to
maintain consistent decision boundaries by interchanging class-wise centroids.
These centroids are central features of local data on each device, which are
aligned by the server every communication round. Updating local models with the
aligned centroids helps to form consistent decision boundaries among local
models, although the noise distributions in clients' data are different from
each other. To improve local model performance, we introduce a novel approach
to select confident samples that are used for updating the model with given
labels. Furthermore, we propose a global-guided pseudo-labeling method to
update labels of unconfident samples by exploiting the global model. Our
experimental results on the noisy CIFAR-10 dataset and the Clothing1M dataset
show that our approach is noticeably effective in federated learning with noisy
labels.

提出了一种新的联邦学习方案，其中服务器与本地模型合作，通过交换类别的中心来保持一致的决策边界，实现了在网络中使用带有给定噪声的标签的一致决策边界。同时，还提出了选择有自信的样本来更新模型以及全局引导的伪标签方法来更新不自信的样本标签。在嘈杂的 CIFAR-10 数据集和 Clothing1M 数据集上的实验证明，该方法在使用有噪声的标签的联邦学习中非常有效。

带有噪声标签的鲁棒联邦学习

Robust Federated Learning with Noisy Labels

A new algorithm is proposed which accelerates the mini-batch k-means
algorithm of Sculley (2010) by using the distance bounding approach of Elkan
(2003). We argue that, when incorporating distance bounds into a mini-batch
algorithm, already used data should preferentially be reused. To this end we
propose using nested mini-batches, whereby data in a mini-batch at iteration t
is automatically reused at iteration t+1.
Using nested mini-batches presents two difficulties. The first is that
unbalanced use of data can bias estimates, which we resolve by ensuring that
each data sample contributes exactly once to centroids. The second is in
choosing mini-batch sizes, which we address by balancing premature fine-tuning
of centroids with redundancy induced slow-down. Experiments show that the
resulting nmbatch algorithm is very effective, often arriving within 1% of the
empirical minimum 100 times earlier than the standard mini-batch algorithm.

通过使用 Elkan（2003）的距离界限方法来加速 Sculley（2010）的 Mini-Batch K-Means 算法，提出了一种新算法。使用嵌套的 Mini-Batches 提出了两个困难。实验表明，得到的嵌套 Mini-Batch 算法非常有效，通常比标准 Mini-Batch 算法早 100 次到达经验最小值的 1%。