量子计算为某些问题提供了指数加速的潜力。但是，许多具有可证明加速的现有算法都需要当前不可用的耐故障量子计算机。我们提出了NISQ-TDA，这是第一个完全实现的量子机学习算法，其在任意经典（非手动）数据上具有可证明的指数加速，并且仅需要线性电路深度。我们报告了我们的NISQ-TDA算法的成功执行，该算法应用于在量子计算设备以及嘈杂的量子模拟器上运行的小数据集。我们从经验上证实，该算法对噪声是可靠的，并提供了目标深度和噪声水平，以实现现实世界中问题的近期，无耐受耐受性的量子优势。我们独特的数据加载投影方法是噪声鲁棒性的主要来源，引入了一种新的自我校正数据加载方法。

我们实施和解释各种有涉及实际二次领域的监督学习实验，具有1、2和3。我们从数据科学的角度量化了匹配/不同奇偶校验的类别的相对困难，应用功能分析的方法论组件分析，并使用符号分类来开发适用于我们数据集的1、2和3类的机器学习公式。

论一般相对论中的长期分类问题，我们采用机器学习和现代数据科学的富有成效技术采取小说视角。特别是，我们模拟Petrov的分类时间的分类，并表明前馈神经网络可以实现高度的成功。我们还展示了数据可视化技术如何具有维度降低的技术可以帮助分析不同类型的刻度的结构中的底层图案。

我们将机器学习应用于寻找数值卡拉比市度量的问题。我们在使用Donaldson算法计算近似Ricci-FLAN度量的学习近似Ricci-Flat度量，以更加准确的“最佳”度量标准的“最佳”的“最佳”指标来扩展。我们表明，机器学习能够预测只有一个小型训练数据样本的Calabi-yau度量的K \“Ahler潜力。

我们重新审视加权P4的经典数据库，该加权P4允许卡拉巴 - yau 3折过高度，从机器学习工具箱中配备了各种工具。无监督的技术识别出于对重量拓扑数据的意外几乎线性依赖性。然后，这允许我们在Calabi-yau数据中识别先前未被注意的群集。监督技术是成功预测超细的拓扑参数，其重量具有R ^ 2> 95％的精度。监督学习还允许我们识别加权P4，通过利用聚类行为支持的分区来识别Calabi-Yau过度覆盖到100％的准确性。

我们通过在调整方案中找到有效的相似性测量，提出了一种朝向弦景观的真空退化问题的新方法。使用一百万个Calabi-yau歧管作为具体例子，少量机器学习和暹罗神经网络的范式代表它们作为R（3）的点，其中两个歧管之间的相似度得分是它们之间的欧几里德距离r（3）代表。使用这些方法，我们可以通过仅在几百个数据点上进行培训，将搜索空间压缩以获得极度罕见的歧管，以百分比在原始数据的一个百分比内。我们还展示了如何应用这些方法来表征真空代表的“典型性”。

我们应用机器学习方法，例如神经网络，流形学习和图像处理，以研究代数几何和弦理论中的二维变形虫。在嵌入歧管投影的帮助下，我们恢复了从所谓的偏斜性获得的复杂条件。在某些情况下，它甚至可以达到$ \ sim99 \％$的精度，尤其是对于$ f_0 $的不平衡的变形虫，并具有正系数，我们将其放置为主要重点。使用权重和偏见，我们还找到了良好的近似值，以较低的计算成本来确定变形虫的属。通常，这些模型可以轻松预测超过$ 90 \％$精确度的属。通过类似的技术，我们还直接研究了成员资格问题和图像处理。

Designing experiments often requires balancing between learning about the true treatment effects and earning from allocating more samples to the superior treatment. While optimal algorithms for the Multi-Armed Bandit Problem (MABP) provide allocation policies that optimally balance learning and earning, they tend to be computationally expensive. The Gittins Index (GI) is a solution to the MABP that can simultaneously attain optimality and computationally efficiency goals, and it has been recently used in experiments with Bernoulli and Gaussian rewards. For the first time, we present a modification of the GI rule that can be used in experiments with exponentially-distributed rewards. We report its performance in simulated 2- armed and 3-armed experiments. Compared to traditional non-adaptive designs, our novel GI modified design shows operating characteristics comparable in learning (e.g. statistical power) but substantially better in earning (e.g. direct benefits). This illustrates the potential that designs using a GI approach to allocate participants have to improve participant benefits, increase efficiencies, and reduce experimental costs in adaptive multi-armed experiments with exponential rewards.

Transformer has achieved impressive successes for various computer vision tasks. However, most of existing studies require to pretrain the Transformer backbone on a large-scale labeled dataset (e.g., ImageNet) for achieving satisfactory performance, which is usually unavailable for medical images. Additionally, due to the gap between medical and natural images, the improvement generated by the ImageNet pretrained weights significantly degrades while transferring the weights to medical image processing tasks. In this paper, we propose Bootstrap Own Latent of Transformer (BOLT), a self-supervised learning approach specifically for medical image classification with the Transformer backbone. Our BOLT consists of two networks, namely online and target branches, for self-supervised representation learning. Concretely, the online network is trained to predict the target network representation of the same patch embedding tokens with a different perturbation. To maximally excavate the impact of Transformer from limited medical data, we propose an auxiliary difficulty ranking task. The Transformer is enforced to identify which branch (i.e., online/target) is processing the more difficult perturbed tokens. Overall, the Transformer endeavours itself to distill the transformation-invariant features from the perturbed tokens to simultaneously achieve difficulty measurement and maintain the consistency of self-supervised representations. The proposed BOLT is evaluated on three medical image processing tasks, i.e., skin lesion classification, knee fatigue fracture grading and diabetic retinopathy grading. The experimental results validate the superiority of our BOLT for medical image classification, compared to ImageNet pretrained weights and state-of-the-art self-supervised learning approaches.

Text clustering and topic extraction are two important tasks in text mining. Usually, these two tasks are performed separately. For topic extraction to facilitate clustering, we can first project texts into a topic space and then perform a clustering algorithm to obtain clusters. To promote topic extraction by clustering, we can first obtain clusters with a clustering algorithm and then extract cluster-specific topics. However, this naive strategy ignores the fact that text clustering and topic extraction are strongly correlated and follow a chicken-and-egg relationship. Performing them separately fails to make them mutually benefit each other to achieve the best overall performance. In this paper, we propose an unsupervised text clustering and topic extraction framework (ClusTop) which integrates text clustering and topic extraction into a unified framework and can achieve high-quality clustering result and extract topics from each cluster simultaneously. Our framework includes four components: enhanced language model training, dimensionality reduction, clustering and topic extraction, where the enhanced language model can be viewed as a bridge between clustering and topic extraction. On one hand, it provides text embeddings with a strong cluster structure which facilitates effective text clustering; on the other hand, it pays high attention on the topic related words for topic extraction because of its self-attention architecture. Moreover, the training of enhanced language model is unsupervised. Experiments on two datasets demonstrate the effectiveness of our framework and provide benchmarks for different model combinations in this framework.