The central question in representation learning is what constitutes a good or meaningful representation. In this work we argue that if we consider data with inherent cluster structures, where clusters can be characterized through different means and covariances, those data structures should be represented in the embedding as well. While Autoencoders (AE) are widely used in practice for unsupervised representation learning, they do not fulfil the above condition on the embedding as they obtain a single representation of the data. To overcome this we propose a meta-algorithm that can be used to extend an arbitrary AE architecture to a tensorized version (TAE) that allows for learning cluster-specific embeddings while simultaneously learning the cluster assignment. For the linear setting we prove that TAE can recover the principle components of the different clusters in contrast to principle component of the entire data recovered by a standard AE. We validated this on planted models and for general, non-linear and convolutional AEs we empirically illustrate that tensorizing the AE is beneficial in clustering and de-noising tasks.

学习和分析统计模型的一种常见方法是考虑模型参数空间中的操作。但是，如果我们在参数空间中进行优化，并且在参数空间和基础统计模型空间之间没有一对一的映射会发生什么？这些情况经常发生在包括统计混合物或随机神经网络的分层模型中，据说这些模型是单数的。奇异模型在机器学习中揭示了几个重要且研究的问题，例如由于吸引者行为而导致学习轨迹的收敛速度的降低。在这项工作中，我们提出了一种参数空间的相对重新聚集技术，该技术产生了一种从单数模型中提取常规子模型的一般方法。我们的方法在训练过程中实施了模型可识别性，并研究了在相对参数化下为高斯混合模型（GMM）的梯度下降和期望最大化的学习动力学，显示了更快的实验收敛性和围绕奇异性的动态的改善。将分析扩展到GMM之外，我们进一步分析了在相对重新聚体化及其对概括误差的影响下的Fisher信息矩阵，并显示该方法如何应用于更复杂的模型，例如深层神经网络。

近年来，监督学习环境的几个结果表明，古典统计学习 - 理论措施，如VC维度，不充分解释深度学习模型的性能，促使在无限宽度和迭代制度中的工作摆动。但是，对于超出监督环境之外的神经网络成功几乎没有理论解释。在本文中，我们认为，在一些分布假设下，经典学习 - 理论措施可以充分解释转导造型中的图形神经网络的概括。特别是，我们通过分析节点分类问题图卷积网络的概括性特性，对神经网络的性能进行严格分析神经网络。虽然VC维度确实导致该设置中的琐碎泛化误差界限，但我们表明转导变速器复杂性可以解释用于随机块模型的图形卷积网络的泛化特性。我们进一步使用基于转换的Rademacher复杂性的泛化误差界限来展示图形卷积和网络架构在实现较小的泛化误差方面的作用，并在图形结构可以帮助学习时提供洞察。本文的调查结果可以重新新的兴趣在学习理论措施方面对神经网络的概括，尽管在特定问题中。

在分析参数统计模型时，有用的方法包括在几何上建模参数空间。然而，即使对于统计混合物或随机深度神经网络等非常简单且常用的分层模型，歧管的平滑度呈呈现在参数空间中的非平滑邻域的奇异点。这些奇异模型已经在学习动态的背景下进行了分析，其中奇点可以充当学习轨迹上的吸引子，因此，对模型的收敛速度产生负面影响。我们提出了一种通过使用Stratifolds，来自代数拓扑的概念来规避奇点引起的问题的一般方法，以正式模拟奇异参数空间。我们使用特定的Stratifolds配备了分辨率的特定方法来构造奇异空间的平滑歧管近似。我们经验证明，使用（自然）梯度下降在平滑歧管近似而不是奇异空间允许我们避免吸引子行为，从而提高学习中的收敛速度。

Explanations are crucial parts of deep neural network (DNN) classifiers. In high stakes applications, faithful and robust explanations are important to understand and gain trust in DNN classifiers. However, recent work has shown that state-of-the-art attribution methods in text classifiers are susceptible to imperceptible adversarial perturbations that alter explanations significantly while maintaining the correct prediction outcome. If undetected, this can critically mislead the users of DNNs. Thus, it is crucial to understand the influence of such adversarial perturbations on the networks' explanations and their perceptibility. In this work, we establish a novel definition of attribution robustness (AR) in text classification, based on Lipschitz continuity. Crucially, it reflects both attribution change induced by adversarial input alterations and perceptibility of such alterations. Moreover, we introduce a wide set of text similarity measures to effectively capture locality between two text samples and imperceptibility of adversarial perturbations in text. We then propose our novel TransformerExplanationAttack (TEA), a strong adversary that provides a tight estimation for attribution robustness in text classification. TEA uses state-of-the-art language models to extract word substitutions that result in fluent, contextual adversarial samples. Finally, with experiments on several text classification architectures, we show that TEA consistently outperforms current state-of-the-art AR estimators, yielding perturbations that alter explanations to a greater extent while being more fluent and less perceptible.

Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines fully aware of data constraints and symmetries. We introduce a class of persistence-based neural network layers. Persistence-based layers allow the users to easily inject knowledge about symmetries (equivariance) respected by the data, are equipped with learnable weights, and can be composed with state-of-the-art neural architectures.

Deep Reinforcement Learning is emerging as a promising approach for the continuous control task of robotic arm movement. However, the challenges of learning robust and versatile control capabilities are still far from being resolved for real-world applications, mainly because of two common issues of this learning paradigm: the exploration strategy and the slow learning speed, sometimes known as "the curse of dimensionality". This work aims at exploring and assessing the advantages of the application of Quantum Computing to one of the state-of-art Reinforcement Learning techniques for continuous control - namely Soft Actor-Critic. Specifically, the performance of a Variational Quantum Soft Actor-Critic on the movement of a virtual robotic arm has been investigated by means of digital simulations of quantum circuits. A quantum advantage over the classical algorithm has been found in terms of a significant decrease in the amount of required parameters for satisfactory model training, paving the way for further promising developments.

Algorithms and technologies are essential tools that pervade all aspects of our daily lives. In the last decades, health care research benefited from new computer-based recruiting methods, the use of federated architectures for data storage, the introduction of innovative analyses of datasets, and so on. Nevertheless, health care datasets can still be affected by data bias. Due to data bias, they provide a distorted view of reality, leading to wrong analysis results and, consequently, decisions. For example, in a clinical trial that studied the risk of cardiovascular diseases, predictions were wrong due to the lack of data on ethnic minorities. It is, therefore, of paramount importance for researchers to acknowledge data bias that may be present in the datasets they use, eventually adopt techniques to mitigate them and control if and how analyses results are impacted. This paper proposes a method to address bias in datasets that: (i) defines the types of data bias that may be present in the dataset, (ii) characterizes and quantifies data bias with adequate metrics, (iii) provides guidelines to identify, measure, and mitigate data bias for different data sources. The method we propose is applicable both for prospective and retrospective clinical trials. We evaluate our proposal both through theoretical considerations and through interviews with researchers in the health care environment.

The current trend of applying transfer learning from CNNs trained on large datasets can be an overkill when the target application is a custom and delimited problem with enough data to train a network from scratch. On the other hand, the training of custom and lighter CNNs requires expertise, in the from-scratch case, and or high-end resources, as in the case of hardware-aware neural architecture search (HW NAS), limiting access to the technology by non-habitual NN developers. For this reason, we present Colab NAS, an affordable HW NAS technique for producing lightweight task-specific CNNs. Its novel derivative-free search strategy, inspired by Occam's razor, allows it to obtain state-of-the-art results on the Visual Wake Word dataset in just 4.5 GPU hours using free online GPU services such as Google Colaboratory and Kaggle Kernel.

We propose a novel approach for deep learning-based Multi-View Stereo (MVS). For each pixel in the reference image, our method leverages a deep architecture to search for the corresponding point in the source image directly along the corresponding epipolar line. We denote our method DELS-MVS: Deep Epipolar Line Search Multi-View Stereo. Previous works in deep MVS select a range of interest within the depth space, discretize it, and sample the epipolar line according to the resulting depth values: this can result in an uneven scanning of the epipolar line, hence of the image space. Instead, our method works directly on the epipolar line: this guarantees an even scanning of the image space and avoids both the need to select a depth range of interest, which is often not known a priori and can vary dramatically from scene to scene, and the need for a suitable discretization of the depth space. In fact, our search is iterative, which avoids the building of a cost volume, costly both to store and to process. Finally, our method performs a robust geometry-aware fusion of the estimated depth maps, leveraging a confidence predicted alongside each depth. We test DELS-MVS on the ETH3D, Tanks and Temples and DTU benchmarks and achieve competitive results with respect to state-of-the-art approaches.