Existing analyses of neural network training often operate under the unrealistic assumption of an extremely small learning rate. This lies in stark contrast to practical wisdom and empirical studies, such as the work of J. Cohen et al. (ICLR 2021), which exhibit startling new phenomena (the "edge of stability" or "unstable convergence") and potential benefits for generalization in the large learning rate regime. Despite a flurry of recent works on this topic, however, the latter effect is still poorly understood. In this paper, we take a step towards understanding genuinely non-convex training dynamics with large learning rates by performing a detailed analysis of gradient descent for simplified models of two-layer neural networks. For these models, we provably establish the edge of stability phenomenon and discover a sharp phase transition for the step size below which the neural network fails to learn "threshold-like" neurons (i.e., neurons with a non-zero first-layer bias). This elucidates one possible mechanism by which the edge of stability can in fact lead to better generalization, as threshold neurons are basic building blocks with useful inductive bias for many tasks.

我们提出了一项合成任务，乐高（学习平等和小组操作），该任务封装了遵循推理链的问题，我们研究了变压器体系结构如何学习这项任务。我们特别注意数据效应，例如预处理（看似无关的NLP任务）和数据集组成（例如，训练和测试时间时的链长度不同），以及体系结构变体，例如重量绑定层或添加卷积组件。我们研究了受过训练的模型最终如何在任务中取得成功，尤其是我们能够在某种程度上（一定程度地）理解一些注意力头以及网络中的信息如何流动。基于这些观察结果，我们提出了一个假设，即在这里进行预训练仅是因为是智能初始化而不是网络中存储的深层知识。我们还观察到，在某些数据制度中，受过训练的变压器发现“快捷方式”解决方案遵循推理链，这阻碍了该模型将其推广到主要任务的简单变体的能力，而且我们发现人们可以防止适当的快捷方式架构修改或仔细的数据准备。在我们的发现的激励下，我们开始探索学习执行C程序的任务，在此过程中，对变压器进行了卷积修改，即在密钥/查询/值图中添加卷积结构，显示出令人鼓舞的优势。

数据增强是机器学习管道的基石，但其理论基础尚不清楚。它只是人为增加数据集大小的一种方法吗？还是鼓励模型满足某些不变性？在这项工作中，我们考虑了另一个角度，我们研究了数据增强对学习过程动态的影响。我们发现，数据增强可以改变各种功能的相对重要性，从而有效地使某些信息性但难以学习的功能更有可能在学习过程中捕获。重要的是，我们表明，对于非线性模型，例如神经网络，这种效果更为明显。我们的主要贡献是对Allen-Zhu和Li [2020]最近提出的多视图数据模型中两层卷积神经网络的学习动态数据的详细分析。我们通过进一步的实验证据来补充这一分析，证明数据增加可以看作是特征操纵。

Classically, data interpolation with a parametrized model class is possible as long as the number of parameters is larger than the number of equations to be satisfied. A puzzling phenomenon in deep learning is that models are trained with many more parameters than what this classical theory would suggest. We propose a partial theoretical explanation for this phenomenon. We prove that for a broad class of data distributions and model classes, overparametrization is necessary if one wants to interpolate the data smoothly. Namely we show that smooth interpolation requires $d$ times more parameters than mere interpolation, where $d$ is the ambient data dimension. We prove this universal law of robustness for any smoothly parametrized function class with polynomial size weights, and any covariate distribution verifying isoperimetry. In the case of two-layers neural networks and Gaussian covariates, this law was conjectured in prior work by Bubeck, Li and Nagaraj. We also give an interpretation of our result as an improved generalization bound for model classes consisting of smooth functions.

We introduce the XPER (eXplainable PERformance) methodology to measure the specific contribution of the input features to the predictive or economic performance of a model. Our methodology offers several advantages. First, it is both model-agnostic and performance metric-agnostic. Second, XPER is theoretically founded as it is based on Shapley values. Third, the interpretation of the benchmark, which is inherent in any Shapley value decomposition, is meaningful in our context. Fourth, XPER is not plagued by model specification error, as it does not require re-estimating the model. Fifth, it can be implemented either at the model level or at the individual level. In an application based on auto loans, we find that performance can be explained by a surprisingly small number of features. XPER decompositions are rather stable across metrics, yet some feature contributions switch sign across metrics. Our analysis also shows that explaining model forecasts and model performance are two distinct tasks.

We introduce a parametric view of non-local two-step denoisers, for which BM3D is a major representative, where quadratic risk minimization is leveraged for unsupervised optimization. Within this paradigm, we propose to extend the underlying mathematical parametric formulation by iteration. This generalization can be expected to further improve the denoising performance, somehow curbed by the impracticality of repeating the second stage for all two-step denoisers. The resulting formulation involves estimating an even larger amount of parameters in a unsupervised manner which is all the more challenging. Focusing on the parameterized form of NL-Ridge, the simplest but also most efficient non-local two-step denoiser, we propose a progressive scheme to approximate the parameters minimizing the risk. In the end, the denoised images are made up of iterative linear combinations of patches. Experiments on artificially noisy images but also on real-world noisy images demonstrate that our method compares favorably with the very best unsupervised denoisers such as WNNM, outperforming the recent deep-learning-based approaches, while being much faster.

The French National Institute of Geographical and Forest Information (IGN) has the mission to document and measure land-cover on French territory and provides referential geographical datasets, including high-resolution aerial images and topographic maps. The monitoring of land-cover plays a crucial role in land management and planning initiatives, which can have significant socio-economic and environmental impact. Together with remote sensing technologies, artificial intelligence (IA) promises to become a powerful tool in determining land-cover and its evolution. IGN is currently exploring the potential of IA in the production of high-resolution land cover maps. Notably, deep learning methods are employed to obtain a semantic segmentation of aerial images. However, territories as large as France imply heterogeneous contexts: variations in landscapes and image acquisition make it challenging to provide uniform, reliable and accurate results across all of France. The FLAIR-one dataset presented is part of the dataset currently used at IGN to establish the French national reference land cover map "Occupation du sol \`a grande \'echelle" (OCS- GE).

Reflection high-energy electron diffraction (RHEED) is a powerful tool in molecular beam epitaxy (MBE), but RHEED images are often difficult to interpret, requiring experienced operators. We present an approach for automated surveillance of GaAs substrate deoxidation in MBE reactors using deep learning based RHEED image-sequence classification. Our approach consists of an non-supervised auto-encoder (AE) for feature extraction, combined with a supervised convolutional classifier network. We demonstrate that our lightweight network model can accurately identify the exact deoxidation moment. Furthermore we show that the approach is very robust and allows accurate deoxidation detection during months without requiring re-training. The main advantage of the approach is that it can be applied to raw RHEED images without requiring further information such as the rotation angle, temperature, etc.

近年来，关于如何在公平限制下学习机器学习模型的越来越多的工作，通常在某些敏感属性方面表达。在这项工作中，我们考虑了对手对目标模型具有黑箱访问的设置，并表明对手可以利用有关该模型公平性的信息，以增强他对训练数据敏感属性的重建。更确切地说，我们提出了一种通用的重建校正方法，该方法将其作为对手进行的初始猜测，并纠正它以符合某些用户定义的约束（例如公平信息），同时最大程度地减少了对手猜测的变化。提出的方法对目标模型的类型，公平感知的学习方法以及对手的辅助知识不可知。为了评估我们的方法的适用性，我们对两种最先进的公平学习方法进行了彻底的实验评估，使用四个具有广泛公差的不同公平指标以及三个不同大小和敏感属性的数据集。实验结果证明了提出的方法改善训练集敏感属性的重建的有效性。

为了减轻模型中不希望的偏差的影响，几种方法建议预先处理输入数据集，以通过防止敏感属性的推断来减少歧视风险。不幸的是，这些预处理方法中的大多数导致一代新分布与原始分布有很大不同，因此通常导致不切实际的数据。作为副作用，这种新的数据分布意味着需要重新训练现有模型才能做出准确的预测。为了解决这个问题，我们提出了一种新颖的预处理方法，我们将根据保护组的分布转换为所选目标一个，并具有附加的隐私约束，其目的是防止敏感敏感的推断属性。更确切地说，我们利用Wasserstein Gan和Attgan框架的最新作品来实现数据点的最佳运输以及强制保护属性推断的歧视器。我们提出的方法可以保留数据的可解释性，并且可以在不定义敏感组的情况下使用。此外，我们的方法可以专门建模现有的最新方法，从而提出对这些方法的统一观点。最后，关于真实和合成数据集的一些实验表明，我们的方法能够隐藏敏感属性，同时限制数据的变形并改善了后续数据分析任务的公平性。