Graph Neural Networks (GNNs) have shown great potential in the field of graph representation learning. Standard GNNs define a local message-passing mechanism which propagates information over the whole graph domain by stacking multiple layers. This paradigm suffers from two major limitations, over-squashing and poor long-range dependencies, that can be solved using global attention but significantly increases the computational cost to quadratic complexity. In this work, we propose an alternative approach to overcome these structural limitations by leveraging the ViT/MLP-Mixer architectures introduced in computer vision. We introduce a new class of GNNs, called Graph MLP-Mixer, that holds three key properties. First, they capture long-range dependency and mitigate the issue of over-squashing as demonstrated on the Long Range Graph Benchmark (LRGB) and the TreeNeighbourMatch datasets. Second, they offer better speed and memory efficiency with a complexity linear to the number of nodes and edges, surpassing the related Graph Transformer and expressive GNN models. Third, they show high expressivity in terms of graph isomorphism as they can distinguish at least 3-WL non-isomorphic graphs. We test our architecture on 4 simulated datasets and 7 real-world benchmarks, and show highly competitive results on all of them.

随着社交媒体的出现，每天都会上传大量的视频剪辑，并使用语言查询来检索最相关的视觉内容变得至关重要。大多数方法旨在学习纯文本和视觉内容的联合嵌入空间，而无需充分利用其模式内结构和模式间相关性。本文提出了一种新颖的变压器，将文本和视频明确地将文本和视频分解为对象，空间环境和时间上下文的语义角色，并具有注意力方案，以学习三个角色之间的内部和角色间相关性，以发现歧视性特征，以发现与不同的匹配水平。流行的YouCook2的初步结果表明，我们的方法超过了当前的最新方法，所有指标的利润很高。它还可以用两个指标覆盖两种SOTA方法。

我们提供了一个理论框架来研究我们称之为单发概括的现象。这种现象是指算法在单个任务中执行转移学习的能力，这意味着它正确地对训练集中具有单个示例的测试点进行了分类。我们提出了一个简单的数据模型，并使用它以两种方式研究这种现象。首先，我们证明了一种非反应基碱线 - 基于最近的邻分类的内核方法无法执行单发概括，而与核的选择无关，并且训练集的大小。其次，我们从经验上表明，我们数据模型最直接的神经网络体系结构几乎完美地执行了单发概括。这种鲜明的差异使我们相信，单发概括机制是对神经网络的经验成功的部分原因。

In the last few years, graph neural networks (GNNs) have become the standard toolkit for analyzing and learning from data on graphs. This emerging field has witnessed an extensive growth of promising techniques that have been applied with success to computer science, mathematics, biology, physics and chemistry. But for any successful field to become mainstream and reliable, benchmarks must be developed to quantify progress. This led us in March 2020 to release a benchmark framework that i) comprises of a diverse collection of mathematical and real-world graphs, ii) enables fair model comparison with the same parameter budget to identify key architectures, iii) has an open-source, easy-to-use and reproducible code infrastructure, and iv) is flexible for researchers to experiment with new theoretical ideas. As of December 2022, the GitHub repository has reached 2,000 stars and 380 forks, which demonstrates the utility of the proposed open-source framework through the wide usage by the GNN community. In this paper, we present an updated version of our benchmark with a concise presentation of the aforementioned framework characteristics, an additional medium-sized molecular dataset AQSOL, similar to the popular ZINC, but with a real-world measured chemical target, and discuss how this framework can be leveraged to explore new GNN designs and insights. As a proof of value of our benchmark, we study the case of graph positional encoding (PE) in GNNs, which was introduced with this benchmark and has since spurred interest of exploring more powerful PE for Transformers and GNNs in a robust experimental setting.

In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain connectomes or words' embedding, represented by graphs. We present a formulation of CNNs in the context of spectral graph theory, which provides the necessary mathematical background and efficient numerical schemes to design fast localized convolutional filters on graphs. Importantly, the proposed technique offers the same linear computational complexity and constant learning complexity as classical CNNs, while being universal to any graph structure. Experiments on MNIST and 20NEWS demonstrate the ability of this novel deep learning system to learn local, stationary, and compositional features on graphs.

This paper is devoted to the numerical resolution of McKean-Vlasov control problems via the class of mean-field neural networks introduced in our companion paper [25] in order to learn the solution on the Wasserstein space. We propose several algorithms either based on dynamic programming with control learning by policy or value iteration, or backward SDE from stochastic maximum principle with global or local loss functions. Extensive numerical results on different examples are presented to illustrate the accuracy of each of our eight algorithms. We discuss and compare the pros and cons of all the tested methods.

This paper describes the system developed at the Universitat Polit\`ecnica de Catalunya for the Workshop on Machine Translation 2022 Sign Language Translation Task, in particular, for the sign-to-text direction. We use a Transformer model implemented with the Fairseq modeling toolkit. We have experimented with the vocabulary size, data augmentation techniques and pretraining the model with the PHOENIX-14T dataset. Our system obtains 0.50 BLEU score for the test set, improving the organizers' baseline by 0.38 BLEU. We remark the poor results for both the baseline and our system, and thus, the unreliability of our findings.

This paper studies the infinite-width limit of deep linear neural networks initialized with random parameters. We obtain that, when the number of neurons diverges, the training dynamics converge (in a precise sense) to the dynamics obtained from a gradient descent on an infinitely wide deterministic linear neural network. Moreover, even if the weights remain random, we get their precise law along the training dynamics, and prove a quantitative convergence result of the linear predictor in terms of the number of neurons. We finally study the continuous-time limit obtained for infinitely wide linear neural networks and show that the linear predictors of the neural network converge at an exponential rate to the minimal $\ell_2$-norm minimizer of the risk.

Recent advances in deep learning models for sequence classification have greatly improved their classification accuracy, specially when large training sets are available. However, several works have suggested that under some settings the predictions made by these models are poorly calibrated. In this work we study binary sequence classification problems and we look at model calibration from a different perspective by asking the question: Are deep learning models capable of learning the underlying target class distribution? We focus on sparse sequence classification, that is problems in which the target class is rare and compare three deep learning sequence classification models. We develop an evaluation that measures how well a classifier is learning the target class distribution. In addition, our evaluation disentangles good performance achieved by mere compression of the training sequences versus performance achieved by proper model generalization. Our results suggest that in this binary setting the deep-learning models are indeed able to learn the underlying class distribution in a non-trivial manner, i.e. by proper generalization beyond data compression.

The combination of machine learning models with physical models is a recent research path to learn robust data representations. In this paper, we introduce p$^3$VAE, a generative model that integrates a perfect physical model which partially explains the true underlying factors of variation in the data. To fully leverage our hybrid design, we propose a semi-supervised optimization procedure and an inference scheme that comes along meaningful uncertainty estimates. We apply p$^3$VAE to the semantic segmentation of high-resolution hyperspectral remote sensing images. Our experiments on a simulated data set demonstrated the benefits of our hybrid model against conventional machine learning models in terms of extrapolation capabilities and interpretability. In particular, we show that p$^3$VAE naturally has high disentanglement capabilities. Our code and data have been made publicly available at https://github.com/Romain3Ch216/p3VAE.