At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit (16; 4; 7; 13; 6), thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: during gradient descent on the parameters of an ANN, the network function f θ (which maps input vectors to output vectors) follows the kernel gradient of the functional cost (which is convex, in contrast to the parameter cost) w.r.t. a new kernel: the Neural Tangent Kernel (NTK). This kernel is central to describe the generalization features of ANNs. While the NTK is random at initialization and varies during training, in the infinite-width limit it converges to an explicit limiting kernel and it stays constant during training. This makes it possible to study the training of ANNs in function space instead of parameter space. Convergence of the training can then be related to the positive-definiteness of the limiting NTK. We prove the positive-definiteness of the limiting NTK when the data is supported on the sphere and the non-linearity is non-polynomial. We then focus on the setting of least-squares regression and show that in the infinitewidth limit, the network function f θ follows a linear differential equation during training. The convergence is fastest along the largest kernel principal components of the input data with respect to the NTK, hence suggesting a theoretical motivation for early stopping. Finally we study the NTK numerically, observe its behavior for wide networks, and compare it to the infinite-width limit.

View-dependent effects such as reflections pose a substantial challenge for image-based and neural rendering algorithms. Above all, curved reflectors are particularly hard, as they lead to highly non-linear reflection flows as the camera moves. We introduce a new point-based representation to compute Neural Point Catacaustics allowing novel-view synthesis of scenes with curved reflectors, from a set of casually-captured input photos. At the core of our method is a neural warp field that models catacaustic trajectories of reflections, so complex specular effects can be rendered using efficient point splatting in conjunction with a neural renderer. One of our key contributions is the explicit representation of reflections with a reflection point cloud which is displaced by the neural warp field, and a primary point cloud which is optimized to represent the rest of the scene. After a short manual annotation step, our approach allows interactive high-quality renderings of novel views with accurate reflection flow. Additionally, the explicit representation of reflection flow supports several forms of scene manipulation in captured scenes, such as reflection editing, cloning of specular objects, reflection tracking across views, and comfortable stereo viewing. We provide the source code and other supplemental material on https://repo-sam.inria.fr/ fungraph/neural_catacaustics/

Lenia is a family of cellular automata (CA) generalizing Conway's Game of Life to continuous space, time and states. Lenia has attracted a lot of attention because of the wide diversity of self-organizing patterns it can generate. Among those, some spatially localized patterns (SLPs) resemble life-like artificial creatures. However, those creatures are found in only a small subspace of the Lenia parameter space and are not trivial to discover, necessitating advanced search algorithms. We hypothesize that adding a mass conservation constraint could facilitate the emergence of SLPs. We propose here an extension of the Lenia model, called Flow Lenia, which enables mass conservation. We show a few observations demonstrating its effectiveness in generating SLPs with complex behaviors. Furthermore, we show how Flow Lenia enables the integration of the parameters of the CA update rules within the CA dynamics, making them dynamic and localized. This allows for multi-species simulations, with locally coherent update rules that define properties of the emerging creatures, and that can be mixed with neighbouring rules. We argue that this paves the way for the intrinsic evolution of self-organized artificial life forms within continuous CAs.

Humans have been able to tackle biosphere complexities by acting as ecosystem engineers, profoundly changing the flows of matter, energy and information. This includes major innovations that allowed to reduce and control the impact of extreme events. Modelling the evolution of such adaptive dynamics can be challenging given the potentially large number of individual and environmental variables involved. This paper shows how to address this problem by using fire as the source of external, bursting and wide fluctuations. Fire propagates on a spatial landscape where a group of agents harvest and exploit trees while avoiding the damaging effects of fire spreading. The agents need to solve a conflict to reach a group-level optimal state: while tree harvesting reduces the propagation of fires, it also reduces the availability of resources provided by trees. It is shown that the system displays two major evolutionary innovations that end up in an ecological engineering strategy that favours high biomass along with the suppression of large fires. The implications for potential A.I. management of complex ecosystems are discussed.

We consider a model where a signal (discrete or continuous) is observed with an additive Gaussian noise process. The signal is issued from a linear combination of a finite but increasing number of translated features. The features are continuously parameterized by their location and depend on some scale parameter. First, we extend previous prediction results for off-the-grid estimators by taking into account here that the scale parameter may vary. The prediction bounds are analogous, but we improve the minimal distance between two consecutive features locations in order to achieve these bounds. Next, we propose a goodness-of-fit test for the model and give non-asymptotic upper bounds of the testing risk and of the minimax separation rate between two distinguishable signals. In particular, our test encompasses the signal detection framework. We deduce upper bounds on the minimal energy, expressed as the 2-norm of the linear coefficients, to successfully detect a signal in presence of noise. The general model considered in this paper is a non-linear extension of the classical high-dimensional regression model. It turns out that, in this framework, our upper bound on the minimax separation rate matches (up to a logarithmic factor) the lower bound on the minimax separation rate for signal detection in the high dimensional linear model associated to a fixed dictionary of features. We also propose a procedure to test whether the features of the observed signal belong to a given finite collection under the assumption that the linear coefficients may vary, but do not change to opposite signs under the null hypothesis. A non-asymptotic upper bound on the testing risk is given. We illustrate our results on the spikes deconvolution model with Gaussian features on the real line and with the Dirichlet kernel, frequently used in the compressed sensing literature, on the torus.

HTR models development has become a conventional step for digital humanities projects. The performance of these models, often quite high, relies on manual transcription and numerous handwritten documents. Although the method has proven successful for Latin scripts, a similar amount of data is not yet achievable for scripts considered poorly-endowed, like Arabic scripts. In that respect, we are introducing and assessing a new modus operandi for HTR models development and fine-tuning dedicated to the Arabic Maghrib{\=i} scripts. The comparison between several state-of-the-art HTR demonstrates the relevance of a word-based neural approach specialized for Arabic, capable to achieve an error rate below 5% with only 10 pages manually transcribed. These results open new perspectives for Arabic scripts processing and more generally for poorly-endowed languages processing. This research is part of the development of RASAM dataset in partnership with the GIS MOMM and the BULAC.

Accurate diagnosis and prognosis of Alzheimer's disease are crucial to develop new therapies and reduce the associated costs. Recently, with the advances of convolutional neural networks, methods have been proposed to automate these two tasks using structural MRI. However, these methods often suffer from lack of interpretability, generalization, and can be limited in terms of performance. In this paper, we propose a novel deep framework designed to overcome these limitations. Our framework consists of two stages. In the first stage, we propose a deep grading model to extract meaningful features. To enhance the robustness of these features against domain shift, we introduce an innovative collective artificial intelligence strategy for training and evaluating steps. In the second stage, we use a graph convolutional neural network to better capture AD signatures. Our experiments based on 2074 subjects show the competitive performance of our deep framework compared to state-of-the-art methods on different datasets for both AD diagnosis and prognosis.

To apply federated learning to drug discovery we developed a novel platform in the context of European Innovative Medicines Initiative (IMI) project MELLODDY (grant n{\deg}831472), which was comprised of 10 pharmaceutical companies, academic research labs, large industrial companies and startups. The MELLODDY platform was the first industry-scale platform to enable the creation of a global federated model for drug discovery without sharing the confidential data sets of the individual partners. The federated model was trained on the platform by aggregating the gradients of all contributing partners in a cryptographic, secure way following each training iteration. The platform was deployed on an Amazon Web Services (AWS) multi-account architecture running Kubernetes clusters in private subnets. Organisationally, the roles of the different partners were codified as different rights and permissions on the platform and administrated in a decentralized way. The MELLODDY platform generated new scientific discoveries which are described in a companion paper.

本文通过采取完全几何学的角度引入了对变异自动编码器框架的新解释。我们认为，香草vae自然而然地揭示了其潜在空间中的riemannian结构，并且考虑到这些几何方面可以导致更好的插值和改进的生成程序。这种新提出的采样方法包括从统一分布中的采样组成，该分布本质地从学到的利曼式潜在空间中得出，我们表明，使用此方案可以使香草VAE竞争性且比几个基准数据集中更先进的版本更好。由于已知生成模型对训练样品的数量很敏感，因此我们还强调了该方法在低数据状态下的鲁棒性。

在自动驾驶的背景下，车辆本质上肯定会遇到更多的极端天气，在此期间必须确保公共安全。随着气候迅速变化，大暴风雪的频率有望增加，并成为安全导航的主要威胁。尽管有许多文献旨在提高对冬季条件的导航弹性，但缺乏标准指标来量化与降水有关的LIDAR传感器的可见性丧失。本章提出了一个新颖的指标，以实时量化LIDAR可见性损失，并依赖气象研究领域的可见性概念。我们在加拿大不良驾驶条件（CADC）数据集上评估了该指标，将其与基于最先进的激光雷达的本地化算法的性能相关联，并评估在本地化过程之前过滤点云的好处。我们表明，迭代最接近的点（ICP）算法令人惊讶地抵抗降雪，但是突然的事件（例如雪地）可以极大地阻碍其准确性。我们讨论了此类事件，并证明需要更好地关注这些极端事件以量化其效果。