在随机子集总和问题中，给定$ n $ i.i.d.随机变量$ x_1，...，x_n $，我们希望将[-1,1] $ in [-1,1] $的任何点$ z \作为合适子集的总和$ x_ {i_1（z）}，...，x_ {i_s（z）} $的$，最多$ \ varepsilon $。尽管有简单的陈述，但这个问题还是理论计算机科学和统计力学的基本兴趣。最近，它因其在人工神经网络理论中的影响而引起了人们的重新关注。该问题的一个明显的多维概括是考虑$ n $ i.i.d. \ $ d $ - 二维随机向量，目的是近似于[-1,1]^d $的每个点$ \ Mathbf {z} \。令人惊讶的是，在Lueker的1998年证明，在一维设置中，$ n = o（\ log \ frac 1 \ varepsilon）$ samples $ samples $ samples具有很高可能性的近似属性，在实现上述概括方面几乎没有进展。在这项工作中，我们证明，在$ d $ dimensions中，$ n = o（d^3 \ log \ frac 1 \ varepsilon \ cdot（\ log \ frac 1 \ frac 1 \ varepsilon + log d d））$ samples $ sample近似属性具有很高的概率。作为强调该结果潜在兴趣的应用程序，我们证明了最近提出的神经网络模型表现出\ emph {通用}：具有很高的概率，该模型可以在参数数量中近似多项式开销中的任何神经网络。

我们重新审视块世界中的规划问题，我们为此任务实施了一个已知的启发式。重要的是，我们的实施是生物学上可言论的，因此它仅通过神经元的尖峰进行。尽管在过去五十年中，在块世界中已经在块世界中完成了很多，但我们认为这是它的第一个算法。输入是编码初始块堆栈以及目标集合的符号序列，并且输出是一系列运动命令，例如“将顶部块放在桌子上的堆栈1中”。该程序是在组装微积分中写入的，最近提出的计算框架通过弥合神经活动与认知功能之间的差距来模拟大脑中的计算。其基本对象是神经元的组件（稳定的神经元组，其同时射击表示该主题正在考虑对象，概念，单词等），其命令包括项目和合并，其执行模型基于广泛接受的原则神经科学。该框架中的一个程序基本上建立了神经元的动态系统和最终具有高概率，实现任务的神经元和突触。这项工作的目的是凭经验建立了大会微积分中的合理大计划可以正确可靠地执行;这相当现实 - 如果理想化 - 更高的认知功能，例如在块世界中规划，可以通过这些程序成功实现。

Self-supervised learning is a popular and powerful method for utilizing large amounts of unlabeled data, for which a wide variety of training objectives have been proposed in the literature. In this study, we perform a Bayesian analysis of state-of-the-art self-supervised learning objectives and propose a unified formulation based on likelihood learning. Our analysis suggests a simple method for integrating self-supervised learning with generative models, allowing for the joint training of these two seemingly distinct approaches. We refer to this combined framework as GEDI, which stands for GEnerative and DIscriminative training. Additionally, we demonstrate an instantiation of the GEDI framework by integrating an energy-based model with a cluster-based self-supervised learning model. Through experiments on synthetic and real-world data, including SVHN, CIFAR10, and CIFAR100, we show that GEDI outperforms existing self-supervised learning strategies in terms of clustering performance by a wide margin. We also demonstrate that GEDI can be integrated into a neural-symbolic framework to address tasks in the small data regime, where it can use logical constraints to further improve clustering and classification performance.

With more and more data being collected, data-driven modeling methods have been gaining in popularity in recent years. While physically sound, classical gray-box models are often cumbersome to identify and scale, and their accuracy might be hindered by their limited expressiveness. On the other hand, classical black-box methods, typically relying on Neural Networks (NNs) nowadays, often achieve impressive performance, even at scale, by deriving statistical patterns from data. However, they remain completely oblivious to the underlying physical laws, which may lead to potentially catastrophic failures if decisions for real-world physical systems are based on them. Physically Consistent Neural Networks (PCNNs) were recently developed to address these aforementioned issues, ensuring physical consistency while still leveraging NNs to attain state-of-the-art accuracy. In this work, we scale PCNNs to model building temperature dynamics and propose a thorough comparison with classical gray-box and black-box methods. More precisely, we design three distinct PCNN extensions, thereby exemplifying the modularity and flexibility of the architecture, and formally prove their physical consistency. In the presented case study, PCNNs are shown to achieve state-of-the-art accuracy, even outperforming classical NN-based models despite their constrained structure. Our investigations furthermore provide a clear illustration of NNs achieving seemingly good performance while remaining completely physics-agnostic, which can be misleading in practice. While this performance comes at the cost of computational complexity, PCNNs on the other hand show accuracy improvements of 17-35% compared to all other physically consistent methods, paving the way for scalable physically consistent models with state-of-the-art performance.

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.

Timely and effective feedback within surgical training plays a critical role in developing the skills required to perform safe and efficient surgery. Feedback from expert surgeons, while especially valuable in this regard, is challenging to acquire due to their typically busy schedules, and may be subject to biases. Formal assessment procedures like OSATS and GEARS attempt to provide objective measures of skill, but remain time-consuming. With advances in machine learning there is an opportunity for fast and objective automated feedback on technical skills. The SimSurgSkill 2021 challenge (hosted as a sub-challenge of EndoVis at MICCAI 2021) aimed to promote and foster work in this endeavor. Using virtual reality (VR) surgical tasks, competitors were tasked with localizing instruments and predicting surgical skill. Here we summarize the winning approaches and how they performed. Using this publicly available dataset and results as a springboard, future work may enable more efficient training of surgeons with advances in surgical data science. The dataset can be accessed from https://console.cloud.google.com/storage/browser/isi-simsurgskill-2021.

A tractogram is a virtual representation of the brain white matter. It is composed of millions of virtual fibers, encoded as 3D polylines, which approximate the white matter axonal pathways. To date, tractograms are the most accurate white matter representation and thus are used for tasks like presurgical planning and investigations of neuroplasticity, brain disorders, or brain networks. However, it is a well-known issue that a large portion of tractogram fibers is not anatomically plausible and can be considered artifacts of the tracking procedure. With Verifyber, we tackle the problem of filtering out such non-plausible fibers using a novel fully-supervised learning approach. Differently from other approaches based on signal reconstruction and/or brain topology regularization, we guide our method with the existing anatomical knowledge of the white matter. Using tractograms annotated according to anatomical principles, we train our model, Verifyber, to classify fibers as either anatomically plausible or non-plausible. The proposed Verifyber model is an original Geometric Deep Learning method that can deal with variable size fibers, while being invariant to fiber orientation. Our model considers each fiber as a graph of points, and by learning features of the edges between consecutive points via the proposed sequence Edge Convolution, it can capture the underlying anatomical properties. The output filtering results highly accurate and robust across an extensive set of experiments, and fast; with a 12GB GPU, filtering a tractogram of 1M fibers requires less than a minute. Verifyber implementation and trained models are available at https://github.com/FBK-NILab/verifyber.

Semi-supervised learning methods can train high-accuracy machine learning models with a fraction of the labeled training samples required for traditional supervised learning. Such methods do not typically involve close review of the unlabeled training samples, making them tempting targets for data poisoning attacks. In this paper we investigate the vulnerabilities of semi-supervised learning methods to backdoor data poisoning attacks on the unlabeled samples. We show that simple poisoning attacks that influence the distribution of the poisoned samples' predicted labels are highly effective - achieving an average attack success rate as high as 96.9%. We introduce a generalized attack framework targeting semi-supervised learning methods to better understand and exploit their limitations and to motivate future defense strategies.

Extreme wildfires continue to be a significant cause of human death and biodiversity destruction within countries that encompass the Mediterranean Basin. Recent worrying trends in wildfire activity (i.e., occurrence and spread) suggest that wildfires are likely to be highly impacted by climate change. In order to facilitate appropriate risk mitigation, it is imperative to identify the main drivers of extreme wildfires and assess their spatio-temporal trends, with a view to understanding the impacts of global warming on fire activity. To this end, we analyse the monthly burnt area due to wildfires over a region encompassing most of Europe and the Mediterranean Basin from 2001 to 2020, and identify high fire activity during this period in eastern Europe, Algeria, Italy and Portugal. We build an extreme quantile regression model with a high-dimensional predictor set describing meteorological conditions, land cover usage, and orography, for the domain. To model the complex relationships between the predictor variables and wildfires, we make use of a hybrid statistical deep-learning framework that allows us to disentangle the effects of vapour-pressure deficit (VPD), air temperature, and drought on wildfire activity. Our results highlight that whilst VPD, air temperature, and drought significantly affect wildfire occurrence, only VPD affects extreme wildfire spread. Furthermore, to gain insights into the effect of climate change on wildfire activity in the near future, we perturb VPD and temperature according to their observed trends and find evidence that global warming may lead to spatially non-uniform changes in wildfire activity.

Reinforcement Learning (RL) generally suffers from poor sample complexity, mostly due to the need to exhaustively explore the state space to find good policies. On the other hand, we postulate that expert knowledge of the system to control often allows us to design simple rules we expect good policies to follow at all times. In this work, we hence propose a simple yet effective modification of continuous actor-critic RL frameworks to incorporate such prior knowledge in the learned policies and constrain them to regions of the state space that are deemed interesting, thereby significantly accelerating their convergence. Concretely, we saturate the actions chosen by the agent if they do not comply with our intuition and, critically, modify the gradient update step of the policy to ensure the learning process does not suffer from the saturation step. On a room temperature control simulation case study, these modifications allow agents to converge to well-performing policies up to one order of magnitude faster than classical RL agents while retaining good final performance.