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We obtain essentially matching upper and lower bounds for the expected max-sliced 1-Wasserstein distance between a probability measure on a separable Hilbert space and its empirical distribution from $n$ samples. By proving a Banach space version of this result, we also obtain an upper bound, that is sharp up to a log factor, for the expected max-sliced 2-Wasserstein distance between a symmetric probability measure $\mu$ on a Euclidean space and its symmetrized empirical distribution in terms of the norm of the covariance matrix of $\mu$ and the diameter of the support of $\mu$.

Weakly supervised surgical instrument segmentation with only instrument presence labels has been rarely explored in surgical domain. To mitigate the highly under-constrained challenges, we extend a two-stage weakly supervised segmentation paradigm with temporal attributes from two perspectives. From a temporal equivariance perspective, we propose a prototype-based temporal equivariance regulation loss to enhance pixel-wise consistency between adjacent features. From a semantic continuity perspective, we propose a class-aware temporal semantic continuity loss to constrain the semantic consistency between a global view of target frame and local non-discriminative regions of adjacent reference frame. To the best of our knowledge, WeakSurg is the first instrument-presence-only weakly supervised segmentation architecture to take temporal information into account for surgical scenarios. Extensive experiments are validated on Cholec80, an open benchmark for phase and instrument recognition. We annotate instance-wise instrument labels with fixed time-steps which are double checked by a clinician with 3-years experience. Our results show that WeakSurg compares favorably with state-of-the-art methods not only on semantic segmentation metrics but also on instance segmentation metrics.

This paper develops an in-depth treatment concerning the problem of approximating the Gaussian smoothing and Gaussian derivative computations in scale-space theory for application on discrete data. With close connections to previous axiomatic treatments of continuous and discrete scale-space theory, we consider three main ways discretizing these scale-space operations in terms of explicit discrete convolutions, based on either (i) sampling the Gaussian kernels and the Gaussian derivative kernels, (ii) locally integrating the Gaussian kernels and the Gaussian derivative kernels over each pixel support region and (iii) basing the scale-space analysis on the discrete analogue of the Gaussian kernel, and then computing derivative approximations by applying small-support central difference operators to the spatially smoothed image data. We study the properties of these three main discretization methods both theoretically and experimentally, and characterize their performance by quantitative measures, including the results they give rise to with respect to the task of scale selection, investigated for four different use cases, and with emphasis on the behaviour at fine scales. The results show that the sampled Gaussian kernels and derivatives as well as the integrated Gaussian kernels and derivatives perform very poorly at very fine scales. At very fine scales, the discrete analogue of the Gaussian kernel with its corresponding discrete derivative approximations performs substantially better. The sampled Gaussian kernel and the sampled Gaussian derivatives do, on the other hand, lead to numerically very good approximations of the corresponding continuous results, when the scale parameter is sufficiently large, in the experiments presented in the paper, when the scale parameter is greater than a value of about 1, in units of the grid spacing.

We present experimental results on the single file motion of a group of robots interacting with each other through position sensors. We successfully replicate the fundamental diagram typical of these systems, with a transition from free flow to congested traffic as the density of the system increases. In the latter scenario we also observe the characteristic stop-and-go waves. The unique advantages of this novel system, such as experimental stability and repeatability, allow for extended experimental runs, facilitating a comprehensive statistical analysis of the global dynamics. Above a certain density, we observe a divergence of the average jam duration and the average number of robots involved in it. This discovery enables us to precisely identify another transition: from congested intermittent flow (for intermediate densities) to a totally congested scenario for high densities. Beyond this finding, the present work demonstrates the suitability of robot swarms to model complex behaviors in many particle systems.

Markov networks are probabilistic graphical models that employ undirected graphs to depict conditional independence relationships among variables. Our focus lies in constraint-based structure learning, which entails learning the undirected graph from data through the execution of conditional independence tests. We establish theoretical limits concerning two critical aspects of constraint-based learning of Markov networks: the number of tests and the sizes of the conditioning sets. These bounds uncover an exciting interplay between the structural properties of the graph and the amount of tests required to learn a Markov network. The starting point of our work is that the graph parameter maximum pairwise connectivity, $\kappa$, that is, the maximum number of vertex-disjoint paths connecting a pair of vertices in the graph, is responsible for the sizes of independence tests required to learn the graph. On one hand, we show that at least one test with the size of the conditioning set at least $\kappa$ is always necessary. On the other hand, we prove that any graph can be learned by performing tests of size at most $\kappa$. This completely resolves the question of the minimum size of conditioning sets required to learn the graph. When it comes to the number of tests, our upper bound on the sizes of conditioning sets implies that every $n$-vertex graph can be learned by at most $n^{\kappa}$ tests with conditioning sets of sizes at most $\kappa$. We show that for any upper bound $q$ on the sizes of the conditioning sets, there exist graphs with $O(n q)$ vertices that require at least $n^{\Omega(\kappa)}$ tests to learn. This lower bound holds even when the treewidth and the maximum degree of the graph are at most $\kappa+2$. On the positive side, we prove that every graph of bounded treewidth can be learned by a polynomial number of tests with conditioning sets of sizes at most $2\kappa$.

Curiosity-driven learning has shown significant positive effects on students' learning experiences and outcomes. But despite this importance, reports show that children lack this skill, especially in formal educational settings. To address this challenge, we propose an 8-session workshop that aims to enhance children's curiosity through training a set of specific metacognitive skills we hypothesize are involved in its process. Our workshop contains animated videos presenting declarative knowledge about curiosity and the said metacognitive skills as well as practice sessions to apply these skills during a reading-comprehension task, using a web platform designed for this study (e.g. expressing uncertainty, formulating questions, etc). We conduct a pilot study with 15 primary school students, aged between 8 and 10. Our first results show a positive impact on children's metacognitive efficiency and their ability to express their curiosity through question-asking behaviors.

Recently pre-trained language representation models such as BERT have shown great success when fine-tuned on downstream tasks including information retrieval (IR). However, pre-training objectives tailored for ad-hoc retrieval have not been well explored. In this paper, we propose Pre-training with Representative wOrds Prediction (PROP) for ad-hoc retrieval. PROP is inspired by the classical statistical language model for IR, specifically the query likelihood model, which assumes that the query is generated as the piece of text representative of the "ideal" document. Based on this idea, we construct the representative words prediction (ROP) task for pre-training. Given an input document, we sample a pair of word sets according to the document language model, where the set with higher likelihood is deemed as more representative of the document. We then pre-train the Transformer model to predict the pairwise preference between the two word sets, jointly with the Masked Language Model (MLM) objective. By further fine-tuning on a variety of representative downstream ad-hoc retrieval tasks, PROP achieves significant improvements over baselines without pre-training or with other pre-training methods. We also show that PROP can achieve exciting performance under both the zero- and low-resource IR settings. The code and pre-trained models are available at //github.com/Albert-Ma/PROP.

Recent work pre-training Transformers with self-supervised objectives on large text corpora has shown great success when fine-tuned on downstream NLP tasks including text summarization. However, pre-training objectives tailored for abstractive text summarization have not been explored. Furthermore there is a lack of systematic evaluation across diverse domains. In this work, we propose pre-training large Transformer-based encoder-decoder models on massive text corpora with a new self-supervised objective. In PEGASUS, important sentences are removed/masked from an input document and are generated together as one output sequence from the remaining sentences, similar to an extractive summary. We evaluated our best PEGASUS model on 12 downstream summarization tasks spanning news, science, stories, instructions, emails, patents, and legislative bills. Experiments demonstrate it achieves state-of-the-art performance on all 12 downstream datasets measured by ROUGE scores. Our model also shows surprising performance on low-resource summarization, surpassing previous state-of-the-art results on 6 datasets with only 1000 examples. Finally we validated our results using human evaluation and show that our model summaries achieve human performance on multiple datasets.

We present a simple self-training method that achieves 87.4% top-1 accuracy on ImageNet, which is 1.0% better than the state-of-the-art model that requires 3.5B weakly labeled Instagram images. On robustness test sets, it improves ImageNet-A top-1 accuracy from 16.6% to 74.2%, reduces ImageNet-C mean corruption error from 45.7 to 31.2, and reduces ImageNet-P mean flip rate from 27.8 to 16.1. To achieve this result, we first train an EfficientNet model on labeled ImageNet images and use it as a teacher to generate pseudo labels on 300M unlabeled images. We then train a larger EfficientNet as a student model on the combination of labeled and pseudo labeled images. We iterate this process by putting back the student as the teacher. During the generation of the pseudo labels, the teacher is not noised so that the pseudo labels are as good as possible. But during the learning of the student, we inject noise such as data augmentation, dropout, stochastic depth to the student so that the noised student is forced to learn harder from the pseudo labels.

Training a deep architecture using a ranking loss has become standard for the person re-identification task. Increasingly, these deep architectures include additional components that leverage part detections, attribute predictions, pose estimators and other auxiliary information, in order to more effectively localize and align discriminative image regions. In this paper we adopt a different approach and carefully design each component of a simple deep architecture and, critically, the strategy for training it effectively for person re-identification. We extensively evaluate each design choice, leading to a list of good practices for person re-identification. By following these practices, our approach outperforms the state of the art, including more complex methods with auxiliary components, by large margins on four benchmark datasets. We also provide a qualitative analysis of our trained representation which indicates that, while compact, it is able to capture information from localized and discriminative regions, in a manner akin to an implicit attention mechanism.