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Learning dynamics is at the heart of many important applications of machine learning (ML), such as robotics and autonomous driving. In these settings, ML algorithms typically need to reason about a physical system using high dimensional observations, such as images, without access to the underlying state. Recently, several methods have proposed to integrate priors from classical mechanics into ML models to address the challenge of physical reasoning from images. In this work, we take a sober look at the current capabilities of these models. To this end, we introduce a suite consisting of 17 datasets with visual observations based on physical systems exhibiting a wide range of dynamics. We conduct a thorough and detailed comparison of the major classes of physically inspired methods alongside several strong baselines. While models that incorporate physical priors can often learn latent spaces with desirable properties, our results demonstrate that these methods fail to significantly improve upon standard techniques. Nonetheless, we find that the use of continuous and time-reversible dynamics benefits models of all classes.

Efficiently approximating local curvature information of the loss function is a key tool for optimization and compression of deep neural networks. Yet, most existing methods to approximate second-order information have high computational or storage costs, which can limit their practicality. In this work, we investigate matrix-free, linear-time approaches for estimating Inverse-Hessian Vector Products (IHVPs) for the case when the Hessian can be approximated as a sum of rank-one matrices, as in the classic approximation of the Hessian by the empirical Fisher matrix. We propose two new algorithms as part of a framework called M-FAC: the first algorithm is tailored towards network compression and can compute the IHVP for dimension $d$, if the Hessian is given as a sum of $m$ rank-one matrices, using $O(dm^2)$ precomputation, $O(dm)$ cost for computing the IHVP, and query cost $O(m)$ for any single element of the inverse Hessian. The second algorithm targets an optimization setting, where we wish to compute the product between the inverse Hessian, estimated over a sliding window of optimization steps, and a given gradient direction, as required for preconditioned SGD. We give an algorithm with cost $O(dm + m^2)$ for computing the IHVP and $O(dm + m^3)$ for adding or removing any gradient from the sliding window. These two algorithms yield state-of-the-art results for network pruning and optimization with lower computational overhead relative to existing second-order methods. Implementations are available at [9] and [17].

In this article, we show and discuss the results of a quantitative and qualitative analysis of citations to retracted publications in the humanities domain. Our study was conducted by selecting retracted papers in the humanities domain and marking their main characteristics (e.g., retraction reason). Then, we gathered the citing entities and annotated their basic metadata (e.g., title, venue, subject, etc.) and the characteristics of their in-text citations (e.g., intent, sentiment, etc.). Using these data, we performed a quantitative and qualitative study of retractions in the humanities, presenting descriptive statistics and a topic modeling analysis of the citing entities' abstracts and the in-text citation contexts. As part of our main findings, we noticed a continuous increment in the overall number of citations after the retraction year, with few entities which have either mentioned the retraction or expressed a negative sentiment toward the cited entities. In addition, on several occasions we noticed a higher concern and awareness when it was about citing a retracted article, by the citing entities belonging to the health sciences domain, if compared to the humanities and the social sciences domains. Philosophy, arts, and history are the humanities areas that showed the higher concerns toward the retraction.

We introduce the category of information structures, whose objects are suitable diagrams of measurable sets that encode the possible outputs of a given family of observables and their mutual relationships of refinement; they serve as mathematical models of contextuality in classical and quantum settings. Each information structure can be regarded as a ringed site with trivial topology; the structure ring is generated by the observables themselves and its multiplication corresponds to joint measurement. We extend Baudot and Bennequin's definition of information cohomology to this setting, as a derived functor in the category of modules over the structure ring, and show explicitly that the bar construction gives a projective resolution in that category, recovering in this way the cochain complexes previously considered in the literature. Finally, we study the particular case of a one-parameter family of coefficients made of functions of probability distributions. The only 1-cocycles are Shannon entropy or Tsallis $\alpha$-entropy, depending on the value of the parameter.

Hesitant fuzzy linguistic preference relation (HFLPR) is of interest because it provides an efficient way for opinion expression under uncertainty. For enhancing the theory of decision making with HFLPR, the paper introduces an algorithm for group decision making with HFLPRs based on the acceptable consistency and consensus measurements, which involves (1) defining a hesitant fuzzy linguistic geometric consistency index (HFLGCI) and proposing a procedure for consistency checking and inconsistency improving for HFLPR; (2) measuring the group consensus based on the similarity between the original individual HFLPRs and the overall perfect HFLPR, then establishing a procedure for consensus ensuring including the determination of decision-makers weights. The convergence and monotonicity of the proposed two procedures have been proved. Some experiments are furtherly performed to investigate the critical values of the defined HFLGCI, and comparative analyses are conducted to show the effectiveness of the proposed algorithm. A case concerning the performance evaluation of venture capital guiding funds is given to illustrate the availability of the proposed algorithm. As an application of our work, an online decision-making portal is finally provided for decision-makers to utilize the proposed algorithms to solve decision-making problems.

The single-site dynamics are a canonical class of Markov chains for sampling from high-dimensional probability distributions, e.g. the ones represented by graphical models. We give a simple and generic parallel algorithm that can faithfully simulate single-site dynamics. When the chain asymptotically satisfies the $\ell_p$-Dobrushin's condition, specifically, when the Dobrushin's influence matrix has constantly bounded $\ell_p$-induced operator norm for an arbitrary $p\in[1,\infty]$, the parallel simulation of $N$ steps of single-site updates succeeds within $O\left({N}/{n}+\log n\right)$ depth of parallel computing using $\tilde{O}(m)$ processors, where $n$ is the number of sites and $m$ is the size of graphical model. Since the Dobrushin's condition is almost always satisfied asymptotically by mixing chains, this parallel simulation algorithm essentially transforms single-site dynamics with optimal $O(n\log n)$ mixing time to RNC algorithms for sampling. In particular we obtain RNC samplers, for the Ising models on general graphs in the uniqueness regime, and for satisfying solutions of CNF formulas in a local lemma regime. With non-adaptive simulated annealing, these RNC samplers can be transformed routinely to RNC algorithms for approximate counting. A key step in our parallel simulation algorithm, is a so-called "universal coupling" procedure, which tries to simultaneously couple all distributions over the same sample space. We construct such a universal coupling, that for every pair of distributions the coupled probability is at least their Jaccard similarity. We also prove this is optimal in the worst case. The universal coupling and its applications are of independent interests.

For rare events described in terms of Markov processes, truly unbiased estimation of the rare event probability generally requires the avoidance of numerical approximations of the Markov process. Recent work in the exact and $\varepsilon$-strong simulation of diffusions, which can be used to almost surely constrain sample paths to a given tolerance, suggests one way to do this. We specify how such algorithms can be combined with the classical multilevel splitting method for rare event simulation. This provides unbiased estimations of the probability in question. We discuss the practical feasibility of the algorithm with reference to existing $\varepsilon$-strong methods and provide proof-of-concept numerical examples.

We employ a toolset -- dubbed Dr. Frankenstein -- to analyse the similarity of representations in deep neural networks. With this toolset, we aim to match the activations on given layers of two trained neural networks by joining them with a stitching layer. We demonstrate that the inner representations emerging in deep convolutional neural networks with the same architecture but different initializations can be matched with a surprisingly high degree of accuracy even with a single, affine stitching layer. We choose the stitching layer from several possible classes of linear transformations and investigate their performance and properties. The task of matching representations is closely related to notions of similarity. Using this toolset, we also provide a novel viewpoint on the current line of research regarding similarity indices of neural network representations: the perspective of the performance on a task.

The problem of Approximate Nearest Neighbor (ANN) search is fundamental in computer science and has benefited from significant progress in the past couple of decades. However, most work has been devoted to pointsets whereas complex shapes have not been sufficiently treated. Here, we focus on distance functions between discretized curves in Euclidean space: they appear in a wide range of applications, from road segments to time-series in general dimension. For $\ell_p$-products of Euclidean metrics, for any $p$, we design simple and efficient data structures for ANN, based on randomized projections, which are of independent interest. They serve to solve proximity problems under a notion of distance between discretized curves, which generalizes both discrete Fr\'echet and Dynamic Time Warping distances. These are the most popular and practical approaches to comparing such curves. We offer the first data structures and query algorithms for ANN with arbitrarily good approximation factor, at the expense of increasing space usage and preprocessing time over existing methods. Query time complexity is comparable or significantly improved by our algorithms, our algorithm is especially efficient when the length of the curves is bounded.