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This paper addresses the problem of estimating entropy-regularized optimal transport (EOT) maps with squared-Euclidean cost between source and target measures that are subGaussian. In the case that the target measure is compactly supported or strongly log-concave, we show that for a recently proposed in-sample estimator, the expected squared $L^2$-error decays at least as fast as $O(n^{-1/3})$ where $n$ is the sample size. For the general subGaussian case we show that the expected $L^1$-error decays at least as fast as $O(n^{-1/6})$, and in both cases we have polynomial dependence on the regularization parameter. While these results are suboptimal compared to known results in the case of compactness of both the source and target measures (squared $L^2$-error converging at a rate $O(n^{-1})$) and for when the source is subGaussian while the target is compactly supported (squared $L^2$-error converging at a rate $O(n^{-1/2})$), their importance lie in eliminating the compact support requirements. The proof technique makes use of a bias-variance decomposition where the variance is controlled using standard concentration of measure results and the bias is handled by T1-transport inequalities along with sample complexity results in estimation of EOT cost under subGaussian assumptions. Our experimental results point to a looseness in controlling the variance terms and we conclude by posing several open problems.

The influence of natural image transformations on receptive field responses is crucial for modelling visual operations in computer vision and biological vision. In this regard, covariance properties with respect to geometric image transformations in the earliest layers of the visual hierarchy are essential for expressing robust image operations and for formulating invariant visual operations at higher levels. This paper defines and proves a joint covariance property under compositions of spatial scaling transformations, spatial affine transformations, Galilean transformations and temporal scaling transformations, which makes it possible to characterize how different types of image transformations interact with each other. Specifically, the derived relations show how the receptive field parameters need to be transformed, in order to match the output from spatio-temporal receptive fields with the underlying spatio-temporal image transformations.

This paper studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under a high-dimensional factor structure. We provide asymptotic distributions for the top eigenvalues of bootstrapped sample covariance matrix under mild conditions. After bootstrap, the spiked eigenvalues which are driven by common factors will converge weakly to Gaussian limits after proper scaling and centralization. However, the largest non-spiked eigenvalue is mainly determined by the order statistics of the bootstrap resampling weights, and follows extreme value distribution. Based on the disparate behavior of the spiked and non-spiked eigenvalues, we propose innovative methods to test the number of common factors. Indicated by extensive numerical and empirical studies, the proposed methods perform reliably and convincingly under the existence of both weak factors and cross-sectionally correlated errors. Our technical details contribute to random matrix theory on spiked covariance model with convexly decaying density and unbounded support, or with general elliptical distributions.

Autoregressive Markov switching (ARMS) time series models are used to represent real-world signals whose dynamics may change over time. They have found application in many areas of the natural and social sciences, as well as in engineering. In general, inference in this kind of systems involves two problems: (a) detecting the number of distinct dynamical models that the signal may adopt and (b) estimating any unknown parameters in these models. In this paper, we introduce a class of ARMS time series models that includes many systems resulting from the discretisation of stochastic delay differential equations (DDEs). Remarkably, this class includes cases in which the discretisation time grid is not necessarily aligned with the delays of the DDE, resulting in discrete-time ARMS models with real (non-integer) delays. We describe methods for the maximum likelihood detection of the number of dynamical modes and the estimation of unknown parameters (including the possibly non-integer delays) and illustrate their application with an ARMS model of El Ni\~no--southern oscillation (ENSO) phenomenon.

In the pursuit of designing highly effective decoders for short LDPC codes nearing maximum likelihood performance, we employ a relayed decoding strategy. A neural min-sum decoder initiates the decoding process, and its errors undergo postprocessing through an adaptive ordered statistics decoding. Several key initiatives supporting the latter are emphasized. Firstly, soft information at each iteration of the neural min-sum decoder is gathered and input into a convolutional neural network to enhance bit reliability estimates. This process identifies error-prone bits, either excluding them from the most reliable basis or concentrating them at the forefront, both advantageous for the adaptive ordered statistical decoding. Additionally, a decoding path, comprising a list of order patterns, directs the postprocessing process. Adjustable path length and refined constraints on associated order patterns offer diverse means of complexity management. Simultaneously, a novel auxiliary criterion is introduced to significantly reduce the list size of codeword candidates in the adaptive ordered statistics decoding. Extensive experimental results and complexity analysis validate the serial architecture, equipped with these innovations, as a formidable contender against state-of-the-art decoders for short LDPC codes.

The influence of natural image transformations on receptive field responses is crucial for modelling visual operations in computer vision and biological vision. In this regard, covariance properties with respect to geometric image transformations in the earliest layers of the visual hierarchy are essential for expressing robust image operations and for formulating invariant visual operations at higher levels. This paper defines and proves a joint covariance property under compositions of spatial scaling transformations, spatial affine transformations, Galilean transformations and temporal scaling transformations, which makes it possible to characterize how different types of image transformations interact with each other. Specifically, the derived relations show the receptive field parameters need to be transformed, in order to match the output from spatio-temporal receptive fields with the underlying spatio-temporal image transformations.

A central task in knowledge compilation is to compile a CNF-SAT instance into a succinct representation format that allows efficient operations such as testing satisfiability, counting, or enumerating all solutions. Useful representation formats studied in this area range from ordered binary decision diagrams (OBDDs) to circuits in decomposable negation normal form (DNNFs). While it is known that there exist CNF formulas that require exponential size representations, the situation is less well studied for other types of constraints than Boolean disjunctive clauses. The constraint satisfaction problem (CSP) is a powerful framework that generalizes CNF-SAT by allowing arbitrary sets of constraints over any finite domain. The main goal of our work is to understand for which type of constraints (also called the constraint language) it is possible to efficiently compute representations of polynomial size. We answer this question completely and prove two tight characterizations of efficiently compilable constraint languages, depending on whether target format is structured. We first identify the combinatorial property of ``strong blockwise decomposability'' and show that if a constraint language has this property, we can compute DNNF representations of linear size. For all other constraint languages we construct families of CSP-instances that provably require DNNFs of exponential size. For a subclass of ``strong uniformly blockwise decomposable'' constraint languages we obtain a similar dichotomy for structured DNNFs. In fact, strong (uniform) blockwise decomposability even allows efficient compilation into multi-valued analogs of OBDDs and FBDDs, respectively. Thus, we get complete characterizations for all knowledge compilation classes between O(B)DDs and DNNFs.

Advancements in materials play a crucial role in technological progress. However, the process of discovering and developing materials with desired properties is often impeded by substantial experimental costs, extensive resource utilization, and lengthy development periods. To address these challenges, modern approaches often employ machine learning (ML) techniques such as Bayesian Optimization (BO), which streamline the search for optimal materials by iteratively selecting experiments that are most likely to yield beneficial results. However, traditional BO methods, while beneficial, often struggle with balancing the trade-off between exploration and exploitation, leading to sub-optimal performance in material discovery processes. This paper introduces a novel Threshold-Driven UCB-EI Bayesian Optimization (TDUE-BO) method, which dynamically integrates the strengths of Upper Confidence Bound (UCB) and Expected Improvement (EI) acquisition functions to optimize the material discovery process. Unlike the classical BO, our method focuses on efficiently navigating the high-dimensional material design space (MDS). TDUE-BO begins with an exploration-focused UCB approach, ensuring a comprehensive initial sweep of the MDS. As the model gains confidence, indicated by reduced uncertainty, it transitions to the more exploitative EI method, focusing on promising areas identified earlier. The UCB-to-EI switching policy dictated guided through continuous monitoring of the model uncertainty during each step of sequential sampling results in navigating through the MDS more efficiently while ensuring rapid convergence. The effectiveness of TDUE-BO is demonstrated through its application on three different material datasets, showing significantly better approximation and optimization performance over the EI and UCB-based BO methods in terms of the RMSE scores and convergence efficiency, respectively.

We present ResMLP, an architecture built entirely upon multi-layer perceptrons for image classification. It is a simple residual network that alternates (i) a linear layer in which image patches interact, independently and identically across channels, and (ii) a two-layer feed-forward network in which channels interact independently per patch. When trained with a modern training strategy using heavy data-augmentation and optionally distillation, it attains surprisingly good accuracy/complexity trade-offs on ImageNet. We will share our code based on the Timm library and pre-trained models.

Nowadays, the Convolutional Neural Networks (CNNs) have achieved impressive performance on many computer vision related tasks, such as object detection, image recognition, image retrieval, etc. These achievements benefit from the CNNs outstanding capability to learn the input features with deep layers of neuron structures and iterative training process. However, these learned features are hard to identify and interpret from a human vision perspective, causing a lack of understanding of the CNNs internal working mechanism. To improve the CNN interpretability, the CNN visualization is well utilized as a qualitative analysis method, which translates the internal features into visually perceptible patterns. And many CNN visualization works have been proposed in the literature to interpret the CNN in perspectives of network structure, operation, and semantic concept. In this paper, we expect to provide a comprehensive survey of several representative CNN visualization methods, including Activation Maximization, Network Inversion, Deconvolutional Neural Networks (DeconvNet), and Network Dissection based visualization. These methods are presented in terms of motivations, algorithms, and experiment results. Based on these visualization methods, we also discuss their practical applications to demonstrate the significance of the CNN interpretability in areas of network design, optimization, security enhancement, etc.