Miracle-dz/UniFAR-FTUs huggingface dataset:
Fast and Interpretable Nonlocal Neural Networks for Image Denoising via Group-Sparse Convolutional Dictionary Learning

Nonlocal self-similarity within natural images has become an increasingly popular prior in deep-learning models. Despite their successful image restoration performance, such models remain largely uninterpretable due to their black-box construction. Our previous studies have shown that interpretable construction of a fully convolutional denoiser (CDLNet), with performance on par with state-of-the-art black-box counterparts, is achievable by unrolling a dictionary learning algorithm. In this manuscript, we seek an interpretable construction of a convolutional network with a nonlocal self-similarity prior that performs on par with black-box nonlocal models. We show that such an architecture can be effectively achieved by upgrading the $\ell 1$ sparsity prior of CDLNet to a weighted group-sparsity prior. From this formulation, we propose a novel sliding-window nonlocal operation, enabled by sparse array arithmetic. In addition to competitive performance with black-box nonlocal DNNs, we demonstrate the proposed sliding-window sparse attention enables inference speeds greater than an order of magnitude faster than its competitors.
A unified analysis of likelihood-based estimators in the Plackett--Luce model

The Plackett--Luce model is a popular approach for ranking data analysis, where a utility vector is employed to determine the probability of each outcome based on Luce's choice axiom. In this paper, we investigate the asymptotic theory of utility vector estimation by maximizing different types of likelihood, such as the full-, marginal-, and quasi-likelihood. We provide a rank-matching interpretation for the estimating equations of these estimators and analyze their asymptotic behavior as the number of items being compared tends to infinity. In particular, we establish the uniform consistency of these estimators under conditions characterized by the topology of the underlying comparison graph sequence and demonstrate that the proposed conditions are sharp for common sampling scenarios such as the nonuniform random hypergraph model and the hypergraph stochastic block model; we also obtain the asymptotic normality of these estimators and discuss the trade-off between statistical efficiency and computational complexity for practical uncertainty quantification. Both results allow for nonuniform and inhomogeneous comparison graphs with varying edge sizes and different asymptotic orders of edge probabilities. We verify our theoretical findings by conducting detailed numerical experiments.
On Approximability of Steiner Tree in $\ell_p$-metrics

In the Continuous Steiner Tree problem (CST), we are given as input a set of points (called terminals) in a metric space and ask for the minimum-cost tree connecting them. Additional points (called Steiner points) from the metric space can be introduced as nodes in the solution. In the Discrete Steiner Tree problem (DST), we are given in addition to the terminals, a set of facilities, and any solution tree connecting the terminals can only contain the Steiner points from this set of facilities. Trevisan [SICOMP'00] showed that CST and DST are APX-hard when the input lies in the $\ell_1$-metric (and Hamming metric). Chleb\'ik and Chleb\'ikov\'a [TCS'08] showed that DST is NP-hard to approximate to factor of $96/95\approx 1.01$ in the graph metric (and consequently $\ell_\infty$-metric). Prior to this work, it was unclear if CST and DST are APX-hard in essentially every other popular metric! In this work, we prove that DST is APX-hard in every $\ell_p$-metric. We also prove that CST is APX-hard in the $\ell_{\infty}$-metric. Finally, we relate CST and DST, showing a general reduction from CST to DST in $\ell_p$-metrics. As an immediate consequence, this yields a $1.39$-approximation polynomial time algorithm for CST in $\ell_p$-metrics.
Calib-Anything: Zero-training LiDAR-Camera Extrinsic Calibration Method Using Segment Anything

The research on extrinsic calibration between Light Detection and Ranging(LiDAR) and camera are being promoted to a more accurate, automatic and generic manner. Since deep learning has been employed in calibration, the restrictions on the scene are greatly reduced. However, data driven method has the drawback of low transfer-ability. It cannot adapt to dataset variations unless additional training is taken. With the advent of foundation model, this problem can be significantly mitigated. By using the Segment Anything Model(SAM), we propose a novel LiDAR-camera calibration method, which requires zero extra training and adapts to common scenes. With an initial guess, we opimize the extrinsic parameter by maximizing the consistency of points that are projected inside each image mask. The consistency includes three properties of the point cloud: the intensity, normal vector and categories derived from some segmentation methods. The experiments on different dataset have demonstrated the generality and comparable accuracy of our method. The code is available at https://github.com/OpenCalib/CalibAnything.
HireVAE: An Online and Adaptive Factor Model Based on Hierarchical and Regime-Switch VAE

Factor model is a fundamental investment tool in quantitative investment, which can be empowered by deep learning to become more flexible and efficient in practical complicated investing situations. However, it is still an open question to build a factor model that can conduct stock prediction in an online and adaptive setting, where the model can adapt itself to match the current market regime identified based on only point-in-time market information. To tackle this problem, we propose the first deep learning based online and adaptive factor model, HireVAE, at the core of which is a hierarchical latent space that embeds the underlying relationship between the market situation and stock-wise latent factors, so that HireVAE can effectively estimate useful latent factors given only historical market information and subsequently predict accurate stock returns. Across four commonly used real stock market benchmarks, the proposed HireVAE demonstrate superior performance in terms of active returns over previous methods, verifying the potential of such online and adaptive factor model.
Long-term normalized difference urban index (NDUI) data time series for urban studies

Keeping continuous, long-term data to examine changes in urban surroundings is crucial as cities expand and develop. The DMSP OLS nighttime lights data and the Landsat NDVI were used to create the Normalized Difference Urbanization Index (NDUI), which has proven to be an invaluable resource for studying urban areas. However, DMSP's reach and usefulness are constrained by the fact that data collecting ended in 2014 while VIIRS has continued to collect the nighttime lights data since 2012. The unavailability of DMSP translates to a challenge in performing urban studies using the NDUI. In this work, we address this difficulty and suggest a novel approach to bringing the NDUI time series up to date. We first map the VIIRS to DMSP using 2012 as a calibration year and then construct an updated NDUI time series. ClimateDownscaleSuite is used and Swin Transformer is selected as the best model for the mapping. The Swin Transformer model and the sophisticated machine learning capabilities it offers are used in conjunction with the VIIRS evening lighting data collected after 2012. By using this strategy, not only is the NDUI time series extended, but the potential of AI in filling in data gaps and boosting urban studies is also highlighted.
Complexity of Block Coordinate Descent with Proximal Regularization and Applications to Wasserstein CP-dictionary Learning

We consider the block coordinate descent methods of Gauss-Seidel type with proximal regularization (BCD-PR), which is a classical method of minimizing general nonconvex objectives under constraints that has a wide range of practical applications. We theoretically establish the worst-case complexity bound for this algorithm. Namely, we show that for general nonconvex smooth objectives with block-wise constraints, the classical BCD-PR algorithm converges to an epsilon-stationary point within O(1/epsilon) iterations. Under a mild condition, this result still holds even if the algorithm is executed inexactly in each step. As an application, we propose a provable and efficient algorithm for `Wasserstein CP-dictionary learning', which seeks a set of elementary probability distributions that can well-approximate a given set of d-dimensional joint probability distributions. Our algorithm is a version of BCD-PR that operates in the dual space, where the primal problem is regularized both entropically and proximally.
Rigorous derivation of weakly dispersive shallow water models with large amplitude topography variations

We derive rigorously from the water waves equations new irrotational shallow water models for the propagation of surface waves in the case of uneven topography in horizontal dimensions one and two. The systems are made to capture the possible change in the waves' propagation, which can occur in the case of large amplitude topography. The main contribution of this work is the construction of new multi-scale shallow water approximations of the Dirichlet-Neumann operator. We prove that the precision of these approximations is given at the order $O(\mu \varepsilon)$, $O(\mu\varepsilon +\mu^2\beta^2)$ and $O(\mu^2\varepsilon+\mu \varepsilon \beta+ \mu^2\beta^2)$. Here $\mu$, $\varepsilon$, and $\beta$ denote respectively the shallow water parameter, the nonlinear parameter, and the bathymetry parameter. From these approximations, we derive models with the same precision as the ones above. The model with precision $O(\mu \varepsilon)$ is coupled with an elliptic problem, while the other models do not present this inconvenience.
Graph Fourier MMD for Signals on Graphs

While numerous methods have been proposed for computing distances between probability distributions in Euclidean space, relatively little attention has been given to computing such distances for distributions on graphs. However, there has been a marked increase in data that either lies on graph (such as protein interaction networks) or can be modeled as a graph (single cell data), particularly in the biomedical sciences. Thus, it becomes important to find ways to compare signals defined on such graphs. Here, we propose Graph Fourier MMD (GFMMD), a novel distance between distributions and signals on graphs. GFMMD is defined via an optimal witness function that is both smooth on the graph and maximizes the difference in expectation between the pair of distributions on the graph. We find an analytical solution to this optimization problem as well as an embedding of distributions that results from this method. We also prove several properties of this method including scale invariance and applicability to disconnected graphs. We showcase it on graph benchmark datasets as well on single cell RNA-sequencing data analysis. In the latter, we use the GFMMD-based gene embeddings to find meaningful gene clusters. We also propose a novel type of score for gene selection called gene localization score which helps select genes for cellular state space characterization.
Moving object detection method based on background subtraction

Combining the thoughts of image intensity normalization and two-dimensional cross-entropy,a moving object detection algorithm,which is robust against illumination changes,is presented.The intensity of each video frame image is normalized.The background is initialized by an improved mean filtering method,which can get a satisfying background image even if an object appears.The background is updated automatically.The moving objects are detected by using an adaptive threshold based on two-dimensional cross-entropy to segment the background subtraction image.Experimental results demonstrate that this algorithm is quick,effective and robust against changes of illumination.
Exploring the Impact of Model Scaling on Parameter-Efficient Tuning

Parameter-efficient tuning (PET) methods can effectively drive extremely large pre-trained language models (PLMs) by training only minimal parameters. Different PET methods utilize different manually designed tunable modules. In small PLMs, there are usually noticeable performance differences among PET methods. Nevertheless, as the model scale increases, the performance differences become marginal. Hence, we hypothesize that model scaling mitigates the impact of design differences on PET methods. To investigate this hypothesis, we introduce a more flexible PET method called Arbitrary PET (APET) method. The APET method is compatible with a tunable module, which consists of any number of parameters distributed in arbitrary positions. Then, we utilize it and conduct experiments on 11 NLP tasks across 3 representative PLMs. Our investigations reveal that model scaling (1) mitigates the effects of the positions of tunable parameters on performance, and (2) enables tuning methods to achieve performance comparable to full-parameter fine-tuning by optimizing fewer tunable parameters. Intriguingly, we also observe that tuning methods optimize the similar number of tunable parameters to exceed random guess performance on different tasks. We collectively discuss this phenomenon and the two aforementioned findings from an optimization perspective to understand the underlying mechanisms. These conclusions enhance our understanding of the impact of model scaling on PET and assist in designing more effective and efficient PET methods for PLMs of different scales. The source code can be obtained from this GitHub repository: \url{https://github.com/yushengsu-thu/PET_Scaling}.
Enhance Diffusion to Improve Robust Generalization

Deep neural networks are susceptible to human imperceptible adversarial perturbations. One of the strongest defense mechanisms is Adversarial Training (AT). In this paper, we aim to address two predominant problems in AT. First, there is still little consensus on how to set hyperparameters with a performance guarantee for AT research, and customized settings impede a fair comparison between different model designs in AT research. Second, the robustly trained neural networks struggle to generalize well and suffer from tremendous overfitting. This paper focuses on the primary AT framework - Projected Gradient Descent Adversarial Training (PGD-AT). We approximate the dynamic of PGD-AT by a continuous-time Stochastic Differential Equation (SDE), and show that the diffusion term of this SDE determines the robust generalization. An immediate implication of this theoretical finding is that robust generalization is positively correlated with the ratio between learning rate and batch size. We further propose a novel approach, Diffusion Enhanced Adversarial Training (DEAT), to manipulate the diffusion term to improve robust generalization with virtually no extra computational burden. We theoretically show that DEAT obtains a tighter generalization bound than PGD-AT. Our empirical investigation is extensive and firmly attests that DEAT universally outperforms PGD-AT by a significant margin.
Bayesian Learning of Optimal Policies in Markov Decision Processes with Countably Infinite State-Space

Models of many real-life applications, such as queuing models of communication networks or computing systems, have a countably infinite state-space. Algorithmic and learning procedures that have been developed to produce optimal policies mainly focus on finite state settings, and do not directly apply to these models. To overcome this lacuna, in this work we study the problem of optimal control of a family of discrete-time countable state-space Markov Decision Processes (MDPs) governed by an unknown parameter $\theta\in\Theta$, and defined on a countably-infinite state space $\mathcal X=\mathbb{Z}_+^d$, with finite action space $\mathcal A$, and an unbounded cost function. We take a Bayesian perspective with the random unknown parameter $\boldsymbol{\theta}^*$ generated via a given fixed prior distribution on $\Theta$. To optimally control the unknown MDP, we propose an algorithm based on Thompson sampling with dynamically-sized episodes: at the beginning of each episode, the posterior distribution formed via Bayes' rule is used to produce a parameter estimate, which then decides the policy applied during the episode. To ensure the stability of the Markov chain obtained by following the policy chosen for each parameter, we impose ergodicity assumptions. From this condition and using the solution of the average cost Bellman equation, we establish an $\tilde O(dh^d\sqrt{|\mathcal A|T})$ upper bound on the Bayesian regret of our algorithm, where $T$ is the time-horizon. Finally, to elucidate the applicability of our algorithm, we consider two different queuing models with unknown dynamics, and show that our algorithm can be applied to develop approximately optimal control algorithms.
Truly Multivariate Structured Additive Distributional Regression

Generalized additive models for location, scale and shape (GAMLSS) are a popular extension to mean regression models where each parameter of an arbitrary distribution is modelled through covariates. While such models have been developed for univariate and bivariate responses, the truly multivariate case remains extremely challenging for both computational and theoretical reasons. Alternative approaches to GAMLSS may allow for higher dimensional response vectors to be modelled jointly but often assume a fixed dependence structure not depending on covariates or are limited with respect to modelling flexibility or computational aspects. We contribute to this gap in the literature and propose a truly multivariate distributional model, which allows one to benefit from the flexibility of GAMLSS even when the response has dimension larger than two or three. Building on copula regression, we model the dependence structure of the response through a Gaussian copula, while the marginal distributions can vary across components. Our model is highly parameterized but estimation becomes feasible with Bayesian inference employing shrinkage priors. We demonstrate the competitiveness of our approach in a simulation study and illustrate how it complements existing models along the examples of childhood malnutrition and a yet unexplored data set on traffic detection in Berlin.
Aiming towards the minimizers: fast convergence of SGD for overparametrized problems

Modern machine learning paradigms, such as deep learning, occur in or close to the interpolation regime, wherein the number of model parameters is much larger than the number of data samples. In this work, we propose a regularity condition within the interpolation regime which endows the stochastic gradient method with the same worst-case iteration complexity as the deterministic gradient method, while using only a single sampled gradient (or a minibatch) in each iteration. In contrast, all existing guarantees require the stochastic gradient method to take small steps, thereby resulting in a much slower linear rate of convergence. Finally, we demonstrate that our condition holds when training sufficiently wide feedforward neural networks with a linear output layer.
Enhanced Distribution Modelling via Augmented Architectures For Neural ODE Flows

While the neural ODE formulation of normalizing flows such as in FFJORD enables us to calculate the determinants of free form Jacobians in O(D) time, the flexibility of the transformation underlying neural ODEs has been shown to be suboptimal. In this paper, we present AFFJORD, a neural ODE-based normalizing flow which enhances the representation power of FFJORD by defining the neural ODE through special augmented transformation dynamics which preserve the topology of the space. Furthermore, we derive the Jacobian determinant of the general augmented form by generalizing the chain rule in the continuous sense into the Cable Rule, which expresses the forward sensitivity of ODEs with respect to their initial conditions. The cable rule gives an explicit expression for the Jacobian of a neural ODE transformation, and provides an elegant proof of the instantaneous change of variable. Our experimental results on density estimation in synthetic and high dimensional data, such as MNIST, CIFAR-10 and CelebA 32x32, show that AFFJORD outperforms the baseline FFJORD through the improved flexibility of the underlying vector field.
Model-Aided Federated Reinforcement Learning for Multi-UAV Trajectory Planning in IoT Networks

Deploying teams of unmanned aerial vehicles (UAVs) to harvest data from distributed Internet of Things (IoT) devices requires efficient trajectory planning and coordination algorithms. Multi-agent reinforcement learning (MARL) has emerged as a solution, but requires extensive and costly real-world training data. To tackle this challenge, we propose a novel model-aided federated MARL algorithm to coordinate multiple UAVs on a data harvesting mission with only limited knowledge about the environment. The proposed algorithm alternates between building an environment simulation model from real-world measurements, specifically learning the radio channel characteristics and estimating unknown IoT device positions, and federated QMIX training in the simulated environment. Each UAV agent trains a local QMIX model in its simulated environment and continuously consolidates it through federated learning with other agents, accelerating the learning process. A performance comparison with standard MARL algorithms demonstrates that our proposed model-aided FedQMIX algorithm reduces the need for real-world training experiences by around three magnitudes while attaining similar data collection performance.
Learning Probabilistic Symmetrization for Architecture Agnostic Equivariance

We present a novel framework to overcome the limitations of equivariant architectures in learning functions with group symmetries. In contrary to equivariant architectures, we use an arbitrary base model (such as an MLP or a transformer) and symmetrize it to be equivariant to the given group by employing a small equivariant network that parameterizes the probabilistic distribution underlying the symmetrization. The distribution is end-to-end trained with the base model which can maximize performance while reducing sample complexity of symmetrization. We show that this approach ensures not only equivariance to given group but also universal approximation capability in expectation. We implement our method on a simple patch-based transformer that can be initialized from pretrained vision transformers, and test it for a wide range of symmetry groups including permutation and Euclidean groups and their combinations. Empirical tests show competitive results against tailored equivariant architectures, suggesting the potential for learning equivariant functions for diverse groups using a non-equivariant universal base architecture. We further show evidence of enhanced learning in symmetric modalities, like graphs, when pretrained from non-symmetric modalities, like vision. Our implementation will be open-sourced at https://github.com/jw9730/lps.