To mitigate global warming, greenhouse gas sources need to be resolved at a high spatial resolution and monitored in time to ensure the reduction and ultimately elimination of the pollution source. However, the complexity of computation in resolving high-resolution wind fields left the simulations impractical to test different time lengths and model configurations. This study presents a preliminary development of a physics-informed super-resolution (SR) generative adversarial network (GAN) that super-resolves the three-dimensional (3D) low-resolution wind fields by upscaling x9 times. We develop a pixel-wise self-attention (PWA) module that learns 3D weather dynamics via a self-attention computation followed by a 2D convolution. We also employ a loss term that regularizes the self-attention map during pretraining, capturing the vertical convection process from input wind data. The new PWA SR-GAN shows the high-fidelity super-resolved 3D wind data, learns a wind structure at the high-frequency domain, and reduces the computational cost of a high-resolution wind simulation by x89.7 times.
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End-to-End (E2E) unrolled optimization frameworks show promise for Magnetic Resonance (MR) image recovery, but suffer from high memory usage during training. In addition, these deterministic approaches do not offer opportunities for sampling from the posterior distribution. In this paper, we introduce a memory-efficient approach for E2E learning of the posterior distribution. We represent this distribution as the combination of a data-consistency-induced likelihood term and an energy model for the prior, parameterized by a Convolutional Neural Network (CNN). The CNN weights are learned from training data in an E2E fashion using maximum likelihood optimization. The learned model enables the recovery of images from undersampled measurements using the Maximum A Posteriori (MAP) optimization. In addition, the posterior model can be sampled to derive uncertainty maps about the reconstruction. Experiments on parallel MR image reconstruction show that our approach performs comparable to the memory-intensive E2E unrolled algorithm, performs better than its memory-efficient counterpart, and can provide uncertainty maps. Our framework paves the way towards MR image reconstruction in 3D and higher dimensions
We consider the graphon mean-field system introduced in the work of Bayraktar, Chakraborty, and Wu. It is the large-population limit of a heterogeneously interacting diffusive particle system, where the interaction is of mean-field type with weights characterized by an underlying graphon function. Observing continuous-time trajectories of a finite-population particle system, we build plug-in estimators of the particle densities, drift coefficients, and graphon interaction weights of the mean-field system. Our estimators for the densities and drifts are direct results of kernel interpolation on the empirical data, and a deconvolution method leads to an estimator of the underlying graphon function. We prove that the estimator converges to the true graphon function as the number of particles tends to infinity, when all other parameters are properly chosen. Besides, we also justify the pointwise optimality of the density estimator via a minimax analysis over a particular class of particle systems.
Understanding the mechanisms through which neural networks extract statistics from input-label pairs is one of the most important unsolved problems in supervised learning. Prior works have identified that the gram matrices of the weights in trained neural networks of general architectures are proportional to the average gradient outer product of the model, in a statement known as the Neural Feature Ansatz (NFA). However, the reason these quantities become correlated during training is poorly understood. In this work, we explain the emergence of this correlation. We identify that the NFA is equivalent to alignment between the left singular structure of the weight matrices and a significant component of the empirical neural tangent kernels associated with those weights. We establish that the NFA introduced in prior works is driven by a centered NFA that isolates this alignment. We show that the speed of NFA development can be predicted analytically at early training times in terms of simple statistics of the inputs and labels. Finally, we introduce a simple intervention to increase NFA correlation at any given layer, which dramatically improves the quality of features learned.
Augmented reality for laparoscopic liver resection is a visualisation mode that allows a surgeon to localise tumours and vessels embedded within the liver by projecting them on top of a laparoscopic image. Preoperative 3D models extracted from CT or MRI data are registered to the intraoperative laparoscopic images during this process. In terms of 3D-2D fusion, most of the algorithms make use of anatomical landmarks to guide registration. These landmarks include the liver's inferior ridge, the falciform ligament, and the occluding contours. They are usually marked by hand in both the laparoscopic image and the 3D model, which is time-consuming and may contain errors if done by a non-experienced user. Therefore, there is a need to automate this process so that augmented reality can be used effectively in the operating room. We present the Preoperative-to-Intraoperative Laparoscopic Fusion Challenge (P2ILF), held during the Medical Imaging and Computer Assisted Interventions (MICCAI 2022) conference, which investigates the possibilities of detecting these landmarks automatically and using them in registration. The challenge was divided into two tasks: 1) A 2D and 3D landmark detection task and 2) a 3D-2D registration task. The teams were provided with training data consisting of 167 laparoscopic images and 9 preoperative 3D models from 9 patients, with the corresponding 2D and 3D landmark annotations. A total of 6 teams from 4 countries participated, whose proposed methods were evaluated on 16 images and two preoperative 3D models from two patients. All the teams proposed deep learning-based methods for the 2D and 3D landmark segmentation tasks and differentiable rendering-based methods for the registration task. Based on the experimental outcomes, we propose three key hypotheses that determine current limitations and future directions for research in this domain.
We present a demonstration of image classification using an echo-state network (ESN) relying on a single simulated spintronic nanostructure known as the vortex-based spin-torque oscillator (STVO) delayed in time. We employ an ultrafast data-driven simulation framework called the data-driven Thiele equation approach (DD-TEA) to simulate the STVO dynamics. This allows us to avoid the challenges associated with repeated experimental manipulation of such a nanostructured system. We showcase the versatility of our solution by successfully applying it to solve classification challenges with the MNIST, EMNIST-letters and Fashion MNIST datasets. Through our simulations, we determine that within an ESN with numerous learnable parameters the results obtained using the STVO dynamics as an activation function are comparable to the ones obtained with other conventional nonlinear activation functions like the reLU and the sigmoid. While achieving state-of-the-art accuracy levels on the MNIST dataset, our model's performance on EMNIST-letters and Fashion MNIST is lower due to the relative simplicity of the system architecture and the increased complexity of the tasks. We expect that the DD-TEA framework will enable the exploration of deeper architectures, ultimately leading to improved classification accuracy.
The interest in network analysis of bibliographic data has grown substantially in recent years, yet comprehensive statistical models for examining the complete dynamics of scientific networks based on bibliographic data are generally lacking. Current empirical studies often focus on models restricting analysis either to paper citation networks (paper-by-paper) or author networks (author-by-author). However, such networks encompass not only direct connections between papers, but also indirect relationships between the references of papers connected by a citation link. In this paper, we extend recently developed relational hyperevent models (RHEM) for analyzing scientific networks. We introduce new covariates representing theoretically meaningful and empirically interesting sub-network configurations. The model accommodates testing hypotheses considering: (i) the polyadic nature of scientific publication events, and (ii) the interdependencies between authors and references of current and prior papers. We implement the model using purpose-built, publicly available open-source software, demonstrating its empirical value in an analysis of a large publicly available scientific network dataset. Assessing the relative strength of various effects reveals that both the hyperedge structure of publication events, as well as the interconnection between authors and references significantly improve our understanding and interpretation of collaborative scientific production.
We devise a policy-iteration algorithm for deterministic two-player discounted and mean-payoff games, that runs in polynomial time with high probability, on any input where each payoff is chosen independently from a sufficiently random distribution. This includes the case where an arbitrary set of payoffs has been perturbed by a Gaussian, showing for the first time that deterministic two-player games can be solved efficiently, in the sense of smoothed analysis. More generally, we devise a condition number for deterministic discounted and mean-payoff games, and show that our algorithm runs in time polynomial in this condition number. Our result confirms a previous conjecture of Boros et al., which was claimed as a theorem and later retracted. It stands in contrast with a recent counter-example by Christ and Yannakakis, showing that Howard's policy-iteration algorithm does not run in smoothed polynomial time on stochastic single-player mean-payoff games. Our approach is inspired by the analysis of random optimal assignment instances by Frieze and Sorkin, and the analysis of bias-induced policies for mean-payoff games by Akian, Gaubert and Hochart.
An emerging trend in approximate counting is to show that certain `low-temperature' problems are easy on typical instances, despite worst-case hardness results. For the class of regular graphs one usually shows that expansion can be exploited algorithmically, and since random regular graphs are good expanders with high probability the problem is typically tractable. Inspired by approaches used in subexponential-time algorithms for Unique Games, we develop an approximation algorithm for the partition function of the ferromagnetic Potts model on graphs with a small-set expansion condition. In such graphs it may not suffice to explore the state space of the model close to ground states, and a novel feature of our method is to efficiently find a larger set of `pseudo-ground states' such that it is enough to explore the model around each pseudo-ground state.
Hashing has been widely used in approximate nearest search for large-scale database retrieval for its computation and storage efficiency. Deep hashing, which devises convolutional neural network architecture to exploit and extract the semantic information or feature of images, has received increasing attention recently. In this survey, several deep supervised hashing methods for image retrieval are evaluated and I conclude three main different directions for deep supervised hashing methods. Several comments are made at the end. Moreover, to break through the bottleneck of the existing hashing methods, I propose a Shadow Recurrent Hashing(SRH) method as a try. Specifically, I devise a CNN architecture to extract the semantic features of images and design a loss function to encourage similar images projected close. To this end, I propose a concept: shadow of the CNN output. During optimization process, the CNN output and its shadow are guiding each other so as to achieve the optimal solution as much as possible. Several experiments on dataset CIFAR-10 show the satisfying performance of SRH.
Recommender systems play a crucial role in mitigating the problem of information overload by suggesting users' personalized items or services. The vast majority of traditional recommender systems consider the recommendation procedure as a static process and make recommendations following a fixed strategy. In this paper, we propose a novel recommender system with the capability of continuously improving its strategies during the interactions with users. We model the sequential interactions between users and a recommender system as a Markov Decision Process (MDP) and leverage Reinforcement Learning (RL) to automatically learn the optimal strategies via recommending trial-and-error items and receiving reinforcements of these items from users' feedbacks. In particular, we introduce an online user-agent interacting environment simulator, which can pre-train and evaluate model parameters offline before applying the model online. Moreover, we validate the importance of list-wise recommendations during the interactions between users and agent, and develop a novel approach to incorporate them into the proposed framework LIRD for list-wide recommendations. The experimental results based on a real-world e-commerce dataset demonstrate the effectiveness of the proposed framework.
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