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Slicing distribution selection has been used as an effective technique to improve the performance of parameter estimators based on minimizing sliced Wasserstein distance in applications. Previous works either utilize expensive optimization to select the slicing distribution or use slicing distributions that require expensive sampling methods. In this work, we propose an optimization-free slicing distribution that provides a fast sampling for the Monte Carlo estimation of expectation. In particular, we introduce the random-path projecting direction (RPD) which is constructed by leveraging the normalized difference between two random vectors following the two input measures. From the RPD, we derive the random-path slicing distribution (RPSD) and two variants of sliced Wasserstein, i.e., the Random-Path Projection Sliced Wasserstein (RPSW) and the Importance Weighted Random-Path Projection Sliced Wasserstein (IWRPSW). We then discuss the topological, statistical, and computational properties of RPSW and IWRPSW. Finally, we showcase the favorable performance of RPSW and IWRPSW in gradient flow and the training of denoising diffusion generative models on images.

A novel Follow-the-Perturbed-Leader type algorithm is proposed and analyzed for solving general long-term constrained optimization problems in online manner, where the objective and constraints are arbitrarily generated and not necessarily convex. In each period, random linear perturbation and strongly concave perturbation are incorporated in primal and dual directions, respectively, to the offline oracle, and a global minimax point is searched as the solution. Based on a proposed expected static cumulative regret, we derive the first sublinear $O(T^{8/9})$ regret complexity for this class of problems. The proposed algorithm is applied to tackle a long-term (extreme value) constrained river pollutant source identification problem, validate the theoretical results and exhibit superior performance compared to existing methods.

Collaborative filtering (CF) methods for recommendation systems have been extensively researched, ranging from matrix factorization and autoencoder-based to graph filtering-based methods. Recently, lightweight methods that require almost no training have been recently proposed to reduce overall computation. However, existing methods still have room to improve the trade-offs among accuracy, efficiency, and robustness. In particular, there are no well-designed closed-form studies for \emph{balanced} CF in terms of the aforementioned trade-offs. In this paper, we design SVD-AE, a simple yet effective singular vector decomposition (SVD)-based linear autoencoder, whose closed-form solution can be defined based on SVD for CF. SVD-AE does not require iterative training processes as its closed-form solution can be calculated at once. Furthermore, given the noisy nature of the rating matrix, we explore the robustness against such noisy interactions of existing CF methods and our SVD-AE. As a result, we demonstrate that our simple design choice based on truncated SVD can be used to strengthen the noise robustness of the recommendation while improving efficiency. Code is available at //github.com/seoyoungh/svd-ae.

For models consisting of a classifier in some representation space, learning online from a non-stationary data stream often necessitates changes in the representation. So, the question arises of what is the best way to adapt the classifier to shifts in representation. Current methods only slowly change the classifier to representation shift, introducing noise into learning as the classifier is misaligned to the representation. We propose DeepCCG, an empirical Bayesian approach to solve this problem. DeepCCG works by updating the posterior of a class conditional Gaussian classifier such that the classifier adapts in one step to representation shift. The use of a class conditional Gaussian classifier also enables DeepCCG to use a log conditional marginal likelihood loss to update the representation. To perform the update to the classifier and representation, DeepCCG maintains a fixed number of examples in memory and so a key part of DeepCCG is selecting what examples to store, choosing the subset that minimises the KL divergence between the true posterior and the posterior induced by the subset. We explore the behaviour of DeepCCG in online continual learning (CL), demonstrating that it performs well against a spectrum of online CL methods and that it reduces the change in performance due to representation shift.

Contemporary accelerator designs exhibit a high degree of spatial localization, wherein two-dimensional physical distance determines communication costs between processing elements. This situation presents considerable algorithmic challenges, particularly when managing sparse data, a pivotal component in progressing data science. The spatial computer model quantifies communication locality by weighting processor communication costs by distance, introducing a term named energy. Moreover, it integrates depth, a widely-utilized metric, to promote high parallelism. We propose and analyze a framework for efficient spatial tree algorithms within the spatial computer model. Our primary method constructs a spatial tree layout that optimizes the locality of the neighbors in the compute grid. This approach thereby enables locality-optimized messaging within the tree. Our layout achieves a polynomial factor improvement in energy compared to utilizing a PRAM approach. Using this layout, we develop energy-efficient treefix sum and lowest common ancestor algorithms, which are both fundamental building blocks for other graph algorithms. With high probability, our algorithms exhibit near-linear energy and poly-logarithmic depth. Our contributions augment a growing body of work demonstrating that computations can have both high spatial locality and low depth. Moreover, our work constitutes an advancement in the spatial layout of irregular and sparse computations.

Where dual-numbers forward-mode automatic differentiation (AD) pairs each scalar value with its tangent value, dual-numbers reverse-mode AD attempts to achieve reverse AD using a similarly simple idea: by pairing each scalar value with a backpropagator function. Its correctness and efficiency on higher-order input languages have been analysed by Brunel, Mazza and Pagani, but this analysis used a custom operational semantics for which it is unclear whether it can be implemented efficiently. We take inspiration from their use of linear factoring to optimise dual-numbers reverse-mode AD to an algorithm that has the correct complexity and enjoys an efficient implementation in a standard functional language with support for mutable arrays, such as Haskell. Aside from the linear factoring ingredient, our optimisation steps consist of well-known ideas from the functional programming community. We demonstrate the use of our technique by providing a practical implementation that differentiates most of Haskell98. Where previous work on dual numbers reverse AD has required sequentialisation to construct the reverse pass, we demonstrate that we can apply our technique to task-parallel source programs and generate a task-parallel derivative computation.

Autonomous driving perception models are typically composed of multiple functional modules that interact through complex relationships to accomplish environment understanding. However, perception models are predominantly optimized as a black box through end-to-end training, lacking independent evaluation of functional modules, which poses difficulties for interpretability and optimization. Pioneering in the issue, we propose an evaluation method based on feature map analysis to gauge the convergence of model, thereby assessing functional modules' training maturity. We construct a quantitative metric named as the Feature Map Convergence Score (FMCS) and develop Feature Map Convergence Evaluation Network (FMCE-Net) to measure and predict the convergence degree of models respectively. FMCE-Net achieves remarkable predictive accuracy for FMCS across multiple image classification experiments, validating the efficacy and robustness of the introduced approach. To the best of our knowledge, this is the first independent evaluation method for functional modules, offering a new paradigm for the training assessment towards perception models.

V2X cooperation, through the integration of sensor data from both vehicles and infrastructure, is considered a pivotal approach to advancing autonomous driving technology. Current research primarily focuses on enhancing perception accuracy, often overlooking the systematic improvement of accident prediction accuracy through end-to-end learning, leading to insufficient attention to the safety issues of autonomous driving. To address this challenge, this paper introduces the UniE2EV2X framework, a V2X-integrated end-to-end autonomous driving system that consolidates key driving modules within a unified network. The framework employs a deformable attention-based data fusion strategy, effectively facilitating cooperation between vehicles and infrastructure. The main advantages include: 1) significantly enhancing agents' perception and motion prediction capabilities, thereby improving the accuracy of accident predictions; 2) ensuring high reliability in the data fusion process; 3) superior end-to-end perception compared to modular approaches. Furthermore, We implement the UniE2EV2X framework on the challenging DeepAccident, a simulation dataset designed for V2X cooperative driving.

Fine-grained image analysis (FGIA) is a longstanding and fundamental problem in computer vision and pattern recognition, and underpins a diverse set of real-world applications. The task of FGIA targets analyzing visual objects from subordinate categories, e.g., species of birds or models of cars. The small inter-class and large intra-class variation inherent to fine-grained image analysis makes it a challenging problem. Capitalizing on advances in deep learning, in recent years we have witnessed remarkable progress in deep learning powered FGIA. In this paper we present a systematic survey of these advances, where we attempt to re-define and broaden the field of FGIA by consolidating two fundamental fine-grained research areas -- fine-grained image recognition and fine-grained image retrieval. In addition, we also review other key issues of FGIA, such as publicly available benchmark datasets and related domain-specific applications. We conclude by highlighting several research directions and open problems which need further exploration from the community.

Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.