Optimal Transport has sparked vivid interest in recent years, in particular thanks to the Wasserstein distance, which provides a geometrically sensible and intuitive way of comparing probability measures. For computational reasons, the Sliced Wasserstein (SW) distance was introduced as an alternative to the Wasserstein distance, and has seen uses for training generative Neural Networks (NNs). While convergence of Stochastic Gradient Descent (SGD) has been observed practically in such a setting, there is to our knowledge no theoretical guarantee for this observation. Leveraging recent works on convergence of SGD on non-smooth and non-convex functions by Bianchi et al. (2022), we aim to bridge that knowledge gap, and provide a realistic context under which fixed-step SGD trajectories for the SW loss on NN parameters converge. More precisely, we show that the trajectories approach the set of (sub)-gradient flow equations as the step decreases. Under stricter assumptions, we show a much stronger convergence result for noised and projected SGD schemes, namely that the long-run limits of the trajectories approach a set of generalised critical points of the loss function.
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There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems. Iterative methods are particularly well-suited for parallel solves of such systems. However, fast and stable convergence of iterative methods is reliant on the application of a high-quality preconditioner that reduces the spread and increase the clustering of the eigenvalues of the target matrix. To improve the performance of these approaches, we present a new parallel-friendly symmetric stair preconditioner. We prove that our preconditioner has advantageous theoretical properties when used in conjunction with iterative methods for trajectory optimization such as a more clustered eigenvalue spectrum. Numerical experiments with typical trajectory optimization problems reveal that as compared to the best alternative parallel preconditioner from the literature, our symmetric stair preconditioner provides up to a 34% reduction in condition number and up to a 25% reduction in the number of resulting linear system solver iterations.
The recent Facebook rebranding to Meta has drawn renewed attention to the metaverse. Technology giants, amongst others, are increasingly embracing the vision and opportunities of a hybrid social experience that mixes physical and virtual interactions. As the metaverse gains in traction, it is expected that everyday objects may soon connect more closely with virtual elements. However, discovering this "hidden" virtual world will be a crucial first step to interacting with it in this new augmented world. In this paper, we address the problem of connecting physical objects with their virtual counterparts, especially through connections built upon visual markers. We propose a unified recognition framework that guides approaches to the metaverse access points. We illustrate the use of the framework through experimental studies under different conditions, in which an interactive and visually attractive decoration pattern, an Artcode, is used as the approach to enable the connection. This paper will be of interest to, amongst others, researchers working in Interaction Design or Augmented Reality who are seeking techniques or guidelines for augmenting physical objects in an unobtrusive, complementary manner.
For Prognostics and Health Management (PHM) of Lithium-ion (Li-ion) batteries, many models have been established to characterize their degradation process. The existing empirical or physical models can reveal important information regarding the degradation dynamics. However, there are no general and flexible methods to fuse the information represented by those models. Physics-Informed Neural Network (PINN) is an efficient tool to fuse empirical or physical dynamic models with data-driven models. To take full advantage of various information sources, we propose a model fusion scheme based on PINN. It is implemented by developing a semi-empirical semi-physical Partial Differential Equation (PDE) to model the degradation dynamics of Li-ion batteries. When there is little prior knowledge about the dynamics, we leverage the data-driven Deep Hidden Physics Model (DeepHPM) to discover the underlying governing dynamic models. The uncovered dynamics information is then fused with that mined by the surrogate neural network in the PINN framework. Moreover, an uncertainty-based adaptive weighting method is employed to balance the multiple learning tasks when training the PINN. The proposed methods are verified on a public dataset of Li-ion Phosphate (LFP)/graphite batteries.
Navigating in the latent space of StyleGAN has shown effectiveness for face editing. However, the resulting methods usually encounter challenges in complicated navigation due to the entanglement among different attributes in the latent space. To address this issue, this paper proposes a novel framework, termed SDFlow, with a semantic decomposition in original latent space using continuous conditional normalizing flows. Specifically, SDFlow decomposes the original latent code into different irrelevant variables by jointly optimizing two components: (i) a semantic encoder to estimate semantic variables from input faces and (ii) a flow-based transformation module to map the latent code into a semantic-irrelevant variable in Gaussian distribution, conditioned on the learned semantic variables. To eliminate the entanglement between variables, we employ a disentangled learning strategy under a mutual information framework, thereby providing precise manipulation controls. Experimental results demonstrate that SDFlow outperforms existing state-of-the-art face editing methods both qualitatively and quantitatively. The source code is made available at //github.com/phil329/SDFlow.
Advanced Driver Assistance Systems (ADAS) are increasingly important in improving driving safety and comfort, with Adaptive Cruise Control (ACC) being one of the most widely used. However, pre-defined ACC settings may not always align with driver's preferences and habits, leading to discomfort and potential safety issues. Personalized ACC (P-ACC) has been proposed to address this problem, but most existing research uses historical driving data to imitate behaviors that conform to driver preferences, neglecting real-time driver feedback. To bridge this gap, we propose a cloud-vehicle collaborative P-ACC framework that incorporates driver feedback adaptation in real time. The framework is divided into offline and online parts. The offline component records the driver's naturalistic car-following trajectory and uses inverse reinforcement learning (IRL) to train the model on the cloud. In the online component, driver feedback is used to update the driving gap preference in real time. The model is then retrained on the cloud with driver's takeover trajectories, achieving incremental learning to better match driver's preference. Human-in-the-loop (HuiL) simulation experiments demonstrate that our proposed method significantly reduces driver intervention in automatic control systems by up to 62.8%. By incorporating real-time driver feedback, our approach enhances the comfort and safety of P-ACC, providing a personalized and adaptable driving experience.
Diffusion Probabilistic Models (DPMs) have achieved considerable success in generation tasks. As sampling from DPMs is equivalent to solving diffusion SDE or ODE which is time-consuming, numerous fast sampling methods built upon improved differential equation solvers are proposed. The majority of such techniques consider solving the diffusion ODE due to its superior efficiency. However, stochastic sampling could offer additional advantages in generating diverse and high-quality data. In this work, we engage in a comprehensive analysis of stochastic sampling from two aspects: variance-controlled diffusion SDE and linear multi-step SDE solver. Based on our analysis, we propose SA-Solver, which is an improved efficient stochastic Adams method for solving diffusion SDE to generate data with high quality. Our experiments show that SA-Solver achieves: 1) improved or comparable performance compared with the existing state-of-the-art sampling methods for few-step sampling; 2) SOTA FID scores on substantial benchmark datasets under a suitable number of function evaluations (NFEs).
We present an expanded study of the performance of FLASH when using Linux Kernel Hugepages on Ookami, an HPE Apollo 80 A64FX platform. FLASH is a multi-scale, multi-physics simulation code written principally in modern Fortran and makes use of the PARAMESH library to manage a block-structured adaptive mesh. Our initial study used only the Fujitsu compiler to utilize standard hugepages (hp), but further investigation allowed us to utilize hp for multiple compilers by linking to the Fujitsu library libmpg and transparent hugepages (thp) by enabling it at the node level. By comparing the results of hardware counters and in-code timers, we found that hp and thp do not significantly impact the runtime performance of FLASH. Interestingly, there is a significant reduction in the TLB misses, differences in cache and memory access counters, and strange behavior is observed when using thp.
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We prove that the well-known (strong) fully-concurrent bisimilarity and the novel i-causal-net bisimilarity, which is a sligtlhy coarser variant of causal-net bisimilarity, are decidable for finite bounded Petri nets. The proofs are based on a generalization of the ordered marking proof technique that Vogler used to demonstrate that (strong) fully-concurrent bisimilarity (or, equivalently, history-preserving bisimilarity) is decidable on finite safe nets.
Large Language Models (LLMs) have emerged as powerful tools in the field of Natural Language Processing (NLP) and have recently gained significant attention in the domain of Recommendation Systems (RS). These models, trained on massive amounts of data using self-supervised learning, have demonstrated remarkable success in learning universal representations and have the potential to enhance various aspects of recommendation systems by some effective transfer techniques such as fine-tuning and prompt tuning, and so on. The crucial aspect of harnessing the power of language models in enhancing recommendation quality is the utilization of their high-quality representations of textual features and their extensive coverage of external knowledge to establish correlations between items and users. To provide a comprehensive understanding of the existing LLM-based recommendation systems, this survey presents a taxonomy that categorizes these models into two major paradigms, respectively Discriminative LLM for Recommendation (DLLM4Rec) and Generative LLM for Recommendation (GLLM4Rec), with the latter being systematically sorted out for the first time. Furthermore, we systematically review and analyze existing LLM-based recommendation systems within each paradigm, providing insights into their methodologies, techniques, and performance. Additionally, we identify key challenges and several valuable findings to provide researchers and practitioners with inspiration.
Deep Convolutional Neural Networks (CNNs) are a special type of Neural Networks, which have shown state-of-the-art results on various competitive benchmarks. The powerful learning ability of deep CNN is largely achieved with the use of multiple non-linear feature extraction stages that can automatically learn hierarchical representation from the data. Availability of a large amount of data and improvements in the hardware processing units have accelerated the research in CNNs and recently very interesting deep CNN architectures are reported. The recent race in deep CNN architectures for achieving high performance on the challenging benchmarks has shown that the innovative architectural ideas, as well as parameter optimization, can improve the CNN performance on various vision-related tasks. In this regard, different ideas in the CNN design have been explored such as use of different activation and loss functions, parameter optimization, regularization, and restructuring of processing units. However, the major improvement in representational capacity is achieved by the restructuring of the processing units. Especially, the idea of using a block as a structural unit instead of a layer is gaining substantial appreciation. This survey thus focuses on the intrinsic taxonomy present in the recently reported CNN architectures and consequently, classifies the recent innovations in CNN architectures into seven different categories. These seven categories are based on spatial exploitation, depth, multi-path, width, feature map exploitation, channel boosting and attention. Additionally, it covers the elementary understanding of the CNN components and sheds light on the current challenges and applications of CNNs.
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