This paper presents a novel approach for propagating uncertainties in dynamical systems building on high-order Taylor expansions of the flow and moment-generating functions (MGFs). Unlike prior methods that focus on Gaussian distributions, our approach leverages the relationship between MGFs and distribution moments to extend high-order uncertainty propagation techniques to non-Gaussian scenarios. This significantly broadens the applicability of these methods to a wider range of problems and uncertainty types. High-order moment computations are performed one-off and symbolically, reducing the computational burden of the technique to the calculation of Taylor series coefficients around a nominal trajectory, achieved by efficiently integrating the system's variational equations. Furthermore, the use of the proposed approach in combination with event transition tensors, allows for accurate propagation of uncertainties at specific events, such as the landing surface of a celestial body, the crossing of a predefined Poincar\'e section, or the trigger of an arbitrary event during the propagation. Via numerical simulations we demonstrate the effectiveness of our method in various astrodynamics applications, including the unperturbed and perturbed two-body problem, and the circular restricted three-body problem, showing that it accurately propagates non-Gaussian uncertainties both at future times and at event manifolds.
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Custom Non-Linear Model Predictive Control for Obstacle Avoidance in Indoor and Outdoor Environments
Navigating complex environments requires Unmanned Aerial Vehicles (UAVs) and autonomous systems to perform trajectory tracking and obstacle avoidance in real-time. While many control strategies have effectively utilized linear approximations, addressing the non-linear dynamics of UAV, especially in obstacle-dense environments, remains a key challenge that requires further research. This paper introduces a Non-linear Model Predictive Control (NMPC) framework for the DJI Matrice 100, addressing these challenges by using a dynamic model and B-spline interpolation for smooth reference trajectories, ensuring minimal deviation while respecting safety constraints. The framework supports various trajectory types and employs a penalty-based cost function for control accuracy in tight maneuvers. The framework utilizes CasADi for efficient real-time optimization, enabling the UAV to maintain robust operation even under tight computational constraints. Simulation and real-world indoor and outdoor experiments demonstrated the NMPC ability to adapt to disturbances, resulting in smooth, collision-free navigation.
Information Retrieval (IR) systems used in search and recommendation platforms frequently employ Learning-to-Rank (LTR) models to rank items in response to user queries. These models heavily rely on features derived from user interactions, such as clicks and engagement data. This dependence introduces cold start issues for items lacking user engagement and poses challenges in adapting to non-stationary shifts in user behavior over time. We address both challenges holistically as an online learning problem and propose BayesCNS, a Bayesian approach designed to handle cold start and non-stationary distribution shifts in search systems at scale. BayesCNS achieves this by estimating prior distributions for user-item interactions, which are continuously updated with new user interactions gathered online. This online learning procedure is guided by a ranker model, enabling efficient exploration of relevant items using contextual information provided by the ranker. We successfully deployed BayesCNS in a large-scale search system and demonstrated its efficacy through comprehensive offline and online experiments. Notably, an online A/B experiment showed a 10.60% increase in new item interactions and a 1.05% improvement in overall success metrics over the existing production baseline.
Existing 3D facial emotion modeling have been constrained by limited emotion classes and insufficient datasets. This paper introduces "Emo3D", an extensive "Text-Image-Expression dataset" spanning a wide spectrum of human emotions, each paired with images and 3D blendshapes. Leveraging Large Language Models (LLMs), we generate a diverse array of textual descriptions, facilitating the capture of a broad spectrum of emotional expressions. Using this unique dataset, we conduct a comprehensive evaluation of language-based models' fine-tuning and vision-language models like Contranstive Language Image Pretraining (CLIP) for 3D facial expression synthesis. We also introduce a new evaluation metric for this task to more directly measure the conveyed emotion. Our new evaluation metric, Emo3D, demonstrates its superiority over Mean Squared Error (MSE) metrics in assessing visual-text alignment and semantic richness in 3D facial expressions associated with human emotions. "Emo3D" has great applications in animation design, virtual reality, and emotional human-computer interaction.
We introduce LogicAsker, a novel approach for evaluating and enhancing the logical reasoning capabilities of large language models (LLMs) such as ChatGPT and GPT-4. Despite LLMs' prowess in tasks like writing assistance, code generation, and machine translation, assessing their ability to reason has been challenging. Traditional evaluations often prioritize accuracy on downstream tasks over direct assessments of reasoning processes. LogicAsker addresses this gap by employing a set of atomic reasoning skills grounded in propositional and predicate logic to systematically examine and improve the reasoning prowess of LLMs. Our methodology reveals significant gaps in LLMs' learning of logical rules, with identified reasoning failures ranging from 29\% to 90\% across different models. Moreover, we leverage these findings to construct targeted demonstration examples and fine-tune data, notably enhancing logical reasoning in models like GPT-4o by up to 5\%. To our knowledge, this is the first effort to utilize test case outcomes to effectively refine LLMs' formal reasoning capabilities. We make our code, data, and results publicly available (//github.com/yxwan123/LogicAsker) to facilitate further research and replication of our findings.
This paper presents a control variate-based Markov chain Monte Carlo algorithm for efficient sampling from the probability simplex, with a focus on applications in large-scale Bayesian models such as latent Dirichlet allocation. Standard Markov chain Monte Carlo methods, particularly those based on Langevin diffusions, suffer from significant discretization errors near the boundaries of the simplex, which are exacerbated in sparse data settings. To address this issue, we propose an improved approach based on the stochastic Cox--Ingersoll--Ross process, which eliminates discretization errors and enables exact transition densities. Our key contribution is the integration of control variates, which significantly reduces the variance of the stochastic gradient estimator in the Cox--Ingersoll--Ross process, thereby enhancing the accuracy and computational efficiency of the algorithm. We provide a theoretical analysis showing the variance reduction achieved by the control variates approach and demonstrate the practical advantages of our method in data subsampling settings. Empirical results on large datasets show that the proposed method outperforms existing approaches in both accuracy and scalability.
We present CD-NGP, which is a fast and scalable representation for 3D reconstruction and novel view synthesis in dynamic scenes. Inspired by continual learning, our method first segments input videos into multiple chunks, followed by training the model chunk by chunk, and finally, fuses features of the first branch and subsequent branches. Experiments on the prevailing DyNeRF dataset demonstrate that our proposed novel representation reaches a great balance between memory consumption, model size, training speed, and rendering quality. Specifically, our method consumes $85\%$ less training memory ($<14$GB) than offline methods and requires significantly lower streaming bandwidth ($<0.4$MB/frame) than other online alternatives.
Diffusion models have revolted the field of text-to-image generation recently. The unique way of fusing text and image information contributes to their remarkable capability of generating highly text-related images. From another perspective, these generative models imply clues about the precise correlation between words and pixels. In this work, a simple but effective method is proposed to utilize the attention mechanism in the denoising network of text-to-image diffusion models. Without re-training nor inference-time optimization, the semantic grounding of phrases can be attained directly. We evaluate our method on Pascal VOC 2012 and Microsoft COCO 2014 under weakly-supervised semantic segmentation setting and our method achieves superior performance to prior methods. In addition, the acquired word-pixel correlation is found to be generalizable for the learned text embedding of customized generation methods, requiring only a few modifications. To validate our discovery, we introduce a new practical task called "personalized referring image segmentation" with a new dataset. Experiments in various situations demonstrate the advantages of our method compared to strong baselines on this task. In summary, our work reveals a novel way to extract the rich multi-modal knowledge hidden in diffusion models for segmentation.
This paper introduces a method for detecting vulnerabilities in smart contracts using static analysis and a multi-objective optimization algorithm. We focus on four types of vulnerabilities: reentrancy, call stack overflow, integer overflow, and timestamp dependencies. Initially, smart contracts are compiled into an abstract syntax tree to analyze relationships between contracts and functions, including calls, inheritance, and data flow. These analyses are transformed into static evaluations and intermediate representations that reveal internal relations. Based on these representations, we examine contract's functions, variables, and data dependencies to detect the specified vulnerabilities. To enhance detection accuracy and coverage, we apply a multi-objective optimization algorithm to the static analysis process. This involves assigning initial numeric values to input data and monitoring changes in statement coverage and detection accuracy. Using coverage and accuracy as fitness values, we calculate Pareto front and crowding distance values to select the best individuals for the new parent population, iterating until optimization criteria are met. We validate our approach using an open-source dataset collected from Etherscan, containing 6,693 smart contracts. Experimental results show that our method outperforms state-of-the-art tools in terms of coverage, accuracy, efficiency, and effectiveness in detecting the targeted vulnerabilities.
The advent of large language models marks a revolutionary breakthrough in artificial intelligence. With the unprecedented scale of training and model parameters, the capability of large language models has been dramatically improved, leading to human-like performances in understanding, language synthesizing, and common-sense reasoning, etc. Such a major leap-forward in general AI capacity will change the pattern of how personalization is conducted. For one thing, it will reform the way of interaction between humans and personalization systems. Instead of being a passive medium of information filtering, large language models present the foundation for active user engagement. On top of such a new foundation, user requests can be proactively explored, and user's required information can be delivered in a natural and explainable way. For another thing, it will also considerably expand the scope of personalization, making it grow from the sole function of collecting personalized information to the compound function of providing personalized services. By leveraging large language models as general-purpose interface, the personalization systems may compile user requests into plans, calls the functions of external tools to execute the plans, and integrate the tools' outputs to complete the end-to-end personalization tasks. Today, large language models are still being developed, whereas the application in personalization is largely unexplored. Therefore, we consider it to be the right time to review the challenges in personalization and the opportunities to address them with LLMs. In particular, we dedicate this perspective paper to the discussion of the following aspects: the development and challenges for the existing personalization system, the newly emerged capabilities of large language models, and the potential ways of making use of large language models for personalization.
We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.
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