arXiv subjects

Jing Yang

Publications and source records attributed to Jing Yang.

At least 181 records · Page 10Linked to original sources

arXiv2024

An Algorithm for Discriminating the Complete Multiplicities of a Parametric Univariate Polynomial

In this paper, we tackle the parametric complete multiplicity problem for a univariate polynomial. Our approach to the parametric complete multiplicity problem has a significant difference from the classical method, which relies on repeated gcd computation. Instead, we introduce a novel technique that uses incremental gcds of the given polynomial and its high-order derivatives. This approach, formulated as non-nested subresultants, sidesteps the exponential expansion of polynomial degrees in the generated condition. We also uncover the hidden structure between the incremental gcds and pseudo-remainders. Our analysis reveals that the conditions produced by our new algorithm are simpler than those generated by the classical approach in most cases. Experiments show that our algorithm is faster than the one based on repeated gcd computation for problems with relatively big size.

cs.SC↗

arXiv2024

RFPPO: Motion Dynamic RRT based Fluid Field - PPO for Dynamic TF/TA Routing Planning

Existing local dynamic route planning algorithms, when directly applied to terrain following/terrain avoidance, or dynamic obstacle avoidance for large and medium-sized fixed-wing aircraft, fail to simultaneously meet the requirements of real-time performance, long-distance planning, and the dynamic constraints of large and medium-sized aircraft. To deal with this issue, this paper proposes the Motion Dynamic RRT based Fluid Field - PPO for dynamic TF/TA routing planning. Firstly, the action and state spaces of the proximal policy gradient algorithm are redesigned using disturbance flow fields and artificial potential field algorithms, establishing an aircraft dynamics model, and designing a state transition process based on this model. Additionally, a reward function is designed to encourage strategies for obstacle avoidance, terrain following, terrain avoidance, and safe flight. Experimental results on real DEM data demonstrate that our algorithm can complete long-distance flight tasks through collision-free trajectory planning that complies with dynamic constraints, without the need for prior global planning.

cs.RO↗

arXiv2024

Acquisition of Spatially-Varying Reflectance and Surface Normals via Polarized Reflectance Fields

Accurately measuring the geometry and spatially-varying reflectance of real-world objects is a complex task due to their intricate shapes formed by concave features, hollow engravings and diverse surfaces, resulting in inter-reflection and occlusion when photographed. Moreover, issues like lens flare and overexposure can arise from interference from secondary reflections and limitations of hardware even in professional studios. In this paper, we propose a novel approach using polarized reflectance field capture and a comprehensive statistical analysis algorithm to obtain highly accurate surface normals (within 0.1mm/px) and spatially-varying reflectance data, including albedo, specular separation, roughness, and anisotropy parameters for realistic rendering and analysis. Our algorithm removes image artifacts via analytical modeling and further employs both an initial step and an optimization step computed on the whole image collection to further enhance the precision of per-pixel surface reflectance and normal measurement. We showcase the captured shapes and reflectance of diverse objects with a wide material range, spanning from highly diffuse to highly glossy - a challenge unaddressed by prior techniques. Our approach enhances downstream applications by offering precise measurements for realistic rendering and provides a valuable training dataset for emerging research in inverse rendering. We will release the polarized reflectance fields of several captured objects with this work.

cs.CV↗

arXiv2024

FedDW: Distilling Weights through Consistency Optimization in Heterogeneous Federated Learning

Federated Learning (FL) is an innovative distributed machine learning paradigm that enables neural network training across devices without centralizing data. While this addresses issues of information sharing and data privacy, challenges arise from data heterogeneity across clients and increasing network scale, leading to impacts on model performance and training efficiency. Previous research shows that in IID environments, the parameter structure of the model is expected to adhere to certain specific consistency principles. Thus, identifying and regularizing these consistencies can mitigate issues from heterogeneous data. We found that both soft labels derived from knowledge distillation and the classifier head parameter matrix, when multiplied by their own transpose, capture the intrinsic relationships between data classes. These shared relationships suggest inherent consistency. Therefore, the work in this paper identifies the consistency between the two and leverages it to regulate training, underpinning our proposed FedDW framework. Experimental results show FedDW outperforms 10 state-of-the-art FL methods, improving accuracy by an average of 3% in highly heterogeneous settings. Additionally, we provide a theoretical proof that FedDW offers higher efficiency, with the additional computational load from backpropagation being negligible. The code is available at https://github.com/liuvvvvv1/FedDW.

cs.LG↗

arXiv2024

Revisiting Generative Policies: A Simpler Reinforcement Learning Algorithmic Perspective

Generative models, particularly diffusion models, have achieved remarkable success in density estimation for multimodal data, drawing significant interest from the reinforcement learning (RL) community, especially in policy modeling in continuous action spaces. However, existing works exhibit significant variations in training schemes and RL optimization objectives, and some methods are only applicable to diffusion models. In this study, we compare and analyze various generative policy training and deployment techniques, identifying and validating effective designs for generative policy algorithms. Specifically, we revisit existing training objectives and classify them into two categories, each linked to a simpler approach. The first approach, Generative Model Policy Optimization (GMPO), employs a native advantage-weighted regression formulation as the training objective, which is significantly simpler than previous methods. The second approach, Generative Model Policy Gradient (GMPG), offers a numerically stable implementation of the native policy gradient method. We introduce a standardized experimental framework named GenerativeRL. Our experiments demonstrate that the proposed methods achieve state-of-the-art performance on various offline-RL datasets, offering a unified and practical guideline for training and deploying generative policies.

cs.LG↗

arXiv2024

Implication of nano-Hertz stochastic gravitational wave background on ultralight axion particles

Recently, the Hellings Downs correlation has been observed by different pulsar timing array (PTA) collaborations, such as NANOGrav, European PTA, Parkes PTA, and Chinese PTA. These PTA measurements of the most precise pulsars within the Milky Way show the first evidence for the stochastic gravitational wave background of our Universe. We study the ultralight axion interpretation of the new discovery by investigating the gravitational wave from axion transitions between different energy levels of the gravitational atoms, which are composed of cosmic populated Kerr black holes and their surrounding axion clouds formed through the superradiant process. By Bayesian analysis, we demonstrate that this new observation naturally admits an ultralight axion interpretation around $10^{-21}$eV, which is consistent in magnitude with the typical mass of fuzzy dark matter.

hep-ph↗

arXiv2024

Decision Feedback In-Context Symbol Detection over Block-Fading Channels

Pre-trained Transformers, through in-context learning (ICL), have demonstrated exceptional capabilities to adapt to new tasks using example prompts \textit{without model update}. Transformer-based wireless receivers, where prompts consist of the pilot data in the form of transmitted and received signal pairs, have shown high estimation accuracy when pilot data are abundant. However, pilot information is often costly and limited in practice. In this work, we propose the \underline{DE}cision \underline{F}eedback \underline{IN}-Cont\underline{E}xt \underline{D}etection (DEFINED) solution as a new wireless receiver design, which bypasses channel estimation and directly performs symbol detection using the (sometimes extremely) limited pilot data. The key innovation in DEFINED is the proposed decision feedback mechanism in ICL, where we sequentially incorporate the detected symbols into the prompts to improve the detections for subsequent symbols. Extensive experiments across a broad range of wireless communication settings demonstrate that DEFINED achieves significant performance improvements, in some cases only needing a single pilot pair.

cs.IT↗

arXiv2024

SPEA -- an analytical thermodynamic model for defect phase diagram

We propose an analytical thermodynamic model for describing defect phase transformations, which we term the statistical phase evaluation approach (SPEA). The SPEA model assumes a Boltzmann distribution of finite size phase fractions and calculates their statistical average. To benchmark the performance of the model, we apply it to construct binary surface phase diagrams of metal alloys. Two alloy systems are considered: a Mg surface with Ca substitutions and a Ni surface with Nb substitutions. To construct a firm basis against which the performance of the analytical model can be leveled, we first perform Monte Carlo (MC) simulations coupled with cluster expansion of density functional theory dataset. We then demonstrate the SPEA model to reproduce the MC results accurately. Specifically, it correctly predicts the surface order-disorder transitions as well as the coexistence of the 1/3 ordered phase and the disordered phase. Finally, we compare the SPEA method to the sublattice model commonly used in the CALPHAD approach to describe ordered and random solution phases and their transitions. The proposed SPEA model provides a highly efficient approach for modeling defect phase transformations.

cond-mat.mtrl-sci↗

arXiv2024

Multi-Type Preference Learning: Empowering Preference-Based Reinforcement Learning with Equal Preferences

Preference-Based reinforcement learning (PBRL) learns directly from the preferences of human teachers regarding agent behaviors without needing meticulously designed reward functions. However, existing PBRL methods often learn primarily from explicit preferences, neglecting the possibility that teachers may choose equal preferences. This neglect may hinder the understanding of the agent regarding the task perspective of the teacher, leading to the loss of important information. To address this issue, we introduce the Equal Preference Learning Task, which optimizes the neural network by promoting similar reward predictions when the behaviors of two agents are labeled as equal preferences. Building on this task, we propose a novel PBRL method, Multi-Type Preference Learning (MTPL), which allows simultaneous learning from equal preferences while leveraging existing methods for learning from explicit preferences. To validate our approach, we design experiments applying MTPL to four existing state-of-the-art baselines across ten locomotion and robotic manipulation tasks in the DeepMind Control Suite. The experimental results indicate that simultaneous learning from both equal and explicit preferences enables the PBRL method to more comprehensively understand the feedback from teachers, thereby enhancing feedback efficiency. Project page: \url{https://github.com/FeiCuiLengMMbb/paper_MTPL}

cs.LG↗

arXiv2024

Transformers as Game Players: Provable In-context Game-playing Capabilities of Pre-trained Models

The in-context learning (ICL) capability of pre-trained models based on the transformer architecture has received growing interest in recent years. While theoretical understanding has been obtained for ICL in reinforcement learning (RL), the previous results are largely confined to the single-agent setting. This work proposes to further explore the in-context learning capabilities of pre-trained transformer models in competitive multi-agent games, i.e., in-context game-playing (ICGP). Focusing on the classical two-player zero-sum games, theoretical guarantees are provided to demonstrate that pre-trained transformers can provably learn to approximate Nash equilibrium in an in-context manner for both decentralized and centralized learning settings. As a key part of the proof, constructional results are established to demonstrate that the transformer architecture is sufficiently rich to realize celebrated multi-agent game-playing algorithms, in particular, decentralized V-learning and centralized VI-ULCB.

stat.ML↗

arXiv2024

MGMapNet: Multi-Granularity Representation Learning for End-to-End Vectorized HD Map Construction

The construction of Vectorized High-Definition (HD) map typically requires capturing both category and geometry information of map elements. Current state-of-the-art methods often adopt solely either point-level or instance-level representation, overlooking the strong intrinsic relationships between points and instances. In this work, we propose a simple yet efficient framework named MGMapNet (Multi-Granularity Map Network) to model map element with a multi-granularity representation, integrating both coarse-grained instance-level and fine-grained point-level queries. Specifically, these two granularities of queries are generated from the multi-scale bird's eye view (BEV) features using a proposed Multi-Granularity Aggregator. In this module, instance-level query aggregates features over the entire scope covered by an instance, and the point-level query aggregates features locally. Furthermore, a Point Instance Interaction module is designed to encourage information exchange between instance-level and point-level queries. Experimental results demonstrate that the proposed MGMapNet achieves state-of-the-art performance, surpassing MapTRv2 by 5.3 mAP on nuScenes and 4.4 mAP on Argoverse2 respectively.

cs.CV↗

arXiv2024

Take It Easy: Label-Adaptive Self-Rationalization for Fact Verification and Explanation Generation

Computational methods to aid journalists in the task often require adapting a model to specific domains and generating explanations. However, most automated fact-checking methods rely on three-class datasets, which do not accurately reflect real-world misinformation. Moreover, fact-checking explanations are often generated based on text summarization of evidence, failing to address the relationship between the claim and the evidence. To address these issues, we extend the self-rationalization method--typically used in natural language inference (NLI) tasks--to fact verification. We propose a label-adaptive learning approach: first, we fine-tune a model to learn veracity prediction with annotated labels (step-1 model). Then, we fine-tune the step-1 model again to learn self-rationalization, using the same data and additional annotated explanations. Our results show that our label-adaptive approach improves veracity prediction by more than ten percentage points (Macro F1) on both the PubHealth and AVeriTec datasets, outperforming the GPT-4 model. Furthermore, to address the high cost of explanation annotation, we generated 64 synthetic explanations from three large language models: GPT-4-turbo, GPT-3.5-turbo, and Llama-3-8B and few-shot fine-tune our step-1 model. The few-shot synthetic explanation fine-tuned model performed comparably to the fully fine-tuned self-rationalization model, demonstrating the potential of low-budget learning with synthetic data. Our label-adaptive self-rationalization approach presents a promising direction for future research on real-world explainable fact-checking with different labeling schemes.

cs.CL↗

arXiv2024

Non-asymptotic Convergence of Training Transformers for Next-token Prediction

Transformers have achieved extraordinary success in modern machine learning due to their excellent ability to handle sequential data, especially in next-token prediction (NTP) tasks. However, the theoretical understanding of their performance in NTP is limited, with existing studies focusing mainly on asymptotic performance. This paper provides a fine-grained non-asymptotic analysis of the training dynamics of a one-layer transformer consisting of a self-attention module followed by a feed-forward layer. We first characterize the essential structural properties of training datasets for NTP using a mathematical framework based on partial orders. Then, we design a two-stage training algorithm, where the pre-processing stage for training the feed-forward layer and the main stage for training the attention layer exhibit fast convergence performance. Specifically, both layers converge sub-linearly to the direction of their corresponding max-margin solutions. We also show that the cross-entropy loss enjoys a linear convergence rate. Furthermore, we show that the trained transformer presents non-trivial prediction ability with dataset shift, which sheds light on the remarkable generalization performance of transformers. Our analysis technique involves the development of novel properties on the attention gradient and further in-depth analysis of how these properties contribute to the convergence of the training process. Our experiments further validate our theoretical findings.

cs.LG↗

arXiv2024

Federated Online Prediction from Experts with Differential Privacy: Separations and Regret Speed-ups

We study the problems of differentially private federated online prediction from experts against both stochastic adversaries and oblivious adversaries. We aim to minimize the average regret on $m$ clients working in parallel over time horizon $T$ with explicit differential privacy (DP) guarantees. With stochastic adversaries, we propose a Fed-DP-OPE-Stoch algorithm that achieves $\sqrt{m}$-fold speed-up of the per-client regret compared to the single-player counterparts under both pure DP and approximate DP constraints, while maintaining logarithmic communication costs. With oblivious adversaries, we establish non-trivial lower bounds indicating that collaboration among clients does not lead to regret speed-up with general oblivious adversaries. We then consider a special case of the oblivious adversaries setting, where there exists a low-loss expert. We design a new algorithm Fed-SVT and show that it achieves an $m$-fold regret speed-up under both pure DP and approximate DP constraints over the single-player counterparts. Our lower bound indicates that Fed-SVT is nearly optimal up to logarithmic factors. Experiments demonstrate the effectiveness of our proposed algorithms. To the best of our knowledge, this is the first work examining the differentially private online prediction from experts in the federated setting.

cs.LG↗

arXiv2024

A Generalization of Habicht's Theorem for Subresultants of Several Univariate Polynomials

Subresultants of two univariate polynomials are one of the most classic and ubiquitous objects in computational algebra and algebraic geometry. In 1948, Habicht discovered and proved interesting relationships among subresultants. Those relationships were found to be useful for both structural understanding and efficient computation. Often one needs to consider several (possibly more than two) polynomials. It is rather straightforward to generalize the notion of subresultants to several polynomials. However, it is not obvious (in fact, quite challenging) to generalize the Habicht's result to several polynomials. The main contribution of this paper is to provide such a generalization.

cs.SC↗

arXiv2024

Subresultants of Several Univariate Polynomials in Newton Basis

In this paper, we consider the problem of formulating the subresultant polynomials for several univariate polynomials in Newton basis. It is required that the resulting subresultant polynomials be expressed in the same Newton basis as that used in the input polynomials. To solve the problem, we devise a particular matrix with the help of the companion matrix of a polynomial in Newton basis. Meanwhile, the concept of determinantal polynomial in power basis for formulating subresultant polynomials is extended to that in Newton basis. It is proved that the generalized determinantal polynomial of the specially designed matrix provides a new formula for the subresultant polynomial in Newton basis, which is equivalent to the subresultant polynomial in power basis. Furthermore, we show an application of the new formula in devising a basis-preserving method for computing the gcd of several Newton polynomials.

cs.SC↗

arXiv2024

Computing greatest common divisor of several parametric univariate polynomials via generalized subresultant polynomials

In this paper, we tackle the following problem: compute the gcd for several univariate polynomials with parametric coefficients. It amounts to partitioning the parameter space into ``cells'' so that the gcd has a uniform expression over each cell and constructing a uniform expression of gcd in each cell. We tackle the problem as follows. We begin by making a natural and obvious extension of subresultant polynomials of two polynomials to several polynomials. Then we develop the following structural theories about them. 1. We generalize Sylvester's theory to several polynomials, in order to obtain an elegant relationship between generalized subresultant polynomials and the gcd of several polynomials, yielding an elegant algorithm. 2. We generalize Habicht's theory to several polynomials, in order to obtain a systematic relationship between generalized subresultant polynomials and pseudo-remainders, yielding an efficient algorithm. Using the generalized theories, we present a simple (structurally elegant) algorithm which is significantly more efficient (both in the output size and computing time) than algorithms based on previous approaches.

cs.SC↗

arXiv2024

CSR-dMRI: Continuous Super-Resolution of Diffusion MRI with Anatomical Structure-assisted Implicit Neural Representation Learning

Deep learning-based dMRI super-resolution methods can effectively enhance image resolution by leveraging the learning capabilities of neural networks on large datasets. However, these methods tend to learn a fixed scale mapping between low-resolution (LR) and high-resolution (HR) images, overlooking the need for radiologists to scale the images at arbitrary resolutions. Moreover, the pixel-wise loss in the image domain tends to generate over-smoothed results, losing fine textures and edge information. To address these issues, we propose a novel continuous super-resolution method for dMRI, called CSR-dMRI, which utilizes an anatomical structure-assisted implicit neural representation learning approach. Specifically, the CSR-dMRI model consists of two components. The first is the latent feature extractor, which primarily extracts latent space feature maps from LR dMRI and anatomical images while learning structural prior information from the anatomical images. The second is the implicit function network, which utilizes voxel coordinates and latent feature vectors to generate voxel intensities at corresponding positions. Additionally, a frequency-domain-based loss is introduced to preserve the structural and texture information, further enhancing the image quality. Extensive experiments on the publicly available HCP dataset validate the effectiveness of our approach. Furthermore, our method demonstrates superior generalization capability and can be applied to arbitrary-scale super-resolution, including non-integer scale factors, expanding its applicability beyond conventional approaches.

eess.IV↗