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Yang Tian

Publications and source records attributed to Yang Tian.

At least 73 records · Page 4Linked to original sources
arXiv2024

Simplex path integral and simplex renormalization group for high-order interactions

Modern theories of phase transitions and scale-invariance are rooted in path integral formulation and renormalization group (RG). Despite the applicability of these approaches on simple systems with only pairwise interactions, they are less effective on complex systems with un-decomposable high-order interactions (i.e., interactions among arbitrary sets of units). To precisely characterize the universality of high-order interacting systems, we propose simplex path integral and simplex renormalization group (SRG) as the generalizations of classic approaches to arbitrary high-order and heterogeneous interactions. We first formalize the trajectories of units governed by high-order interactions to define path integrals on corresponding simplices based on a high-order propagator. Then we develop a method to integrate out short-range high-order interactions in the momentum space, accompanied by a coarse graining procedure functioning on the simplex structure generated by high-order interactions. The proposed SRG, equipped with a divide-and-conquer framework, can deal with the absence of ergodicity arised from the sparse distribution of high-order interactions and renormalize a system with intertwined high-order interactions on the $p$-order according to its properties on the $q$-order ($p\leq q$). The associated scaling relation and its corollaries support to differentiate among scale-invariant, weakly scale-invariant, and scale-dependent systems across different orders. We have validated our theory in multi-order scale-invariance verification, topological invariance discovery, organizational structure identification, and information bottleneck analysis. These experiments demonstrate the capacity of our theory for identifying intrinsic statistical and topological properties of high-order interacting systems during system reduction.

cond-mat.stat-mech↗
arXiv2024

Koopman neural operator as a mesh-free solver of non-linear partial differential equations

The lacking of analytic solutions of diverse partial differential equations (PDEs) gives birth to a series of computational techniques for numerical solutions. Although numerous latest advances are accomplished in developing neural operators, a kind of neural-network-based PDE solver, these solvers become less accurate and explainable while learning long-term behaviors of non-linear PDE families. In this paper, we propose the Koopman neural operator (KNO), a new neural operator, to overcome these challenges. With the same objective of learning an infinite-dimensional mapping between Banach spaces that serves as the solution operator of the target PDE family, our approach differs from existing models by formulating a non-linear dynamic system of equation solution. By approximating the Koopman operator, an infinite-dimensional operator governing all possible observations of the dynamic system, to act on the flow mapping of the dynamic system, we can equivalently learn the solution of a non-linear PDE family by solving simple linear prediction problems. We validate the KNO in mesh-independent, long-term, and5zero-shot predictions on five representative PDEs (e.g., the Navier-Stokes equation and the Rayleigh-B{é}nard convection) and three real dynamic systems (e.g., global water vapor patterns and western boundary currents). In these experiments, the KNO exhibits notable advantages compared with previous state-of-the-art models, suggesting the potential of the KNO in supporting diverse science and engineering applications (e.g., PDE solving, turbulence modelling, and precipitation forecasting).

cs.LG↗
arXiv2024

RoboKeyGen: Robot Pose and Joint Angles Estimation via Diffusion-based 3D Keypoint Generation

Estimating robot pose and joint angles is significant in advanced robotics, enabling applications like robot collaboration and online hand-eye calibration.However, the introduction of unknown joint angles makes prediction more complex than simple robot pose estimation, due to its higher dimensionality.Previous methods either regress 3D keypoints directly or utilise a render&compare strategy. These approaches often falter in terms of performance or efficiency and grapple with the cross-camera gap problem.This paper presents a novel framework that bifurcates the high-dimensional prediction task into two manageable subtasks: 2D keypoints detection and lifting 2D keypoints to 3D. This separation promises enhanced performance without sacrificing the efficiency innate to keypoint-based techniques.A vital component of our method is the lifting of 2D keypoints to 3D keypoints. Common deterministic regression methods may falter when faced with uncertainties from 2D detection errors or self-occlusions.Leveraging the robust modeling potential of diffusion models, we reframe this issue as a conditional 3D keypoints generation task. To bolster cross-camera adaptability, we introduce theNormalised Camera Coordinate Space (NCCS), ensuring alignment of estimated 2D keypoints across varying camera intrinsics.Experimental results demonstrate that the proposed method outperforms the state-of-the-art render\&compare method and achieves higher inference speed.Furthermore, the tests accentuate our method's robust cross-camera generalisation capabilities.We intend to release both the dataset and code in https://nimolty.github.io/Robokeygen/

cs.RO↗
arXiv2024

Fast renormalizing the structures and dynamics of ultra-large systems via random renormalization group

Criticality and symmetry, studied by the renormalization groups, lie at the heart of modern physics theories of matters and complex systems. However, surveying these properties with massive experimental data is bottlenecked by the intolerable costs of computing renormalization groups on real systems. Here, we develop a time- and memory-efficient framework, termed as the random renormalization group, for renormalizing ultra-large systems (e.g., with millions of units) within minutes. This framework is based on random projections, hashing techniques, and kernel representations, which support the renormalization governed by linear and non-linear correlations. For system structures, it exploits the correlations among local topology in kernel spaces to unfold the connectivity of units, identify intrinsic system scales, and verify the existences of symmetries under scale transformation. For system dynamics, it renormalizes units into correlated clusters to analyze scaling behaviours, validate scaling relations, and investigate potential criticality. Benefiting from hashing-function-based designs, our framework significantly reduces computational complexity compared with classic renormalization groups, realizing a single-step acceleration of two orders of magnitude. Meanwhile, the efficient representation of different kinds of correlations in kernel spaces realized by random projections ensures the capacity of our framework to capture diverse unit relations. As shown by our experiments, the random renormalization group helps identify non-equilibrium phase transitions, criticality, and symmetry in diverse large-scale genetic, neural, material, social, and cosmological systems.

cond-mat.stat-mech↗
arXiv2023

GLIME: General, Stable and Local LIME Explanation

As black-box machine learning models grow in complexity and find applications in high-stakes scenarios, it is imperative to provide explanations for their predictions. Although Local Interpretable Model-agnostic Explanations (LIME) [22] is a widely adpoted method for understanding model behaviors, it is unstable with respect to random seeds [35,24,3] and exhibits low local fidelity (i.e., how well the explanation approximates the model's local behaviors) [21,16]. Our study shows that this instability problem stems from small sample weights, leading to the dominance of regularization and slow convergence. Additionally, LIME's sampling neighborhood is non-local and biased towards the reference, resulting in poor local fidelity and sensitivity to reference choice. To tackle these challenges, we introduce GLIME, an enhanced framework extending LIME and unifying several prior methods. Within the GLIME framework, we derive an equivalent formulation of LIME that achieves significantly faster convergence and improved stability. By employing a local and unbiased sampling distribution, GLIME generates explanations with higher local fidelity compared to LIME. GLIME explanations are independent of reference choice. Moreover, GLIME offers users the flexibility to choose a sampling distribution based on their specific scenarios.

cs.LG↗
arXiv2023

Thermodynamics of percolation in interacting systems

Interacting systems can be studied as the networks where nodes are system units and edges denote correlated interactions. Although percolation on network is a unified way to model the emergence and propagation of correlated behaviours, it remains unknown how the dynamics characterized by percolation is related to the thermodynamics of phase transitions. It is non-trivial to formalize thermodynamics for most complex systems, not to mention calculating thermodynamic quantities and verifying scaling relations during percolation. In this work, we develop a formalism to quantify the thermodynamics of percolation in interacting systems, which is rooted in a discovery that percolation transition is a process for the system to lose the freedom degrees associated with ground state configurations. We derive asymptotic formulas to accurately calculate entropy and specific heat under our framework, which enables us to detect phase transitions and demonstrate the Rushbrooke equality (i.e., $α+2β+γ=2$) in six representative complex systems (e.g., Bernoulli and bootstrap percolation, classical and quantum synchronization, non-linear oscillations with damping, and cellular morphogenesis). These results suggest the general applicability of our framework in analyzing diverse interacting systems and percolation processes.

cond-mat.stat-mech↗
arXiv2023

OriWheelBot: An origami-wheeled robot

Origami-inspired robots with multiple advantages, such as being lightweight, requiring less assembly, and exhibiting exceptional deformability, have received substantial and sustained attention. However, the existing origami-inspired robots are usually of limited functionalities and developing feature-rich robots is very challenging. Here, we report an origami-wheeled robot (OriWheelBot) with variable width and outstanding sand walking versatility. The OriWheelBot's ability to adjust wheel width over obstacles is achieved by origami wheels made of Miura origami. An improved version, called iOriWheelBot, is also developed to automatically judge the width of the obstacles. Three actions, namely direct pass, variable width pass, and direct return, will be carried out depending on the width of the channel between the obstacles. We have identified two motion mechanisms, i.e., sand-digging and sand-pushing, with the latter being more conducive to walking on the sand. We have systematically examined numerous sand walking characteristics, including carrying loads, climbing a slope, walking on a slope, and navigating sand pits, small rocks, and sand traps. The OriWheelBot can change its width by 40%, has a loading-carrying ratio of 66.7% on flat sand and can climb a 17-degree sand incline. The OriWheelBot can be useful for planetary subsurface exploration and disaster area rescue.

cs.RO↗
arXiv2023

Network comparison via encoding, decoding, and causality

Quantifying the relations (e.g., similarity) between complex networks paves the way for studying the latent information shared across networks. However, fundamental relation metrics are not well-defined between networks. As a compromise, prevalent techniques measure network relations in data-driven manners, which are inapplicable to analytic derivations in physics. To resolve this issue, we present a theory for obtaining an optimal characterization of network topological properties. We show that a network can be fully represented by a Gaussian variable defined by a function of the Laplacian, which simultaneously satisfies network-topology-dependent smoothness and maximum entropy properties. Based on it, we can analytically measure diverse relations between complex networks. As illustrations, we define encoding (e.g., information divergence and mutual information), decoding (e.g., Fisher information), and causality (e.g., Granger causality and conditional mutual information) between networks. We validate our framework on representative networks (e.g., random networks, protein structures, and chemical compounds) to demonstrate that a series of science and engineering challenges (e.g., network evolution, embedding, and query) can be tackled from a new perspective. An implementation of our theory is released as a multi-platform toolbox.

cs.SI↗
arXiv2023

Theoretical foundations of studying criticality in the brain

Criticality is hypothesized as a physical mechanism underlying efficient transitions between cortical states and remarkable information processing capacities in the brain. While considerable evidence generally supports this hypothesis, non-negligible controversies persist regarding the ubiquity of criticality in neural dynamics and its role in information processing. Validity issues frequently arise during identifying potential brain criticality from empirical data. Moreover, the functional benefits implied by brain criticality are frequently misconceived or unduly generalized. These problems stem from the non-triviality and immaturity of the physical theories that analytically derive brain criticality and the statistic techniques that estimate brain criticality from empirical data. To help solve these problems, we present a systematic review and reformulate the foundations of studying brain criticality, i.e., ordinary criticality (OC), quasi-criticality (qC), self-organized criticality (SOC), and self-organized quasi-criticality (SOqC), using the terminology of neuroscience. We offer accessible explanations of the physical theories and statistic techniques of brain criticality, providing step-by-step derivations to characterize neural dynamics as a physical system with avalanches. We summarize error-prone details and existing limitations in brain criticality analysis and suggest possible solutions. Moreover, we present a forward-looking perspective on how optimizing the foundations of studying brain criticality can deepen our understanding of various neuroscience questions.

q-bio.NC↗
arXiv2023

Laplacian dynamics of convergent and divergent swarm behaviors

Swarming phenomena are ubiquitous in various physical, biological, and social systems, where simple local interactions between individual units lead to complex global patterns. A common feature of diverse swarming phenomena is that the units exhibit either convergent or divergent evolution in their behaviors, i.e., becoming increasingly similar or distinct, respectively. The associated dynamics changes across time, leading to complex consequences on a global scale. In this study, we propose a generalized Laplacian dynamics model to describe both convergent and divergent swarm behaviors, where the trends of convergence and divergence compete with each other and jointly determine the evolution of global patterns. We empirically observe non-trivial phase-transition-like phenomena between the convergent and divergent evolution phases, which are controlled by local interaction properties. We also propose a conjecture regarding the underlying phase transition mechanisms and outline the main theoretical difficulties for testing this conjecture. Overall, our framework may serve as a minimal model of swarm behaviors and their intricate phase transition dynamics.

cond-mat.stat-mech↗
arXiv2023

KoopmanLab: machine learning for solving complex physics equations

Numerous physics theories are rooted in partial differential equations (PDEs). However, the increasingly intricate physics equations, especially those that lack analytic solutions or closed forms, have impeded the further development of physics. Computationally solving PDEs by classic numerical approaches suffers from the trade-off between accuracy and efficiency and is not applicable to the empirical data generated by unknown latent PDEs. To overcome this challenge, we present KoopmanLab, an efficient module of the Koopman neural operator family, for learning PDEs without analytic solutions or closed forms. Our module consists of multiple variants of the Koopman neural operator (KNO), a kind of mesh-independent neural-network-based PDE solvers developed following dynamic system theory. The compact variants of KNO can accurately solve PDEs with small model sizes while the large variants of KNO are more competitive in predicting highly complicated dynamic systems govern by unknown, high-dimensional, and non-linear PDEs. All variants are validated by mesh-independent and long-term prediction experiments implemented on representative PDEs (e.g., the Navier-Stokes equation and the Bateman-Burgers equation in fluid mechanics) and ERA5 (i.e., one of the largest high-resolution global-scale climate data sets in earth physics). These demonstrations suggest the potential of KoopmanLab to be a fundamental tool in diverse physics studies related to equations or dynamic systems.

cs.LG↗
arXiv2022

Video Interpolation by Event-driven Anisotropic Adjustment of Optical Flow

Video frame interpolation is a challenging task due to the ever-changing real-world scene. Previous methods often calculate the bi-directional optical flows and then predict the intermediate optical flows under the linear motion assumptions, leading to isotropic intermediate flow generation. Follow-up research obtained anisotropic adjustment through estimated higher-order motion information with extra frames. Based on the motion assumptions, their methods are hard to model the complicated motion in real scenes. In this paper, we propose an end-to-end training method A^2OF for video frame interpolation with event-driven Anisotropic Adjustment of Optical Flows. Specifically, we use events to generate optical flow distribution masks for the intermediate optical flow, which can model the complicated motion between two frames. Our proposed method outperforms the previous methods in video frame interpolation, taking supervised event-based video interpolation to a higher stage.

cs.CV↗
arXiv2022

Statistical Physics of Deep Neural Networks: Initialization toward Optimal Channels

In deep learning, neural networks serve as noisy channels between input data and its representation. This perspective naturally relates deep learning with the pursuit of constructing channels with optimal performance in information transmission and representation. While considerable efforts are concentrated on realizing optimal channel properties during network optimization, we study a frequently overlooked possibility that neural networks can be initialized toward optimal channels. Our theory, consistent with experimental validation, identifies primary mechanics underlying this unknown possibility and suggests intrinsic connections between statistical physics and deep learning. Unlike the conventional theories that characterize neural networks applying the classic mean-filed approximation, we offer analytic proof that this extensively applied simplification scheme is not valid in studying neural networks as information channels. To fill this gap, we develop a corrected mean-field framework applicable for characterizing the limiting behaviors of information propagation in neural networks without strong assumptions on inputs. Based on it, we propose an analytic theory to prove that mutual information maximization is realized between inputs and propagated signals when neural networks are initialized at dynamic isometry, a case where information transmits via norm-preserving mappings. These theoretical predictions are validated by experiments on real neural networks, suggesting the robustness of our theory against finite-size effects. Finally, we analyze our findings with information bottleneck theory to confirm the precise relations among dynamic isometry, mutual information maximization, and optimal channel properties in deep learning.

cs.LG↗
arXiv2022

A feasibility study of multi-electrode high-purity germanium detector for Ge-76 neutrinoless double beta decay searching

Experiments to search for neutrinoless double-beta (0ν\b{eta}\b{eta}) decay of 76Ge using a high-purity germanium (HPGe) detector rely heavily on background suppression technologies to enhance their sensitivities. In this work, we proposed a pulse-shape analysis method based on a neural network (NN) and a light gradient boosting machine (lightGBM; LGB) to discriminate single-electron (background) and double-electrons (0ν\b{eta}\b{eta} signal) events in a multi-electrode HPGe detector. In this paper, we describe a multi-electrode HPGe detector system, a data-processing system, and pulse-shape simulation procedures. We built a fully connected (FC) neural network and an LGB model to classify the single- and double-electron events. The FC network is trained with simulated single- and double-electron-induced pulses and tested in an independent dataset generated by the pulse-shape simulation. The discrimination efficiency of the FC neural network in the test set for the 0ν\b{eta}\b{eta} double-electron events signal was 77.4%, the precision was 57.7%, and the training time was 430 min. The discrimination efficiency of LGB model was 73.1%, the precision was 64.0%, and the training time was 1.5 min. This study demonstrated that it is feasible to realize single- and double-electron discrimination on multi-electrode HPGe detectors using an FC neural network and LGB model. These results can be used as a reference for future 76Ge 0ν\b{eta}\b{eta} experiments.

physics.ins-det↗
arXiv2022

In-orbit Radiation Damage Characterization of SiPMs in the GRID-02 CubeSat Detector

Recently, silicon photomultipliers (SiPMs) have been used in several space-borne missions, owing to their solid state, compact size, low operating voltage, and insensitivity to magnetic fields. However, operating SiPMs in space results in radiation damage and degraded performance. In-orbit quantitative studies on these effects are limited. In this study, we present in-orbit SiPM characterization results obtained by the second detector of the Gamma-Ray Integrated Detectors (GRID-02), which was launched on 6 November 2020. An increase in dark current of $\sim$100 $μ$A/year per SiPM chip (model MicroFJ-60035-TSV) at 28.5 V and 5 $^{\circ}$C was observed. Consequently, the overall noise level (sigma) of the GRID-02 detector increased by $\sim$7.5 keV/year. The estimate of this increase is $\sim$40 $μ$A/year per SiPM chip at -20 $^{\circ}$C, highlighting the positive effect of using a cooling system.

physics.ins-det↗
arXiv2022

Bridging the information and dynamics attributes of neural activities

The brain works as a dynamic system to process information. Various challenges remain in understanding the connection between information and dynamics attributes in the brain. The present research pursues exploring how the characteristics of neural information functions are linked to neural dynamics. We attempt to bridge dynamics (e.g., Kolmogorov-Sinai entropy) and information (e.g., mutual information and Fisher information) metrics on the stimulus-triggered stochastic dynamics in neural populations. On the one hand, our unified analysis identifies various essential features of the information-processing-related neural dynamics. We discover spatiotemporal differences in the dynamic randomness and chaotic degrees of neural dynamics during neural information processing. On the other hand, our framework reveals the fundamental role of neural dynamics in shaping neural information processing. The neural dynamics creates an oppositely directed variation of encoding and decoding properties under specific conditions, and it determines the neural representation of stimulus distribution. Overall, our findings demonstrate a potential direction to explain the emergence of neural information processing from neural dynamics and help understand the intrinsic connections between the informational and the physical brain.

q-bio.NC↗
arXiv2022

Resilience in Industrial Internet of Things Systems: A Communication Perspective

Industrial Internet of Things is an ultra-large-scale system that is much more sophisticated and fragile than conventional industrial platforms. The effective management of such a system relies heavily on the resilience of the network, especially the communication part. Imperative as resilient communication is, there is not enough attention from literature and a standardized framework is still missing. In awareness of these, this paper intends to provide a systematic overview of resilience in IIoT with a communication perspective, aiming to answer the questions of why we need it, what it is, how to enhance it, and where it can be applied. Specifically, we emphasize the urgency of resilience studies via examining existing literature and analyzing malfunction data from a real satellite communication system. Resilience-related concepts and metrics, together with standardization efforts are then summarized and discussed, presenting a basic framework for analyzing the resilience of the system before, during, and after disruptive events. On the basis of the framework, key resilience concerns associated with the design, deployment, and operation of IIoT are briefly described to shed light on the methods for resilience enhancement. Promising resilient applications in different IIoT sectors are also introduced to highlight the opportunities and challenges in practical implementations.

eess.SY↗