arXiv subjects

Tiejun Li

Publications and source records attributed to Tiejun Li.

At least 37 records · Page 2Linked to original sources

arXiv2025

Variational Regularized Unbalanced Optimal Transport: Single Network, Least Action

Recovering the dynamics from a few snapshots of a high-dimensional system is a challenging task in statistical physics and machine learning, with important applications in computational biology. Many algorithms have been developed to tackle this problem, based on frameworks such as optimal transport and the Schrödinger bridge. A notable recent framework is Regularized Unbalanced Optimal Transport (RUOT), which integrates both stochastic dynamics and unnormalized distributions. However, since many existing methods do not explicitly enforce optimality conditions, their solutions often struggle to satisfy the principle of least action and meet challenges to converge in a stable and reliable way. To address these issues, we propose Variational RUOT (Var-RUOT), a new framework to solve the RUOT problem. By incorporating the optimal necessary conditions for the RUOT problem into both the parameterization of the search space and the loss function design, Var-RUOT only needs to learn a scalar field to solve the RUOT problem and can search for solutions with lower action. We also examined the challenge of selecting a growth penalty function in the widely used Wasserstein-Fisher-Rao metric and proposed a solution that better aligns with biological priors in Var-RUOT. We validated the effectiveness of Var-RUOT on both simulated data and real single-cell datasets. Compared with existing algorithms, Var-RUOT can find solutions with lower action while exhibiting faster convergence and improved training stability. Our code is available at https://github.com/ZerooVector/VarRUOT.

cs.LG↗

arXiv2025

Spin-NeuroMem: A Low-Power Neuromorphic Associative Memory Design Based on Spintronic Devices

Biologically-inspired computing models have made significant progress in recent years, but the conventional von Neumann architecture is inefficient for the large-scale matrix operations and massive parallelism required by these models. This paper presents Spin-NeuroMem, a low-power circuit design of Hopfield network for the function of associative memory. Spin-NeuroMem is equipped with energy-efficient spintronic synapses which utilize magnetic tunnel junctions (MTJs) to store weight matrices of multiple associative memories. The proposed synapse design achieves as low as 17.4% power consumption compared to the state-of-the-art synapse designs. Spin-NeuroMem also encompasses a novel voltage converter with a 53.3% reduction in transistor usage for effective Hopfield network computation. In addition, we propose an associative memory simulator for the first time, which achieves a 5Mx speedup with a comparable associative memory effect. By harnessing the potential of spintronic devices, this work paves the way for the development of energy-efficient and scalable neuromorphic computing systems.

cs.AR↗

arXiv2025

NeuroPDE: A Neuromorphic PDE Solver Based on Spintronic and Ferroelectric Devices

In recent years, new methods for solving partial differential equations (PDEs) such as Monte Carlo random walk methods have gained considerable attention. However, due to the lack of hardware-intrinsic randomness in the conventional von Neumann architecture, the performance of PDE solvers is limited. In this paper, we introduce NeuroPDE, a hardware design for neuromorphic PDE solvers that utilizes emerging spintronic and ferroelectric devices. NeuroPDE incorporates spin neurons that are capable of probabilistic transmission to emulate random walks, along with ferroelectric synapses that store continuous weights non-volatilely. The proposed NeuroPDE achieves a variance of less than 1e-2 compared to analytical solutions when solving diffusion equations, demonstrating a performance advantage of 3.48x to 315x speedup in execution time and an energy consumption advantage of 2.7x to 29.8x over advanced CMOS-based neuromorphic chips. By leveraging the inherent physical stochasticity of emerging devices, this study paves the way for future probabilistic neuromorphic computing systems.

cs.AR↗

arXiv2025

Learning stochastic dynamics from snapshots through regularized unbalanced optimal transport

Reconstructing dynamics using samples from sparsely time-resolved snapshots is an important problem in both natural sciences and machine learning. Here, we introduce a new deep learning approach for solving regularized unbalanced optimal transport (RUOT) and inferring continuous unbalanced stochastic dynamics from observed snapshots. Based on the RUOT form, our method models these dynamics without requiring prior knowledge of growth and death processes or additional information, allowing them to be learned directly from data. Theoretically, we explore the connections between the RUOT and Schrödinger bridge problem and discuss the key challenges and potential solutions. The effectiveness of our method is demonstrated with a synthetic gene regulatory network, high-dimensional Gaussian Mixture Model, and single-cell RNA-seq data from blood development. Compared with other methods, our approach accurately identifies growth and transition patterns, eliminates false transitions, and constructs the Waddington developmental landscape. Our code is available at: https://github.com/zhenyiizhang/DeepRUOT.

cs.LG↗

arXiv2025

Integrating Dynamical Systems Modeling with Spatiotemporal scRNA-seq Data Analysis

Understanding the dynamic nature of biological systems is fundamental to deciphering cellular behavior, developmental processes, and disease progression. Single-cell RNA sequencing (scRNA-seq) has provided static snapshots of gene expression, offering valuable insights into cellular states at a single time point. Recent advancements in temporally resolved scRNA-seq, spatial transcriptomics (ST), and time-series spatial transcriptomics (temporal-ST) have further revolutionized our ability to study the spatiotemporal dynamics of individual cells. These technologies, when combined with computational frameworks such as Markov chains, stochastic differential equations (SDEs), and generative models like optimal transport and Schrödinger bridges, enable the reconstruction of dynamic cellular trajectories and cell fate decisions. This review discusses how these dynamical system approaches offer new opportunities to model and infer cellular dynamics from a systematic perspective.

q-bio.QM↗

arXiv2024

Quasi-Newton OMP Approach for Super-Resolution Channel Estimation and Extrapolation

Channel estimation and extrapolation are fundamental issues in MIMO communication systems. In this paper, we proposed the quasi-Newton orthogonal matching pursuit (QNOMP) approach to overcome these issues with high efficiency while maintaining accuracy. The algorithm consists of two stages on the super-resolution recovery: we first performed a cheap on-grid OMP estimation of channel parameters in the sparsity domain (e.g., delay or angle), then an off-grid optimization to achieve the super-resolution. In the off-grid stage, we employed the BFGS quasi-Newton method to jointly estimate the parameters through a multipath model, which improved the speed and accuracy significantly. Furthermore, we derived the optimal extrapolated solution in the linear minimum mean squared estimator criterion, revealed its connection with Slepian basis, and presented a practical algorithm to realize the extrapolation based on the QNOMP results. Special treatment utilizing the block sparsity nature of the considered channels was also proposed. Numerical experiments on the simulated models and CDL-C channels demonstrated the high performance and low computational complexity of QNOMP.

eess.SP↗

arXiv2024

DMRA: An Adaptive Line Spectrum Estimation Method through Dynamical Multi-Resolution of Atoms

We proposed a novel dense line spectrum super-resolution algorithm, the DMRA, that leverages dynamical multi-resolution of atoms technique to address the limitation of traditional compressed sensing methods when handling dense point-source signals. The algorithm utilizes a smooth $\tanh$ relaxation function to replace the $\ell_0$ norm, promoting sparsity and jointly estimating the frequency atoms and complex gains. To reduce computational complexity and improve frequency estimation accuracy, a two-stage strategy was further introduced to dynamically adjust the number of the optimized degrees of freedom. The strategy first increases candidate frequencies through local refinement, then applies a sparse selector to eliminate insignificant frequencies, thereby adaptively adjusting the degrees of freedom to improve estimation accuracy. Theoretical analysis were provided to validate the proposed method for multi-parameter estimations. Computational results demonstrated that this algorithm achieves good super-resolution performance in various practical scenarios and outperforms the state-of-the-art methods in terms of frequency estimation accuracy and computational efficiency.

eess.SP↗

arXiv2024

RHS-TRNG: A Resilient High-Speed True Random Number Generator Based on STT-MTJ Device

High-quality random numbers are very critical to many fields such as cryptography, finance, and scientific simulation, which calls for the design of reliable true random number generators (TRNGs). Limited by entropy source, throughput, reliability, and system integration, existing TRNG designs are difficult to be deployed in real computing systems to greatly accelerate target applications. This study proposes a TRNG circuit named RHS-TRNG based on spin-transfer torque magnetic tunnel junction (STT-MTJ). RHS-TRNG generates resilient and high-speed random bit sequences exploiting the stochastic switching characteristics of STT-MTJ. By circuit/system co-design, we integrate RHS-TRNG into a RISC-V processor as an acceleration component, which is driven by customized random number generation instructions. Our experimental results show that a single cell of RHS-TRNG has a random bit generation speed of up to 303 Mb/s, which is the highest among existing MTJ-based TRNGs. Higher throughput can be achieved by exploiting cell-level parallelism. RHS-TRNG also shows strong resilience against PVT variations thanks to our designs using bidirectional switching currents and dual generator units. In addition, our system evaluation results using gem5 simulator suggest that the system equipped with RHS-TRNG can achieve 3.4-12x higher performance in speeding up option pricing programs than software implementations of random number generation.

cs.AR↗

arXiv2024

EPR-Net: Constructing non-equilibrium potential landscape via a variational force projection formulation

We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state (NESS) systems. EPR-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product space. Remarkably, our loss function has an intimate connection with the steady entropy production rate (EPR), enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness, and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an 8D limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics.

physics.bio-ph↗

arXiv2023

Revisiting the central limit theorems for the SGD-type methods

We revisited the central limit theorem (CLT) for stochastic gradient descent (SGD) type methods, including the vanilla SGD, momentum SGD and Nesterov accelerated SGD methods with constant or vanishing damping parameters. By taking advantage of Lyapunov function technique and $L^p$ bound estimates, we established the CLT under more general conditions on learning rates for broader classes of SGD methods compared with previous results. The CLT for the time average was also investigated, and we found that it held in the linear case, while it was not generally true in nonlinear situation. Numerical tests were also carried out to verify our theoretical analysis.

math.OC↗

arXiv2023

On the Mathematics of RNA Velocity II: Algorithmic Aspects

In a previous paper [CSIAM Trans. Appl. Math. 2 (2021), 1-55], the authors proposed a theoretical framework for the analysis of RNA velocity, which is a promising concept in scRNA-seq data analysis to reveal the cell state-transition dynamical processes underlying snapshot data. The current paper is devoted to the algorithmic study of some key components in RNA velocity workflow. Four important points are addressed in this paper: (1) We construct a rational time-scale fixation method which can determine the global gene-shared latent time for cells. (2) We present an uncertainty quantification strategy for the inferred parameters obtained through the EM algorithm. (3) We establish the optimal criterion for the choice of velocity kernel bandwidth with respect to the sample size in the downstream analysis and discuss its implications. (4) We propose a temporal distance estimation approach between two cell clusters along the cellular development path. Some illustrative numerical tests are also carried out to verify our analysis. These results are intended to provide tools and insights in further development of RNA velocity type methods in the future.

math.NA↗

arXiv2022

Intrinsically Motivated Self-supervised Learning in Reinforcement Learning

In vision-based reinforcement learning (RL) tasks, it is prevalent to assign auxiliary tasks with a surrogate self-supervised loss so as to obtain more semantic representations and improve sample efficiency. However, abundant information in self-supervised auxiliary tasks has been disregarded, since the representation learning part and the decision-making part are separated. To sufficiently utilize information in auxiliary tasks, we present a simple yet effective idea to employ self-supervised loss as an intrinsic reward, called Intrinsically Motivated Self-Supervised learning in Reinforcement learning (IM-SSR). We formally show that the self-supervised loss can be decomposed as exploration for novel states and robustness improvement from nuisance elimination. IM-SSR can be effortlessly plugged into any reinforcement learning with self-supervised auxiliary objectives with nearly no additional cost. Combined with IM-SSR, the previous underlying algorithms achieve salient improvements on both sample efficiency and generalization in various vision-based robotics tasks from the DeepMind Control Suite, especially when the reward signal is sparse.

cs.LG↗

arXiv2022

Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks

In this paper, we consider the eigenvalue PDE problem of the infinitesimal generators of metastable diffusion processes. We propose a numerical algorithm based on training artificial neural networks for solving the leading eigenvalues and eigenfunctions of such high-dimensional eigenvalue problem. The algorithm is able to find multiple leading eigenpairs by solving a single training task. It is useful in understanding the dynamical behaviors of metastable processes on large timescales. We demonstrate the capability of our algorithm on a high-dimensional model problem, and on the simple molecular system alanine dipeptide.

math.OC↗

arXiv2021

Transition path theory for Langevin dynamics on manifold: optimal control and data-driven solver

We present a data-driven point of view for rare events, which represent conformational transitions in biochemical reactions modeled by over-damped Langevin dynamics on manifolds in high dimensions. We first reinterpret the transition state theory and the transition path theory from the optimal control viewpoint. Given point clouds sampled from a reaction dynamics, we construct a discrete Markov process based on an approximated Voronoi tesselation. We use the constructed Markov process to compute a discrete committor function whose level set automatically orders the point clouds. Then based on the committor function, an optimally controlled random walk on point clouds is constructed and utilized to efficiently sample transition paths, which become an almost sure event in $O(1)$ time instead of a rare event in the original reaction dynamics. To compute the mean transition path efficiently, a local averaging algorithm based on the optimally controlled random walk is developed, which adapts the finite temperature string method to the controlled Monte Carlo samples. Numerical examples on sphere/torus including a conformational transition for the alanine dipeptide in vacuum are conducted to illustrate the data-driven solver for the transition path theory on point clouds. The mean transition path obtained via the controlled Monte Carlo simulations highly coincides with the computed dominant transition path in the transition path theory.

math.OC↗

arXiv2020

The Graph Limit of The Minimizer of The Onsager-Machlup Functional and Its Computation

The Onsager-Machlup (OM) functional is well-known for characterizing the most probable transition path of a diffusion process with non-vanishing noise. However, it suffers from a notorious issue that the functional is unbounded below when the specified transition time $T$ goes to infinity. This hinders the interpretation of the results obtained by minimizing the OM functional. We provide a new perspective on this issue. Under mild conditions, we show that although the infimum of the OM functional becomes unbounded when $T$ goes to infinity, the sequence of minimizers does contain convergent subsequences on the space of curves. The graph limit of this minimizing subsequence is an extremal of the abbreviated action functional, which is related to the OM functional via the Maupertuis principle with an optimal energy. We further propose an energy-climbing geometric minimization algorithm (EGMA) which identifies the optimal energy and the graph limit of the transition path simultaneously. This algorithm is successfully applied to several typical examples in rare event studies. Some interesting comparisons with the Freidlin-Wentzell action functional are also made.

math.PR↗

arXiv2016

City traffic forecasting using taxi GPS data: A coarse-grained cellular automata model

City traffic is a dynamic system of enormous complexity. Modeling and predicting city traffic flow remains to be a challenge task and the main difficulties are how to specify the supply and demands and how to parameterize the model. In this paper we attempt to solve these problems with the help of large amount of floating car data. We propose a coarse-grained cellular automata model that simulates vehicles moving on uniform grids whose size are much larger compared with the microscopic cellular automata model. The car-car interaction in the microscopic model is replaced by the coupling between vehicles and coarse-grained state variables in our model. To parameterize the model, flux-occupancy relations are fitted from the historical data at every grids, which serve as the coarse-grained fundamental diagrams coupling the occupancy and speed. To evaluate the model, we feed it with the historical travel demands and trajectories obtained from the floating car data and use the model to predict road speed one hour into the future. Numerical results show that our model can capture the traffic flow pattern of the entire city and make reasonable predictions. The current work can be considered a prototype for a model-based forecasting system for city traffic.

cs.OH↗

arXiv2016

Comment on "On Uniqueness of SDE Decomposition in A-type Stochastic Integration" [arXiv:1603.07927v1]

The uniqueness issue of SDE decomposition theory proposed by Ao and his co-workers has recently been discussed. A comprehensive study to investigate connections among different landscape theories [J. Chem. Phys. 144, 094109 (2016)] has pointed out that the decomposition is generally not unique, while Ao et al. (arXiv:1603.07927v1) argues that such conclusions are "incorrect" because of the missing boundary conditions. In this comment, we will combine literatures research and concrete examples to show that the concrete and effective boundary conditions have not been proposed to guarantee the uniqueness, hence the arguments in [arXiv:1603.07927v1] are not sufficient. Moreover, we show that the "uniqueness" of the O-U process decomposition referred by YTA paper is unable to serve as a counterexample to ZL's result since additional assumptions have been made implicitly beyond the original SDE decomposition framework, which cannot be applied to general nonlinear cases. Some other issues such as the failure of gradient expansion method will also be discussed. Our demonstration contributes to better understanding of the relevant papers as well as the SDE decomposition theory.

cond-mat.stat-mech↗

arXiv2016

Large deviations for two scale chemical kinetic processes

We formulate the large deviations for a class of two scale chemical kinetic processes motivated from biological applications. The result is successfully applied to treat a genetic switching model with positive feedbacks. The corresponding Hamiltonian is convex with respect to the momentum variable as a by-product of the large deviation theory. This property ensures its superiority in the rare event simulations compared with the result obtained by formal WKB asymptotics. The result is of general interest to understand the large deviations for multiscale problems.

math.PR↗