arXiv subjects

Hong Qian

Publications and source records attributed to Hong Qian.

At least 55 records · Page 3Linked to original sources

arXiv2023

Cell Population Growth Kinetics in the Presence of Stochastic Heterogeneity of Cell Phenotype

Recent studies at individual cell resolution have revealed phenotypic heterogeneity in nominally clonal tumor cell populations. The heterogeneity affects cell growth behaviors, which can result in departure from the idealized uniform exponential growth of the cell population. Here we measured the stochastic time courses of growth of an ensemble of populations of HL60 leukemia cells in cultures, starting with distinct initial cell numbers to capture a departure from the {uniform exponential growth model for the initial growth (``take-off'')}. Despite being derived from the same cell clone, we observed significant variations in the early growth patterns of individual cultures with statistically significant differences in growth dynamics, which could be explained by the presence of inter-converting subpopulations with different growth rates, and which could last for many generations. Based on the hypothesis of existence of multiple subpopulations, we developed a branching process model that was consistent with the experimental observations.

q-bio.PE↗

arXiv2023

Scaling Multi-Objective Security Games Provably via Space Discretization Based Evolutionary Search

In the field of security, multi-objective security games (MOSGs) allow defenders to simultaneously protect targets from multiple heterogeneous attackers. MOSGs aim to simultaneously maximize all the heterogeneous payoffs, e.g., life, money, and crime rate, without merging heterogeneous attackers. In real-world scenarios, the number of heterogeneous attackers and targets to be protected may exceed the capability of most existing state-of-the-art methods, i.e., MOSGs are limited by the issue of scalability. To this end, this paper proposes a general framework called SDES based on many-objective evolutionary search to scale up MOSGs to large-scale targets and heterogeneous attackers. SDES consists of four consecutive key components, i.e., discretization, optimization, evaluation, and refinement. Specifically, SDES first discretizes the originally high-dimensional continuous solution space to the low-dimensional discrete one by the maximal indifference property in game theory. This property helps evolutionary algorithms (EAs) bypass the high-dimensional step function and ensure a well-convergent Pareto front. Then, a many-objective EA is used for optimization in the low-dimensional discrete solution space to obtain a well-spaced Pareto front. To evaluate solutions, SDES restores solutions back to the original space via greedily optimizing a novel divergence measurement. Finally, the refinement in SDES boosts the optimization performance with acceptable cost. Theoretically, we prove the optimization consistency and convergence of SDES. Experiment results show that SDES is the first linear-time MOSG algorithm for both large-scale attackers and targets. SDES is able to solve up to 20 attackers and 100 targets MOSG problems, while the state-of-the-art (SOTA) methods can only solve up to 8 attackers and 25 targets ones. Ablation study verifies the necessity of all components in SDES.

cs.LG↗

arXiv2022

Mathematical Representation of Clausius' and Kelvin's Statements of the Second Law and Irreversibility

We provide a stochastic mathematical representation for Clausius' and Kelvin-Planck's statements of the Second Law of Thermodynamics in terms of the entropy productions of a finite, compact driven Markov system and its lift. A surjective map is rigorously established through the lift when the state space is either a discrete graph or a continuous n-dimensional torus T^n. The corresponding lifted processes have detailed balance thus a natural potential function but no stationary probability. We show that in the long-time limit the entropy production of the finite driven system precisely equals the potential energy decrease in the lifted system. This theorem provides a dynamic foundation for the two equivalent statements of Second Law of Thermodynamics, a la Kelvin's and Clausius'. It suggests a modernized, combined statement: "A mesoscopic engine that works in completing irreversible internal cycles statistically has necessarily an external effect that lowering a weight accompanied by passing heat from a warmer to a colder body."

math.PR↗

arXiv2022

BBTv2: Towards a Gradient-Free Future with Large Language Models

Most downstream adaptation methods tune all or part of the parameters of pre-trained models (PTMs) through gradient descent, where the tuning cost increases linearly with the growth of the model size. By contrast, gradient-free methods only require the forward computation of the PTM to tune the prompt, retaining the benefits of efficient tuning and deployment. Though, past work on gradient-free tuning often introduces gradient descent to seek a good initialization of prompt and lacks versatility across tasks and PTMs. In this paper, we present BBTv2, an improved version of Black-Box Tuning, to drive PTMs for few-shot learning. We prepend continuous prompts to every layer of the PTM and propose a divide-and-conquer gradient-free algorithm to optimize the prompts at different layers alternately. Extensive experiments across various tasks and PTMs show that BBTv2 can achieve comparable performance to full model tuning and state-of-the-art parameter-efficient methods (e.g., Adapter, LoRA, BitFit, etc.) under few-shot settings while maintaining much fewer tunable parameters.

cs.CL↗

arXiv2022

Internal Energy, Fundamental Thermodynamic Relation, and Gibbs' Ensemble Theory as Laws of Statistical Counting

Counting ad infinitum is the holographic observable to a statistical dynamics with finite states under independent repeated sampling. Entropy provides the infinitesimal probability for an observed frequency $\hat{\boldsymbolν}$ w.r.t. a probability prior ${\bf p}$. Following Callen's postulate and through Legendre-Fenchel transform, without help from mechanics, we show an internal energy $\boldsymbolμ$ emerges; it provides a linear representation of real-valued observables with full or partial information. Gibbs' fundamental thermodynamic relation and theory of ensembles follow mathematically. $\boldsymbolμ$ is to $\hat{\boldsymbolν}$ what $ω$ is to $t$ in Fourier analysis.

cond-mat.stat-mech↗

arXiv2022

Unified Policy Optimization for Continuous-action Reinforcement Learning in Non-stationary Tasks and Games

This paper addresses policy learning in non-stationary environments and games with continuous actions. Rather than the classical reward maximization mechanism, inspired by the ideas of follow-the-regularized-leader (FTRL) and mirror descent (MD) update, we propose a no-regret style reinforcement learning algorithm PORL for continuous action tasks. We prove that PORL has a last-iterate convergence guarantee, which is important for adversarial and cooperative games. Empirical studies show that, in stationary environments such as MuJoCo locomotion controlling tasks, PORL performs equally well as, if not better than, the soft actor-critic (SAC) algorithm; in non-stationary environments including dynamical environments, adversarial training, and competitive games, PORL is superior to SAC in both a better final policy performance and a more stable training process.

cs.LG↗

arXiv2022

Black-Box Tuning for Language-Model-as-a-Service

Extremely large pre-trained language models (PTMs) such as GPT-3 are usually released as a service. It allows users to design task-specific prompts to query the PTMs through some black-box APIs. In such a scenario, which we call Language-Model-as-a-Service (LMaaS), the gradients of PTMs are usually unavailable. Can we optimize the task prompts by only accessing the model inference APIs? This paper proposes the black-box tuning framework to optimize the continuous prompt prepended to the input text via derivative-free optimization. Instead of optimizing in the original high-dimensional prompt space, which is intractable for traditional derivative-free optimization, we perform optimization in a randomly generated subspace due to the low intrinsic dimensionality of large PTMs. The experimental results show that the black-box tuning with RoBERTa on a few labeled samples not only significantly outperforms manual prompt and GPT-3's in-context learning, but also surpasses the gradient-based counterparts, i.e., prompt tuning and full model tuning.

cs.CL↗

arXiv2022

ZOOpt: Toolbox for Derivative-Free Optimization

Recent advances in derivative-free optimization allow efficient approximation of the global-optimal solutions of sophisticated functions, such as functions with many local optima, non-differentiable and non-continuous functions. This article describes the ZOOpt (Zeroth Order Optimization) toolbox that provides efficient derivative-free solvers and is designed easy to use. ZOOpt provides single-machine parallel optimization on the basis of python core and multi-machine distributed optimization for time-consuming tasks by incorporating with the Ray framework -- a famous platform for building distributed applications. ZOOpt particularly focuses on optimization problems in machine learning, addressing high-dimensional and noisy problems such as hyper-parameter tuning and direct policy search. The toolbox is maintained toward a ready-to-use tool in real-world machine learning tasks.

cs.LG↗

arXiv2022

$2^{1296}$ Exponentially Complex Quantum Many-Body Simulation via Scalable Deep Learning Method

For decades, people are developing efficient numerical methods for solving the challenging quantum many-body problem, whose Hilbert space grows exponentially with the size of the problem. However, this journey is far from over, as previous methods all have serious limitations. The recently developed deep learning methods provide a very promising new route to solve the long-standing quantum many-body problems. We report that a deep learning based simulation protocol can achieve the solution with state-of-the-art precision in the Hilbert space as large as $2^{1296}$ for spin system and $3^{144}$ for fermion system , using a HPC-AI hybrid framework on the new Sunway supercomputer. With highly scalability up to 40 million heterogeneous cores, our applications have measured 94% weak scaling efficiency and 72% strong scaling efficiency. The accomplishment of this work opens the door to simulate spin models and Fermion models on unprecedented lattice size with extreme high precision.

quant-ph↗

arXiv2022

Emergence and Breaking of Duality Symmetry in Generalized Fundamental Thermodynamic Relations

Thermodynamics as limiting behaviors of statistics is generalized to arbitrary system with probability {\it a priori} where thermodynamic infinite-size limit is replaced by multiple-measurement limit. A duality symmetry between Massieu's and Gibbs' entropy arises in the limit of infinitely repeated observations, yielding the Gibbs equation and Hill-Gibbs-Duhem equation (HGDE) as dual pair. If a system has thermodynamic limit satisfying Callen's postulate, entropy being an Eulerian function, the symmetry is lost: the HGDE reduces to the Gibbs-Duhem equation. This theory provides a de-mechanized foundation for classical and nanothermodynamics and offers a framework for distilling emergence from large data, free from underlying details.

cond-mat.stat-mech↗

arXiv2022

On the Posterior Distribution of a Random Process Conditioned on Empirical Frequencies of a Finite Path: the i.i.d and finite Markov chain case

We obtain the posterior distribution of a random process conditioned on observing the empirical frequencies of a finite sample path. We find under a rather broad assumption on the "dependence structure" of the process, {\em c.f.} independence or Markovian, the posterior marginal distribution of the process at a given time index can be identified as certain empirical distribution computed from the observed empirical frequencies of the sample path. We show that in both cases of discrete-valued i.i.d. sequence and finite Markov chain, a certain "conditional symmetry" given by the observation of the empirical frequencies leads to the desired result on the posterior distribution. Results for both finite-time observations and its asymptotic infinite-time limit are connected via the idea of Gibbs conditioning. Finally, since our results demonstrate a central role of the empirical frequency in understanding the information content of data, we use the Large Deviations Principle (LDP) to construct a general notion of "data-driven entropy", from which one can apply a formalism from the recent study of statistical thermodynamics to data.

math.PR↗

arXiv2021

Thermodynamic Behavior of Statistical Event Counting in Time: Independent and Correlated Measurements

We introduce an entropy analysis of time series, repeated measurements of statistical observables, based on an Eulerian homogeneous degree-one entropy function $Φ(t,n)$ of time $t$ and number of events $n$. The duality of $Φ$, in terms of conjugate variables $η=-Φ'_t$ and $μ=Φ'_n$, yields an ``equation of state'' (EoS) in differential form that resembles the Gibbs-Duhem relation in classical thermodynamics: $t dη-n dμ= 0$. For simple Poisson counting with rate $r$, $η=r(e^μ-1)$. The conjugate variable $η$ is then identified as being equal to the Hamiltonian function in a Hamilton-Jacobi equation for $Φ(t,n)$. Applying the same logic to the entropy function of time correlated events yields a Hamiltonian as the principal eigenvalue of a matrix. For time reversible case it is the sum of a symmetric Markovian part $\sqrt{π_i}q_{ij}/\sqrt{π_j}$ and the conjugate variables $μ_iδ_{ij}$. The eigenvector, as a posterior to the naive counting measure used as the prior, suggests a set of intrinsic characteristics of Markov states.

cond-mat.stat-mech↗

arXiv2021

Stochastic Dynamics, Large Deviations Principle, and Non-equilibrium Thermodynamics

By examining the deterministic limit of a general $ε$-dependent generator for Markovian dynamics, which includes the continuous Fokker-Planck equations and discrete chemical master equations as two special cases, the intrinsic connections among mesoscopic stochastic dynamics, deterministic ODEs or PDEs, large deviations rate function, and macroscopic thermodynamic potential are established. Our result not only solves the long-lasting question on the origin of entropy function in classical irreversible thermodynamics, but also reveals an emergent feature that arises automatically during the deterministic limit, through its large deviations rate function, with both time-reversible dynamics equipped with a Hamiltonian function and time-irreversible dynamics equipped with an entropy function.

math.PR↗

arXiv2021

Duality Symmetry, Two Entropy Functions, and an Eigenvalue Problem in Gibbs' Theory

We generalize the convex duality symmetry in Gibbs' statistical ensemble formulation, between Massieu's free entropy $Φ_{V,N} (β)$ and the Gibbs entropy $φ_{V,N}(u)$ as a function of mean internal energy $u$. The duality tells us that Gibbs thermodynamic entropy is to the law of large numbers (LLN) for arithmetic sample means what Shannon's information entropy is to the LLN for empirical counting frequencies. Following the same logic, we identify $u$ as the conjugate variable to counting frequency, a Hamilton-Jacobi equation for Shannon entropy as an equation of state, and suggest an eigenvalue problem for modeling statistical frequencies of correlated data.

cond-mat.stat-mech↗

arXiv2021

Generalized Boltzmann distributions for systems strongly coupled to large finite bath -- a microcanonical approach

The theory of probability shows that, as the fraction $X_n/Y\to 0$, the conditional probability for $X_n$, given $X_n+Y \in h_δ:=[h, h+δ]$, has a limit law $f_{X_n}(x)e^{-ψ_n(h_δ)x}$, where $ψ_n(h_δ) $ equals to $[\partial \ln P(Y \in y_δ)/\partial y]_{y=h}$ plus an additional term, contributed from the correlation between $X_n$ and bath $Y$. By applying this limit law to an isolated composite system consisting of two strongly coupled parts, a system of interest and a large but finite bath, we derive the generalized Boltzmann distribution law for the system of interest in the exponential form of a redefined Hamiltonian and corrected Boltzmann temperature that reflects the modification due to strong system-bath coupling and the large but finite bath.

math-ph↗

arXiv2021

Nonequilibrium Stationary Process and Fluctuation-Dissipation Relations

A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent mechanisms contributing to the overall fluctuations of the dynamics, representing the uncertainties in the past and in the future. A generalized Einstein relation is a consequence solely because the dynamics being stationary; and the Green-Kubo formula reflects a balance between the two mechanisms. Equilibrium with reversibility is characterized by a novel covariance symmetry.

cond-mat.stat-mech↗

arXiv2021

Intermittent Synchronization in finite-state random networks under Markov Perturbations

By introducing extrinsic noise as well as intrinsic uncertainty into a network with stochastic events, this paper studies the dynamics of the resulting Markov random network and characterizes a novel phenomenon of intermittent synchronization and desynchronization that is due to an interplay of the two forms of randomness in the system. On a finite state space and in discrete time, the network allows for unperturbed (or "deterministic") randomness that represents the extrinsic noise but also for small intrinsic uncertainties modelled by a Markov perturbation. It is shown that if the deterministic random network is synchronized (resp., uniformly synchronized), then for almost all realizations of its extrinsic noise the stochastic trajectories of the perturbed network synchronize along almost all (resp., along all) time sequences after a certain time, with high probability. That is, both the probability of synchronization and the proportion of time spent in synchrony are arbitrarily close to one. Under smooth Markov perturbations, high-probability synchronization and low-probability desynchronization occur intermittently in time, which can both be precisely described via an asymptotic expansion of the invariant distribution. Existence and uniqueness of invariant distributions are established, as well as their convergence as the perturbation parameter vanishes. An explicit asymptotic expansion is derived. Ergodicity of the extrinsic noise dynamics is seen to be crucial for the characterization of (de)synchronization sets and their respective relative frequencies. An example of a smooth Markov perturbation of a synchronized probabilistic Boolean network is provided to illustrate the intermittency between high-probability synchronization and low-probability desynchronization.

math.DS↗

arXiv2021

Revealing and controlling nuclear dynamics following inner-shell photoionization of N2

In this work, we apply the Monte Carlo wave packet method to study the ultrafast nuclear dynamics following inner-shell photoionization of N2 exposed to an ultrashort intense X-ray pulse. The photon energy of the X-ray pulse is large enough to remove a 1s electron from the N atom in N2. The intermediate state in N+2 is highly excited so that autoionization takes place from this state to the dissociative or non-dissociative electronic states of ungerade and gerade symmetries in N++2. The possible vibrational resonances allowed by the non-dissociative states prevents a direct extraction of the nuclear kinetic release (KER) spectrum from the nuclear wave packets in N++2. Therefore, we propose a hybrid technique by combining the advantages of two energy analysis strategies to obtain the final nuclear KER spectrum of the process. A femtosecond IR probe pulse, which couples the electronic states in N++2 together, is applied to achieve a time-resolved imaging and controlling of the ultrafast dynamics that takes place during double ionization of N2. The influence of the laser parameters including the peak intensity, pulse duration and pump-probe delay, on the nuclear dynamics is also investigated.

physics.atom-ph↗