arXiv subjects

Zixiang Liu

Publications and source records attributed to Zixiang Liu.

8 recordsLinked to original sources

arXiv2026

ESPO: Early-Stopping Proximal Policy Optimization

When a large language model under reinforcement learning commits a wrong reasoning step early in a trajectory, standard algorithms force it to keep generating until the maximum horizon, spending compute on tokens that never receive positive reward and polluting advantage estimates with post-failure noise. We propose ESPO (Early-Stopping Proximal Policy Optimization), which detects trajectory failure on-the-fly and terminates rollouts early. At each generation step, ESPO computes a surrogate regret using only the logits already computed during sampling, and terminates when the smoothed cumulative regret significantly exceeds its estimated values. Truncated trajectories are treated as absorbing failure states with a terminal reward, concentrating negative temporal-difference (TD) errors near the detected failure step without any additional reward model or human annotation. On DeepSeek-R1-Distill-Qwen-7B trained for mathematical reasoning, ESPO surpasses PPO on AIME~2024 (46.28% vs. 45.25%), AMC~2023 (85.83% vs. 82.94%), and MATH-500 (87.42% vs. 85.43%), while saving more than 20% rollout tokens cumulatively.

cs.LG↗

arXiv2025

MCPAgentBench: A Real-world Task Benchmark for Evaluating LLM Agent MCP Tool Use

Large Language Models (LLMs) are increasingly serving as autonomous agents, and their utilization of external tools via the Model Context Protocol (MCP) is considered a future trend. Current MCP evaluation sets suffer from issues such as reliance on external MCP services and a lack of difficulty awareness. To address these limitations, we propose MCPAgentBench, a benchmark based on real-world MCP definitions designed to evaluate the tool-use capabilities of agents. We construct a dataset containing authentic tasks and simulated MCP tools. The evaluation employs a dynamic sandbox environment that presents agents with candidate tool lists containing distractors, thereby testing their tool selection and discrimination abilities. Furthermore, we introduce comprehensive metrics to measure both task completion rates and execution efficiency. Experiments conducted on various latest mainstream Large Language Models reveal significant performance differences in handling complex, multi-step tool invocations. All code is open-source at Github.

cs.AI↗

arXiv2025

Proof2Hybrid: Automatic Mathematical Benchmark Synthesis for Proof-Centric Problems

Evaluating the mathematical capability of Large Language Models (LLMs) is a critical yet challenging frontier. Existing benchmarks fall short, particularly for proof-centric problems, as manual creation is unscalable and costly, leaving the true mathematical abilities of LLMs largely unassessed. To overcome these barriers, we propose Proof2Hybrid, the first fully automated framework that synthesizes high-quality, proof-centric benchmarks from natural language mathematical corpora. The key novelty of our solution is Proof2X, a roadmap of converting mathematical proofs into various kinds of questions that are easy to verify. Instructed by this roadmap, we propose a new type of hybrid-formatted questions, named ``$m$-out-of-$n$ multiple judge questions'', specifically designed to enable robust, automatic evaluation while being resilient to guessing and superficial pattern matching inherent in traditional formats. As a demonstration of our framework, we introduce AlgGeoTest, a benchmark for algebraic geometry--a frontier domain of modern mathematics--comprising 456 challenging items. Our extensive evaluations on state-of-the-art LLMs using AlgGeoTest reveal profound deficits in their comprehension of algebraic geometry, providing a more precise measure of their true mathematical capabilities. Our framework and benchmark pave the way for a new wave of in-depth research into the mathematical intelligence of AI systems.

cs.CL↗

arXiv2019

A unified analysis of nano-to-microscale particle dispersion in tubular blood flow

Transport of solid particles in blood flow exhibits qualitative differences in the transport mechanism when the particle varies from nanoscale to microscale size comparable to the red blood cell (RBC). The effect of microscale particle margination has been investigated by several groups. Also, the transport of nanoscale particles (NPs) in blood has received considerable attention in the past. This study attempts to bridge the gap by quantitatively showing how the transport mechanism varies with particle size from nano- to microscale. Using a three-dimensional (3D) multiscale method, the dispersion of particles in microscale tubular flows is investigated for various hematocrits, vessel diameters and particle sizes. NPs exhibit a nonuniform, smoothly-dispersed distribution across the tube radius due to severe Brownian motion. The near-wall concentration of NPs can be moderately enhanced by increasing hematocrit and confinement. Moreover, there exists a critical particle size ($\sim$1 $μ$m) that leads to excessive retention of particles in the cell-free region near the wall, i.e., margination. Above this threshold, the margination propensity increases with the particle size. The dominance of RBC-enhanced shear-induced diffusivity (RESID) over Brownian diffusivity (BD) results in 10 times higher radial diffusion rates in the RBC-laden region compared to that in the cell-free layer, correlated with the high margination propensity of microscale particles. This work captures the particle size-dependent transition from Brownian-motion dominant dispersion to margination using a unified 3D multiscale computational approach, and highlights the linkage between the radial distribution of RESID and the margination of particles in confined blood flows.

cond-mat.soft↗

arXiv2019

Multiscale method based on coupled lattice-Boltzmann and Langevin-dynamics for direct simulation of nanoscale particle/polymer suspensions in complex flows

A hybrid computational method coupling the lattice-Boltzmann (LB) method and a Langevin-dynamics (LD) method is developed to simulate nanoscale particle and polymer (NPP) suspensions in the presence of both thermal fluctuation and long-range many-body hydrodynamic interactions (HI). Brownian motion of the NPP is explicitly captured by a stochastic forcing term in the LD method. The LD method is two-way coupled to the non-fluctuating LB fluid through a discrete LB forcing source distribution to capture the long-range HI. To ensure intrinsically linear scalability with respect to the number of particles, an Eulerian-host algorithm for short-distance particle neighbor search and interaction is developed and embedded to LB-LD framework. The validity and accuracy of the LB-LD approach are demonstrated through several sample problems. The simulation results show good agreements with theory and experiment. The LB-LD approach can be favorably incorporated into complex multiscale computational frameworks for efficiently simulating multiscale, multicomponent particulate suspension systems such as complex blood suspensions.

physics.flu-dyn↗

arXiv2019

Nanoparticle diffusion in sheared cellular blood flow

Using a multiscale blood flow solver, the complete diffusion tensor of nanoparticle (NP) in sheared cellular blood flow is calculated over a wide range of shear rate and haematocrit. In the short-time regime, NPs exhibit anomalous dispersive behaviors under high shear and high haematocrit due to the transient elongation and alignment of the red blood cells (RBCs). In the long-time regime, the NP diffusion tensor features high anisotropy. Particularly, there exists a critical shear rate ($\sim$100 $s^{-1}$) around which the shear-rate dependence of the diffusivity tensor changes from linear to nonlinear scale. Above the critical shear rate, the cross-stream diffusivity terms vary sublinearly with shear rate, while the longitudinal term varies superlinearly. The dependence on haematocrit is linear in general except at high shear rates, where a sublinear scale is found for the vorticity term and a quadratic scale for the longitudinal term. Through analysis of the suspension microstructure and numerical experiments, the nonlinear hemorheological dependence of the NP diffusion tensor is attributed to the streamwise elongation and cross-stream contraction of RBCs under high shear, quantified by a Capillary number. The RBC size is shown to be the characteristic length scale affecting the RBC-enhanced shear-induced diffusion (RESID), while the NP size at submicron exhibits negligible influence on the RESID. Based on the observed scaling behaviors, empirical correlations are proposed to bridge the NP diffusion tensor to specific shear rate and haematocrit. The characterized NP diffusion tensor provides a constitutive relation that can lead to more effective continuum models to tackle large-scale NP biotransport applications.

physics.bio-ph↗

arXiv2018

Conformational dynamics of charged polymers interacting with charged nanoparticles

The transition from globular to elongated states of biopolymers in shear flow occurs at a distinct critical shear rate, $\dot{γ}^{*}$. The magnitude of $\dot{γ}^{*}$ depends on the internal potential and the polymer length. For example, the critical shear is much larger for von Willebrand Factor (vWF) compared to DNA. Furthermore, it is shown through computational analysis of vWF (model-vWF) that $\dot{γ}^{*}\sim N^{1/3}$, where N is the number of dimeric units in the vWF. In this study, we show that in the presence of charged nanoparticles (CNP) and polymer, the critical shear rate scales differently depending on the polymer length and the charge-strength of the CNP. It is shown that CNP alter the conformational dynamics of polymers under shear flow when the polymer beads have an opposite charge. The introduction of CNP shifts the critical shear rate and alters the scaling. Furthermore, it is shown that the critical zeta potential of CNP, $ζ^{*}$, scales linearly with shear rate, and scales cubically with ratio $β$ between final CNP-polymer composite size and original polymer size, that is $ζ^{*}\sim \dot{γ}β^{-3}$.

physics.comp-ph↗

arXiv2018

Nanoparticle Transport in Cellular Blood Flow

The biotransport of the intravascular nanoparticle (NP) is influenced by both the complex cellular flow environment and the NP characteristics. Being able to computationally simulate such intricate transport phenomenon with high efficiency is of far-reaching significance to the development of nanotherapeutics, yet challenging due to large length-scale discrepancies between NP and red blood cell (RBC) as well as the complexity of NP dynamics. Recently, a lattice-Boltzmann (LB) based multiscale simulation method has been developed to capture both NP scale and cellular level transport phenomenon at high computational efficiency. The basic components of this method include the LB treatment for the fluid phase, a spectrin-link method for RBCs, and a Langevin dynamics (LD) approach to capturing the motion of the suspended NPs. Comprehensive two-way coupling schemes are established to capture accurate interactions between each component. The accuracy and robustness of the LB-LD coupling method are demonstrated through the relaxation of a single NP with initial momentum and self-diffusion of NPs. This approach is then applied to study the migration of NPs in a capillary vessel under physiological conditions. It is shown that Brownian motion is most significant for the NP distribution in capillary vessels. For 1~100 nm particles, the Brownian diffusion is the dominant radial diffusive mechanism compared to the RBC-enhanced diffusion. For ~500 nm particles, the Brownian diffusion and RBC-enhanced diffusion are comparable drivers for the particle radial diffusion process.

physics.flu-dyn↗