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Jin Jia

Publications and source records attributed to Jin Jia.

5 recordsLinked to original sources
arXiv2026

Multi-Dimensional Structural Stability of Mixed Riemann Configurations Containing Centered Rarefaction Waves and Surfaces of Discontinuities of Gas Dynamics

For 2D compressible Euler equations of isentropic gas, we prove the structural stability of mixed Riemann configurations containing centered rarefaction waves and surfaces of discontinuities (such as shock waves or vortex sheets), by deriving simultaneous energy estimates for acoustic and vorticity waves within the rarefaction wave region \emph{without loss of derivatives} and examinations of the nonlinear superpositions of rarefaction waves with other waves such as shock waves or vortex sheets. The nonlinear superpositions of \emph{shock wave-rarefaction wave} and \emph{rarefaction wave-vortex sheet-rarefaction wave} are achieved by reducing the problems in corner regions to the Cauchy problems with the data prescribed on the plane $\Sigma_0=\{(t, x_1, x_2): t=0, (x_1, x_2)\in \mathbb{R}\times\mathbb{R}/2\pi\mathbb{Z}\}$ with discontinuities at $\mathbf{S}_*:=\{(t,x_{1},x_{2})\mid t=0,\ x_{1}=0, x_2\in\mathbb{R}/2\pi\mathbb{Z} \}$.

math.AP↗
arXiv2026

MAS-FIRE: Fault Injection and Reliability Evaluation for LLM-Based Multi-Agent Systems

As LLM-based Multi-Agent Systems (MAS) are increasingly deployed for complex tasks, ensuring their reliability has become a pressing challenge. Since MAS coordinate through unstructured natural language rather than rigid protocols, they are prone to semantic failures (e.g., hallucinations, misinterpreted instructions, and reasoning drift) that propagate silently without raising runtime exceptions. Prevailing evaluation approaches, which measure only end-to-end task success, offer limited insight into how these failures arise or how effectively agents recover from them. To bridge this gap, we propose MAS-FIRE, a systematic framework for fault injection and reliability evaluation of MAS. We define a taxonomy of 15 fault types covering intra-agent cognitive errors and inter-agent coordination failures, and inject them via three non-invasive mechanisms: prompt modification, response rewriting, and message routing manipulation. Applying MAS-FIRE to three representative MAS architectures, we uncover a rich set of fault-tolerant behaviors that we organize into four tiers: mechanism, rule, prompt, and reasoning. This tiered view enables fine-grained diagnosis of where and why systems succeed or fail. Our findings reveal that stronger foundation models do not uniformly improve robustness. We further show that architectural topology plays an equally decisive role, with iterative, closed-loop designs neutralizing over 40% of faults that cause catastrophic collapse in linear workflows. MAS-FIRE provides the process-level observability and actionable guidance needed to systematically improve multi-agent systems.

cs.SE↗
arXiv2025

Alada: Alternating Adaptation of Momentum Method for Memory-Efficient Matrix Optimization

This work proposes Alada, an adaptive momentum method for stochastic optimization over large-scale matrices. Alada employs a rank-one factorization approach to estimate the second moment of gradients, where factors are updated alternatively to minimize the estimation error. Alada achieves sublinear memory overheads and can be readily extended to optimizing tensor-shaped variables.We also equip Alada with a first moment estimation rule, which enhances the algorithm's robustness without incurring additional memory overheads. The theoretical performance of Alada aligns with that of traditional methods such as Adam. Numerical studies conducted on several natural language processing tasks demonstrate the reduction in memory overheads and the robustness in training large models relative to Adam and its variants.

cs.LG↗
arXiv2024

Radiation fields for semilinear Dirac equations with spinor null forms

Inthispaper,weinvestigatethescatteringtheoryofhalf-spinwavesthroughtheuse of radiation fields. We define the radiation fields for semilinear Dirac equations with spinor null forms and establish a nonlinear isomorphism between the weighted energy space of initial data and the weighted energy space of radiation fields. The proof relies on a detailed examination of the linear Dirac radiation fields and the use of a suitable functional framework.

math.AP↗