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Ruijia Zhang

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math.DG Artificial Intelligence math.AP cs.CY Distributed, Parallel, and Cluster Computing Machine Learning

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preprint2026arXiv

LLM Agents in Law: Taxonomy, Applications, and Challenges

Large language models (LLMs) have precipitated a dramatic improvement in the legal domain, yet the deployment of standalone models faces significant limitations regarding hallucination, outdated information, and verifiability. Recently, LLM agents have attracted significant attention as a solution to these challenges, utilizing advanced capabilities such as planning, memory, and tool usage to meet the rigorous standards of legal practice. In this paper, we present a comprehensive survey of LLM agents for legal tasks, analyzing how these architectures bridge the gap between technical capabilities and domain-specific needs. Our major contributions include: (1) systematically analyzing the technical transition from standard legal LLMs to legal agents; (2) presenting a structured taxonomy of current agent applications across distinct legal practice areas; (3) discussing evaluation methodologies specifically for agentic performance in law; and (4) identifying open challenges and outlining future directions for developing robust and autonomous legal assistants.

preprint2026arXiv

MinT: Managed Infrastructure for Training and Serving Millions of LLMs

We present MindLab Toolkit (MinT), a managed infrastructure system for Low-Rank Adaptation (LoRA) post-training and online serving. MinT targets a setting where many trained policies are produced over a small number of expensive base-model deployments. Instead of materializing each policy as a merged full checkpoint, MinT keeps the base model resident and moves exported LoRA adapter revisions through rollout, update, export, evaluation, serving, and rollback, hiding distributed training, serving, scheduling, and data movement behind a service interface. MinT scales this path along three axes. Scale Up extends LoRA RL to frontier-scale dense and MoE architectures, including MLA and DSA attention paths, with training and serving validated beyond 1T total parameters. Scale Down moves only the exported LoRA adapter, which can be under 1% of base-model size in rank-1 settings; adapter-only handoff reduces the measured step by 18.3x on a 4B dense model and 2.85x on a 30B MoE, while concurrent multi-policy GRPO shortens wall time by 1.77x and 1.45x without raising peak memory. Scale Out separates durable policy addressability from CPU/GPU working sets: a tensor-parallel deployment supports 10^6-scale addressable catalogs (measured single-engine sweeps through 100K) and thousand-adapter active waves at cluster scale, with cold loading treated as scheduled service work and packed MoE LoRA tensors improving live engine loading by 8.5-8.7x. MinT thus manages million-scale LoRA policy catalogs while training and serving selected adapter revisions over shared 1T-class base models.

preprint2023arXiv

A unified flow approach to smooth $L^p$ Christoffel-Minkowski problem for $p>1$

In this paper we study an anisotropic expanding flow of smooth, closed, uniformly convex hypersurfaces in $\mathbb{R}^{n+1}$ with speed $ψσ_k(λ)^α$, where $α$ is a positive constant, $σ_k(λ)$ is the $k$-th elementary symmetric polynomial of the principal radii of curvature and $ψ$ is a preassigned positive smooth function defined on $\mathbb{S}^n$. We prove that under some assumptions of $ψ$, the solution to the flow after normalisation exists for all time and converges smoothly to a solution of the well-known $L^p$ Christoffel-Minkowski problem $u^{1-p}( x ) σ_k \left( \nabla^2u+uI\right)=cψ(x)$ for $p>1$.

preprint2022arXiv

A flow approach to the prescribed Gaussian curvature problem in $\mathbb{H}^{n+1}$

In this paper, we study the following prescribed Gaussian curvature problem $$K=\frac{\tilde{f}(θ)}{ϕ(ρ)^{α-2}\sqrt{ϕ(ρ)^2+|\bar{\nabla}ρ|^2}},$$ a generalization of the Alexandrov problem ($α=n+1$) in hyperbolic space, where $\tilde{f}$ is a smooth positive function on $\mathbb{S}^{n}$, $ρ$ is the radial function of the hypersurface, $ϕ(ρ)=\sinhρ$ and $K$ is the Gauss curvature. By a flow approach, we obtain the existence and uniqueness of solutions to the above equations when $α\geq n+1$. Our argument provides a parabolic proof in smooth category for the Alexandrov problem in $\mathbb{H}^{n+1}$. We also consider the cases $2<α\leq n+1$ under the evenness assumption of $\tilde{f}$ and prove the existence of solutions to the above equations.

preprint2021arXiv

Asymptotic convergence for a class of anisotropic curvature flows

In this paper, by using new auxiliary functions, we study a class of contracting flows of closed, star-shaped hypersurfaces in $\mathbb{R}^{n+1}$ with speed $r^{\fracαβ}σ_k^{\frac{1}β}$, where $σ_k$ is the $k$-th elementary symmetric polynomial of the principal curvatures, $α$, $β$ are positive constants and $r$ is the distance from points on the hypersurface to the origin. We obtain convergence results under some assumptions of $k$, $α$, $β$. When $k\geq2$, $0<β\leq 1$, $α\geq β+k$, we prove that the $k$-convex solution to the flow exists for all time and converges smoothly to a sphere after normalization, in particular, we generalize Li-Sheng-Wang's result from uniformly convex to $k$-convex. When $k \geq 2$, $β=k$, $α\geq 2k$, we prove that the $k$-convex solution to the flow exists for all time and converges smoothly to a sphere after normalization, in particular, we generalize Ling Xiao's result from $k=2$ to $k \geq 2$.