We introduce NAGO, a noise-aware generative operator for efficient sampling from invariant measures of stochastic partial differential equations (SPDEs) in function space. Our central idea is to treat the source measure as a design variable rather than a fixed Gaussian default. We establish admissibility conditions for well-defined infinite-dimensional flows and show that the finite-band source--target covariance ratio controls the spectral stiffness of the marginal velocity field. This analysis yields an admissibility-constrained spectral-matching rule: choose a source that is sufficiently rough for well-posedness, then minimize covariance mismatch over the resolved Fourier modes. On three representative stochastic-field benchmarks, this source design improves few-step spectral accuracy and several complementary distributional and physical statistics. In a controlled Matern-field ablation, it reduces the accurate RK4 budget from about 30 steps for Gaussian functional flow matching to 3--5 steps, a $6$--$10\times$ reduction in neural ODE evaluations. These gains are strongest for stationary multiscale fields and depend on the metric, resolution, and guidance protocol.
Senbo Zhang, Qiqi Wang Nankai University, Fanghao Lou Nankai University, Guanyu Chen, Yihong Pan University of Auckland, Huijia Li, Qian Liu University of Auckland
A defence opinion is an essential step in criminal proceedings, yet it has not been systematically formulated or evaluated as a specific LegalAI task. Grounded in legal principles and practice, we formulate this task as generating a structured defence opinion conditioned jointly on an indictment and the defendant’s stated opinion, which often present conflicting claims. We formalize this setting as a dual-perspective generation problem and introduce DefGen-Bench, a benchmark comprising several Chinese criminal cases with expert-reviewed reference defence opinions. We evaluate eight large language models (LLMs) on this task and observe that existing models tend to mirror the defendant’s opinion, thereby overlooking more appropriate defence strategies. To address this challenge, we propose Knowledge-Enhanced Highlighted Indictment (KHI), a legal knowledge–guided input enhancement method applicable to both open- and closed-source LLMs. Experiments demonstrate consistent improvements across all evaluated LLMs, validating the effectiveness of the proposed approach.
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cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表