Jiayi Li, Penghao Jiang, Baiyu Chen, Yifan Duan, Hira Saleem, Zhaonan Wang, Piotr Koniusz, Flora D. Salim
Neural operators efficiently simulate dynamical systems by repeatedly predicting the next state. However, small errors at each step can accumulate, causing long-term predictions to drift from the true trajectory. Long-term error reflects both the propagation of earlier prediction errors and new errors introduced at each step. How to reduce these errors is therefore a critical question. We propose the Spectral Generator Neural Operator (SGNO), which combines a linear estimate of the next state with a learned correction. The linear component uses consecutive states in the training data to fit a map from the current state to the next. A neural network corrects this prediction by learning changes that the linear model does not capture, including nonlinear interactions. Both components are trained jointly toward the same next-state target. Experiments across 13 periodic PDE configurations in one to three dimensions show that SGNO accurately learns state evolution on linear tasks and reduces 100-step rollout error by 13-74% over the strongest baseline under the main comparison protocol on each nonlinear task. Longer-horizon extrapolation tests show lower late-window prediction errors on several nonlinear tasks. These results show that combining fitted propagation with learned state-dependent correction can improve long-horizon autoregressive prediction on the evaluated PDE tasks. Code is available at https://github.com/cruiseresearchgroup/SGNO.
Yifan Li, YuKai Gu, Yingqian Min, Zikang Liu, Yifan Du, Kun Zhou University of California, San Diego, Min Yang Bytedance, Xin Zhao Renmin University of China 等 9 位作者
Recent breakthroughs in video generation have demonstrated an emerging capability termed Chain-of-Frames (CoF) reasoning, where models resolve complex tasks through the generation of continuous frames. While these models show promise for Generative Video Reasoning (GVR), existing evaluation frameworks often rely on single-frame assessments, which can lead to outcome-hacking, where a model reaches a correct conclusion through an erroneous process. To address this, we propose a process-aware evaluation paradigm. We introduce VIPER, a comprehensive benchmark spanning 16 tasks across temporal, structural, symbolic, spatial, physics, and planning reasoning. Furthermore, we propose Process-outcome Consistency (POC@r), a new metric that utilizes VLM-as-Judge with a hierarchical rubric to evaluate both the validity of the intermediate steps and the final result. Our experiments reveal that state-of-the-art video models achieve POC@1.0 only about 20% and exhibit a significant outcome-hacking. We further explore the impact of test-time scaling and sampling robustness, highlighting a substantial gap between current video generation and true generalized visual reasoning. Our benchmark are released at https://github.com/RUCAIBox/VIPER.
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Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表