Koopman operator theory provides a principled framework for reduced-order modeling of nonlinear spatiotemporal dynamics through linear evolution in an observable space. In practice, however, learned finite-dimensional representations are typically approximately invariant, causing unresolved dynamics and accumulated closure errors. Recent approaches, inspired by the Mori-Zwanzig formalism, address these effects through deterministic memory or closure modeling, yet robust extrapolation beyond the training horizon remains challenging. Here, we propose KoopFlow, an efficient prediction-correction framework based on the key insight that finite-dimensional Koopman error accumulation can be reinterpreted as a progressive distributional degradation process. Accordingly, KoopFlow treats Koopman predictions as noisy intermediate estimates, which are then transported toward the target latent distribution through a generative model, thereby mitigating accumulated errors while retaining computational efficiency and temporal flexibility. Moreover, we reveal a non-monotonic relationship between Koopman spectral coherence and predictive accuracy. Experiments across diverse nonlinear dynamical systems demonstrate improved long-horizon prediction accuracy and stability over representative baselines, particularly beyond the training horizon.
Saurabh Kataria, Yi Wu, Zhaoliang Chen, Hyunjung Gloria Kwak, Yuhao Xu, Lovely Yeswanth Panchumarthi, Ran Xiao, Jiaying Lu 等 26 位作者
Time-series Foundation Models (FMs) are pretrained on either heterogeneous corpora or specific signal domains. Using Photoplethysmography (PPG) as a representative modality, we compare generalist time-series FMs, PPG-specialist FMs, and traditional machine learning (ML) baselines for PPG-based health assessment. We conduct a two-stage benchmark. First, we evaluate multiple FM families across 23 downstream evaluations (e.g., atrial fibrillation detection, vital-sign estimation). Second, we conduct a focused four-FM comparison (MOMENT, Chronos-2, GPT-PPG, MOMENT-PPG) at multiple model sizes on an expanded 51-task suite, under both frozen-backbone and full-model tuning, to study tuning strategy, model scaling, and cross-dataset transfer. The multi-model benchmark shows that PPG-specialist FMs achieve the strongest aggregate performance, but their advantage is not uniform: generalist FMs remain competitive on several tasks, and traditional ML baselines outperform FMs on selected clinical regression tasks. The focused analysis shows that the advantage of PPG-specific pretraining appears mainly with frozen backbones and on targets that the waveform directly reflects, such as atrial fibrillation and vital signs. Full-model tuning narrows this advantage, model rankings change with the tuning strategy, and the largest model variant is the best choice in only about one-third of cases. Additionally, controlled experiments with two generalist models show that initializing PPG pretraining from generalist checkpoints provides an early advantage over training from scratch, even when the pretrained features offer little downstream benefit. Together, these findings suggest that PPG-specific pretraining is useful but task-dependent, and that FMs should be evaluated against simpler statistical, traditional ML, and clinical history-based baselines.
LLM agents learn by interacting with environments, yet existing environments are designed for specific tasks and fail to generalize to new ones. Recent methods automate environment construction with LLMs. However, they generate each environment from scratch, neither reusing parts shared across environments nor carrying a fix from one environment to the rest. To address this, we propose a new paradigm of evolving environment atoms, which composes environments from reusable atoms (intent, rule, data and server) and evolves the atoms when an environment fails to give reliable feedback (e.g., an application lacks a tool the task requires). To instantiate this paradigm, we introduce LegoEnv, which builds 5,465 verified environments over 223 applications, and one round of evolution raises the share of solvable environments from 71.6% to 88.3%. On AutomationBench, SFT on these environments lifts Qwen3.6-27B from 16.0% to 32.0%, and RL with their verifiers lifts Qwen3.8-27B from 37.6% to 40.3%. Further analyses show steady gains with corpus size, transfer to unseen applications, and failures concentrated in a few shared root causes.
Recursive self-improvement requires models not only to acquire useful training experience, but also to decide when their current experience has ceased to be useful. Existing methods often focus on what experience to generate next, while paying less attention to when fresh experience should be introduced. Many also construct training targets through self-consistency or majority voting, making supervision depend on the model's own uncertain predictions. We address these two questions separately: training dynamics determine when to acquire new experience, while the answers to new tasks remain independently checkable. A-RSI monitors reward variation and accuracy in training logs to refresh a task pool when its learning signal declines, without consulting validation or test scores. A static library of model-authored programs produces multimodal questions and derives their reference answers; we specify the task-generation contract, automatically verify chosen properties of the reward and refresh rules, and separately audit the generated answers. The training loop uses no external training examples or human-written answer labels. On the primary eleven-benchmark suite, A-RSI raises the performance average from 57.77 to 61.05 with 800 fresh tasks.