发表机构
Peking University–Tsinghua University–National Institute of Biological Sciences Joint Graduate Program; Academy for Advanced Interdisciplinary Studies; Center for Bioinformatics; School of Life Sciences; National Laboratory of Protein Engineering and Plant Genetic Engineering; Center for Quantitative Biology; NYU-ECNU Institute of Mathematical Sciences; New York University Shanghai; NYU-ECNU Institute of Brain and Cognitive Science（北京大学-清华大学-中国生物科学研究院联合研究生项目; 先进跨学科研究院; 生物信息中心; 生命科学学院; 蛋白质工程与植物基因工程国家实验室; 定量生物学中心; 纽约大学-复旦大学数学科学研究院; 纽约大学上海分校; 纽约大学-复旦大学脑与认知科学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究复杂系统参数与可观测量关系，将兼容参数集形式化为可行参数流形，用条件分数扩散模型训练并采样，以Lorenz等模型为例揭示系统补偿几何等，为研究提供工具。
AI 中文摘要
复杂系统模型参数多但受实验可测可观测量限制，兼容参数集可形式化为可行参数流形。我们在模拟参数-特征对上训练条件分数扩散模型并用作加权可行集的摊销采样器，通过多个模型揭示了相关几何结构及特性，扩散模型为研究提供实用工具。
英文摘要
Models of complex systems often have many parameters, yet are constrained by far fewer experimentally accessible observables; consequently, similar activity can emerge from coordinated parameter changes. We formalize these compatible parameter sets as \emph{viable parameter manifolds}: the inverse images of target dynamical features under a parameter-to-feature map. The relevant codimension is not the number of reported features, but the effective rank of that map at the target scale. Locally redundant features lower the effective codimension, while poor conditioning, high curvature, or regime mixing degrade learnability. We train conditional score-based diffusion models on simulated parameter--feature pairs and use them as amortized samplers of prior-weighted viable sets. In the Lorenz system, scalar trajectory statistics generate thin viable sheets, and a finite-tolerance conditioning localizes a transition-adjacent corridor. In the Izhikevich neuron model, four firing descriptors lie close to a nearly two-dimensional family of features, and the learned inverse images reveal distinct regular and irregular compensation geometries. In a deterministic ODE reduction of finite spiking networks, the same framework reveals excitatory--inhibitory compensation, timescale--coupling tradeoffs, and viable manifolds across 4--12 parameter dimensions. In this view, robustness, compensation, and hidden parameter dependencies are organized as inverse geometry, with diffusion models providing practical tools for sampling, visualizing, and interrogating that geometry.
Comments25 pages, 7 figures
