用视觉嵌入捕捉随机模式的不变性,反推系统演化参数。
Solving Inverse Problems in Stochastic Self-Organizing Systems through Invariant Representations
- 通过视觉嵌入构建对称性不变表征空间
- 在三类自组织系统中成功恢复未知参数
- 适合研究复杂随机模式形成的理论与实验工作者
自组织系统展示简单局部规则如何生成复杂的随机模式。许多自然系统依赖此类动力学,使自组织成为理解自然复杂性的核心。建模中的根本挑战是逆问题:从宏观观测中推断未知因果参数。当观测具有强随机性时,不同结果产生多样但等价的模式,传统逆方法失效,因像素级度量无法捕捉变量结果间的特征相似性。本文提出一种新逆建模方法,专为处理可观测空间的随机性设计,利用视觉嵌入能力生成鲁棒表征,捕捉感知不变性。通过将模式表征映射到不变嵌入空间,可有效恢复未知因果参数,无需手工设计目标函数或启发式规则。我们在三类自组织系统上评估:一个物理系统(反应-扩散)、一个生物系统(胚胎发育模型)和一个社会系统(社会隔离代理模型)。结果显示,该方法在模式结果存在随机性的情况下仍能可靠恢复参数。进一步应用于真实生物图案,凸显其作为理论与实验研究者探究复杂随机模式形成机制的潜力。
原文摘要 · Abstract (English)
Self-organizing systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organization central to understanding natural complexity. A fundamental challenge in modeling such systems is solving the inverse problem: finding the unknown causal parameters from macroscopic observations. This task becomes particularly difficult when observations have a strong stochastic component, yielding diverse yet equivalent patterns. Traditional inverse methods fail in this setting, as pixel-wise metrics cannot capture feature similarities between variable outcomes. In this work, we introduce a novel inverse modeling method specifically designed to handle stochasticity in the observable space, leveraging the capacity of visual embeddings to produce robust representations that capture perceptual invariances. By mapping the pattern representations onto an invariant embedding space, we can effectively recover unknown causal parameters without the need for handcrafted objective functions or heuristics. We evaluate the method on three self-organizing systems: a physical, a biological, and a social one; namely, a reaction-diffusion system, a model of embryonic development, and an agent-based model of social segregation. We show that the method reliably recovers parameters despite stochasticity in the pattern outcomes. We further apply the method to real biological patterns, highlighting its potential as a tool for both theorists and experimentalists to investigate the dynamics underlying complex stochastic pattern formation.
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