Modern generative machine learning models demonstrate surprising ability to
create realistic outputs far beyond their training data, such as photorealistic
artwork, accurate protein structures, or conversational text. These successes
suggest that generative models learn to effectively parametrize and sample
arbitrarily complex distributions. Beginning half a century ago, foundational
works in nonlinear dynamics used tools from information theory to infer
properties of chaotic attractors from time series, motivating the development
of algorithms for parametrizing chaos in real datasets. In this perspective, we
aim to connect these classical works to emerging themes in large-scale
generative statistical learning. We first consider classical attractor
reconstruction, which mirrors constraints on latent representations learned by
state space models of time series. We next revisit early efforts to use
symbolic approximations to compare minimal discrete generators underlying
complex processes, a problem relevant to modern efforts to distill and
interpret black-box statistical models. Emerging interdisciplinary works bridge
nonlinear dynamics and learning theory, such as operator-theoretic methods for
complex fluid flows, or detection of broken detailed balance in biological
datasets. We anticipate that future machine learning techniques may revisit
other classical concepts from nonlinear dynamics, such as transinformation
decay and complexity-entropy tradeoffs.

现代生成式机器学习模型展示出令人惊讶的能力，能够创造出超越其训练数据的逼真产出，如逼真的艺术作品、精确的蛋白结构或对话文本。这些成功表明生成模型学会了有效地参数化和采样任意复杂的分布。本文旨在将经典作品与大规模生成统计学习中的新兴主题联系起来，包括经典吸引子重构、隐空间模型中的潜在表示学习等。还介绍了早期利用符号近似进行比较的努力，与现代努力进行黑盒统计模型的精简和解释相关。新兴的跨学科研究桥接了非线性动力学和学习理论，如用于复杂流体流动的算子理论方法，或者检测生物数据集中打破了详细平衡的情况。我们预计未来的机器学习技术可能会重新审视非线性动力学中的其他经典概念，如信息传输衰减和复杂性 - 熵权衡问题。