Attractor dynamics are a hallmark of many complex systems, including the brain. Understanding how such self-organizing dynamics emerge from first principles is crucial for advancing our understanding of neuronal computations and the design of artificial intelligence systems. Here we formalize how attractor networks emerge from the free energy principle applied to a universal partitioning of random dynamical systems. Our approach obviates the need for explicitly imposed learning and inference rules and identifies emergent, but efficient and biologically plausible inference and learning dynamics for such self-organizing systems. These result in a collective, multi-level Bayesian active inference process. Attractors on the free energy landscape encode prior beliefs; inference integrates sensory data into posterior beliefs; and learning fine-tunes couplings to minimize long-term surprise. Analytically and via simulations, we establish that the proposed networks favor approximately orthogonalized attractor representations, a consequence of simultaneously optimizing predictive accuracy and model complexity. These attractors efficiently span the input subspace, enhancing generalization and the mutual information between hidden causes and observable effects. Furthermore, while random data presentation leads to symmetric and sparse couplings, sequential data fosters asymmetric couplings and non-equilibrium steady-state dynamics, offering a natural generalization of conventional Boltzmann Machines. Our findings offer a unifying theory of self-organizing attractor networks, providing novel insights for AI and neuroscience.

翻译：吸引子动力学是包括大脑在内的许多复杂系统的标志。理解这种自组织动力学如何从第一性原理涌现，对于推进我们对神经计算的理解以及人工智能系统的设计至关重要。本文形式化了吸引子网络如何从应用于随机动力系统普适划分的自由能原理中涌现。我们的方法无需显式施加学习和推理规则，并为这类自组织系统识别出涌现的、高效且具有生物合理性的推理和学习动力学。这些过程产生了一个集体的、多层次贝叶斯主动推理过程。自由能景观上的吸引子编码先验信念；推理将感觉数据整合为后验信念；而学习则微调耦合以最小化长期惊讶。通过解析分析和数值模拟，我们证明了所提出的网络倾向于近似正交化的吸引子表示，这是同时优化预测精度和模型复杂度的结果。这些吸引子高效地张成输入子空间，增强了泛化能力以及隐藏原因与可观测效应之间的互信息。此外，随机数据呈现会导致对称且稀疏的耦合，而序列数据则促进非对称耦合和非平衡稳态动力学，从而为传统玻尔兹曼机提供了一种自然的推广。我们的发现为自组织吸引子网络提供了一个统一的理论，为人工智能和神经科学提供了新的见解。