用递归高斯过程建模大脑预测计算，连接贝叶斯推理与神经机制。
Recursive Gaussian Processes and the Bayesian Brain
- 通过递归高斯过程实现分层贝叶斯推断，避免表示崩溃。
- 模型自动传播不确定性并加权预测误差，符合神经动态。
- 可解释皮层微环路机制，适合研究大脑预测编码的生物基础。
预测编码为皮层计算提供了强大框架，但满足贝叶斯精确性与神经生物学约束的可扩展实现仍稀缺。本文通过将预测编码正式关联到递归高斯过程（RGPs）来弥合这一差距。RGPs使用一个由层级索引和输入值共同索引的单一高斯过程 $ g(t, \cdot) $，防止标准深度高斯过程中的表示崩溃，并通过 $ r_{1g} $ 实现可学习的跨层依赖。我们证明，RGPs天然实现分层贝叶斯推断、不确定性传播和精度加权预测误差。关键的是，我们将RGP组件——共享高斯过程、稀疏-板式变量选择和MCMC动力学——映射到经典的皮层微环路，为其计算提供神经生物学基础。基于自由能原理，我们证明RGP推断最小化变分自由能，正式链接贝叶斯力学与神经动力学。本合成使RGPs成为既具原则性的计算工具，也作为大脑预测机制的候选模型，生成关于分层特异性动态和前馈/反馈处理频谱不对称性的可检验预测。
原文摘要 · Abstract (English)
Predictive coding offers a powerful framework for cortical computation, yet scalable implementations that respect both Bayesian exactness and neurobiological constraints remain scarce. We bridge this gap by formally connecting predictive coding to Recursive Gaussian Processes (RGPs). RGPs employ a single Gaussian process \( g(t, \cdot) \) indexed by layer index and input value, preventing the representational collapse of standard deep Gaussian processes while allowing learnable cross-layer dependence via \( r_{1g} \). We demonstrate that RGPs intrinsically implement hierarchical Bayesian inference, uncertainty propagation, and precision-weighted prediction error. Critically, we map RGP components---the shared GP, spike-and-slab variable selection, and MCMC dynamics---onto the canonical cortical microcircuit, providing a neurobiological substrate for these computations. Drawing on the free energy principle, we show that RGP inference minimizes variational free energy, formally linking Bayesian mechanics to neuronal dynamics. Our synthesis positions RGPs as both a principled computational tool and a candidate model for the brain's predictive machinery, generating testable predictions for laminar-specific dynamics and spectral asymmetries between feedforward and feedback processing.
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