发表机构
Indian Institute of Management, Udaipur; Ashoka University; Indian Statistical Institute（乌代布尔印度管理学院; 阿肖克大学; 印度统计研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将预测编码与递归高斯过程（RGPs）形式化关联，证明RGPs可实现分层贝叶斯推理等功能，将其组成部分映射到皮层微回路，定位其为计算工具与大脑预测机制模型，可产生可检验的神经动力学预测。
AI 中文摘要
预测编码为皮层计算提供了强大框架，但同时兼顾贝叶斯精确性与神经生物学约束的可扩展实现仍较为稀缺。我们通过将预测编码与递归高斯过程（Recursive Gaussian Processes, RGPs）建立形式化联系，弥合了这一缺口。RGPs采用以层索引和输入值为索引的单一高斯过程\boldsymbol{g(t, \boldsymbol{\bullet})}，可避免标准深度高斯过程的表征崩溃，同时通过\boldsymbol{r_{1g}}实现可学习的跨层依赖。我们证明RGPs本质上可实现分层贝叶斯推理、不确定性传播及精度加权预测误差。关键在于，我们将RGPs的组成部分——共享高斯过程、尖峰-板条变量选择及马尔可夫链蒙特卡洛（MCMC）动力学——映射到经典皮层微回路，为这些计算提供了神经生物学基底。基于自由能原理，我们表明RGP推理可最小化变分自由能，将贝叶斯力学与神经元动力学建立形式化联系。我们的综合研究将RGPs定位为兼具原则性的计算工具与大脑预测机制候选模型，可产生针对层特异性动力学及前馈与反馈处理间频谱不对称性的可检验预测。
英文摘要
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.
CommentsWhat is your thought process? The Bayesian Recursive Gaussian process?
