ActPC-Geom：借助信息几何与多样化认知机制加速主动预测编码，迈向可扩展的在线神经-符号学习
ActPC-Geom: Towards Scalable Online Neural-Symbolic Learning via Accelerating Active Predictive Coding with Information Geometry & Diverse Cognitive Mechanisms
AI总结：
本文提出 ActPC-Geom，用 Wasserstein 度量、神经近似、kPCA 与超向量/FCA 格机制加速 ActPC，实现可扩展的实时在线神经-符号学习与少样本审慎推理。
摘要：
本文介绍 ActPC-Geom，这是一种通过融合信息几何来加速神经网络中主动预测编码（Active Predictive Coding，ActPC）的方法，具体采用基于 Wasserstein 度量的方法处理依赖于测度的梯度流。我们提议将 ActPC 预测误差评估中的 KL 散度替换为 Wasserstein 度量，并认为这可能增强网络的鲁棒性。为使其在计算上可行，我们提出若干策略，包括：（1）用于逆的、依赖于测度的 Laplace 算子的神经近似器；（2）近似核 PCA（kPCA）嵌入，用于为这些近似器提供低秩近似；以及（3）由 kPCA 输出导出的组合超向量嵌入，其代数针对模糊 FCA 格进行了优化，而这些格通过分析网络状态的神经架构学习得到。由此形成的 ActPC 架构能够进行实时在线学习，并整合连续型（例如类似 transformer 或类似 Hopfield 网络的）与离散符号型 ActPC 网络，包括用于算法化学演化的 OpenCog Hyperon 或 ActPC-Chem 等框架。共享的概率模型、概念格模型和超向量模型使符号—亚符号整合成为可能。关键特性包括：（1）在类似 transformer 的架构中通过超向量嵌入实现组合推理，以处理常识推理等任务；（2）Hopfield 网络动力学支持联想长期记忆和吸引子驱动的认知特性。我们概述了 ActPC-Geom 如何将少样本学习与在线权重更新相结合，从而实现审慎思维以及无缝的符号—亚符号推理。文中还探索了来自 Galois 连接的思想，以实现高效的混合 ActPC/ActPC-Chem 处理。最后，我们提出一种专门的 HPC 设计，针对 ActPC-Geom 的需求进行优化，以支持实时集中注意和审慎推理。
英文摘要：
This paper introduces ActPC-Geom, an approach to accelerate Active Predictive Coding (ActPC) in neural networks by integrating information geometry, specifically using Wasserstein-metric-based methods for measure-dependent gradient flows. We propose replacing KL-divergence in ActPC's predictive error assessment with the Wasserstein metric, suggesting this may enhance network robustness. To make this computationally feasible, we present strategies including: (1) neural approximators for inverse measure-dependent Laplacians, (2) approximate kernel PCA embeddings for low-rank approximations feeding into these approximators, and (3) compositional hypervector embeddings derived from kPCA outputs, with algebra optimized for fuzzy FCA lattices learned through neural architectures analyzing network states. This results in an ActPC architecture capable of real-time online learning and integrating continuous (e.g., transformer-like or Hopfield-net-like) and discrete symbolic ActPC networks, including frameworks like OpenCog Hyperon or ActPC-Chem for algorithmic chemistry evolution. Shared probabilistic, concept-lattice, and hypervector models enable symbolic-subsymbolic integration. Key features include (1) compositional reasoning via hypervector embeddings in transformer-like architectures for tasks like commonsense reasoning, and (2) Hopfield-net dynamics enabling associative long-term memory and attractor-driven cognitive features. We outline how ActPC-Geom combines few-shot learning with online weight updates, enabling deliberative thinking and seamless symbolic-subsymbolic reasoning. Ideas from Galois connections are explored for efficient hybrid ActPC/ActPC-Chem processing. Finally, we propose a specialized HPC design optimized for real-time focused attention and deliberative reasoning tailored to ActPC-Geom's demands.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
