Supplemental File from Symmetry and complexity in object-centric deep active inference models

Humans perceive and interact with hundreds of objects every day. In doing so, they need to employ mental models of these objects and often exploit symmetries in the object’s shape and appearance in order to learn generalizable and transferable skills. Active inference is a first principles approach to understanding and modelling sentient agents. It states that agents entertain a generative model of their environment, and learn and act by minimizing an upper bound on their surprisal, i.e. their Free Energy. The Free Energy decomposes into an accuracy and complexity term, meaning that agents favour the least complex model, that can accurately explain their sensory observations. In this paper, we investigate how inherent symmetries of particular objects also emerge as symmetries in the latent state space of the generative model learnt under deep active inference. In particular, we focus on object-centric representations, which are trained from pixels to predict novel object views as the agent moves its viewpoint. First, we investigate the relation between model complexity and symmetry exploitation in the state space. Second, we do a principal component analysis to demonstrate how the model encodes the principal axis of symmetry of the object in the latent space. Finally, we also demonstrate how more symmetrical representations can be exploited for better generalization in the context of manipulation.

人类每日感知并与数百种物体交互。在此过程中，人类需要构建这些物体的心理模型，并常利用物体形状与外观上的对称性，以习得可泛化、可迁移的技能。主动推理（Active Inference）是一种用于理解与建模感知智能体的第一性原理范式。该范式指出，智能体拥有对自身所处环境的生成模型（generative model），并通过最小化自身惊讶度（surprisal）的上界——即自由能（Free Energy）——来进行学习与行动。自由能可分解为准确度项与复杂度项，这意味着智能体倾向于选择能够准确解释自身感官观测结果的最简模型。本文旨在探究特定物体的固有对称性，如何在基于深度主动推理训练得到的生成模型的隐状态空间（latent state space）中，以对称性的形式涌现出来。具体而言，我们聚焦于以物体为中心的表征（object-centric representations）——这类表征从像素数据中训练得到，可在智能体移动视点时预测物体的全新视角。首先，我们探究模型复杂度与状态空间中对称性利用之间的关联。其次，我们通过主成分分析（Principal Component Analysis, PCA），展示模型如何在隐空间中编码物体的对称主轴。最后，我们还将展示，在操控任务场景中，如何利用更具对称性的表征以实现更优异的泛化性能。