This supplementary material provides implementation details, hyper-parameters settings, additional results and visualisations. Section A presents a focus on the design choices we use for IMGEP-HOLMES Section B provides implementation details for the main paper evaluation procedure - B.1: Quantitative evaluation of diversity - B.2: Quantitative evaluation of Representational Similarity - D.1: Complete RSA analysis of the hierarchy of behavioral characterizations learned Figure 6: Focus on the different design choices made for the HOLMES architecture. We summarize those components in Figure 6. The connection scheme is summarized in Figure 6. There are two main choices: when to split a node and how to redirect the patterns toward either the left or right children.

Self-organization of complex morphological patterns from local interactions is a fascinating phenomenon in many natural and artificial systems. In the artificial world, typical examples of such morphogenetic systems are cellular automata. Yet, their mechanisms are often very hard to grasp and so far scientific discoveries of novel patterns have primarily been relying on manual tuning and ad hoc exploratory search. The problem of automated diversity-driven discovery in these systems was recently introduced [26, 61], highlighting that two key ingredients are autonomous exploration and unsupervised representation learning to describe "relevant" degrees of variations in the patterns. In this paper, we motivate the need for what we call Meta-diversity search, arguing that there is not a unique ground truth interesting diversity as it strongly depends on the final observer and its motives. Using a continuous game-of-life system for experiments, we provide empirical evidences that relying on monolithic architectures for the behavioral embedding design tends to bias the final discoveries (both for hand-defined and unsupervisedly-learned features) which are unlikely to be aligned with the interest of a final end-user. To address these issues, we introduce a novel dynamic and modular architecture that enables unsupervised learning of a hierarchy of diverse representations. Combined with intrinsically motivated goal exploration algorithms, we show that this system forms a discovery assistant that can efficiently adapt its diversity search towards preferences of a user using only a very small amount of user feedback.

Designing agent that can autonomously discover and learn a diversity of structures and skills in unknown changing environments is key for lifelong machine learning. A central challenge is how to learn incrementally representations in order to progressively build a map of the discovered structures and re-use it to further explore. To address this challenge, we identify and target several key functionalities. First, we aim to build lasting representations and avoid catastrophic forgetting throughout the exploration process. Secondly we aim to learn a diversity of representations allowing to discover a "diversity of diversity" of structures (and associated skills) in complex high-dimensional environments. Thirdly, we target representations that can structure the agent discoveries in a coarse-to-fine manner. Finally, we target the reuse of such representations to drive exploration toward an "interesting" type of diversity, for instance leveraging human guidance. Current approaches in state representation learning rely generally on monolithic architectures which do not enable all these functionalities. Therefore, we present a novel technique to progressively construct a Hierarchy of Observation Latent Models for Exploration Stratification, called HOLMES. This technique couples the use of a dynamic modular model architecture for representation learning with intrinsically-motivated goal exploration processes (IMGEPs). The paper shows results in the domain of automated discovery of diverse self-organized patterns, considering as testbed the experimental framework from Reinke et al. (2019).