They had four primitive actions: north, south, east, and west. Multi-Floor Office is an extension of Office to multiple floors. Pick-up and put-down have the intended effect when appropriate; otherwise they do not change the state. T owers of Hanoi contains four discs of different sizes, placed on three poles. Options generated using alternative methods called primitive actions directly.

They had four primitive actions: north, south, east, and west. Multi-Floor Office is an extension of Office to multiple floors. Pick-up and put-down have the intended effect when appropriate; otherwise they do not change the state. T owers of Hanoi contains four discs of different sizes, placed on three poles. Options generated using alternative methods called primitive actions directly.

What is a useful skill hierarchy for an autonomous agent?

The explosive growth of complex datasets across various modalities necessitates advanced analytical tools that not only group data effectively but also provide human-understandable insights into the discovered structures. We introduce HERCULES (Hierarchical Embedding-based Recursive Clustering Using LLMs for Efficient Summarization), a novel algorithm and Python package designed for hierarchical k-means clustering of diverse data types, including text, images, and numeric data (processed one modality per run). HERCULES constructs a cluster hierarchy by recursively applying k-means clustering, starting from individual data points at level 0. A key innovation is its deep integration of Large Language Models (LLMs) to generate semantically rich titles and descriptions for clusters at each level of the hierarchy, significantly enhancing interpretability. The algorithm supports two main representation modes: `direct' mode, which clusters based on original data embeddings or scaled numeric features, and `description' mode, which clusters based on embeddings derived from LLM-generated summaries. Users can provide a `topic\_seed' to guide LLM-generated summaries towards specific themes. An interactive visualization tool facilitates thorough analysis and understanding of the clustering results. We demonstrate HERCULES's capabilities and discuss its potential for extracting meaningful, hierarchical knowledge from complex datasets.

Hierarchical clustering is a powerful tool for exploratory data analysis, organizing data into a tree of clusterings from which a partition can be chosen. This paper generalizes these ideas by proving that, for any reasonable hierarchy, one can optimally solve any center-based clustering objective over it (such as $k$-means). Moreover, these solutions can be found exceedingly quickly and are themselves necessarily hierarchical. Thus, given a cluster tree, we show that one can quickly access a plethora of new, equally meaningful hierarchies. Just as in standard hierarchical clustering, one can then choose any desired partition from these new hierarchies. We conclude by verifying the utility of our proposed techniques across datasets, hierarchies, and partitioning schemes.

What is a useful skill hierarchy for an autonomous agent? We propose an answer based on the graphical structure of an agent's interaction with its environment. Our approach uses hierarchical graph partitioning to expose the structure of the graph at varying timescales, producing a skill hierarchy with multiple levels of abstraction. At each level of the hierarchy, skills move the agent between regions of the state space that are well connected within themselves but weakly connected to each other. We illustrate the utility of the proposed skill hierarchy in a wide variety of domains in the context of reinforcement learning.

Knowledge graphs have emerged as a widely adopted medium for storing relational data, making methods for automatically reasoning with them highly desirable. In this paper, we present a novel approach for inducing a hierarchy of subject clusters, building upon our earlier work done in taxonomy induction. Our method first constructs a tag hierarchy before assigning subjects to clusters on this hierarchy. We quantitatively demonstrate our method's ability to induce a coherent cluster hierarchy on three real-world datasets.

We present an approach to model-based hierarchical clustering by formulating an objective function based on a Bayesian analysis. This model organizes the data into a cluster hierarchy while specifying a complex feature-set partitioning that is a key component of our model. Features can have either a unique distribution in every cluster or a common distribution over some (or even all) of the clusters. The cluster subsets over which these features have such a common distribution correspond to the nodes (clusters) of the tree representing the hierarchy. We apply this general model to the problem of document clustering for which we use a multinomial likelihood function and Dirichlet priors. Our algorithm consists of a two-stage process wherein we first perform a flat clustering followed by a modified hierarchical agglomerative merging process that includes determining the features that will have common distributions over the merged clusters. The regularization induced by using the marginal likelihood automatically determines the optimal model structure including number of clusters, the depth of the tree and the subset of features to be modeled as having a common distribution at each node.