Date: Nov 28, 2018 3:00pm-4:30pm
Location: Dunton Tower: Room 2203
Speaker: Michael Vertolli
Title: From Embeddings to Concepts: A Study of Representational Structure in Imagination
Imagination can represent relationships between radically different topics, concepts, and objects with minimal effort. An open question in the study of imagination is how to model this process. Over the course of this talk, I argue that four critical components are required to answer this question in the context of visual imagination.
The first section develops a theory, model and implementation of the basic building blocks of imagination. I show that these building blocks can be represented by graphs that have a strong form of hierarchical compositionality (SHC) consistent with our imagined representations. In the second section, I outline three recent techniques that enable an analysis of SHC graphs and their substructures. The core insight is that current state-of-the-art approaches to similarity only measure surface features. Drawing on topological data analysis, I show that deeper structures can both be identified and compared across SHC graphs. This enables a more detailed examination of the motivating question.
The second half of the talk leverages the resulting tools to propose a theory and model of relationships between representations with fundamentally different surface structures. I introduce the notion of harmony as a structural union of SHC graphs that attaches disparate representations via their deep structural equivalences. Consistent with intuitions of ambiguous images, illusions, and similar visual equivalences, harmonization preserves SHC through the relationships it constructs. I argue that SHC also enables a form of causal independence that is essential for the harmonization process, tightly coupling the concepts.
The final section moves to a discussion of information processing schemes that could compute harmony. My proposed technique exploits hierarchical embeddings to produce the necessary SHC and causal independence required by the theory. This distills another tight conceptual coupling for the topic. I then conclude the section by empirically demonstrating that hierarchical embeddings transform generative adversarial networks from a process of mapping-by-deformation to the desired, structure preserving harmony relation. I call the resulting theory of representational structure conceptual geometries in an effort to differentiate it from traditional approaches for describing structure.