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Deep ARTMAP: Generalized Hierarchical Learning with Adaptive Resonance Theory

Niklas M. Melton, Leonardo Enzo Brito da Silva, Sasha Petrenko, Donald. C. Wunsch

TL;DR

Deep ARTMAP addresses the challenge of learning hierarchical structure from multi-modal data by extending ART-based architectures to a multi-layer, transform-aware framework. It generalizes SMART and ARTMAP through a chain of module blocks driven by arbitrary nonlinear transforms $f_k$, enabling both unsupervised divisive clustering and supervised learning within the same architecture; inter-ART map fields enforce structured cross-layer mappings. The key contributions include showing that Deep ARTMAP reduces to SMART under identity transforms and to ARTMAP for $L=2$, outlining an incremental online training algorithm that processes samples top-down and supports parallelizable inference, and providing open-source software implementations in Python and Julia. This framework offers scalable, continual-learning capable hierarchical clustering for multi-modal data, with potential applications in complex relational tasks and reduced catastrophic forgetting in dynamic environments.

Abstract

This paper presents Deep ARTMAP, a novel extension of the ARTMAP architecture that generalizes the self-consistent modular ART (SMART) architecture to enable hierarchical learning (supervised and unsupervised) across arbitrary transformations of data. The Deep ARTMAP framework operates as a divisive clustering mechanism, supporting an arbitrary number of modules with customizable granularity within each module. Inter-ART modules regulate the clustering at each layer, permitting unsupervised learning while enforcing a one-to-many mapping from clusters in one layer to the next. While Deep ARTMAP reduces to both ARTMAP and SMART in particular configurations, it offers significantly enhanced flexibility, accommodating a broader range of data transformations and learning modalities.

Deep ARTMAP: Generalized Hierarchical Learning with Adaptive Resonance Theory

TL;DR

Deep ARTMAP addresses the challenge of learning hierarchical structure from multi-modal data by extending ART-based architectures to a multi-layer, transform-aware framework. It generalizes SMART and ARTMAP through a chain of module blocks driven by arbitrary nonlinear transforms , enabling both unsupervised divisive clustering and supervised learning within the same architecture; inter-ART map fields enforce structured cross-layer mappings. The key contributions include showing that Deep ARTMAP reduces to SMART under identity transforms and to ARTMAP for , outlining an incremental online training algorithm that processes samples top-down and supports parallelizable inference, and providing open-source software implementations in Python and Julia. This framework offers scalable, continual-learning capable hierarchical clustering for multi-modal data, with potential applications in complex relational tasks and reduced catastrophic forgetting in dynamic environments.

Abstract

This paper presents Deep ARTMAP, a novel extension of the ARTMAP architecture that generalizes the self-consistent modular ART (SMART) architecture to enable hierarchical learning (supervised and unsupervised) across arbitrary transformations of data. The Deep ARTMAP framework operates as a divisive clustering mechanism, supporting an arbitrary number of modules with customizable granularity within each module. Inter-ART modules regulate the clustering at each layer, permitting unsupervised learning while enforcing a one-to-many mapping from clusters in one layer to the next. While Deep ARTMAP reduces to both ARTMAP and SMART in particular configurations, it offers significantly enhanced flexibility, accommodating a broader range of data transformations and learning modalities.

Paper Structure

This paper contains 11 sections, 1 figure, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Adaptive Resonance Theory (ART)
  4. ARTMAP
  5. Simplified ARTMAP
  6. Self-consistent Modular ART (SMART)
  7. DeepARTMAP
  8. Algorithm
  9. Limitations and Considerations
  10. Software Implementation
  11. Acknowledgments

Figures (1)

  • Figure 1: The Deep ARTMAP model. A single input sample is processed by differing nonlinear functions $f_k$ and presented to a set of $L$ ART modules that interact through inter-ARTMAP map fields $1, \ldots, L - 1$. Deep ARTMAP reduces to SMART in the case of identity transforms $f_k(\mathbf{x}) = \mathbf{x}$, and it further reduces to ARTMAP with the use of two ART modules $L = 2$ arranged into a single ARTMAP module during.