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Reducing Diversity to Generate Hierarchical Archetypes

Alfredo Ibias, Hector Antona, Guillem Ramirez-Miranda, Enric Guinovart, Eduard Alarcon

TL;DR

This paper presents a primitive-based framework to automatically generate hierarchies of constructive archetypes, as a theory of how to generate hierarchies of abstractions.

Abstract

The Artificial Intelligence field seldom address the development of a fundamental building piece: a framework, methodology or algorithm to automatically build hierarchies of abstractions. This is a key requirement in order to build intelligent behaviour, as recent neuroscience studies clearly expose. In this paper we present a primitive-based framework to automatically generate hierarchies of constructive archetypes, as a theory of how to generate hierarchies of abstractions. We assume the existence of a primitive with very specific characteristics, and we develop our framework over it. We prove the effectiveness of our framework through mathematical definitions and proofs. Finally, we give a few insights about potential uses of our framework and the expected results.

Reducing Diversity to Generate Hierarchical Archetypes

TL;DR

This paper presents a primitive-based framework to automatically generate hierarchies of constructive archetypes, as a theory of how to generate hierarchies of abstractions.

Abstract

The Artificial Intelligence field seldom address the development of a fundamental building piece: a framework, methodology or algorithm to automatically build hierarchies of abstractions. This is a key requirement in order to build intelligent behaviour, as recent neuroscience studies clearly expose. In this paper we present a primitive-based framework to automatically generate hierarchies of constructive archetypes, as a theory of how to generate hierarchies of abstractions. We assume the existence of a primitive with very specific characteristics, and we develop our framework over it. We prove the effectiveness of our framework through mathematical definitions and proofs. Finally, we give a few insights about potential uses of our framework and the expected results.
Paper Structure (15 sections, 14 theorems, 1 equation, 5 figures)

This paper contains 15 sections, 14 theorems, 1 equation, 5 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. The Diversity Reduction Framework
  4. Proofs
  5. The primitive and its properties
  6. Discriminatory Pyramids
  7. Associative Layers
  8. Case Studies
  9. The Unsupervised Scenario
  10. The Supervised Classification Scenario
  11. The Supervised Regression Scenario
  12. The State-Action Scenario
  13. An Illustrative Example
  14. Limitations
  15. Conclusions

Key Result

Theorem 1

Given a process $\mathcal{P}$, and given an input set $I$, if $\mathcal{P}(I)$ produces an output set $O$, with $|O| \leq |I|$, then $\mathcal{P}$ is equivalent to a surjective function mapping $I \to O$.

Figures (5)

  • Figure 1: Basic structure of a primitive.
  • Figure 2: An example of discriminatory pyramid (left) and of its base case called discriminatory column (right).
  • Figure 3: An example of associative layer.
  • Figure 4: An example of complex architecture.
  • Figure 5: Three architectures for the same dataset. The numbers are the sizes of the corresponding input/output sets.

Theorems & Definitions (34)

  • Definition 1
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Definition 2
  • Theorem 3
  • proof
  • Definition 3
  • Definition 4
  • ...and 24 more