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Simple Auto-Associative Networks Succeed at Universal Generalization of the Identity Function and Reduplication Rule.

Kenneth J Kurtz¹

¹Department of Psychology, Binghamton University.

Cognitive Science

|January 16, 2025

Summary

Standard connectionist models can achieve universal generalization for identity-based relational reasoning. Simple feed-forward networks demonstrate capabilities previously thought impossible, bridging symbolic reasoning and neural network mechanisms.

Keywords:

Autoencoders Connectionist models Connectionist versus symbolic architectures Reduplication Relational reasoning Universal function generalization

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Area of Science:

Cognitive Science
Artificial Intelligence
Neuroscience

Background:

Standard connectionist models are widely considered incapable of identity-based relational reasoning, particularly universal generalization.
This limitation has fueled debate regarding the fundamental nature of cognitive architectures and their ability to support complex reasoning.

Purpose of the Study:

To demonstrate that simple feed-forward auto-associative networks can exhibit universal generalization.
To address two key challenges: universal generalization of the identity function and the reduplication rule within connectionist models.

Main Methods:

Utilized feed-forward auto-associative networks, a basic form of connectionist model.
Provided a clear modeling account and evidence to support the claims of generalization capabilities.

Main Results:

Demonstrated that feed-forward auto-associative networks successfully satisfy universal generalization for the identity function.
Showcased the reduplication rule's fulfillment within these simple network models.

Conclusions:

The findings challenge the established view on connectionist model limitations in relational reasoning.
Suggests that simple connectionist mechanisms can bridge the gap with symbolic reasoning, offering a new perspective on cognitive architecture.