The conceptual basis of function learning and extrapolation: comparison of rule-based and associative-based models

Area of Science:

• Cognitive Psychology
• Machine Learning Theory
• Computational Neuroscience

Background:

• Existing formal theories of function learning have limitations.
• Progress in category learning has not been matched by similar formal approaches in function learning.
• Need for a systematic and integrative framework for function learning.

Purpose of the Study:

• To establish a foundation for a formal, systematic, and integrative approach to function learning.
• To develop and test novel computational models of function learning.
• To identify psychologically plausible learning mechanisms.

Main Methods:

• Critique of existing formal theories of function learning.
• Development of expanded rule-based and associative-based function learning models.
• Specification of psychologically-based learning mechanisms for rule models.
• Design of rigorous tests evaluating model performance based on learning difficulty and extrapolation.
• Analysis of detailed learning performance data for model evaluation.

Main Results:

• A hybrid model, EXAM (Extrapolation via Associative-Memory), is proposed.
• EXAM combines associative learning for input-prediction pairs with rule-based outputs for extrapolation.
• This hybrid model demonstrates superior explanatory power compared to purely associative or rule-based models.

Conclusions:

• The findings support a hybrid approach to function learning, integrating associative and rule-based mechanisms.
• The EXAM model provides a more comprehensive account of human function learning, particularly for extrapolation.
• This work paves the way for more advanced, psychologically grounded models of cognitive learning.