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    Area of Science:

    • Cognitive Science
    • Computational Neuroscience
    • Psychology

    Background:

    • Contingency between cues and outcomes is crucial for causal reasoning and associative learning theories.
    • Rescorla-Wagner models are widely used to study contingency, but their comparison with artificial neural networks (ANNs) is limited.
    • Assumed equivalence between Rescorla-Wagner and delta rule in ANNs has hindered direct mathematical comparison.

    Purpose of the Study:

    • To provide a mathematical analysis comparing ANNs and contingency theory.
    • To investigate how ANNs handle contingency problems, addressing recent findings on the non-straightforward equivalence with Rescorla-Wagner models.
    • To explore the structural and functional relationships between associative learning, contingency theory, and connectionism.

    Main Methods:

    • Mathematical analysis of a simple ANN trained on a basic contingency problem.
    • Comparison of the equilibrium structure of the ANN with that of a Rescorla-Wagner model.
    • Investigating the functional behavior resulting from structural differences.

    Main Results:

    • The equilibrium structure of a simple ANN differs significantly from that of a Rescorla-Wagner model for the same contingency problem.
    • Despite structural differences, the ANN and Rescorla-Wagner model demonstrate functionally equivalent behavior.
    • This finding challenges the assumed straightforward equivalence between the two models.

    Conclusions:

    • The study provides a novel mathematical account of how ANNs process contingency.
    • Structural differences between ANNs and Rescorla-Wagner models do not necessarily lead to functional differences in behavior.
    • Results have implications for understanding the interplay between associative learning, contingency theory, and connectionist approaches.