Invariance, Encodings, and Generalization: Learning Identity Effects With Neural Networks

Area of Science:

• Cognitive Science
• Artificial Intelligence
• Computational Linguistics

Background:

• Well-formedness in language and cognition often relies on identity effects, where component identity determines structural validity.
• Explicitly programming identity effects into AI systems is feasible, but learning them implicitly from data presents a significant challenge.

Purpose of the Study:

• To investigate whether identity effects, crucial for well-formedness, can be learned by AI algorithms without explicit guidance.
• To develop a theoretical framework for analyzing the learnability of identity effects in machine learning models.

Main Methods:

• Developed a formal framework to rigorously prove limitations of certain learning algorithms regarding identity effects.
• Analyzed a broad class of learning algorithms, including deep feedforward neural networks trained with gradient-based methods (e.g., stochastic gradient descent, Adam).
• Utilized adversarial examples to demonstrate cases where networks necessarily misclassify inputs due to encoding-dependent limitations.

Main Results:

• Proved that algorithms meeting specific criteria cannot reliably infer identity effects without explicit programming.
• Demonstrated that deep neural networks, under certain input encodings, satisfy these criteria, hindering their ability to learn identity effects.
• Computational experiments confirmed theoretical predictions, showing how input encoding impacts generalization to novel inputs.

Conclusions:

• Identity effects are difficult for standard AI learning algorithms to acquire implicitly from data.
• The input encoding significantly influences an algorithm's capacity to learn and generalize identity effects.
• Further research into input representations and learning architectures is needed to enable AI systems to master these fundamental cognitive constraints.