What Do Hebbian Learners Learn? Reduction Axioms for Iterated Hebbian Learning
Authors: Caleb Schultz Kisby, Saúl A. Blanco, Lawrence S. Moss
AAAI 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This paper is a contribution to neural network semantics, a foundational framework for neuro-symbolic AI. The key insight of this theory is that logical operators can be mapped to operators on neural network states. In this paper, we do this for a neural network learning operator. We map a dynamic operator [φ] to iterated Hebbian learning, a simple learning policy that updates a neural network by repeatedly applying Hebb s learning rule until the net reaches a fixed-point. Our main result is that we can translate away [φ]-formulas via reduction axioms. This means that completeness for the logic of iterated Hebbian learning follows from completeness of the base logic. These reduction axioms also provide (1) a humaninterpretable description of iterated Hebbian learning as a kind of plausibility upgrade, and (2) an approach to building neural networks with guarantees on what they can learn. |
| Researcher Affiliation | Academia | Caleb Schultz Kisby1, Sa ul A. Blanco1, Lawrence S. Moss2 1Department of Computer Science, Indiana University 2Department of Mathematics, Indiana University Bloomington, IN 47408, USA |
| Pseudocode | No | The paper does not contain structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | The proofs of our main theorem and its major supporting lemmas have been verified using the Lean 4 interactive theorem prover (Moura and Ullrich 2021). The code and installation instructions are available at https://github.com/ais-climber/AAAI2024 |
| Open Datasets | No | This is a theoretical paper focused on logical formalisms and proofs, not empirical experiments. Therefore, it does not involve training models on datasets. |
| Dataset Splits | No | This is a theoretical paper focused on logical formalisms and proofs, not empirical experiments involving dataset splits for validation. |
| Hardware Specification | No | The paper is theoretical and focuses on logical proofs and formal systems. It does not describe any empirical experiments or the specific hardware used for computations or proof verification. |
| Software Dependencies | Yes | The proofs of our main theorem and its major supporting lemmas have been verified using the Lean 4 interactive theorem prover (Moura and Ullrich 2021). |
| Experiment Setup | No | The paper is theoretical and focuses on logical formalisms and proofs. It does not describe an experimental setup with hyperparameters, training configurations, or system-level settings. |