Constructing Efficient Fact-Storing MLPs for Transformers
This work addresses the challenge of improving fact storage mechanisms in large language models, with incremental advancements over prior constructions.
The paper tackles the problem of constructing efficient MLPs for storing factual knowledge in Transformers, resulting in a framework that achieves asymptotically optimal parameter efficiency and identifies a tradeoff between storage capacity and usability.
The success of large language models (LLMs) can be attributed in part to their ability to efficiently store factual knowledge as key-value mappings within their MLP parameters. Recent work has proposed explicit weight constructions to build such fact-storing MLPs, providing an improved understanding of LLM fact storage mechanisms. In this paper, we introduce an MLP construction framework that improves over previous constructions in three areas: it 1) works for all but a measure-zero set of feasible input-output pairs, 2) achieves asymptotically optimal parameter efficiency matching information-theoretic bounds for some embeddings, and 3) maintains usability within Transformers for factual recall. Through our improvements, we 1) discover a metric on value embeddings that characterizes facts-per-parameter scaling for both constructed and gradient-descent-trained MLPs, 2) identify a simple encoder-decoder mechanism that empirically matches gradient-descent MLP facts-per-parameter asymptotics across all the inputs and outputs we test, and 3) uncover a fundamental tradeoff between an MLP's fact-storage capacity and its usability within Transformers. Finally, we demonstrate a proof-of-concept application of fact-storing MLPs: modular fact editing on one-layer Transformers by \textit{replacing entire MLPs at once}.