Efficient Fact-Storing MLPs for Transformers Achieve Optimal Knowledge Storage.

Roberto Garcia, Jerry Liu, Ronny Junkins, Sabri Eyuboglu, Atri Rudra, Christopher R\'e· July 14, 2026 View original

Summary

This research presents a theoretical account and a closed-form construction for fact-storing MLP layers within Transformers, demonstrating optimal information-theoretic storage rates. The proposed MLPs require significantly fewer parameters than prior constructions while maintaining factual recall and enabling modular fact editing.

Researchers have developed a theoretical framework and a practical construction for efficient fact-storing Multi-Layer Perceptrons (MLPs) within Transformer models. This work addresses the empirical observation that Large Language Models (LLMs) store factual knowledge in their MLP layers at an information-theoretically optimal rate, a phenomenon not fully explained by previous models. The new construction is the first Transformer-compatible MLP that achieves optimal fact storage scaling, handles diverse input/output geometries, and functions effectively within Transformer blocks. By analyzing the decoding margin of MLPs, the researchers demonstrate that their method requires 10-104 times fewer parameters for a given fact count compared to prior constructions, under isotropic embeddings. Furthermore, these fact-storing MLPs enable modular fact editing, allowing for the replacement of a Transformer's MLP with a new one to update factual knowledge.

Why it matters

AI engineers and researchers can leverage this understanding and construction method to build more parameter-efficient and interpretable LLMs, facilitating easier knowledge editing and reducing model size for deployment.

How to implement this in your domain

  1. 1Study the theoretical underpinnings of Hebbian learning in MLPs for fact storage.
  2. 2Implement the proposed closed-form construction for fact-storing MLPs within a Transformer architecture.
  3. 3Experiment with replacing existing MLP layers in pre-trained Transformers with these new, efficient fact-storing MLPs.
  4. 4Evaluate the impact on factual recall performance and parameter count reduction.
  5. 5Explore the modular fact editing capabilities by swapping MLPs to update specific knowledge without full model retraining.

Who benefits

AI/ML DevelopmentNatural Language ProcessingSoftware DevelopmentResearch & Development

Key takeaways

  • MLP layers in Transformers can store facts at an information-theoretically optimal rate.
  • A new construction achieves optimal storage scaling with significantly fewer parameters.
  • The method supports arbitrary input/output geometries within Transformers.
  • It enables modular fact editing by swapping MLP layers.

Original post by Roberto Garcia, Jerry Liu, Ronny Junkins, Sabri Eyuboglu, Atri Rudra, Christopher R\'e

"arXiv:2607.10034v1 Announce Type: new Abstract: Large language models (LLMs) store factual knowledge in their parameters. While recent work has shown that this knowledge resides in MLP layers, existing constructive and mechanistic interpretability models of fact-storage in LLMs f…"

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Originally posted by Roberto Garcia, Jerry Liu, Ronny Junkins, Sabri Eyuboglu, Atri Rudra, Christopher R\'e on X · view source

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