On Limitations of the Transformer Architecture

Binghui Peng, Srini Narayanan, Christos Papadimitriou

Research Area: Science of LMs, Compute efficient LMs

Keywords: Transformer, computation complexity, communication complexity

TL;DR: The power and limitation of Transformer architecture

Abstract: What are the root causes of hallucinations in large language models (LLMs)? We use Communication Complexity to prove that the Transformer layer is incapable of composing functions (e.g., identify a grandparent of a person in a genealogy) if the domains of the functions are large enough; we show through examples that this inability is already empirically present when the domains are quite small. We also point out that several mathematical tasks that are at the core of the so-called compositional tasks thought to be hard for LLMs are unlikely to be solvable by Transformers, for large enough instances and assuming that certain well accepted conjectures in the field of Computational Complexity are true.

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the COLM Code of Ethics on https://colmweb.org/CoE.html

Author Guide: I certify that this submission complies with the submission instructions as described on https://colmweb.org/AuthorGuide.html

Submission Number: 229