On Limitations of the Transformer Architecture (2402.08164v2)

Abstract: What are the root causes of hallucinations in 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.

Exploring the Limits of the Transformer Architecture in Function Composition

Overview of Theoretical Limitations

The Transformer architecture has been celebrated for its effectiveness across a broad spectrum of applications in artificial intelligence. However, several studies have revealed its limitations, particularly in handling compositional tasks. This paper provides a comprehensive examination of the Transformer architecture's inherent difficulties in executing function composition tasks. The authors employ techniques from Communication and Computational Complexity to demonstrate that the Transformer's layer structure inherently limits its ability to compose functions when the functions' domains are substantial.

Communication Complexity and Function Composition

The authors utilize Communication Complexity to establish that even a single Transformer attention layer fails to perform function composition tasks accurately with a significant probability when the domain size exceeds certain thresholds related to the model's architecture. Specifically, they prove that the probability of a Transformer layer incorrectly answering a function composition query increases inversely with the domain size of the functions involved. This limitation is attributed primarily to the softmax calculation, a fundamental component of the Transformer's mechanism that restricts the model's capacity to use non-local information efficiently.

Computational Complexity Insights

The paper extends its theoretical analysis through Computational Complexity, exploring the transformer's performance on tasks that require sequential composition of elementary tasks. Through rigorous experimentation, it is shown that Transformers struggle with depth-increasing compositional tasks, such as multiplying multi-digit integers and solving logical puzzles. The authors posit that this limitation stems from the Transformer's computational mechanism being confined mainly to operations that can be executed within logarithmic space.

Implications and Speculations

The findings have profound implications for both the theoretical understanding and practical application of Transformer models. Practically, this paper suggests boundaries to the effectiveness of current Transformer models in handling complex compositional tasks that are prevalent in natural language processing and beyond. Theoretically, it invites a re-examination of the computational paradigms underpinning these models, potentially guiding future research towards developing more capable architectures.

Furthermore, the discussions around the Communication and Computational Complexity results suggest intriguing future directions. One such direction could be the design of alternative attention mechanisms or layer structures that circumvent the identified limitations. Another promising avenue could involve integrating external memory components or more sophisticated computational mechanisms that extend beyond the model's inherent logarithmic space limitations.

Conclusion

This paper provides a critical examination of the Transformer architecture's capabilities, revealing inherent limitations in executing complex compositional tasks. By leveraging theories from Communication and Computational Complexity, it outlines the theoretical boundaries of Transformer models, laying the groundwork for future innovations in model architecture and artificial intelligence research at large. The insights gained from this analysis not only deepen our understanding of the current models' limitations but also chart a course for the development of more advanced computational frameworks capable of tackling an even wider array of AI challenges.