On the Geometric Structure of Layer Updates in Deep Language Models
Summary: arXiv:2604.02459v1 Announce Type: cross
Abstract
In this study, we delve into the geometric structure of layer updates within deep language models. Rather than focusing on what information is encoded in intermediate representations, we shift our attention to the changes that occur in representations as they progress from one layer to the next. Our findings reveal that updates occurring at each layer can be decomposed into a predominant tokenwise component and a residual component that is inadequately represented by restricted tokenwise function classes.
Key Findings
Our research presents several key findings across various architectures, including Transformers and state-space models:
- The complete layer update is almost entirely aligned with the tokenwise component.
- The residual component shows significantly weaker alignment, larger angular deviation, and lower projection onto the dominant tokenwise subspace.
- This indicates that the residual is not simply a minor correction but constitutes a geometrically distinct component of the transformation.
Functional Implications
This geometric distinction has important functional implications. The approximation error resulting from the restricted tokenwise model correlates strongly with output perturbation. We observe Spearman correlations that frequently exceed 0.7 and can reach up to 0.95 in larger models. This suggests that most updates at the layer level behave like structured reparameterizations along a primary direction, while functionally significant computations are concentrated in a geometrically distinct residual component.
Methodology
Our framework introduces a straightforward, architecture-agnostic approach to probing the geometric and functional structure of layer updates in contemporary language models. It allows for a deeper understanding of how different components contribute to the overall functioning of these models.
Conclusion
In summary, our study offers insights into the geometric structure of layer updates in deep language models, revealing a complex interplay between tokenwise components and their residuals. Understanding this relationship not only enhances our comprehension of model architectures but also paves the way for future advancements in the field of natural language processing.