Graph-Aware Isomorphic Attention for Adaptive Dynamics in Transformers
Authors: name: Markus J. Buehler

We present an approach to modifying Transformer architectures by integrating
graph-aware relational reasoning into the attention mechanism, merging concepts
from graph neural networks and language modeling. Building on the inherent
connection between attention and graph theory, we reformulate the Transformer's
attention mechanism as a graph operation and propose Graph-Aware Isomorphic
Attention. This method leverages advanced graph modeling strategies, including
Graph Isomorphism Networks (GIN) and Principal Neighborhood Aggregation (PNA),
to enrich the representation of relational structures. Our approach captures
complex dependencies and generalizes across tasks, as evidenced by a reduced
generalization gap and improved learning performance. Additionally, we expand
the concept of graph-aware attention to introduce Sparse GIN-Attention, a
fine-tuning approach that employs sparse GINs. By interpreting attention
matrices as sparse adjacency graphs, this technique enhances the adaptability
of pre-trained foundational models with minimal computational overhead,
endowing them with graph-aware capabilities. Sparse GIN-Attention fine-tuning
achieves improved training dynamics and better generalization compared to
alternative methods like low-rank adaption (LoRA). We discuss latent graph-like
structures within traditional attention mechanisms, offering a new lens through
which Transformers can be understood. By evolving Transformers as hierarchical
GIN models for relational reasoning. This perspective suggests profound
implications for foundational model development, enabling the design of
architectures that dynamically adapt to both local and global dependencies.
Applications in bioinformatics, materials science, language modeling, and
beyond could benefit from this synthesis of relational and sequential data
modeling, setting the stage for interpretable and generalizable modeling
strategies.