When Do Transformers Learn Heuristics for Graph Connectivity?

Qilin Ye, Deqing Fu, Robin Jia, Vatsal Sharan

When Do Transformers Learn Heuristics for Graph Connectivity?: 4 upvotes on Hugging Face Daily Papers, #34 of 37 papers on 2025-10-23. Day-by-day upvote history.

Transformers often fail to learn generalizable algorithms, instead relying on brittle heuristics. Using graph connectivity as a testbed, we explain this phenomenon both theoretically and empirically. We consider a simplified Transformer architecture, the disentangled Transformer, and prove that an L-layer model has capacity to solve for graphs with diameters up to exactly 3^L, implementing an algorithm equivalent to computing powers of the adjacency matrix. We analyze the training-dynamics, and show that the learned strategy hinges on whether most training instances are within this model capacity. Within-capacity graphs (diameter leq 3^L) drive the learning of a correct algorithmic solution while beyond-capacity graphs drive the learning of a simple heuristic based on node degrees. Finally, we empirically demonstrate that restricting training data within a model's capacity leads to both standard and disentangled transformers learning the exact algorithm rather than the degree-based heuristic.

Paper page on Hugging Face · arXiv

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