Small Language Models as Graph Classifiers: Evaluating and Improving Permutation Robustness

Graph classification is dominated by permutation-invariant graph neural networks. We revisit this problem from a different perspective: can small language models (SLMs) act as graph classifiers when graphs are serialized as text? Unlike GNNs, sequence-based transformers do not encode permutation invariance by construction, raising a fundamental question about structural stability under node relabeling.We provide the first systematic study of permutation robustness in small graph-as-text models. We introduce an evaluation protocol based on Flip Rate and KL-to-Mean divergence to quantify prediction instability across random node permutations. To enforce structural consistency, we propose Permutation-Invariant Training (PIT), a multi-view regularization scheme that aligns predictions across relabeled graph views, and examine its interaction with degree-aware token embeddings as a minimal inductive bias.Across benchmark datasets using parameter-efficient fine-tuning, we show that SLMs achieve competitive classification accuracy, yet standard fine-tuning exhibits non-trivial permutation sensitivity. PIT consistently reduces instability and in most evaluated settings improves accuracy, demonstrating that structural invariance in sequence-based graph models can emerge through explicit regularization.