Distributed Numerical Order Representations in Residual Streams

Our initial question concerns how numerical order is represented spatially, in a manner analogous to humancognition, and how such structure is causally implemented and maintained within large transformer-based languagemodels. Using mechanistic interpretability techniques, including activation patching and targeted ablation of attentionheads on number-sequence inputs, we identified several noteworthy patterns.Consistent with prior work and ”textbook” intuitions, we observe that representations of numerical order emergeprominently in early transformer layers. However, our analyses indicate that this early emergence does not renderintermediate layers negligible. A naive interpretation might suggest that order information is localized within specificattention heads. In contrast, our findings support a different account: numerical order information becomes progres-sively more distributed within the residual stream, such that representations in later layers are robust to localizedattention-head ablations.Overall, our results support a hybrid picture: particular attention heads play a critical role in initially constructingnumerical order, after which the residual stream redundantly preserves and propagates this structure to deeper layers.This work contributes a minimal mechanistic account of numerical structure in transformer architectures and alignswith recent advances in interpretability research.