arXiv study: prediction direction is transformers' hidden geometric anchor

Nelson Guda's new arXiv paper, "Geometric and Behavioral Stratification in Transformer Residual Streams," upends a common assumption about how transformers store and use information. Working across 18 models (dense and mixture-of-experts, 7B-120B, both base and instruction-tuned), Guda shows that residual streams are not uniformly organized. Instead, they form a stratified geometry centered on the prediction direction—the unembedding direction of the token the model is currently predicting. This "privileged anchor" sits nearly orthogonal to the principal variance axes, which is why standard variance-based analyses (like PCA) only partially capture the structure. The shortfall gets worse as prompts become more heterogeneous, suggesting existing interpretability tools may be systematically missing a core organizational principle.

Guda's causal experiments strengthen the case. When he disrupted variance directions closest to the prediction axis, models diverged immediately and frequently shifted task frames. Disrupting the next level down only delayed divergence while preserving the original framing. Meanwhile, prediction-distal regions are weakly aligned to the readout per individual direction, yet they are causally and temporally load-bearing—behavior is driven by direction rather than magnitude. This narrow "prediction interface" concentrates readout-relevant structure and scales remarkably well: the proximal slice stays compact and invariant to model size, while the large distal complement expands with scale. The paper offers a geometric account of how high-dimensional computation coexists with simple linear readout, giving interpretability researchers a concrete target for model introspection and control.