IC-1370MLP0 representations of ordinal-sequence tokens in Pythia-1.4b contain linearly decodable mod-10 features that are causally important for incrementation
Using sparse autoencoders on MLP0 activations, the authors identify ten features f0–f9 such that fn is present in tokens whose ordinal index is congruent to n mod 10. The modal most important feature for each mod-10 class is shared on average by 58.5% of tokens in that class. A linear probe recovers the mod-10 value with 0.70764 average cosine similarity to the SAE features and generalises to 94/102 non-numeric tokens. Vector arithmetic (adding/subtracting mod-10 features to token representations) successfully steers the successor head's output in 53% of month cases and 89% of digit 20–29 cases when the target residue is greater than the source. Ablative experiments on individual MLP0 neurons confirm periodic firing with period 10.
Evidence
interventional
Key metric
modal most important feature shared by 58.5% of tokens in class; linear probe cosine similarity 0.70764; 94/102 non-numeric tokens correct; vector arithmetic success 53% (months) and 89% (digits 20-29); most common neuron firing period 10
Caveat
The mod-10 features do not steer the days and letters tasks; the greater-than bias in the successor head means vector arithmetic fails when the target residue is smaller than the source. The SAE was trained primarily on number tokens, so generalisation to other tasks is partial.