Represented Is Not Computed: A Causal Test of Candidate Algorithmic Intermediates in a Transformer
Structured prompts require integrating components according to task-relevant relations. How a network implements this integration is often hard to judge in language or vision, where those relations are rarely specified precisely enough to define a candidate internal algorithm. Arithmetic offers a cleaner setting. We study a Transformer trained on base-digit extraction: given $N$, $B$, and $D$, it must report the coefficient of $B^D$ in the base-$B$ expansion of $N$. The closed-form solution, $\lfloor N/B^D \rfloor \bmod B$, provides explicit candidate algorithmic intermediates. Across three seeds, the model reaches 99.83% exact-answer accuracy on held-out number-base intersections, establ...
| Authors | Ishita Darade, Sushrut Thorat |
|---|---|
| Primary category | cs.LG |
| Published | 21 May 2026 |
| Last updated at source | 21 May 2026 |
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