Androw of Aces: Mitigating Autoregressive Arithmetic Drift in Large Language Models via Canonical Pre-Sorting and Key-Value Bound Binary Prefix-Sum Scratchpads

Abstract

Autoregressive Large Language Models (LLMs) frequently fail at multi-variable arithmetic aggregation when operating in-context without external code execution. Bounded by circuit complexity class $\mathsf{TC}^0$, standard transformers struggle with sequential carry states across lists of length $N > 3$, suffering from copy-alignment drift. This work introduces Androw of Aces (ACES), a lightweight in-context execution protocol enforcing four invariants: an Autoregressive Conditional Gate ($N > 3$), Canonical Pre-Sorting, Explicit Key-Value Parenthetical Binding, and Sequential Binary Subtotaling. By unrolling multi-term sums into an entity-anchored $\Theta(N)$ prefix-sum scratchpad, ACES achieves zero-variance arithmetic aggregation natively in conversational interfaces.