When Models Decide and When They Bind: A Two-Stage Computation for Multiple-Choice Question-Answering

TL;DR

The paper tackles how instruction-tuned language models perform MCQA by disentangling the tasks of selecting the correct answer content and binding that content to the emitted symbol. Using PCA, linear probes, and probe-aligned activation patching, it identifies a two-stage computation: first, per-option evaluation and winner identification in content space, and second, binding or routing that winner to the appropriate symbol near the emission point. The findings show that option-boundary signals encode correctness and that winner identity becomes decodable before the final emission, with symbol binding emerging closer to the answer prefix. These insights clarify how models separate knowledge of the correct option from the act of emitting its symbol and offer a mechanistic account that can guide future probing and intervention studies in MCQA contexts.

Abstract

Multiple-choice question answering (MCQA) is easy to evaluate but adds a meta-task: models must both solve the problem and output the symbol that *represents* the answer, conflating reasoning errors with symbol-binding failures. We study how language models implement MCQA internally using representational analyses (PCA, linear probes) as well as causal interventions. We find that option-boundary (newline) residual states often contain strong linearly decodable signals related to per-option correctness. Winner-identity probing reveals a two-stage progression: the winning *content position* becomes decodable immediately after the final option is processed, while the *output symbol* is represented closer to the answer emission position. Tests under symbol and content permutations support a two-stage mechanism in which models first select a winner in content space and then bind or route that winner to the appropriate symbol to emit.

Figures (16)

• Figure 1: The first ($x$-axis) and second ($y$-axis) principal components from layerwise PCA in Llama-3.2-3B. Activations extracted at every symbol token position. The "Previous option correct" marker is in the color of the symbol of which the activations are being projected.
• Figure 2: The first two principle components for Qwen3-8B (left) and Llama-3.2-3B-Instruct (right) when extracting the residual stream at the content tokens (upper) and subsequent newlines (lower). Note that, unlike Figure \ref{['fig:pca_symbols']}, this plot tracks the current, not the previous token correct. Plots for all layers in Appendix \ref{['appendix:pca_content_newlines']}.
• Figure 3: Layer-wise performance of binary per-option probes trained for the ARC-Easy dataset with $C=10^{-4}$ on the residual stream. The dashed lines represent random chance baselines.
• Figure 4: Layer-wise performance of multinomial probes trained for the ARC-Easy dataset with $C = 10^{-2}$. Each line corresponds to token positions of \\ n\\ nAnswer: (, right after the model has processed all the MCQA options. Dark gray dashed lines represent random chance baselines.
• Figure 5: Performance of the multinomial probe from Figure \ref{['fig:probing_multi']} on ARC-Easy prompts in which option symbols have been permuted. We probe for (a) the correct output symbol under this permutation as well as for (b) the correct (unchanged) content position.