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arxiv: 2605.22870 · v1 · pith:NSSWMX5Qnew · submitted 2026-05-20 · 💻 cs.LG · cs.AI· cs.CL

The Readout Shortcut: Positional Number Copying Dominates Arithmetic CoT Readout in Small Language Models

Ming Liu This is my paper

Pith reviewed 2026-05-25 06:25 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.CL
keywords chain-of-thoughtarithmetic reasoninglanguage modelspositional shortcutreadout mechanismfaithfulness evaluationGSM8K
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The pith

Small language models achieve most chain-of-thought arithmetic accuracy by copying the final number in the reasoning trace rather than computing it.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper isolates the answer-readout stage in 1-3B instruction-tuned models on arithmetic tasks and shows that chain-of-thought prompting works mainly because the correct answer occupies the last position before the delimiter. Gold-answer presence drives 54-92 percentage points of accuracy, or 89-92 percent of each model's teacher-forcing ceiling. On wrong answers the output still matches the last CoT number 95-96 percent of the time. The copy operation overrides retained context: swapping the trailing number collapses performance to near zero even when all prior steps are correct, while removing the number lets the model recover some genuine single-step arithmetic.

Core claim

In three 1-3B instruction-tuned language models, arithmetic chain-of-thought performance is dominated by a positional readout shortcut: the model copies whichever number occupies the trailing position immediately before the answer delimiter, regardless of the logical content of the preceding steps. Gold-answer presence accounts for 54-92 percentage points of accuracy (89-92 percent of the teacher-forcing ceiling), and the final answer matches the last CoT number on 95-96 percent of incorrect items. The copy channel takes precedence over context completion; replacing the trailing number with an incorrect value drives accuracy to near zero despite correct intermediates, yet removing the number

What carries the argument

the trailing-number copy channel that operates in the answer-readout stage and overrides retained-context completion

If this is right

  • Replacing the trailing number with a wrong value collapses accuracy to near zero despite correct intermediates.
  • Removing the trailing number recovers 5-32 percentage points above the floor, including single-step arithmetic the model can otherwise perform.
  • Qwen and Llama copy novel distractors 87-95 percent of the time; Gemma gates selectively.
  • The effect replicates on GSM-Symbolic, and head-level ablation identifies architecture-specific head sets.
  • On non-arithmetic BBH tasks shuffle retention drops sharply, and at 7-8B content-selective gating emerges.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Step-level faithfulness evaluations may be measuring positional transport rather than genuine computation.
  • The shortcut could be tested by systematically removing or altering final numbers across a wider range of tasks to measure retained computational ability.
  • Larger models may reduce reliance on the shortcut once content-selective gating appears, suggesting a size-dependent transition in readout strategy.

Load-bearing premise

The prefix-completion technique cleanly isolates the readout stage without altering the model's prior internal computation or context retention.

What would settle it

An experiment in which the trailing number is replaced by a distractor while all prior reasoning steps remain correct, followed by measurement of whether accuracy stays high or drops to near zero.

Figures

Figures reproduced from arXiv: 2605.22870 by Ming Liu.

Figure 1
Figure 1. Figure 1: The answer-context-gated positional readout: the model reads whichever number appears in answer￾relevant context at the trailing position before the #### delimiter. (a) When the correct answer is last, the read￾out yields the right output. (b) In Qwen/Llama (1–3B), injecting a wrong number in answer context displaces gold and is copied 87–95% of the time; Gemma instead shows stronger content gating (P(dist… view at source ↗
Figure 2
Figure 2. Figure 2: Answer-position curve (5-position sweep, [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Shuffle hierarchy with bootstrap 95% CIs [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

Chain-of-thought (CoT) prompting is necessary for arithmetic in small language models, yet shuffling its steps preserves most performance. What does CoT contribute if not logical sequencing? In three 1-3B instruction-tuned LMs on GSM8K, we isolate the answer-readout stage via prefix completion and identify a positional shortcut: the model copies whichever number occupies the trailing position before the answer delimiter, regardless of intermediate reasoning. Gold-answer presence accounts for 54-92 pp of accuracy (89-92% of each model's teacher-forcing ceiling); even on incorrect items, the final answer matches the last CoT number 95-96% of the time. The copy channel takes precedence over retained-context completion: replacing the trailing number with a wrong value collapses accuracy to near-zero despite correct intermediates, yet removing it recovers 5-32 pp above that floor--even single-step arithmetic the model can otherwise perform is suppressed when a copyable number is present. Qwen and Llama copy novel distractors 87-95% of the time; Gemma gates selectively. Head-level ablation implicates architecture-specific head sets; the effect replicates on GSM-Symbolic. On non-arithmetic BBH tasks, shuffle retention drops sharply; at 7-8B, content-selective gating emerges. Step-level faithfulness evaluations risk conflating positional answer transport with genuine computation--a failure mode for CoT-based oversight.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that in 1-3B instruction-tuned LMs on GSM8K, CoT primarily enables a positional readout shortcut: the model copies the trailing number before the answer delimiter rather than performing step-by-step reasoning. Using prefix completion to isolate readout, gold-answer presence accounts for 54-92 pp accuracy gains (89-92% of teacher-forcing ceiling); final answers match the last CoT number 95-96% of the time even on errors. Trailing-number replacement collapses accuracy to near zero while removal recovers 5-32 pp; novel distractors are copied 87-95% of the time by Qwen/Llama. Head ablations implicate architecture-specific heads; the effect replicates on GSM-Symbolic. On BBH tasks shuffle retention drops, and at 7-8B content-selective gating appears. The work warns that step-level faithfulness evaluations may conflate positional transport with computation.

Significance. If the central empirical measurements hold, the result is significant for understanding CoT mechanisms in small models and for the reliability of CoT-based oversight techniques. The direct evidence from replacement experiments, high match rates on errors, and replication on GSM-Symbolic are strengths; the head-level ablation and scaling observations to 7-8B add useful granularity. The finding that a copy channel can suppress even single-step arithmetic the model can otherwise perform is a clear, falsifiable observation with implications for interpretability work.

major comments (2)
  1. [prefix-completion experiments] Prefix-completion experiments (abstract and methods): the central claim that gold-answer presence drives 54-92 pp via positional copying of the trailing number depends on the technique cleanly isolating the readout stage without altering prior internal states. In transformers, conditioning on a prefix containing the full CoT plus (possibly altered) final number can modify attention patterns over earlier tokens, so the observed copying may reflect changed computation rather than native readout on unaltered context. The replacement and match-rate results are consistent with copying but do not rule out this confound.
  2. [results on accuracy deltas] Abstract and results sections: the reported accuracy deltas (54-92 pp) and match rates (95-96%) are presented without error bars, full dataset splits, or statistical tests. Given the noted possibility of post-hoc item/model selection, it is difficult to assess whether the effect sizes are robust or whether the 89-92% of teacher-forcing ceiling claim generalizes.
minor comments (2)
  1. [replication paragraph] The abstract states the effect replicates on GSM-Symbolic but does not specify whether the same prefix-completion protocol and replacement controls were applied identically.
  2. [abstract] Notation for 'teacher-forcing ceiling' is used without an explicit definition or equation in the provided abstract; a short methods paragraph would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and for recognizing the potential significance of the empirical measurements. We address each major comment below, proposing revisions where the concerns are valid.

read point-by-point responses

  1. Referee: [prefix-completion experiments] Prefix-completion experiments (abstract and methods): the central claim that gold-answer presence drives 54-92 pp via positional copying of the trailing number depends on the technique cleanly isolating the readout stage without altering prior internal states. In transformers, conditioning on a prefix containing the full CoT plus (possibly altered) final number can modify attention patterns over earlier tokens, so the observed copying may reflect changed computation rather than native readout on unaltered context. The replacement and match-rate results are consistent with copying but do not rule out this confound.

    Authors: We agree that prefix completion could in principle alter attention patterns over earlier tokens. The replacement experiments (which modify only the trailing number while keeping the prefix otherwise fixed) and the 95-96% match rates observed during standard (non-prefix) generation provide convergent evidence that the effect is readout-driven, but these do not fully eliminate the possibility of a confound in the prefix-completion setting itself. We will add an explicit limitations paragraph discussing this architectural consideration and its implications for interpreting the isolation of the readout stage. revision: partial

  2. Referee: [results on accuracy deltas] Abstract and results sections: the reported accuracy deltas (54-92 pp) and match rates (95-96%) are presented without error bars, full dataset splits, or statistical tests. Given the noted possibility of post-hoc item/model selection, it is difficult to assess whether the effect sizes are robust or whether the 89-92% of teacher-forcing ceiling claim generalizes.

    Authors: We acknowledge that the current manuscript lacks error bars, explicit dataset-split details, and statistical tests, which limits assessment of robustness. The models were the primary publicly available 1-3B instruction-tuned checkpoints at the time of the study, and all experiments used the full GSM8K test set; however, we did not pre-register item or model selection criteria. We will revise the abstract and results to report bootstrap confidence intervals, state the exact splits and model selection process, and add a brief discussion of generalizability. revision: yes

Circularity Check

0 steps flagged

No circularity: purely empirical measurements on model behavior

full rationale

The paper reports experimental results from prefix-completion interventions, accuracy deltas, and match rates on GSM8K and other benchmarks. No equations, derivations, fitted parameters renamed as predictions, or self-citation chains appear in the provided text. Claims rest on direct observations (e.g., accuracy drops when trailing number is replaced) rather than any self-referential construction. The prefix-completion technique is an experimental method, not a definitional or fitted step that forces the outcome by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that prefix completion isolates readout without side effects on retained context and that the three tested models are representative of the 1-3B instruction-tuned class.

axioms (1)
  • domain assumption Prefix completion isolates the answer-readout stage without changing the model's internal state or prior computation.
    Invoked when the paper uses prefix completion to measure the contribution of the trailing number.

pith-pipeline@v0.9.0 · 5789 in / 1150 out tokens · 64523 ms · 2026-05-25T06:25:16.148477+00:00 · methodology

discussion (0)

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