Shared circuits predict whether LLMs generalize across formats in arithmetic reasoning
Andrea Gregor de Varda, Sana Pandey, Pengrui Han, Jacob Andreas, Evelina Fedorenko
cs.CL · cs.AI
Quick verdict
Circuit overlap predicts LLM cross-format arithmetic generalization at three levels; strong empirical support, but probe comparisons rest on a single model.
Summary
The paper asks whether a model's internals predict its ability to generalize arithmetic reasoning across surface formats. Using attribution patching on 13 open-weight LLMs (six families, 0.6B–32B), the authors localize per model a 'numeric circuit' — the top 1% of MLP units (scored at the last prompt position) by attribution on symbolic problems like 44+22 — then measure (a) top-1% Jaccard overlap between each verbal format's circuit (English, Spanish, Italian) and the numeric circuit, and (b) each item's loading on it. Attributions derive from the model's own greedy answers via sign-flipped counterfactuals, not gold labels. Results: median accuracy falls from 87.4% (numeric) to 36.4%/17.9%/6.8% (English/Spanish/Italian); overlap mirrors this ordering (means 0.145/0.078/0.069) and predicts model-level accuracy (English r=0.75; Spanish r=0.58; Italian n.s., r=0.47, N=13). Item-level loading correlates with correctness in nearly all model×format pairs, and activation-patching controls (Appendix C) confirm causality. On Llama-3.1-8B only, circuit loading retains significant unique variance against trained probes and confidence measures, though next-token entropy explains more variance in weaker formats (e.g., 20.4% vs 5.3% in Spanish). Balanced-accuracy controls (Appendices E–F) show any format's circuit predicts any target, weakening numeric specificity. Limitations: no explanatory theory; key controls single-model; no stated code release.
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Assessment at a glance
4
risk flags identified
● high 0
● medium 3
● low 1
5 strengths · 5 weaknesses · 5 author questions
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Key claims under review
- The difficulty ordering of verbal formats (English > Spanish > Italian) is mirrored by top-1% Jaccard overlap with each model's numeric circuit in every model tested (§3.1–3.2).
- Model-level verbal accuracy is predicted by overlap with the model's own numeric circuit (English r=0.75/p=0.003; Spanish r=0.58/p=0.04; Italian r=0.47/p=0.10, non-significant; N=13).
- Item-level loading on the numeric circuit predicts per-item correctness in nearly all model×format combinations, and Appendix C activation patching establishes the dependency as causal.
- On Llama-3.1-8B, circuit loading retains significant unique variance beyond trained probes and confidence measures (β=0.127 to 0.030, all p≤0.006), though next-token entropy is the stronger single predictor in weak formats.
- The entire pipeline requires no labeled data: attributions come from the model's own greedy answers on sign-flipped counterfactual prompts (§2.3, Appendix B).
Strengths
Label-free circuit identification
Attributions derive from the model's own greedy answers via a sign-flip preference metric (44+22 vs 44−22; §2.3, Appendix B), so the circuit is well-defined even in formats where the model is mostly wrong — a clean fix for the gold-answer mismatch problem in standard attribution patching.
Causal validation beyond the linear approximation
Appendix C runs true activation patching on all 13 models: the restored preference fraction correlates with item accuracy in 35/38 model×format combos (32 significant), beats size-matched random-unit controls (paired Wilcoxon p<0.001 English/Spanish, p<0.01 Italian), and tracks the AP estimate (r=0.74).
Confound controls on the source circuit
Breadth of the core effect
Candid limitations
Weaknesses
Single-model basis for the headline comparisons
Unadjusted multiplicity and a null under the abstract's claim
Specificity tension with Appendix F
Narrow evaluation surface
No stated code or data release
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Scope & Claims
The paper asks a mechanistic question about a behavioral phenomenon: LLMs solve numeric arithmetic (median 87.4% across 13 base models, 0.6B–32B, six families) far better than verbal renditions in English (36.4%), Spanish (17.9%), and Italian (6.8%) (§3.1). The authors propose that this generalization gap is legible in the internals: how strongly a verbal format recruits the model's own numeric-arithmetic circuit — localized without labels via attribution patching — should predict generalization at three levels: format difficulty ordering, model ranking, and individual items. Claims are stated with unusual precision, and the Limitations section is candid: the authors have correlation plus causal validation but no theory of why the link holds, and their 'circuits' are unit sets not tied to algorithms (Marr's implementation vs. algorithmic levels). The abstract framing 'rivaling supervised probes while requiring no labeled data' is mostly earned, with one asterisk discussed below.
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Frequently asked questions
Why do LLMs fail at 'forty-four plus twenty-two' when they can compute 44+22?
Across 13 open-weight models the paper measures median accuracy of 87.4% on numeric problems but only 36.4% (English), 17.9% (Spanish), and 6.8% (Italian) on verbal versions of the same problems. Internally, verbal formats recruit MLP units that overlap less with the model's numeric-arithmetic circuit, and low overlap or low per-item loading on that circuit predicts failure.
What is attribution patching, and why didn't the authors use gold answers?
Attribution patching is a technique that approximates how much each internal unit matters for a behavior using two forward passes and one backward pass per example, instead of interventions on every unit. Standard versions need a gold answer; this paper instead scores how strongly the model prefers its own answer on a prompt over its answer on a sign-flipped version (44+22 vs 44−22), so the circuit is defined even when the model is usually wrong.
Does a shared circuit mean the LLM computes arithmetic identically in every language?
Only partially. Overlap is modest (mean top-1% Jaccard 0.145 English, 0.078 Spanish, 0.069 Italian), and the balanced-accuracy controls in Appendix F show that any format's circuit predicts any other format's accuracy, suggesting a graded shared arithmetic substrate rather than one identical, format-independent circuit.
Can this method predict LLM failures without any labeled data in practice?
Partially. The circuit metric needs no ground truth and predicts failure confidently (low loading means near-zero accuracy), but next-token entropy — also label-free — explains more variance in weak formats (e.g., 20.4% vs 5.3% in Spanish on Llama-3.1-8B), so circuit loading is best seen as a complementary, mechanistically interpretable signal.
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This is an AI-generated preliminary review by Evolve.Pub, produced from the openly available text of the paper. It is not peer review and does not represent the authors' views. The canonical record of the paper is at the publisher link above.
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