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arxiv: 2606.18453 · v1 · pith:M7WON6B2new · submitted 2026-06-16 · 💻 cs.CL

LLM Parameters for Math Across Languages: Shared or Separate?

Behzad Shomali , Luisa Victor , Tim Selbach , Ali Hamza Bashir , David Berghaus , Joachim Koehler , Mehdi Ali , Markus Frey This is my paper

Pith reviewed 2026-06-27 00:28 UTC · model grok-4.3

classification 💻 cs.CL
keywords multilingual LLMsmathematical reasoningmechanistic interpretabilitycross-lingual analysisparameter overlapLLM layers
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The pith

Math-associated parameters in multilingual LLMs exhibit partial cross-lingual overlap concentrated in intermediate layers.

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

The paper examines whether differences in mathematical reasoning performance across languages in LLMs arise from entirely separate parameters or from a shared mechanism that varies by language. It applies cross-lingual mechanistic analysis to identify and compare the parameters tied to math reasoning. The results show these parameters overlap only partially between languages, with the greatest overlap appearing in the intermediate layers. English consistently involves the largest number of such parameters, while lower-resource languages involve smaller sets. The findings indicate that math-related behavior combines some shared elements with systematic language-dependent differences rather than being fully invariant or fully specific to each language.

Core claim

The extracted math-associated parameters exhibit partial cross-lingual overlap, with the strongest overlap concentrated in intermediate model layers. English consistently produces the largest set of math-relevant parameters, whereas lower-resource languages reveal smaller sets of relevant parameters. These results suggest that math-related behavior in multilingual LLMs is neither fully language-invariant nor fully language-specific, but instead exhibits partial cross-lingual parameter overlap with systematic language-dependent differences.

What carries the argument

Cross-lingual mechanistic analysis that localizes and extracts math-associated parameters for comparison of overlap across languages.

Load-bearing premise

The method for localizing and extracting math-associated parameters correctly distinguishes shared from language-specific parameters without substantial interference from other model behaviors or data artifacts.

What would settle it

An experiment in which ablating the identified overlapping parameters in one language produces no measurable change in math performance for another language would falsify the partial-overlap claim.

Figures

Figures reproduced from arXiv: 2606.18453 by Ali Hamza Bashir, Behzad Shomali, David Berghaus, Joachim Koehler, Luisa Victor, Markus Frey, Mehdi Ali, Tim Selbach.

Figure 1
Figure 1. Figure 1: Math-specific parameters in Llama 1B. Left: Number of isolated parameters per language. Right: Jaccard similarity between language-specific parameter sets. the gap between Hindi and French is smaller than that between Hindi and English. This pattern be￾comes even more pronounced with larger models (Figures F.4, F.5). Finding: The distribution of math-specific pa￾rameters across languages tends to align wit… view at source ↗
Figure 2
Figure 2. Figure 2: Layer-wise distribution of math-reasoning pa [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Effect of pruning isolated math-specific [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

Large language models (LLMs) exhibit substantial cross-lingual variation in mathematical reasoning performance, but it remains unclear whether these differences reflect language-specific parameters or a shared mechanism that manifests differently by language. We present a cross-lingual mechanistic analysis of mathematical reasoning in LLMs, enabling us to localize and compare model parameters that support mathematical reasoning across languages. We find that the extracted math-associated parameters exhibit partial cross-lingual overlap, with the strongest overlap concentrated in intermediate model layers. We further observe that English consistently produces the largest set of math-relevant parameters, whereas lower-resource languages reveal smaller sets of relevant parameters. These results suggest that math-related behavior in multilingual LLMs is neither fully language-invariant nor fully language-specific, but instead exhibits partial cross-lingual parameter overlap with systematic language-dependent differences.

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

1 major / 0 minor

Summary. The paper claims that a cross-lingual mechanistic analysis of mathematical reasoning in LLMs localizes math-associated parameters showing partial overlap across languages, with strongest overlap in intermediate layers; English yields the largest such set while lower-resource languages yield smaller sets. This leads to the conclusion that math-related behavior is neither fully language-invariant nor fully language-specific but exhibits partial cross-lingual parameter overlap with systematic language-dependent differences.

Significance. If the extraction method is shown to be valid and free of the confounds noted in the stress-test, the result would provide a concrete mechanistic account of how multilingual LLMs implement math reasoning, with implications for model editing, cross-lingual transfer, and targeted improvement of low-resource performance. The layer-wise and resource-level patterns are potentially falsifiable predictions that could be tested in follow-up work.

major comments (1)
  1. [Abstract] Abstract (and entire manuscript as presented): the central claim of partial cross-lingual overlap rests on an unspecified 'cross-lingual mechanistic analysis' for localizing and extracting math-associated parameters. No description is given of the intervention or localization procedure, the math tasks or datasets used, model sizes, statistical controls, or validation against tokenization differences, training-data imbalance, or general language-modeling activations. Without these details the reported overlap and the English-vs.-lower-resource size difference cannot be distinguished from artifacts.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and for identifying the need for greater methodological transparency. We agree that the abstract is too high-level and that the presentation of the localization procedure requires expansion to allow proper evaluation of the claims. We will revise accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract (and entire manuscript as presented): the central claim of partial cross-lingual overlap rests on an unspecified 'cross-lingual mechanistic analysis' for localizing and extracting math-associated parameters. No description is given of the intervention or localization procedure, the math tasks or datasets used, model sizes, statistical controls, or validation against tokenization differences, training-data imbalance, or general language-modeling activations. Without these details the reported overlap and the English-vs.-lower-resource size difference cannot be distinguished from artifacts.

    Authors: We accept this criticism. The abstract is intentionally concise and therefore omits procedural specifics; the body of the manuscript contains a Methods section that describes the intervention technique, but we agree the description is not sufficiently detailed or prominent for the central claim. In the revision we will (1) expand the abstract with a one-sentence summary of the localization method, (2) add an explicit subsection detailing the intervention procedure, the math tasks and datasets (including how they were translated), the models and sizes examined, and the statistical controls employed, and (3) include new validation experiments that directly test for confounds arising from tokenization, training-data imbalance, and non-math language-modeling activations. These additions will make it possible to evaluate whether the reported overlap exceeds what would be expected from such artifacts. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical localization method stands independent of its outputs

full rationale

The paper reports results from a cross-lingual mechanistic analysis that localizes math-associated parameters and measures their overlap across languages. No equations, fitted parameters renamed as predictions, or self-citations appear in the provided abstract or description. The central claim (partial overlap strongest in intermediate layers, English yielding largest set) is presented as an observation from the analysis rather than a quantity derived by construction from its own inputs. The method itself is not shown to be self-definitional or to smuggle an ansatz via prior self-citation. This is the normal case of an empirical paper whose validity hinges on the soundness of its experimental procedure, not on definitional circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no information on free parameters, background axioms, or new postulated entities.

pith-pipeline@v0.9.1-grok · 5679 in / 1033 out tokens · 39288 ms · 2026-06-27T00:28:09.042883+00:00 · methodology

discussion (0)

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Reference graph

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