Disentangling Mathematical Reasoning in LLMs: A Methodological Investigation of Internal Mechanisms

Tanja Baeumel , Josef van Genabith , Simon Ostermann

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Pith reviewed 2026-05-10 08:52 UTC · model grok-4.3

classification 💻 cs.CL

keywords modelsarithmeticmechanismsinternalllmstasksattentioncapabilities

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The pith

Proficient LLMs detect arithmetic tasks early but output correct answers only in final layers, with attention and MLP modules dividing labor in a way absent from less proficient models.

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

Large language models can solve math problems, but researchers want to know what happens inside their many layers during that process. This study applies early decoding, a technique that peeks at the model's next-word guesses at every stage instead of waiting until the end. The key observation is that models spot the arithmetic task quickly in early layers, yet only produce the right numerical answer in the very last layers. In models that are strong at arithmetic, the attention components mainly carry forward the original numbers and operators, while the MLP components do the actual combining and calculation. Weaker models lack this clear split in responsibilities. The study also notes that stronger models handle harder problems in a way that looks more like step-by-step computation than simple memory lookup from training data. These patterns come from comparing different model sizes and training levels on basic arithmetic examples. The work stays observational, mapping where information flows rather than proving why the split occurs.

Core claim

Notably, models proficient in arithmetic exhibit a clear division of labor between attention and MLP modules, where attention propagates input information and MLP modules aggregate it. This division is absent in less proficient models. Furthermore, successful models appear to process more challenging arithmetic tasks functionally, suggesting reasoning capabilities beyond factual recall.

Load-bearing premise

That early decoding faithfully reveals the model's unaltered internal computation flow and that the observed attention-MLP split is a causal mechanism for proficiency rather than a correlated byproduct of model scale or training data.

Figures

Figures reproduced from arXiv: 2604.15842 by Josef van Genabith, Simon Ostermann, Tanja Baeumel.

**Figure 2.** Figure 2: Visualization of early decoding. The resid [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: Combined probability mass of numerical tokens in the (a) post-ATT and (b) post-MLP intermediate [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: Proportion of numerical tokens in the (a) top 1 and (b) top 10 post-MLP intermediate predictions, averaged [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

**Figure 5.** Figure 5: Absolute error, i.e., difference to correct result, of numerical tokens in the (a) top 1 and (b) top 10 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 6.** Figure 6: Position of correct result in the post-MLP prediction of intermediate layers, averaged over all data points [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗

**Figure 7.** Figure 7: Position of (a) operand 1 and (b) operand 2 in the post-ATT prediction of intermediate layers, averaged [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗

**Figure 8.** Figure 8: Effect of interchange intervention, i.e., source is used to intervene on base, on one of the operands in the [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗

**Figure 9.** Figure 9: Effect of interchange intervention, i.e., source is used to intervene on base, on the operator in the [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗

**Figure 10.** Figure 10: GPT-Neox-20b: Combined probability mass of numerical tokens in the (a) post-ATT and (b) post-MLP [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗

**Figure 11.** Figure 11: GPT-Neox-20b: Proportion of numerical tokens in the (a) top 1 and (b) top 10 post-MLP intermediate [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗

**Figure 12.** Figure 12: GPT-Neox-20b: Absolute error, i.e., difference to correct result, of numerical tokens in the (a) top 1 and [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗

**Figure 13.** Figure 13: GPT-Neox-20b: Position of correct result in the post-MLP prediction of intermediate layers, averaged [PITH_FULL_IMAGE:figures/full_fig_p014_13.png] view at source ↗

**Figure 14.** Figure 14: GPT-2 XL: Combined probability mass of numerical tokens in the (a) post-ATT and (b) post-MLP [PITH_FULL_IMAGE:figures/full_fig_p014_14.png] view at source ↗

**Figure 15.** Figure 15: GPT-2 XL: Absolute error, i.e., difference to correct result, of numerical tokens in the (a) top 1 and (b) [PITH_FULL_IMAGE:figures/full_fig_p014_15.png] view at source ↗

**Figure 16.** Figure 16: GPT-2 XL: Position of operand 1 in the (a) post-ATT and (b) post-MLP prediction of intermediate layers, [PITH_FULL_IMAGE:figures/full_fig_p015_16.png] view at source ↗

read the original abstract

Large language models (LLMs) have demonstrated impressive capabilities, yet their internal mechanisms for handling reasoning-intensive tasks remain underexplored. To advance the understanding of model-internal processing mechanisms, we present an investigation of how LLMs perform arithmetic operations by examining internal mechanisms during task execution. Using early decoding, we trace how next-token predictions are constructed across layers. Our experiments reveal that while the models recognize arithmetic tasks early, correct result generation occurs only in the final layers. Notably, models proficient in arithmetic exhibit a clear division of labor between attention and MLP modules, where attention propagates input information and MLP modules aggregate it. This division is absent in less proficient models. Furthermore, successful models appear to process more challenging arithmetic tasks functionally, suggesting reasoning capabilities beyond factual recall.

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.

Desk Editor's Note private letter to a colleague

The paper uses early decoding to claim proficient LLMs split arithmetic work between attention propagation and MLP aggregation, but the abstract gives almost no experimental details to check it.

read the letter

The main thing to know is that this work applies early decoding to arithmetic in LLMs and reports that proficient models show attention modules passing input information while MLPs aggregate it, a split that weaker models lack. They also suggest stronger models handle hard problems by functional processing rather than pure recall. That proficiency-linked module division is the piece that stands out as new, since earlier interpretability studies have looked at layers and modules but not tied this exact pattern to arithmetic skill this way. The paper does a reasonable job of keeping the description observational and focused on tracing when correct predictions form late in the network. The soft spots are the missing pieces that matter for judging the claims. There is no information on which models were tested, how large the datasets were, how proficiency was measured, or any controls for scale and training data. Without those, the division could easily be a byproduct rather than a mechanism. The assumption that early decoding leaves the internal flow untouched also needs more support than high-level observations provide. This is aimed at people working on LLM interpretability and mechanistic accounts of reasoning. A reader in that area could pick up some concrete ideas for follow-up experiments, but would not treat the findings as settled. I would send it for peer review so the authors can add the methods and results sections and let referees check whether the split holds up under proper controls.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Empirical interpretability study; no mathematical derivations or new theoretical constructs appear in the abstract.

pith-pipeline@v0.9.0 · 5430 in / 1152 out tokens · 56679 ms · 2026-05-10T08:52:38.732014+00:00 · methodology

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Works this paper leans on

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