arxiv: 2604.18203 · v1 · submitted 2026-04-20 · 💻 cs.CL

Recognition: unknown

Multiplication in Multimodal LLMs: Computation with Text, Image, and Audio Inputs

Samuel G. Balter , Ethan Jerzak , Connor T. Jerzak

Authors on Pith no claims yet

Pith reviewed 2026-05-10 04:27 UTC · model grok-4.3

classification 💻 cs.CL

keywords multimodal LLMsmultiplication benchmarkarithmetic loadperception versus computationfactorial designheuristic probingpaired instances

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The pith

Multimodal LLMs perceive numbers accurately across text, images, and audio but fail at exact multiplication as arithmetic load grows.

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

The paper introduces a factorial benchmark that presents identical multiplication problems in paired instances across modalities and representations to isolate whether failures stem from perception or computation. It defines arithmetic load C as the product of total digits and non-zero digits, demonstrating that accuracy declines sharply with rising C and that this single metric predicts performance with R-squared values often above 0.5 across models. Matched-perception checks confirm models recognize the numbers near perfectly even when they cannot multiply them. The work further uses a forced-completion probe to identify favored heuristics such as distributive decomposition. This separation clarifies the source of arithmetic limits in models that otherwise handle multimodal inputs fluently.

Core claim

Multimodal LLMs can accurately perceive numerical content across modalities yet fail to perform exact multi-digit multiplication when the identical underlying arithmetic problem is presented as numerals, number words, images, or audio. A controlled benchmark factorially varies digit length, sparsity, representation, and modality with paired instances from a reproducible generator. Arithmetic load C, the product of total and non-zero digit counts, predicts accuracy drop-off, often nearing zero by C > 100, with R-squared frequently exceeding 0.5. Perception checks reach over 99% accuracy across modalities while multiplication fails, and a loss probe shows preference for decomposition over cues

What carries the argument

The perception-versus-computation decomposition, implemented via matched-perception checks on paired instances, that isolates recognition of numerical content from execution of the arithmetic operations.

If this is right

Multiplication accuracy falls sharply as C grows, nearing zero by C > 100.
C remains predictive of performance across modalities and models, with R-squared often > 0.5.
Decomposition is favored over columnar multiplication or rounding in both text and vision modalities.
Heuristic-specific LoRA adapters produce near-orthogonal updates yet degrade accuracy, indicating a well-tuned internal router in the base model.

Where Pith is reading between the lines

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

Training strategies that incrementally raise arithmetic load could build computational capacity more effectively than uniform data scaling.
The internal router finding suggests it may be possible to steer models toward stronger heuristics with targeted, low-cost interventions rather than full retraining.
The same factorial paired-instance design could be applied to addition, division, or other operations to test whether C generalizes as a load measure.
Efforts to improve multimodal arithmetic should prioritize strengthening execution pathways over further refining input encoders.

Load-bearing premise

The matched-perception checks can be performed without inadvertently engaging computational processes that would confound the separation from multiplication.

What would settle it

If models score below 99% on the matched-perception checks for problems where multiplication accuracy has already dropped, or if C shows no correlation with accuracy when tested on a new set of digit patterns.

Figures

Figures reproduced from arXiv: 2604.18203 by Connor T. Jerzak, Ethan Jerzak, Samuel G. Balter.

**Figure 2.** Figure 2: Probability of correct answer as a function of arithmetic load [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

read the original abstract

Multimodal LLMs can accurately perceive numerical content across modalities yet fail to perform exact multi-digit multiplication when the identical underlying arithmetic problem is presented as numerals, number words, images, or in audio form. Because existing benchmarks often lack systematically paired instances across modalities, it remains difficult to compare genuine arithmetic limits within and across model families. We therefore introduce a controlled multimodal multiplication benchmark that factorially varies digit length, digit sparsity, representation (e.g., numerals vs. number words), and modality (text, rendered images, audio), with paired instances from a reproducible generator. We also define arithmetic load, C, as the product of the total and non-zero digit count as a compact, mechanistically motivated proxy for operation count. Across evaluations, accuracy falls sharply as C grows, often nearing zero by C > 100. Indeed, C remains predictive of performance across modalities and models, with R-squared often > 0.5, nearing the value from more complex measures of arithmetic load that count the number of intermediate arithmetic steps. A separate perception-versus-computation decomposition shows that multimodal degradation is primarily computational rather than perceptual: on matched-perception checks, models are near-perfect (> 99%) across modalities, even when multiplication accuracy drops. Beyond measuring when models fail, we ask which procedures they are predisposed to follow. We introduce a forced-completion loss probe that scores heuristic-specific reasoning prefixes--including columnar multiplication, distributive decomposition, and rounding/compensation. Here, decomposition is favored in both text and vision modalities; heuristic-specific LoRA adapters produce near-orthogonal updates yet degrade accuracy, indicating the base model maintains a well-tuned internal router.

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's main contribution is a controlled multimodal multiplication benchmark that separates perception from computation and shows accuracy collapsing with arithmetic load C.

read the letter

The punchline is straightforward: multimodal LLMs read numbers accurately in text, images, or audio, but exact multiplication accuracy drops sharply once the problem size increases, and the authors supply a factorial benchmark with paired instances to measure that cleanly across modalities. They define arithmetic load C as the product of total digit count and non-zero digit count, which tracks performance with R-squared values often above 0.5 and performs close to more detailed step-counting measures. The perception checks reach over 99 percent accuracy on matched inputs even when multiplication fails, which supports their claim that the bottleneck is computational rather than perceptual. The forced-completion probes also give an initial look at preferred heuristics, with decomposition favored in text and vision, and the LoRA adapter results suggest the base model keeps some internal routing intact. These pieces are new and useful for anyone tracking numerical limits in current models. The design controls for representation and modality in a reproducible way, which existing benchmarks often skip. One soft spot is that C remains a compact proxy rather than an exhaustive operation count, so its predictive edge may vary once fuller step-by-step measures are applied to more models. The heuristic probes are promising but rest on prefix scoring that could still be influenced by surface patterns. The paper is aimed at researchers working on LLM reasoning benchmarks and multimodal capability evaluation. Readers who need a ready-made testbed for arithmetic difficulty across input types will get direct value from the generator and the C metric. It has enough controlled comparisons and new probes to deserve a serious referee rather than a desk reject.

Referee Report

2 major / 2 minor

Summary. The paper introduces a factorial multimodal multiplication benchmark that systematically varies digit length, sparsity, representation (numerals vs. words), and modality (text, image, audio) using paired instances from a reproducible generator. It defines arithmetic load C as the product of total and non-zero digit counts, reports sharp accuracy declines with increasing C (often with R² > 0.5 across models and modalities), demonstrates via matched-perception checks that models achieve near-perfect (>99%) perception accuracy even as multiplication fails, and uses forced-completion loss probes plus LoRA adapters to show a preference for decomposition heuristics with near-orthogonal updates.

Significance. If the central results hold, the work offers a valuable controlled benchmark for isolating computational limits from perceptual ones in multimodal LLMs, along with a mechanistically motivated load proxy and heuristic analysis that could inform interpretability and improvement efforts. The reproducible design and separation of perception from computation are notable strengths for the field.

major comments (2)

[Perception-versus-computation decomposition] Perception-versus-computation decomposition: the manuscript claims matched-perception checks reach >99% accuracy without engaging computation, but provides insufficient detail on task construction and controls to confirm that these checks fully isolate perception (e.g., whether models can solve the checks without performing any arithmetic steps). This is load-bearing for the primary claim that degradation is computational rather than perceptual.
[Arithmetic load and R-squared results] Arithmetic load results: the reported R² values (often >0.5) for C predicting accuracy lack error bars, per-condition sample sizes, confidence intervals, or statistical tests, making it hard to assess robustness of the claim that C is predictive across modalities and models; this is central to the evaluation of the benchmark's utility.

minor comments (2)

[Benchmark and metric definition] The definition of C as a proxy would benefit from an explicit equation or formula in the main text for clarity and reproducibility.
[Benchmark construction] Clarify in the methods whether the factorial design includes any balancing or randomization steps to prevent systematic biases in how different modalities are tokenized or processed by the models.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the constructive and detailed feedback on our manuscript. We address each major comment point by point below and describe the revisions we will make to improve clarity and statistical reporting.

read point-by-point responses

Referee: Perception-versus-computation decomposition: the manuscript claims matched-perception checks reach >99% accuracy without engaging computation, but provides insufficient detail on task construction and controls to confirm that these checks fully isolate perception (e.g., whether models can solve the checks without performing any arithmetic steps). This is load-bearing for the primary claim that degradation is computational rather than perceptual.

Authors: We agree that more explicit documentation of the perception checks is needed to fully substantiate the isolation claim. These checks use identical numerical inputs across modalities but prompt the model only to transcribe or list the digits/numbers present (e.g., 'Output the exact sequence of numbers shown' or 'Transcribe the spoken digits without any further processing'), with instructions that explicitly prohibit arithmetic. Pilot runs and output inspection confirmed no multiplication steps were generated. To address the concern, we will expand the methods and appendix with complete prompt templates, example inputs/outputs for each modality, and additional verification steps such as token-level analysis to rule out implicit computation. These details will be added in the revised manuscript. revision: yes
Referee: Arithmetic load results: the reported R² values (often >0.5) for C predicting accuracy lack error bars, per-condition sample sizes, confidence intervals, or statistical tests, making it hard to assess robustness of the claim that C is predictive across modalities and models; this is central to the evaluation of the benchmark's utility.

Authors: We concur that statistical details would strengthen the presentation of the arithmetic load results. The R² values derive from regressions over the factorial conditions, each containing 100 reproducible paired instances, but accompanying metrics were omitted from the main text for brevity. In the revision we will add bootstrapped error bars to the relevant plots, include a supplementary table with exact per-condition sample sizes and model-modality counts, report 95% confidence intervals on the R² estimates, and provide p-values from the regression models. These changes will allow better evaluation of C's predictive utility. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper defines arithmetic load C a priori as the product of total and non-zero digit counts, then empirically measures its correlation with accuracy (reporting R-squared values as observed outcomes). The perception-versus-computation decomposition relies on separate matched-perception checks that achieve >99% accuracy while multiplication fails, with no equations or claims reducing the central results to their inputs by construction. No self-citations, fitted parameters renamed as predictions, or ansatzes smuggled via prior work are load-bearing in the derivation chain. The factorial benchmark and heuristic probes are introduced as new experimental designs whose outcomes are measured rather than presupposed.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the domain assumption that perception of numerical content can be isolated from arithmetic computation and that the benchmark's controlled variations adequately capture computational load without modality-specific confounds.

axioms (1)

domain assumption Numerical perception can be tested independently of arithmetic computation in LLMs
The perception-versus-computation decomposition and matched-perception checks rely on this separation being feasible and valid.

pith-pipeline@v0.9.0 · 5604 in / 1434 out tokens · 79826 ms · 2026-05-10T04:27:07.405155+00:00 · methodology

discussion (0)

Reference graph

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