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

• URL: http://arxiv.org/abs/2604.18203v1
• Date: Mon, 20 Apr 2026 12:52:07 GMT
• Title: Multiplication in Multimodal LLMs: Computation with Text, Image, and Audio Inputs
• Abstract summary: Multimodal LLMs can accurately perceive numerical content across modalities yet fail to perform exact multi-digit multiplication.<n>We introduce a controlled multimodal multiplication benchmark that factorially varies digit length, digit sparsity, representation.<n>We also define arithmetic load, C, as the product of the total and non-zero digit count.
• Score: 0.8129517423858409
• License: http://creativecommons.org/licenses/by-sa/4.0/
• 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.

Related papers

• Where Does Generative Difficulty Reside? An Empirical Study of Target Representations [62.54876287800644]
  The target representation defines the distribution an image generator must learn, yet it is often treated as an interchangeable interface.<n>We study raw pixels, SD-VAE latents and DINOv2 as well as MAE representation-autoencoder features within a unified masked autoregressive rectified-flow model.<n>Our results show that compression, reconstruction fidelity, token dimensionality, and visible semantic clustering do not individually predict generative behavior.
  arXiv  Detail & Related papers  (2026-08-01T12:32:31Z)
• Testing LLM Arithmetic Reasoning Generalization with Automatic Numeric-Remapping Attacks [2.6659012768342145]
  We introduce an automatic algorithm for generating numeric-remapping attacks on arithmetic word problems.<n>We evaluate DeepSeek-R1 (70B), Gemma4 (31B), and GPT-OSS (120B) on GSM8K, MAWPS, and MultiArith.
  arXiv  Detail & Related papers  (2026-06-02T13:09:44Z)
• Accelerate Speculative Decoding with Sparse Computation in Verification [49.74839681322316]
  Speculative decoding accelerates autoregressive language model inference by verifying multiple draft tokens in parallel.<n>Existing sparsification methods are designed primarily for standard token-by-token autoregressive decoding.<n>We propose a sparse verification framework that jointly sparsifies attention, FFN, and MoE components during the verification stage to reduce the dominant computation cost.
  arXiv  Detail & Related papers  (2025-12-26T07:53:41Z)
• How Focused Are LLMs? A Quantitative Study via Repetitive Deterministic Prediction Tasks [0.9338697277815541]
  We investigate the performance of large language models on repetitive deterministic prediction tasks.<n>Our experiments reveal a sharp double exponential drop beyond a characteristic length scale.<n>This indicates that the models fail to execute each operation independently.
  arXiv  Detail & Related papers  (2025-11-02T01:42:08Z)
• Why Can't Transformers Learn Multiplication? Reverse-Engineering Reveals Long-Range Dependency Pitfalls [54.57326125204404]
  Language models are increasingly capable, yet still fail at a seemingly simple task of multi-digit multiplication.<n>We study why, by reverse-engineering a model that successfully learns multiplication via emphimplicit chain-of-thought'
  arXiv  Detail & Related papers  (2025-09-30T19:03:26Z)
• Numerical Considerations in Weighted Model Counting [0.0]
  We show how to combine multiple numeric representations to efficiently compute weighted model counts that are guaranteed to achieve a user-specified precision.<n>We show that supplementing a standard IEEE double-precision representation with a separate 64-bit exponent, a format we call extended-range double (ERD), avoids the underflow and overflow issues commonly encountered in weighted model counting.
  arXiv  Detail & Related papers  (2025-08-08T12:28:49Z)
• Mathematical Reasoning in Large Language Models: Assessing Logical and Arithmetic Errors across Wide Numerical Ranges [0.0]
  We introduce GSM-Ranges, a dataset generator that systematically perturbs numerical values in math problems to assess model robustness across varying numerical scales.<n>We also propose a novel grading methodology that distinguishes between logical and non-logical errors, offering a more precise evaluation of reasoning processes beyond computational accuracy.
  arXiv  Detail & Related papers  (2025-02-12T09:53:10Z)
• Adaptive Sampled Softmax with Inverted Multi-Index: Methods, Theory and Applications [79.53938312089308]
  The MIDX-Sampler is a novel adaptive sampling strategy based on an inverted multi-index approach.<n>Our method is backed by rigorous theoretical analysis, addressing key concerns such as sampling bias, gradient bias, convergence rates, and generalization error bounds.
  arXiv  Detail & Related papers  (2025-01-15T04:09:21Z)
• Unveiling the Statistical Foundations of Chain-of-Thought Prompting Methods [59.779795063072655]
  Chain-of-Thought (CoT) prompting and its variants have gained popularity as effective methods for solving multi-step reasoning problems. We analyze CoT prompting from a statistical estimation perspective, providing a comprehensive characterization of its sample complexity.
  arXiv  Detail & Related papers  (2024-08-25T04:07:18Z)
• Deep Ensembles Meets Quantile Regression: Uncertainty-aware Imputation for Time Series [45.76310830281876]
  We propose Quantile Sub-Ensembles, a novel method to estimate uncertainty with ensemble of quantile-regression-based task networks. Our method not only produces accurate imputations that is robust to high missing rates, but also is computationally efficient due to the fast training of its non-generative model.
  arXiv  Detail & Related papers  (2023-12-03T05:52:30Z)
• What and How does In-Context Learning Learn? Bayesian Model Averaging, Parameterization, and Generalization [111.55277952086155]
  We study In-Context Learning (ICL) by addressing several open questions. We show that, without updating the neural network parameters, ICL implicitly implements the Bayesian model averaging algorithm. We prove that the error of pretrained model is bounded by a sum of an approximation error and a generalization error.
  arXiv  Detail & Related papers  (2023-05-30T21:23:47Z)
• Berrut Approximated Coded Computing: Straggler Resistance Beyond Polynomial Computing [34.69732430310801]
  We propose Berrut Approximated Coded Computing (BACC) as an alternative approach to deal with stragglers effect. BACC is proven to be numerically stable with low computational complexity. In particular, BACC is used to train a deep neural network on a cluster of servers.
  arXiv  Detail & Related papers  (2020-09-17T14:23:38Z)
• Consistency of a Recurrent Language Model With Respect to Incomplete Decoding [67.54760086239514]
  We study the issue of receiving infinite-length sequences from a recurrent language model. We propose two remedies which address inconsistency: consistent variants of top-k and nucleus sampling, and a self-terminating recurrent language model.
  arXiv  Detail & Related papers  (2020-02-06T19:56:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.