# 多模态大语言模型的乘法运算：基于文本、图像和音频输入的计算

- 来源：HuggingFace Daily Papers（社区热门论文）
- 发布时间：2026-04-20 08:00
- AIHOT 链接：https://aihot.virxact.com/items/cmo82l6vp03lhslmlrvdj6icc
- 原文链接：https://arxiv.org/abs/2604.18203

## AI 摘要

研究人员发布受控多模态乘法基准，系统评估大模型在文本、图像和音频输入下的算术极限。研究定义算术负载指标C（总位数与非零位数乘积），发现当C>100时准确率急剧下降至接近零，且该指标跨模态预测性能R²常超0.5。实验表明模型失败主要源于计算缺陷而非感知能力——匹配感知测试中各模态准确率均超99%。此外，模型倾向于采用分配式分解策略而非传统列式乘法进行计算。

## 正文

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.