# NuCap: A Numerically Aware Captioning Framework for Improved Numerical Reasoning
## 2 Related Work  
**Image Captioning. ** Image captioning is a vision-language task that generates natural language descriptions for a given image. It typically follows an encoder-decoder framework, where the visual encoder extracts semantic features from the image, and the decoder generates a sentence based on these features [1]. Early models relied primarily on CNN-based encoders. However, with the introduction of Transformer architectures, it became possible to effectively model long-range dependencies across visual and linguistic modalities, resulting in significant improvements in caption quality. Since then, various extensions to Transformer-based architectures have been proposed. For instance, ExpansionNet v2 [11] alleviates the fixed-sequence-length constraint by dynamically adjusting decoding length, enabling more flexible and accurate caption generation. Recent efforts have aimed to improve the expressiveness and factuality of captions. These include approaches such as external knowledge integration, retrieval-based captioning, and diffusion-based generation. For example, MeaCap [12] leverages external memory to extract image-relevant concepts and incorporate them into the generation process, thereby reducing hallucinations and producing factually grounded descriptions. Retrieval-Augmented Captioning [13] retrieves semantically similar images to complement a single-image input, improving consistency in expressions involving quantities and relationships. Prefix-diffusion [14] injects prefix tokens into the denoising process of diffusion models, allowing efficient and diverse caption generation with fewer parameters. Despite these advancements, most existing models still struggle to generate accurate numerical expressions, such as object counts, distances, or temporal attributes. This limitation largely stems from the characteristics of widely used datasets such as COCO [9] and Visual Genome [10], which prioritize general scene descriptions rather than numerical precision. The gap becomes especially apparent in applications that explicitly require quantitative information. **Object Counting. ** Object counting is a core task in computer vision, typically approached through detection-based or density map-based methods [15]. In recent years, various approaches have been proposed to improve generalization and enable open-vocabulary counting. CLIP-Count [16] leverages image-text alignment in CLIP to build a text-guided zero-shot counting framework. It employs patch-text contrastive learning and hierarchical interactions to generate high-quality density maps for open-vocabulary object categories. CountGD [17] introduces a multi-modal counting framework that flexibly uses prompts in the form of text, visual exemplars, or both. PseCo [18] integrates the Segment Anything Model (SAM) with CLIP to enable effective few-shot and zero-shot counting, demonstrating strong performance particularly in dense scenes and with small objects. Additionally, diffusion-based data augmentation [19] generates synthetic data from location-conditioned dot maps using a diffusion model, mitigating data scarcity and improving numerical prediction accuracy in crowd counting tasks. Despite their strong numerical estimation capabilities, these models differ fundamentally from captioning systems in both objective and output. Counting models aim for precise quantitative prediction, whereas captioning models prioritize linguistic fluency, often at the expense of numeric accuracy. This gap is particularly evident in applications where accurate quantity descriptions are essential, highlighting the need for captioning approaches that can reliably incorporate numerical information. **Numerical Reasoning in Vision-Language Tasks. ** Numerical reasoning in vision-language tasks remains a significant challenge despite the progress of large-scale VLMs. Models such as BLIP [20], mPLUG-Owl3 [21], and Idefics2 [22] have demonstrated strong language understanding and effective multi-modal alignment.