# A Fixed-Point Approach to Unified Prompt-Based Counting

arXiv: https://arxiv.org/abs/2403.10236 · HTML: https://mlsanity.com/paper/2403.10236/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 45 references that are in the map.
- First posted on arXiv 15 Mar 2024.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [LLaMA-Adapter V2: Parameter-Efficient Visual Instruction Model](https://mlsanity.com/paper/2304.15010/) (2023)
- [Extract Free Dense Labels from CLIP](https://mlsanity.com/paper/2112.01071/) (2021)
- [Drone-based Object Counting by Spatially Regularized Regional Proposal Network](https://mlsanity.com/paper/1707.05972/) (2017)
- [NWPU-Crowd: A Large-Scale Benchmark for Crowd Counting and Localization](https://mlsanity.com/paper/2001.03360/) (2020)
- [Learning To Count Everything](https://mlsanity.com/paper/2104.08391/) (2021)
- [Class-Agnostic Counting](https://mlsanity.com/paper/1811.00472/) (2018)
- [Represent, Compare, and Learn: A Similarity-Aware Framework for Class-Agnostic Counting](https://mlsanity.com/paper/2203.08354/) (2022)
- [CounTR: Transformer-based Generalised Visual Counting](https://mlsanity.com/paper/2208.13721/) (2022)
- [Precise Detection in Densely Packed Scenes](https://mlsanity.com/paper/1904.00853/) (2019)
- [Improving Object-centric Learning with Query Optimization](https://mlsanity.com/paper/2210.08990/) (2022)
- [Few-shot Object Counting and Detection](https://mlsanity.com/paper/2207.10988/) (2022)
- [Object Representations as Fixed Points: Training Iterative Refinement Algorithms with Implicit Differentiation](https://mlsanity.com/paper/2207.00787/) (2022)
- [Training-free Object Counting with Prompts](https://mlsanity.com/paper/2307.00038/) (2023)
- [Cross-View Cross-Scene Multi-View Crowd Counting](https://mlsanity.com/paper/2205.01551/) (2022)
- [Finding Berries: Segmentation and Counting of Cranberries using Point Supervision and Shape Priors](https://mlsanity.com/paper/2004.08501/) (2020)
- [Counting of Grapevine Berries in Images via Semantic Segmentation using Convolutional Neural Networks](https://mlsanity.com/paper/2004.14010/) (2020)
- [RGB-D Indiscernible Object Counting in Underwater Scenes](https://mlsanity.com/paper/2304.11677/) (2023)

## Built on by (most cited first, 10 of 10)

- [Mind the Prompt: A Novel Benchmark for Prompt-based Class-Agnostic Counting](https://mlsanity.com/paper/2409.15953/) (2024)
- [A Survey on Class-Agnostic Counting: Advancements from Reference-Based to Open-World Text-Guided Approaches](https://mlsanity.com/paper/2501.19184/) (2025)
- [Can Current AI Models Count What We Mean, Not What They See? A Benchmark and Systematic Evaluation](https://mlsanity.com/paper/2509.13939/) (2025)
- [Point-to-Region Loss for Semi-Supervised Point-Based Crowd Counting](https://mlsanity.com/paper/2505.21943/) (2025)
- [Text-promptable Object Counting via Quantity Awareness Enhancement](https://mlsanity.com/paper/2507.06679/) (2025)
- [Does it Really Count? Assessing Semantic Grounding in Text-Guided Class-Agnostic Counting](https://mlsanity.com/paper/2605.02752/) (2026)
- [Decoupling What to Count and Where to See for Referring Expression Counting](https://mlsanity.com/paper/2510.24374/) (2025)
- [Real-Time Crowd Counting for Embedded Systems with Lightweight Architecture](https://mlsanity.com/paper/2510.13250/) (2025)
- [Depth-Guided Video Object Counting in Crowded Scenes](https://mlsanity.com/paper/2608.06236/) (2026)
- [Object Counting Across Modalities: Taxonomies, Benchmarks, Applications, and Open Challenges](https://mlsanity.com/paper/2608.23845/) (2026)

## Abstract (arXiv)

Existing class-agnostic counting models typically rely on a single type of prompt, e.g., box annotations. This paper aims to establish a comprehensive prompt-based counting framework capable of generating density maps for concerned objects indicated by various prompt types, such as box, point, and text. To achieve this goal, we begin by converting prompts from different modalities into prompt masks without requiring training. These masks are then integrated into a class-agnostic counting methodology for predicting density maps. Furthermore, we introduce a fixed-point inference along with an associated loss function to improve counting accuracy, all without introducing new parameters. The effectiveness of this method is substantiated both theoretically and experimentally. Additionally, a contrastive training scheme is implemented to mitigate dataset bias inherent in current class-agnostic counting datasets, a strategy whose effectiveness is confirmed by our ablation study. Our model excels in prominent class-agnostic datasets and exhibits superior performance in cross-dataset adaptation tasks.