# Compact Bilinear Pooling

arXiv: https://arxiv.org/abs/1511.06062 · HTML: https://mlsanity.com/paper/1511.06062/

## Key facts

- Cited by 97 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2015.

## Built on by (most cited first, 30 of 97)

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- [Multi-modal Machine Learning in Engineering Design: A Review and Future Directions](https://mlsanity.com/paper/2302.10909/) (2023)
- [Democratizing Fine-grained Visual Recognition with Large Language Models](https://mlsanity.com/paper/2401.13837/) (2024)
- [Comprehensive Visual Question Answering on Point Clouds through Compositional Scene Manipulation](https://mlsanity.com/paper/2112.11691/) (2021)
- [Learning Gabor Texture Features for Fine-Grained Recognition](https://mlsanity.com/paper/2308.05396/) (2023)
- [Improving Generalization in Visual Reasoning via Self-Ensemble](https://mlsanity.com/paper/2410.20883/) (2024)
- [Dealing with Missing Modalities in the Visual Question Answer-Difference Prediction Task through Knowledge Distillation](https://mlsanity.com/paper/2104.05965/) (2021)
- [VQA and Visual Reasoning: An Overview of Recent Datasets, Methods and Challenges](https://mlsanity.com/paper/2212.13296/) (2022)
- [Improved Random Features for Dot Product Kernels](https://mlsanity.com/paper/2201.08712/) (2022)
- [Improving Fine-Grained Visual Recognition in Low Data Regimes via Self-Boosting Attention Mechanism](https://mlsanity.com/paper/2208.00617/) (2022)
- [Towards Joint Intent Detection and Slot Filling via Higher-order Attention](https://mlsanity.com/paper/2109.08890/) (2021)
- [Temporal-attentive Covariance Pooling Networks for Video Recognition](https://mlsanity.com/paper/2110.14381/) (2021)
- [Pseudo-Pair based Self-Similarity Learning for Unsupervised Person Re-identification](https://mlsanity.com/paper/2207.13035/) (2022)
- [Paying Attention to Activation Maps in Camera Pose Regression](https://mlsanity.com/paper/2103.11477/) (2021)
- [On the Eigenvalues of Global Covariance Pooling for Fine-grained Visual Recognition](https://mlsanity.com/paper/2205.13282/) (2022)
- [RainbowPrompt: Diversity-Enhanced Prompt-Evolving for Continual Learning](https://mlsanity.com/paper/2507.22553/) (2025)
- [Structured Two-stream Attention Network for Video Question Answering](https://mlsanity.com/paper/2206.01017/) (2022)
- [Tuning Pre-trained Model via Moment Probing](https://mlsanity.com/paper/2307.11342/) (2023)
- [Understanding Matrix Function Normalizations in Covariance Pooling through the Lens of Riemannian Geometry](https://mlsanity.com/paper/2407.10484/) (2024)
- [Object-aware Long-short-range Spatial Alignment for Few-Shot Fine-Grained Image Classification](https://mlsanity.com/paper/2108.13098/) (2021)
- [Representing Videos as Discriminative Sub-graphs for Action Recognition](https://mlsanity.com/paper/2201.04027/) (2022)
- [Multi-level Attention Fusion Network for Audio-visual Event Recognition](https://mlsanity.com/paper/2106.06736/) (2021)
- [Part-guided Relational Transformers for Fine-grained Visual Recognition](https://mlsanity.com/paper/2212.13685/) (2022)
- [Learning to Recognize Actions on Objects in Egocentric Video with Attention Dictionaries](https://mlsanity.com/paper/2102.08065/) (2021)
- [FashionVQA: A Domain-Specific Visual Question Answering System](https://mlsanity.com/paper/2208.11253/) (2022)
- [Learning Partial Correlation based Deep Visual Representation for Image Classification](https://mlsanity.com/paper/2304.11597/) (2023)

## Abstract (arXiv)

Bilinear models has been shown to achieve impressive performance on a wide range of visual tasks, such as semantic segmentation, fine grained recognition and face recognition. However, bilinear features are high dimensional, typically on the order of hundreds of thousands to a few million, which makes them impractical for subsequent analysis. We propose two compact bilinear representations with the same discriminative power as the full bilinear representation but with only a few thousand dimensions. Our compact representations allow back-propagation of classification errors enabling an end-to-end optimization of the visual recognition system. The compact bilinear representations are derived through a novel kernelized analysis of bilinear pooling which provide insights into the discriminative power of bilinear pooling, and a platform for further research in compact pooling methods. Experimentation illustrate the utility of the proposed representations for image classification and few-shot learning across several datasets.