Low-rank Random Tensor for Bilinear Pooling

Bilinear pooling is capable of extracting high-order information from data, which makes it suitable for fine-grained visual understanding and information fusion. Despite their effectiveness in various applications, bilinear models with massive number of parameters can easily suffer from curse of dimensionality and intractable computation. In this paper, we propose a novel bilinear model based on low-rank random tensors. The key idea is to effectively combine low-rank tensor decomposition and random projection to reduce the number of parameters while preserving the model representativeness. From the theoretical perspective, we prove that our bilinear model with random tensors can estimate feature maps to reproducing kernel Hilbert spaces (RKHSs) with compositional kernels, grounding the high-dimensional feature fusion with theoretical foundations. From the application perspective, our low-rank tensor operation is lightweight, and can be integrated into standard neural network architectures to enable high-order information fusion. We perform extensive experiments to show that the use of our model leads to state-of-the-art performance on several challenging fine-grained action parsing benchmarks.