Expressing Objects just like Words: Recurrent Visual Embedding for Image-Text Matching

Existing image-text matching approaches typically infer the similarity of an image-text pair by capturing and aggregating the affinities between the text and each independent object of the image. However, they ignore the connections between the objects that are semantically related. These objects may collectively determine whether the image corresponds to a text or not. To address this problem, we propose a Dual Path Recurrent Neural Network (DP-RNN) which processes images and sentences symmetrically by recurrent neural networks (RNN). In particular, given an input image-text pair, our model reorders the image objects based on the positions of their most related words in the text. In the same way as extracting the hidden features from word embeddings, the model leverages RNN to extract high-level object features from the reordered object inputs. We validate that the high-level object features contain useful joint information of semantically related objects, which benefit the retrieval task. To compute the image-text similarity, we incorporate a Multi-attention Cross Matching Model into DP-RNN. It aggregates the affinity between objects and words with cross-modality guided attention and self-attention. Our model achieves the state-of-the-art performance on Flickr30K dataset and competitive performance on MS-COCO dataset. Extensive experiments demonstrate the effectiveness of our model.Comment: Accepted by AAAI-2

Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Products

Developing equivariant neural networks for the E(3) group plays an important role in modeling 3D data across real-world applications. Enforcing this equivariance primarily involves the tensor products of irreducible representations (irreps). However, the computational complexity of such operations increases significantly as higher-order tensors are used. In this work, we propose a systematic approach to substantially accelerate the computation of the tensor products of irreps. We mathematically connect the commonly used Clebsch-Gordan coefficients to the Gaunt coefficients, which are integrals of products of three spherical harmonics. Through Gaunt coefficients, the tensor product of irreps becomes equivalent to the multiplication between spherical functions represented by spherical harmonics. This perspective further allows us to change the basis for the equivariant operations from spherical harmonics to a 2D Fourier basis. Consequently, the multiplication between spherical functions represented by a 2D Fourier basis can be efficiently computed via the convolution theorem and Fast Fourier Transforms. This transformation reduces the complexity of full tensor products of irreps from $\mathcal{O}(L^6)$ to $\mathcal{O}(L^3)$, where $L$ is the max degree of irreps. Leveraging this approach, we introduce the Gaunt Tensor Product, which serves as a new method to construct efficient equivariant operations across different model architectures. Our experiments on the Open Catalyst Project and 3BPA datasets demonstrate both the increased efficiency and improved performance of our approach.Comment: 36 pages; ICLR 2024 (Spotlight Presentation); Code: https://github.com/lsj2408/Gaunt-Tensor-Produc