Transformer-based architectures represent the state of the art in sequence modeling tasks like machine translation and language understanding. Their applicability to multi-modal contexts like image captioning, however, is still largely under-explored. With the aim of filling this gap, we present M$^2$ - a Meshed Transformer with Memory for Image Captioning. The architecture improves both the image encoding and the language generation steps: it learns a multi-level representation of the relationships between image regions integrating learned a priori knowledge, and uses a mesh-like connectivity at decoding stage to exploit low- and high-level features. Experimentally, we investigate the performance of the M$^2$ Transformer and different fully-attentive models in comparison with recurrent ones. When tested on COCO, our proposal achieves a new state of the art in single-model and ensemble configurations on the "Karpathy" test split and on the online test server. We also assess its performances when describing objects unseen in the training set. Trained models and code for reproducing the experiments are publicly available at: https://github.com/aimagelab/meshed-memory-transformer.
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