The deployment of transformers for visual object tracking has shown state-of-the-art results on several benchmarks. However, the transformer-based models are under-utilized for Siamese lightweight tracking due to the computational complexity of their attention blocks. This paper proposes an efficient self and mixed attention transformer-based architecture for lightweight tracking. The proposed backbone utilizes the separable mixed attention transformers to fuse the template and search regions during feature extraction to generate superior feature encoding. Our prediction head performs global contextual modeling of the encoded features by leveraging efficient self-attention blocks for robust target state estimation. With these contributions, the proposed lightweight tracker deploys a transformer-based backbone and head module concurrently for the first time. Our ablation study testifies to the effectiveness of the proposed combination of backbone and head modules. Simulations show that our Separable Self and Mixed Attention-based Tracker, SMAT, surpasses the performance of related lightweight trackers on GOT10k, TrackingNet, LaSOT, NfS30, UAV123, and AVisT datasets, while running at 37 fps on CPU, 158 fps on GPU, and having 3.8M parameters. For example, it significantly surpasses the closely related trackers E.T.Track and MixFormerV2-S on GOT10k-test by a margin of 7.9% and 5.8%, respectively, in the AO metric. The tracker code and model is available at https://github.com/goutamyg/SMAT

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