Objective. This paper proposes a novel approach for the longitudinal registration of PET imaging acquired for the monitoring of patients with metastatic breast cancer. Unlike with other image analysis tasks, the use of deep learning (DL) has not significantly improved the performance of image registration. With this work, we propose a new registration approach to bridge the performance gap between conventional and DL-based methods: medical image registration method regularized by architecture ( MIRRBA ). Approach. MIRRBA is a subject-specific deformable registration method which relies on a deep pyramidal architecture to parametrize the deformation field. Diverging from the usual deep-learning paradigms, MIRRBA does not require a learning database, but only a pair of images to be registered that is used to optimize the network's parameters. We applied MIRRBA on a private dataset of 110 whole-body PET images of patients with metastatic breast cancer. We used different architecture configurations to produce the deformation field and studied the results obtained. We also compared our method to several standard registration approaches: two conventional iterative registration methods (ANTs and Elastix) and two supervised DL-based models (LapIRN and Voxelmorph). Registration accuracy was evaluated using the Dice score, the target registration error, the average Hausdorff distance and the detection rate, while the realism of the registration obtained was evaluated using Jacobian's determinant. The ability of the different methods to shrink disappearing lesions was also computed with the disappearing rate. Main results. MIRRBA significantly improved all metrics when compared to DL-based approaches. The organ and lesion Dice scores of Voxelmorph improved by 6% and 52% respectively, while the ones of LapIRN increased by 5% and 65%. Regarding conventional approaches, MIRRBA presented comparable results showing the feasibility of our method. Significance. In this paper, we also demonstrate the regularizing power of deep architectures and present new elements to understand the role of the architecture in DL methods used for registration.