Allocating limited trainable capacity across convolutional layers is a central challenge in parameter-efficient fine-tuning (PEFT) of pretrained three-dimensional (3D) networks. We propose Residual-Guided Adaptive Tucker Rank Allocation, which jointly selects input- and output-channel ranks under a fixed adapter-parameter budget while preserving the spatial kernel modes. To guide rank selection, we learn task-specific proxy updates from downstream training data and approximate them using candidate Tucker rank pairs. A perturbation analysis bounds the output discrepancy between the fixed proxy network and its Tucker approximation in terms of layerwise reconstruction residuals, motivating residual-based allocation. We normalize each squared residual by the corresponding proxy-update energy to compare relative approximation errors across layers. Dynamic programming minimizes their sum under a global budget constraint that accounts for both channel factors and the Tucker core. This yields a globally optimal allocation over the specified candidate rank pairs. We evaluate the method on the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort for predicting conversion from mild cognitive impairment to Alzheimer's disease within 36 months, using hippocampal segmentation pretraining. Across five random seeds, the proposed method achieves a mean area under the receiver operating characteristic curve (AUC) of 0.7706, compared with 0.7239 for fixed-ratio Tucker adaptation and 0.7430 for full fine-tuning. The total number of trainable parameters is limited to approximately 0.618 million, accounting for only 1.45% of the full model. Adaptive Tucker rank allocation thus provides an effective approach to parameter-efficient transfer learning in 3D medical imaging.

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