Residual-Guided Adaptive Tucker Rank Allocation for Parameter-Efficient MCI Conversion Prediction

Guanghua He, Hancan Zhu, Gaohang Yu, An Zhang

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…