To address the challenge of accurate liver and tumor segmentation in abdominal CT images due to complex anatomy, diverse tumor appearance, and limited annotation data, we introduce HANS-Net (Hyperbolic-convolutions Adaptive-temporal-attention with Neural-representation and Synaptic-plasticity Network), a novel segmentation framework that synergistically combines hyperbolic convolutions for hierarchical geometric representation, a wavelet-inspired decomposition module for multi-scale texture learning, a biologically inspired synaptic plasticity mechanism for adaptive feature enhancement, and implicit neural representation branches that model fine and continuous anatomical boundaries. We also incorporate uncertainty-aware Monte Carlo dropout to quantify prediction confidence and lightweight temporal attention to improve slice-to-slice consistency without compromising efficiency. Extensive evaluation on the LiTS dataset showed that HANS-Net achieved an average Dice score of 93.26%, an IoU of 88.09%, an average symmetry surface distance (ASSD) of 0.72 mm, and a volume overlap error (VOE) of 11.91%. Cross-dataset validation on the AMOS 2022 dataset yielded an average Dice score of 85.09%, an IoU of 76.66%, an ASSD of 19.49 mm, and a VOE of 23.34%, demonstrating strong generalization across different datasets.
