Predicting Functions, Not Features: KANs with Function-Space Joint-Embedding Predictive Learning for Medical Image Segmentation

Kolmogorov--Arnold Networks (KANs) introduce explicit functional representations by parameterizing each network edge as a learnable univariate function. However, existing KAN-based segmentation models optimize edge functions only through objectives defined after edge aggregation, leaving individual functions without an explicit pre-aggregation learning target. To address this limitation, we propose Function-Space Joint-Embedding Predictive Learning (FS-JEPA) for medical image segmentation. Our FS-JEPA framework moves predictive learning into the pre-aggregation function space of KANs. A masked online branch predicts structured signatures of sampled KAN edge functions generated by a full-context exponential moving average target branch, while shared edge indices preserve correspondence between predictions and targets. Rather than predicting an isolated edge response, we represent each sampled edge function using a multi-radius signature composed of function evaluations around its input anchor. This structured representation captures local functional variations that cannot be characterized by a single response and provides a more informative predictive target. The function-space objective is jointly optimized with the segmentation loss during training, while the predictive branch is removed at inference. Experiments on five medical image segmentation benchmarks show that our FS-JEPA achieves the best average Dice and outperforms the strongest competing KAN-based method by +2.25 percentage points.

Decoupling Language Guidance from Backbones for Text-Guided Medical Segmentation

Text-guided medical image segmentation leverages clinical semantics to improve lesion delineation, yet many existing models bind cross-modal fusion, supervision, and decoder design into a task-specific architecture. Such tight coupling makes it difficult to reuse language guidance modules across heterogeneous vision and text backbones, and often requires redesigning the network when the encoder pair changes. This paper presents BTHA, a backbone-transferable hierarchical adapter framework for text-guided medical image segmentation. BTHA is built around a stable feature-level interface: given multi-scale visual features and a text representation, it injects semantic guidance through shape-preserving adapters while maintaining the decoder-side tensor contract. To make this interface effective, we introduce a Hierarchical Coarse-to-Fine Supervision Strategy that decomposes learning into global image-text alignment, multi-scale auxiliary localization, and boundary-aware final mask refinement. We further design a Scale-Adaptive Gated Semantic Guidance (SAGSG) adapter, where resolution-specific gates adaptively control textual injection and channel recalibration suppresses redundant cross-modal responses. Evaluations across diverse vision and text backbones show that the same adapter and supervision design remains effective across convolutional and transformer-based visual encoders as well as different language encoders. Experiments on four public datasets further demonstrate that BTHA improves strong text-guided baselines with modest computational overhead.