Rethinking Convergence in Deep Learning: The Predictive-Corrective Paradigm for Anatomy-Informed Brain MRI Segmentation

TL;DR

This paper challenges traditional end-to-end learning for medical image segmentation by introducing the Predictive-Corrective paradigm, which decouples learning into a lightweight Predictive Prior Module and a powerful Corrective Residual Network. The PCMambaNet architecture implements this paradigm with a symmetry-based PPM focus map and a CRN that refines residuals, achieving state-of-the-art accuracy while converging in as few as 1–5 epochs, especially in data-scarce settings. Theoretical and empirical analyses show reduced hypothesis-space complexity and a smoother loss landscape underpinning faster, more data-efficient learning, with ablations and CAM visualizations highlighting the distinct roles of PPM and CRN. The approach demonstrates strong potential for practical deployment in medical imaging, offering high accuracy, rapid convergence, and robustness under limited labeled data.

Abstract

Despite the remarkable success of the end-to-end paradigm in deep learning, it often suffers from slow convergence and heavy reliance on large-scale datasets, which fundamentally limits its efficiency and applicability in data-scarce domains such as medical imaging. In this work, we introduce the Predictive-Corrective (PC) paradigm, a framework that decouples the modeling task to fundamentally accelerate learning. Building upon this paradigm, we propose a novel network, termed PCMambaNet. PCMambaNet is composed of two synergistic modules. First, the Predictive Prior Module (PPM) generates a coarse approximation at low computational cost, thereby anchoring the search space. Specifically, the PPM leverages anatomical knowledge-bilateral symmetry-to predict a 'focus map' of diagnostically relevant asymmetric regions. Next, the Corrective Residual Network (CRN) learns to model the residual error, focusing the network's full capacity on refining these challenging regions and delineating precise pathological boundaries. Extensive experiments on high-resolution brain MRI segmentation demonstrate that PCMambaNet achieves state-of-the-art accuracy while converging within only 1-5 epochs-a performance unattainable by conventional end-to-end models. This dramatic acceleration highlights that by explicitly incorporating domain knowledge to simplify the learning objective, PCMambaNet effectively mitigates data inefficiency and overfitting.

Figures (7)

• Figure 1: The Efficacy of the Predictive-Corrective (PC) Paradigm. We compare PCMambaNet’s validation-loss curves and its inter-epoch parameter L2-distance trajectories against those of a standard end-to-end baseline.By decoupling the task into a predictive prior and a corrective residual, PCMambaNet is able to achieve its optimal performance within only a few epochs, while simultaneously inducing substantial updates among model parameters.This demonstrates that simplifying the learning objective via domain knowledge dramatically mitigates data inefficiency.
• Figure 2: The architecture of PCMambaNet, designed to instantiate our Predictive-Corrective (PC) paradigm for dramatically accelerated segmentation. The core PCMamba module employs two parallel branches: a Predictive Prior Module (PPM) leverages an anatomy-informed prior for rapid convergence, while a Corrective Residual Network (CRN) ensures precise detail fitting. This design allows our model to achieve state-of-the-art performance in only 5 epochs, surpassing traditional methods that require 200 epochs of training.
• Figure 3: Qualitative comparison of segmentation results on the OASIS-1 and MRBrainS13 datasets. Our proposed PCMambaNet (last column in each set) demonstrates superior performance in boundary delineation and structural coherence compared to several strong baselines. Note our model's ability to produce segmentations that more faithfully match the ground truth (GT), with noticeably fewer false positives and more accurate handling of complex anatomical regions. Red arrows highlight areas where the advantages of our method are particularly evident.
• Figure 4: PCMambaNet demonstrates dramatically accelerated convergence. The validation Dice score of our model (blue curve) reaches near-optimal performance within the first 5 epochs. In contrast, conventional end-to-end models require substantially more training iterations to achieve their peak accuracy. This rapid convergence is a direct result of our Predictive-Corrective paradigm, which creates a smoother and more tractable optimization landscape.
• Figure 5: Visualization of internal feature maps, demonstrating the effectiveness of our Predictive-Corrective paradigm. Features from PCMambaNet (bottom rows), trained for only 5 epochs, show greater attention to salient anatomical structures and suppressed background noise across shallow, middle, and deep layers. The Mamba-UNet (top rows), despite 50 epochs of training, produces less distinct representations. Comparisons are shown on the OASIS-1 (left) and MRBrainS13 (right).

Theorems & Definitions (11)

• Theorem C.1: Standard Generalization Bound (Shalev-Shwartz & Ben-David, 2014)
• Proposition C.2: Complexity Reduction via Structural Priors
• Lemma C.3: Subadditivity of Rademacher Complexity
• Lemma C.4: Complexity of a Singleton Set
• proof
• proof : Proof of Proposition \ref{['prop:complexity']}
• Definition C.5: $L$-smoothness
• Proposition C.6: Improved Smoothness of the PC Objective
• Lemma C.7: Variance Bound via Rademacher Complexity
• Theorem C.8: Bias-Variance Superiority of the PC Paradigm