Binarization-Aware Adjuster: A Theoretical Framework for Bridging Continuous Optimization and Discrete Inference with Application to Edge Detection

In machine learning, discrete decision-making tasks exhibit a fundamental inconsistency between training and inference: models are optimized using continuous-valued outputs, yet evaluated through discrete predictions. This discrepancy arises from the non-differentiability of discretization operations, weakening the alignment between optimization objectives and practical decision outcomes. To address this, we present a theoretical framework for constructing a Binarization-Aware Adjuster (BAA) that integrates binarization behavior directly into gradient-based learning. Central to the approach is a Distance Weight Function (DWF) that dynamically modulates pixel-wise loss contributions based on prediction correctness and proximity to the decision boundary, thereby emphasizing decision-critical regions while de-emphasizing confidently correct samples. Furthermore, a self-adaptive threshold estimation procedure is introduced to better match optimization dynamics with inference conditions. As one of its applications, we implement experiments on the edge detection (ED) task, which also demonstrate the effectiveness of the proposed method experimentally. Beyond binary decision tasks and ED, the proposed framework provides a general strategy for aligning continuous optimization with discrete evaluation and can be extended to multi-valued decision processes in broader structured prediction problems.