Binarization-Aware Adjuster: A Theoretical Framework for Bridging Continuous Optimization and Discrete Inference with Application to Edge Detection
Hao Shu
TL;DR
The paper tackles the mismatch between continuous optimization and discrete inference in binary decision tasks by introducing the Binarization-Aware Adjuster (BAA), which integrates discretization behavior into gradient-based learning via a Distance Weight Function (DWF) and a self-adaptive threshold. The adjusted loss L_{Adj,δ} reweights pixel losses to emphasize decision-critical regions near the binarization boundary while down-weighting confidently correct samples, enabling better alignment with downstream evaluation. The method is theoretically grounded (smooth approximation to thresholding) and empirically validated on edge detection across multiple architectures and datasets, showing robust improvements over standard WBCE, with the self-adaptive variant often delivering the strongest gains. The approach generalizes beyond edge detection to broader discrete structured prediction tasks, offering a principled pathway to bridge continuous optimization and discrete evaluation in practice.
Abstract
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.