Prediction as Feedback: Closed-Loop Deep Unfolding for Visual Classification

Deep unfolding has emerged as a promising paradigm for visual classification by integrating model-based optimization with deep representation learning. However, existing unfolding-based classifiers often retain an open-loop design without an explicit feedback path from intermediate predictions to subsequent solver updates. To bridge this gap, we propose Pre2Inf, a closed-loop deep unfolding framework that uses prediction as feedback to guide subsequent sparse inference, enabling bidirectional interaction between sparse inference and class prediction. Specifically, we formulate a class-aware sparse inference model and unfold its half-quadratic splitting solver into sequential stages. Each stage incorporates tailored modules for the resulting subproblems, with intermediate predictions mapped to sample-adaptive relevance weights that modulate atom-wise regularization in subsequent coefficient updates. Moreover, we analyze the stability of prediction-guided coefficient updates by characterizing their sensitivity to relevance perturbations. Experiments on eight pixel-level and two image-level classification benchmarks demonstrate consistent improvements over existing unfolding methods. Ablation studies further show that prediction feedback improves class separability and reduces reconstruction ambiguity during inference.