A Geometric View of SRC: Learning Representations for Stable Residual Inference 文章

arXiv:2605.29673v1 Announce Type: cross Abstract: Reconstruction-based inference assigns a class by comparing class-wise reconstruction residuals; Sparse Representation Classification (SRC) is a canonical instance whose reliability depends on the geometry of the learned representation. We adopt a strict training-inference separation: SRC is used only as a fixed test-time rule and is never differentiated, unrolled, or optimized during training. In a span-level idealization based on class-conditional spans and their associated projection residuals, we formalize residual-ordering stability through a residual margin and characterize geometric obstructions -- span overlap, dominance, and near-overlap via small principal angles -- that can collapse this margin in worst-case directions. This span-level theory is primary: it specifies when the idealized residual family is well-separated, and it provides a conditional solver-level interpretation for practical residual approximations (e.g.