C 3 DG: Conditional Domain Generalization for Hyperspectral Imagery Classification With Convergence and Constrained-Risk Theories

Hyperspectral imagery (HSI) classification faces the challenge of hyperspectral-monospectra, where distinct classes exhibit similar spectral signatures. The spatial-spectral approach is a common solution but often inflates accuracy due to test pixels overlapping with training patches. While domain generalization shows promise in addressing hyperspectral-monospectra, it still struggles to distinguish spectrally similar samples from different domains. In this work, we address hyperspectral-monospectra using spectral information alone and propose a Convergence- and Error-Constrained Conditional Domain Generalization method (C3DG) for HSI classification. The main contributions of this work are twofold: (1) the Conditional Revising Inference Block (CRIB), and (2) the theoretical guarantees on model convergence and generalization error. CRIB forms the core of our method, employing a shared encoder and multi-branch decoders to fully leverage conditional label distributions during training. This design achieves structural decoupling aligned with the generation mechanisms of HSI. To ensure stable optimization and bounded generalization error, we establish an optimization convergence theorem and a risk upper bound theorem. The convergence theorem shows that the gradients of the loss components consistently align, ensuring stable model optimization. The risk bound theorem establishes a concrete error bound by connecting test-time training with recent developments in sharpness-aware minimization. Experiments on three benchmark datasets demonstrate the superior performance of C3DG. The code is available at github.com/Lab-PANbin/C3DG.