  Hyperspectral imagery (HSI) classification may suffer the challenge of
hyperspectral-monospectra, where different classes present similar spectra.
Joint spatial-spectral feature extraction is a popular solution for the
problem, but this strategy tends to inflate accuracy since test pixels may
exist in training patches. Domain generalization methods show promising
potential, but they still fail to distinguish similar spectra across varying
domains, in addition, the theoretical support is usually ignored. In this
paper, we only rely on spectral information to solve the
hyperspectral-monospectra problem, and propose a Convergence and
Error-Constrained Conditional Domain Generalization method for Hyperspectral
Imagery Classification (C$^3$DG). The major contributions of this paper include
two aspects: the Conditional Revising Inference Block (CRIB), and the
corresponding theories for model convergence and generalization errors. CRIB is
the kernel structure of the proposed method, which employs a shared encoder and
multi-branch decoders to fully leverage the conditional distribution during
training, achieving a decoupling that aligns with the generation mechanisms of
HSI. Moreover, to ensure model convergence and maintain controllable error, we
propose the optimization convergence theorem and risk upper bound theorem. In
the optimization convergence theorem, we ensure the model convergence by
demonstrating that the gradients of the loss terms are not contradictory. In
the risk upper bound theorem, our theoretical analysis explores the
relationship between test-time training and recent related work to establish a
concrete bound for error. Experimental results on three benchmark datasets
indicate the superiority of C$^3$DG.
