Supervised machine learning can help learn topological invariants for topological systems. However, it faces severe limitations when applied to non-Hermitian topological phases. The nonlinear nature of the non-Bloch topological invariant causes a sudden change in non-Hermitian or high-dimensional situations, while supervised machine learning does not have the ability to grasp the rule at this moment. We have rigorously demonstrated the limitation of supervised machine learning and systematically delineated the valid scale range for effective model predictions through generalization error bounds. By integrating the hypothesis space and the underlying physical mechanisms, our work establishes a generalized theoretical framework for evaluating the feasibility of supervised machine learning in topological phase identification.

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• Topological materials
• Machine learning
• Topological tools