Abstract: To enable the online prediction of surface quality during the pulse electrochemical machining (PECM) of TiAl alloys, this study focused on the multi-scale feature mapping between the nonlinear dynamic behavior of electrical signals and the final surface morphology. Conventional methods rely on offline characterization and lack an effective pathway to predict final quality from real-time process signals. Heterogeneous recursive entropy H was introduced as a novel multi-scale feature decoder to quantify both the time-series complexity of the real-time current density signal (H_c) and the spatial complexity of the machined surface morphology (H_s). The experimental results demonstrate that increasing the electrolyte pressure (from 0.2 to 0.5 MPa) significantly reduces the system's chaoticity, the H_c decreases. When the electrolyte pressure is 0.5 MPa, the optimal surface quality with S_a=0.225 μm is achieved. Critically, high-fidelity linear mapping models between the signal complexity (H_c) and both the spatial complexity (H_s) and the surface roughness (S_a) were successfully established. This research confirms the feasibility of using nonlinear features from the current signal for online surface quality prediction. It provides a critical theoretical foundation and technical framework for developing intelligent PECM process optimization and closed-loop control systems.