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Implicit neural representation (INR) has been proposed as an innovative alternative for data representation in full waveform inversion (FWI). However, due to geometrical spreading, the gradient distribution in implicit full waveform inversion (IFWI) is unbalanced, which can lead to instability and slow convergence. Using the chain rule, we isolate the gridded model gradients from the neural parameter gradients. Then, we we apply a pseudo Hessian to compensate for the geometric spreading effects and balance the gradients amplitude. Numerical tests demonstrate that the proposed energy-weighted gradient significantly accelerates the convergence of IFWI and improves the resolution of the inverted models, including deeper in the model, without introducing additional computational cost.