Gradient-Aware Loss Function for Improved Learning in Speech Enhancement

Conventional loss functions for gradient descent are designed mainly to assess output quality, with limited attention to gradient behavior. This study identifies the gradient inconsistency problem in existing loss functions, where gradient magnitude is misaligned with the loss value, causing unstable learning and poor correspondence between optimization and the target metric. To resolve this, we propose a gradient-aware loss function whose gradient is proportional to a chosen evaluation metric, with the loss derived through integration. This design ensures consistent gradients, stable convergence, and alignment with the evaluation metric. Applied to speech enhancement using the log-spectral distance metric, the method achieves faster convergence, greater stability, and higher perceptual quality than conventional approaches, validating the superiority of the proposed formulation.