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Weight averaging is a widely used technique for accelerating training and improving the generalization of deep neural networks (DNNs). While existing approaches like stochastic weight averaging (SWA) rely on pre-set weighting schemes, they can be suboptimal when handling diverse weights. We introduce Trainable Weight Averaging (TWA), a novel optimization method that operates within a reduced subspace spanned by candidate weights and learns optimal weighting coefficients through optimization. TWA offers greater flexibility and can be applied to different training scenarios. For large-scale applications, we develop a distributed training framework that combines parallel computation with low-bit compression for the projection matrix, effectively managing memory and computational demands. TWA can be implemented using either training data (TWA-t) or validation data (TWA-v), with the latter providing more effective averaging. Extensive experiments showcase TWA's advantages: (i) it consistently outperforms SWA in generalization performance and flexibility, (ii) when applied during early training, it reduces training time by over 40\% on CIFAR datasets and 30\% on ImageNet while maintaining comparable performance, and (iii) during fine-tuning, it significantly enhances generalization by weighted averaging of model checkpoints. In summary, we present an efficient and effective framework for trainable weight averaging. The code is available at https://github.com/nblt/TWA.