This paper introduces a deep delta hedging framework for options, using neural networks to learn the residuals between the hedging function and the implied Black-Scholes delta. This approach leverages the smoother properties of these residuals, enhancing deep learning performance. Using ten years of S&P 500 index option data, our empirical analysis shows significant improvements in hedging performance. Even with three years of data, this method matches the results of directly learning the hedging function over ten years.