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Adversarial training for neural networks has been in the limelight in recent years. The advancement in neural network architectures over the last decade has led to significant improvement in their performance. It sparked an interest in their deployment for real-time applications. This process initiated the need to understand the vulnerability of these models to adversarial attacks. It is instrumental in designing models that are robust against adversaries. Recent works have proposed novel techniques to counter the adversaries, most often sacrificing natural accuracy. Most suggest training with an adversarial version of the inputs, constantly moving away from the original distribution. The focus of our work is to use abstract certification to extract a subset of inputs for (hence we call it 'soft') adversarial training. We propose a training framework that can retain natural accuracy without sacrificing robustness in a constrained setting. Our framework specifically targets moderately critical applications which require a reasonable balance between robustness and accuracy. The results testify to the idea of soft adversarial training for the defense against adversarial attacks. At last, we propose the scope of future work for further improvement of this framework.