Deep convolutional neural networks (DCNN) successfully exhibit exceptionally good classification performance, despite their massive size. The effect of a large value of noise term, as irreducible error in Expected Prediction Error (EPE) is first discussed. Through extensive systematic experiments, we show how in extreme conditions the traditional approaches fare at par with large neural networks, which generalize well in practice. Specifically, our experiments establish that state-of-the-art convolutional networks trained for classification barely fit a random labeling of the training data as an extreme condition to learn. This phenomenon is quantitatively unaffected even if we train the CNNs with completely inseparable data. This can be due to large degree of corruption of the entire data by random noise or random labels associated with data due to observation error. We corroborate these experimental findings by showing that depth six CNN (VGG-6) fails to overcome large noise in image signals. © 2017, Springer International Publishing AG.