What do you mean by “size”? Gzipped size? If you simply look at how dark a Mnist image is (count the percentage of dark pixels) you’ll get about 20% accuracy, which is twice better than random guess but a long way from 90’ish %.
Only if your model is outputting a yes/no answer right? And that your definition of accuracy is "class with highest probability" (and not "N classes with highest prob")
If your dataset has more than 2 classes like MNIST, a super low accuracy only tells you to ignore the class the model guesses. It doesn't tell you which of the remaining classes is correct