On Continuity of Robust and Accurate Classifiers

This research paper argues that the real problem with machine learning classifiers isn't that robustness (resistance to adversarial attacks, where small malicious changes trick the AI) and accuracy are fundamentally opposed, but rather that continuous functions (smooth mathematical functions without jumps or breaks) cannot achieve both properties simultaneously. The authors propose that effective robust and accurate classifiers should use discontinuous functions (functions with breaks or sudden changes) instead, and show that understanding this continuity property is crucial for building, analyzing, and testing modern machine learning models.