A fast saddle-point dynamical system approach to robust deep learning.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Deep Learning

Background:

• Deep neural networks (DNNs) are vulnerable to adversarial attacks.
• Current robust training methods often involve computationally expensive min-max optimization.
• High computational cost limits the scalability of existing robust training algorithms.

Purpose of the Study:

• To develop a computationally efficient algorithm for training robust DNNs.
• To alleviate the high computational burden of existing adversarial robustness methods.
• To enable the application of robust training to larger datasets.

Main Methods:

• Exploration of iterative descent-ascent algorithms for simultaneous attack and model optimization.
• Proposal of a novel discrete-time dynamical system-based algorithm to find saddle points in min-max problems.
• Analytical convergence proofs for convex cost functions and concave uncertainties under general adversarial budget constraints (ℓp norm, 1≤p≤∞).

Main Results:

• The proposed algorithm converges asymptotically to the robust optimal solution under specified assumptions.
• A fast robust training algorithm for DNNs was devised based on the theoretical analysis.
• Empirical results demonstrate significant robustness improvements on benchmark datasets compared to state-of-the-art methods.

Conclusions:

• The novel iterative descent-ascent algorithm offers a computationally efficient approach to robust DNN training.
• The method effectively addresses the trade-off between robustness and computational cost.
• The algorithm shows promise for practical deployment in real-world scenarios requiring adversarial robustness.