Adversarially Robust Neural Networks via Optimal Control: Bridging Robustness with Lyapunov Stability
Deep neural networks are known to be vulnerable to adversarial perturbations. In this paper, we bridge adversarial robustness of neural nets with Lyapunov stability of dynamical systems. From this viewpoint, training neural nets is equivalent to finding an optimal control of the discrete dynamical system, which allows one to utilize methods of successive approximations, an optimal control algorithm based on Pontryagin*s maximum principle, to train neural nets. This decoupled training method allows us to add constraints to the optimization, which makes the deep model more robust. The constrained optimization problem can be formulated as a semi-definite programming problem and hence can be solved efficiently. Experiments show that our method effectively improves deep model*s adversarial robustness.
The paper contributes to the robust training of neural networks as follows: 1) The paper uses the theoretical view of a neural network as a discretized ODE to develop a robust control theory aimed at training the network while enforcing robustness; 2) Such an objective is achieved by introducing Lyaponov stability and practically implemented through the method of successive approximations; 3) Empirical evaluation demonstrate that the newly introduced method performs as well as the SOTA in terms of defensive training. The paper is well written and proposes a well motivated and theoretically original strategy to robustly train neural networks against adversarial examples. The strength of the paper is definitively in its theoretical section, it would be really great to see an empirical improvement improvement on the SOTA. However, I do not believe the paper should be penalized for only matching other algorithm as it relies on a tractable and principled theoretical analysis.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Adversarially Robust Neural Networks via Optimal Control: Bridging Robustness with Lyapunov Stability
Deep neural networks are known to be vulnerable to adversarial perturbations. In this paper, we bridge adversarial robustness of neural nets with Lyapunov stability of dynamical systems. From this viewpoint, training neural nets is equivalent to finding an optimal control of the discrete dynamical system, which allows one to utilize methods of successive approximations, an optimal control algorithm based on Pontryagin*s maximum principle, to train neural nets. This decoupled training method allows us to add constraints to the optimization, which makes the deep model more robust. The constrained optimization problem can be formulated as a semi-definite programming problem and hence can be solved efficiently. Experiments show that our method effectively improves deep model*s adversarial robustness.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



The paper contributes to the robust training of neural networks as follows: 1) The paper uses the theoretical view of a neural network as a discretized ODE to develop a robust control theory aimed at training the network while enforcing robustness; 2) Such an objective is achieved by introducing Lyaponov stability and practically implemented through the method of successive approximations; 3) Empirical evaluation demonstrate that the newly introduced method performs as well as the SOTA in terms of defensive training. The paper is well written and proposes a well motivated and theoretically original strategy to robustly train neural networks against adversarial examples. The strength of the paper is definitively in its theoretical section, it would be really great to see an empirical improvement improvement on the SOTA. However, I do not believe the paper should be penalized for only matching other algorithm as it relies on a tractable and principled theoretical analysis.
assistant
The paper contributes to the robust training of neural networks as follows: 1) The paper uses the theoretical view of a neural network as a discretized ODE to develop a robust control theory aimed at training the network while enforcing robustness; 2) Such an objective is achieved by introducing Lyaponov stability and practically implemented through the method of successive approximations; 3) Empirical evaluation demonstrate that the newly introduced method performs as well as the SOTA in terms of defensive training. The paper is well written and proposes a well motivated and theoretically original strategy to robustly train neural networks against adversarial examples. The strength of the paper is definitively in its theoretical section, it would be really great to see an empirical improvement improvement on the SOTA. However, I do not believe the paper should be penalized for only matching other algorithm as it relies on a tractable and principled theoretical analysis.