Zhe Wang

Daniel Schwartz, Dmitriy Bespalov, Zhe Wang et al.

As large language models (LLMs) become increasingly prevalent, ensuring their robustness against adversarial misuse is crucial. This paper introduces the GAP (Graph of Attacks with Pruning) framework, an advanced approach for generating stealthy jailbreak prompts to evaluate and enhance LLM safeguards. GAP addresses limitations in existing tree-based LLM jailbreak methods by implementing an interconnected graph structure that enables knowledge sharing across attack paths. Our experimental evaluation demonstrates GAP's superiority over existing techniques, achieving a 20.8% increase in attack success rates while reducing query costs by 62.7%. GAP consistently outperforms state-of-the-art methods for attacking both open and closed LLMs, with attack success rates of >96%. Additionally, we present specialized variants like GAP-Auto for automated seed generation and GAP-VLM for multimodal attacks. GAP-generated prompts prove highly effective in improving content moderation systems, increasing true positive detection rates by 108.5% and accuracy by 183.6% when used for fine-tuning. Our implementation is available at https://github.com/dsbuddy/GAP-LLM-Safety.

Bin Xu, Junzhe Shi, Sixu Li et al.

Propulsion system electrification revolution has been undergoing in the automotive industry. The electrified propulsion system improves energy efficiency and reduces the dependence on fossil fuel. However, the batteries of electric vehicles experience degradation process during vehicle operation. Research considering both battery degradation and energy consumption in battery/ supercapacitor electric vehicles is still lacking. This study proposes a Q-learning-based strategy to minimize battery degradation and energy consumption. Besides Q-learning, two heuristic energy management methods are also proposed and optimized using Particle Swarm Optimization algorithm. A vehicle propulsion system model is first presented, where the severity factor battery degradation model is considered and experimentally validated with the help of Genetic Algorithm. In the results analysis, Q-learning is first explained with the optimal policy map after learning. Then, the result from a vehicle without ultracapacitor is used as the baseline, which is compared with the results from the vehicle with ultracapacitor using Q-learning, and two heuristic methods as the energy management strategies. At the learning and validation driving cycles, the results indicate that the Q-learning strategy slows down the battery degradation by 13-20% and increases the vehicle range by 1.5-2% compared with the baseline vehicle without ultracapacitor.

Yi Zhou, Zhe Wang, Kaiyi Ji et al.

Various types of parameter restart schemes have been proposed for accelerated gradient algorithms to facilitate their practical convergence in convex optimization. However, the convergence properties of accelerated gradient algorithms under parameter restart remain obscure in nonconvex optimization. In this paper, we propose a novel accelerated proximal gradient algorithm with parameter restart (named APG-restart) for solving nonconvex and nonsmooth problems. Our APG-restart is designed to 1) allow for adopting flexible parameter restart schemes that cover many existing ones; 2) have a global sub-linear convergence rate in nonconvex and nonsmooth optimization; and 3) have guaranteed convergence to a critical point and have various types of asymptotic convergence rates depending on the parameterization of local geometry in nonconvex and nonsmooth optimization. Numerical experiments demonstrate the effectiveness of our proposed algorithm.

Zhe Wang, Yi Zhou, Yingbin Liang et al.

Momentum is a popular technique to accelerate the convergence in practical training, and its impact on convergence guarantee has been well-studied for first-order algorithms. However, such a successful acceleration technique has not yet been proposed for second-order algorithms in nonconvex optimization.In this paper, we apply the momentum scheme to cubic regularized (CR) Newton's method and explore the potential for acceleration. Our numerical experiments on various nonconvex optimization problems demonstrate that the momentum scheme can substantially facilitate the convergence of cubic regularization, and perform even better than the Nesterov's acceleration scheme for CR. Theoretically, we prove that CR under momentum achieves the best possible convergence rate to a second-order stationary point for nonconvex optimization. Moreover, we study the proposed algorithm for solving problems satisfying an error bound condition and establish a local quadratic convergence rate. Then, particularly for finite-sum problems, we show that the proposed algorithm can allow computational inexactness that reduces the overall sample complexity without degrading the convergence rate.

Zhe Wang, Yi Zhou, Yingbin Liang et al.

This note considers the inexact cubic-regularized Newton's method (CR), which has been shown in \cite{Cartis2011a} to achieve the same order-level convergence rate to a secondary stationary point as the exact CR \citep{Nesterov2006}. However, the inexactness condition in \cite{Cartis2011a} is not implementable due to its dependence on future iterates variable. This note fixes such an issue by proving the same convergence rate for nonconvex optimization under an inexact adaptive condition that depends on only the current iterate. Our proof controls the sufficient decrease of the function value over the total iterations rather than each iteration as used in the previous studies, which can be of independent interest in other contexts.

Yi Zhou, Zhe Wang, Yingbin Liang

Cubic-regularized Newton's method (CR) is a popular algorithm that guarantees to produce a second-order stationary solution for solving nonconvex optimization problems. However, existing understandings of the convergence rate of CR are conditioned on special types of geometrical properties of the objective function. In this paper, we explore the asymptotic convergence rate of CR by exploiting the ubiquitous Kurdyka-Lojasiewicz (KL) property of nonconvex objective functions. In specific, we characterize the asymptotic convergence rate of various types of optimality measures for CR including function value gap, variable distance gap, gradient norm and least eigenvalue of the Hessian matrix. Our results fully characterize the diverse convergence behaviors of these optimality measures in the full parameter regime of the KL property. Moreover, we show that the obtained asymptotic convergence rates of CR are order-wise faster than those of first-order gradient descent algorithms under the KL property.

Zhe Wang, Yi Zhou, Yingbin Liang et al.

Cubic regularization (CR) is an optimization method with emerging popularity due to its capability to escape saddle points and converge to second-order stationary solutions for nonconvex optimization. However, CR encounters a high sample complexity issue for finite-sum problems with a large data size. %Various inexact variants of CR have been proposed to improve the sample complexity. In this paper, we propose a stochastic variance-reduced cubic-regularization (SVRC) method under random sampling, and study its convergence guarantee as well as sample complexity. We show that the iteration complexity of SVRC for achieving a second-order stationary solution within $ε$ accuracy is $O(ε^{-3/2})$, which matches the state-of-art result on CR types of methods. Moreover, our proposed variance reduction scheme significantly reduces the per-iteration sample complexity. The resulting total Hessian sample complexity of our SVRC is ${\Oc}(N^{2/3} ε^{-3/2})$, which outperforms the state-of-art result by a factor of $O(N^{2/15})$. We also study our SVRC under random sampling without replacement scheme, which yields a lower per-iteration sample complexity, and hence justifies its practical applicability.