In recent years, quantum computing has emerged as a transformative force in the field of combinatorial optimization, offering novel approaches to tackling complex problems that have long challenged classical computational methods. Among these, the Quantum Approximate Optimization Algorithm (QAOA) stands out for its potential to efficiently solve the Max-Cut problem, a quintessential example of combinatorial optimization. However, practical application faces challenges due to current limitations on quantum computational resource. Our work optimizes QAOA initialization, using Graph Neural Networks (GNN) as a warm-start technique. This sacrifices affordable computational resource on classical computer to reduce quantum computational resource overhead, enhancing QAOA's effectiveness. Experiments with various GNN architectures demonstrate the adaptability and stability of our framework, highlighting the synergy between quantum algorithms and machine learning. Our findings show GNN's potential in improving QAOA performance, opening new avenues for hybrid quantum-classical approaches in quantum computing and contributing to practical applications.

We study level set teleportation, an optimization sub-routine which seeks to accelerate gradient methods by maximizing the gradient norm on a level-set of the objective function. Since the descent lemma implies that gradient descent (GD) decreases the objective proportional to the squared norm of the gradient, level-set teleportation maximizes this one-step progress guarantee. For convex functions satisfying Hessian stability, we prove that GD with level-set teleportation obtains a combined sub-linear/linear convergence rate which is strictly faster than standard GD when the optimality gap is small. This is in sharp contrast to the standard (strongly) convex setting, where we show level-set teleportation neither improves nor worsens convergence rates. To evaluate teleportation in practice, we develop a projected-gradient-type method requiring only Hessian-vector products. We use this method to show that gradient methods with access to a teleportation oracle uniformly out-perform their standard versions on a variety of learning problems.

The integration of deep learning, particularly AI-Generated Content, with high-quality data derived from ab initio calculations has emerged as a promising avenue for transforming the landscape of scientific research. However, the challenge of designing molecular drugs or materials that incorporate multi-modality prior knowledge remains a critical and complex undertaking. Specifically, achieving a practical molecular design necessitates not only meeting the diversity requirements but also addressing structural and textural constraints with various symmetries outlined by domain experts. In this article, we present an innovative approach to tackle this inverse design problem by formulating it as a multi-modality guidance generation/optimization task. Our proposed solution involves a textural-structure alignment symmetric diffusion framework for the implementation of molecular generation/optimization tasks, namely 3DToMolo. 3DToMolo aims to harmonize diverse modalities, aligning them seamlessly to produce molecular structures adhere to specified symmetric structural and textural constraints by experts in the field. Experimental trials across three guidance generation settings have shown a superior hit generation performance compared to state-of-the-art methodologies. Moreover, 3DToMolo demonstrates the capability to generate novel molecules, incorporating specified target substructures, without the need for prior knowledge. This work not only holds general significance for the advancement of deep learning methodologies but also paves the way for a transformative shift in molecular design strategies. 3DToMolo creates opportunities for a more nuanced and effective exploration of the vast chemical space, opening new frontiers in the development of molecular entities with tailored properties and functionalities.

Evolutionary optimization algorithms are often derived from loose biological analogies and struggle to leverage information obtained during the sequential course of optimization. An alternative promising approach is to leverage data and directly discover powerful optimization principles via meta-optimization. In this work, we follow such a paradigm and introduce Evolution Transformer, a causal Transformer architecture, which can flexibly characterize a family of Evolution Strategies. Given a trajectory of evaluations and search distribution statistics, Evolution Transformer outputs a performance-improving update to the search distribution. The architecture imposes a set of suitable inductive biases, i.e. the invariance of the distribution update to the order of population members within a generation and equivariance to the order of the search dimensions. We train the model weights using Evolutionary Algorithm Distillation, a technique for supervised optimization of sequence models using teacher algorithm trajectories. The resulting model exhibits strong in-context optimization performance and shows strong generalization capabilities to otherwise challenging neuroevolution tasks. We analyze the resulting properties of the Evolution Transformer and propose a technique to fully self-referentially train the Evolution Transformer, starting from a random initialization and bootstrapping its own learning progress. We provide an open source implementation under https://github.com/RobertTLange/evosax.

Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these introduce hyperparameters that require manual tuning through trial and error, raising doubts about the successful incorporation of constraints into the generated model. This paper describes in detail the two-stage training method for Neural ODEs, a simple, effective, and penalty parameter-free approach to model constrained systems. In this approach the constrained optimization problem is rewritten as two unconstrained sub-problems that are solved in two stages. The first stage aims at finding feasible NN parameters by minimizing a measure of constraints violation. The second stage aims to find the optimal NN parameters by minimizing the loss function while keeping inside the feasible region. We experimentally demonstrate that our method produces models that satisfy the constraints and also improves their predictive performance. Thus, ensuring compliance with critical system properties and also contributing to reducing data quantity requirements. Furthermore, we show that the proposed method improves the convergence to an optimal solution and improves the explainability of Neural ODE models. Our proposed two-stage training method can be used with any NN architectures.

Sparsifying transforms became in the last decades widely known tools for finding structured sparse representations of signals in certain transform domains. Despite the popularity of classical transforms such as DCT and Wavelet, learning optimal transforms that guarantee good representations of data into the sparse domain has been recently analyzed in a series of papers. Typically, the conditioning number and representation ability are complementary key features of learning square transforms that may not be explicitly controlled in a given optimization model. Unlike the existing approaches from the literature, in our paper, we consider a new sparsifying transform model that enforces explicit control over the data representation quality and the condition number of the learned transforms. We confirm through numerical experiments that our model presents better numerical behavior than the state-of-the-art.

Backdoor attacks have been one of the emerging security threats to deep neural networks (DNNs), leading to serious consequences. One of the mainstream backdoor defenses is model reconstruction-based. Such defenses adopt model unlearning or pruning to eliminate backdoors. However, little attention has been paid to survive from such defenses. To bridge the gap, we propose Venom, the first generic backdoor attack enhancer to improve the survivability of existing backdoor attacks against model reconstruction-based defenses. We formalize Venom as a binary-task optimization problem. The first is the original backdoor attack task to preserve the original attack capability, while the second is the attack enhancement task to improve the attack survivability. To realize the second task, we propose attention imitation loss to force the decision path of poisoned samples in backdoored models to couple with the crucial decision path of benign samples, which makes backdoors difficult to eliminate. Our extensive evaluation on two DNNs and three datasets has demonstrated that Venom significantly improves the survivability of eight state-of-the-art attacks against eight state-of-the-art defenses without impacting the capability of the original attacks.

This paper proposes a scalable distributed policy gradient method and proves its convergence to near-optimal solution in multi-agent linear quadratic networked systems. The agents engage within a specified network under local communication constraints, implying that each agent can only exchange information with a limited number of neighboring agents. On the underlying graph of the network, each agent implements its control input depending on its nearby neighbors' states in the linear quadratic control setting. We show that it is possible to approximate the exact gradient only using local information. Compared with the centralized optimal controller, the performance gap decreases to zero exponentially as the communication and control ranges increase. We also demonstrate how increasing the communication range enhances system stability in the gradient descent process, thereby elucidating a critical trade-off. The simulation results verify our theoretical findings.

This work presents a novel data-driven multi-layered planning and control framework for the safe navigation of a class of unmanned ground vehicles (UGVs) in the presence of unknown stationary obstacles and additive modeling uncertainties. The foundation of this framework is a novel robust model predictive planner, designed to generate optimal collision-free trajectories given an occupancy grid map, and a paired ancillary controller, augmented to provide robustness against model uncertainties extracted from learning data. To tackle modeling discrepancies, we identify both matched (input discrepancies) and unmatched model residuals between the true and the nominal reduced-order models using closed-loop tracking errors as training data. Utilizing conformal prediction, we extract probabilistic upper bounds for the unknown model residuals, which serve to construct a robustifying ancillary controller. Further, we also determine maximum tracking discrepancies, also known as the robust control invariance tube, under the augmented policy, formulating them as collision buffers. Employing a LiDAR-based occupancy map to characterize the environment, we construct a discrepancy-aware cost map that incorporates these collision buffers. This map is then integrated into a sampling-based model predictive path planner that generates optimal and safe trajectories that can be robustly tracked by the augmented ancillary controller in the presence of model mismatches. The effectiveness of the framework is experimentally validated for autonomous high-speed trajectory tracking in a cluttered environment with four different vehicle-terrain configurations. We also showcase the framework's versatility by reformulating it as a driver-assist program, providing collision avoidance corrections based on user joystick commands.

The efficacy of large language models (LLMs) in understanding and generating natural language has aroused a wide interest in developing prompt-based methods to harness the power of black-box LLMs. Existing methodologies usually prioritize a global optimization for finding the global optimum, which however will perform poorly in certain tasks. This thus motivates us to re-think the necessity of finding a global optimum in prompt optimization. To answer this, we conduct a thorough empirical study on prompt optimization and draw two major insights. Contrasting with the rarity of global optimum, local optima are usually prevalent and well-performed, which can be more worthwhile for efficient prompt optimization (Insight I). The choice of the input domain, covering both the generation and the representation of prompts, affects the identification of well-performing local optima (Insight II). Inspired by these insights, we propose a novel algorithm, namely localized zeroth-order prompt optimization (ZOPO), which incorporates a Neural Tangent Kernel-based derived Gaussian process into standard zeroth-order optimization for an efficient search of well-performing local optima in prompt optimization. Remarkably, ZOPO outperforms existing baselines in terms of both the optimization performance and the query efficiency, which we demonstrate through extensive experiments.