The Boolean satisfiability (SAT) problem lies at the core of many applications in combinatorial optimization, software verification, cryptography, and machine learning. While state-of-the-art solvers have demonstrated high efficiency in handling conjunctive normal form (CNF) formulas, numerous applications require non-CNF (hybrid) constraints, such as XOR, cardinality, and Not-All-Equal constraints. Recent work leverages polynomial representations to represent such hybrid constraints, but it relies on box constraints that can limit the use of powerful unconstrained optimizers. In this paper, we propose unconstrained continuous optimization formulations for hybrid SAT solving by penalty terms. We provide theoretical insights into when these penalty terms are necessary and demonstrate empirically that unconstrained optimizers (e.g., Adam) can enhance SAT solving on hybrid benchmarks. Our results highlight the potential of combining continuous optimization and machine-learning-based methods for effective hybrid SAT solving.

Soft Fin-Ray grippers can perform delicate and careful manipulation, which has caused notable attention in different fields. These grippers can handle objects of various forms and sizes safely. The internal structure of the Fin-Ray finger plays a significant role in its adaptability and grasping performance. However, modeling the non-linear grasp force and deformation behaviors for design purposes is challenging. Moreover, when the Fin-Ray finger becomes more rigid and capable of exerting higher forces, it becomes less delicate in handling objects. The contrast between these two objectives gives rise to a multi-objective optimization problem. In this study, we employ finite element method (FEM) to estimate the deflections and contact forces of the Fin-Ray, grasping cylindrical objects. This dataset is then used to construct a multilayer perception (MLP) for prediction of the contact force and the tip displacement. The FEM dataset consists of three input and four target features. The three input features of the MLP and optimization design variables are the thickness of the front and supporting beams, the thickness of the cross beams, and the equal spacing between the cross beams. In addition, the target features are the maximum contact forces and maximum tip displacements in x- and y-directions. The magnitude of maximum contact force and magnitude of maximum tip displacement are the two objectives, showing the trade-off between force and delicate manipulation in soft Fin-Ray grippers. Furthermore, the optimized set of solutions are found using multi-objective optimal techniques. We use non-dominated sorting genetic algorithm (NSGA-II) method for this purpose. Our findings demonstrate that our methodologies can be used to improve the design and gripping performance of soft robotic grippers, helping us to choose a design not only for delicate grasping but also for high-force applications.

Alternating Current Optimal Power Flow (AC-OPF) aims to optimize generator power outputs by utilizing the non-linear relationships between voltage magnitudes and phase angles in a power system. However, current AC-OPF solvers struggle to effectively represent the complex relationship between variable distributions in the constraint space and their corresponding optimal solutions. This limitation in constraint modeling restricts the system's ability to develop diverse knowledge representations. Additionally, modeling the power grid solely based on spatial topology further limits the integration of additional prior knowledge, such as temporal information. To overcome these challenges, we propose DDA-PIGCN (Dynamic Domain Adaptation-Driven Physics-Informed Graph Convolutional Network), a new method designed to address constraint-related issues and build a graph-based learning framework that incorporates spatiotemporal features. DDA-PIGCN improves consistency optimization for features with varying long-range dependencies by applying multi-layer, hard physics-informed constraints. It also uses a dynamic domain adaptation learning mechanism that iteratively updates and refines key state variables under predefined constraints, enabling precise constraint verification. Moreover, it captures spatiotemporal dependencies between generators and loads by leveraging the physical structure of the power grid, allowing for deep integration of topological information across time and space. Extensive comparative and ablation studies show that DDA-PIGCN delivers strong performance across several IEEE standard test cases (such as case9, case30, and case300), achieving mean absolute errors (MAE) from 0.0011 to 0.0624 and constraint satisfaction rates between 99.6% and 100%, establishing it as a reliable and efficient AC-OPF solver.

Long user history is highly valuable signal for recommendation systems, but effectively incorporating it often comes with high cost in terms of data center power consumption and GPU. In this work, we chose offline embedding over end-to-end sequence length optimization methods to enable extremely long user sequence modeling as a cost-effective solution, and propose a new user embedding learning strategy, multi-slicing and summarization, that generates highly generalizable user representation of user's long-term stable interest. History length we encoded in this embedding is up to 70,000 and on average 40,000. This embedding, named as DV365, is proven highly incremental on top of advanced attentive user sequence models deployed in Instagram. Produced by a single upstream foundational model, it is launched in 15 different models across Instagram and Threads with significant impact, and has been production battle-proven for >1 year since our first launch.

Convolutional Neural Networks (CNNs) are pivotal in computer vision and Big Data analytics but demand significant computational resources when trained on large-scale datasets. Conventional training via back-propagation (BP) with losses like Mean Squared Error or Cross-Entropy often requires extensive iterations and may converge sub-optimally. Quantum computing offers a promising alternative by leveraging superposition, tunneling, and entanglement to search complex optimization landscapes more efficiently. In this work, we propose a hybrid optimization method that combines an Unconstrained Binary Quadratic Programming (UBQP) formulation with Stochastic Gradient Descent (SGD) to accelerate CNN training. Evaluated on the MNIST dataset, our approach achieves a 10--15\% accuracy improvement over a standard BP-CNN baseline while maintaining similar execution times. These results illustrate the potential of hybrid quantum-classical techniques in High-Performance Computing (HPC) environments for Big Data and Deep Learning. Fully realizing these benefits, however, requires a careful alignment of algorithmic structures with underlying quantum mechanisms.

The authors deal with a new problem that extends existing problems in a natural way, and present new solutions that extend existing solutions in a natural way; thus in some ways the paper is not very original, but it must be noted that the problem #opt has some surprising properties that make the whole endeavor quite interesting. As for the contribution, it is a valuable piece with new algorithms that have good performance. I really take issue with the emphasis on semirings; I cannot see how this helps the whole effort. Are semirings bringing new insights here? Or are they just more general so that the algorithm applies to other problems?

A solid contribution through a smart formulation to count optimal MAP solutions in graphical models while avoiding to enumerate them. Feedback is satisfactory, even though there were no substantial open questions that would likely change the faith of the manuscript. Techniques are somehow well-known, but the problem is interesting and their application there required some clever work.

We revisit Group Relative Policy Optimization (GRPO) in both on-policy and off-policy optimization regimes. Our motivation comes from recent work on off-policy Proximal Policy Optimization (PPO), which improves training stability, sampling efficiency, and memory usage. In addition, a recent analysis of GRPO suggests that estimating the advantage function with off-policy samples could be beneficial. Building on these observations, we adapt GRPO to the off-policy setting. We show that both on-policy and off-policy GRPO objectives yield an improvement in the reward. This result motivates the use of clipped surrogate objectives in the off-policy version of GRPO. We then compare the empirical performance of reinforcement learning with verifiable rewards in post-training using both GRPO variants. Our results show that off-policy GRPO either significantly outperforms or performs on par with its on-policy counterpart.

The optimization of expensive black-box functions is ubiquitous in science and engineering. A common solution to this problem is Bayesian optimization (BO), which is generally comprised of two components: (i) a surrogate model and (ii) an acquisition function, which generally require expensive re-training and optimization steps at each iteration, respectively. Although recent work enabled in-context surrogate models that do not require re-training, virtually all existing BO methods still require acquisition function maximization to select the next observation, which introduces many knobs to tune, such as Monte Carlo samplers and multi-start optimizers. In this work, we propose a completely in-context, zero-shot solution for BO that does not require surrogate fitting or acquisition function optimization. This is done by using a pre-trained deep generative model to directly sample from the posterior over the optimum point. We show that this process is equivalent to Thompson sampling and demonstrate the capabilities and cost-effectiveness of our foundation model on a suite of real-world benchmarks. We achieve an efficiency gain of more than 35x in terms of wall-clock time when compared with Gaussian process-based BO, enabling efficient parallel and distributed BO, e.g., for high-throughput optimization.

Federated Multi-Task Learning (FMTL) enables multiple clients performing heterogeneous tasks without exchanging their local data, offering broad potential for privacy preserving multi-task collaboration. However, most existing methods focus on building personalized models for each client and unable to support the aggregation of multiple heterogeneous tasks into a unified model. As a result, in real-world scenarios where task objectives, label spaces, and optimization paths vary significantly, conventional FMTL methods struggle to achieve effective joint training. To address this challenge, we propose FedDEA (Federated Decoupled Aggregation), an update-structure-aware aggregation method specifically designed for multi-task model integration. Our method dynamically identifies task-relevant dimensions based on the response strength of local updates and enhances their optimization effectiveness through rescaling. This mechanism effectively suppresses cross-task interference and enables task-level decoupled aggregation within a unified global model. FedDEA does not rely on task labels or architectural modifications, making it broadly applicable and deployment-friendly. Experimental results demonstrate that it can be easily integrated into various mainstream federated optimization algorithms and consistently delivers significant overall performance improvements on widely used NYUD-V2 and PASCAL-Context. These results validate the robustness and generalization capabilities of FedDEA under highly heterogeneous task settings.