Optimizers are crucial for the efficient training of Large Language Models (LLMs). While AdamW is the de facto standard, recent structure-aware optimizers like Muon have emerged, which regularize gradient updates by operating on entire weight matrices. The Muon optimizer balances the gradient updates along all the directions. However, Muon's reliance on the matrix sign function can lead to training instability, exhibits incompatibility when fine-tuning models pre-trained with AdamW. To address these limitations, we propose \textbf{REG}, a novel optimizer that replaces Muon's aggressive matrix sign operator with the Row-and-Column-Scaling (RACS) operator. Theoretically grounded in balancing a matrix, the RACS operator regularizes the update steps in a less drastic manner, making it simpler to implement and more compatible with established training dynamics. Through extensive empirical experiments on LLM training, we demonstrate that our REG optimizer not only achieves superior performance and stability over AdamW, but also maintains consistency with the AdamW training paradigm. This consistency is particularly evident during the fine-tuning stage, where REG optimizer avoids the performance degradation observed with Muon.

Low-discrepancy point sets and digital sequences underpin quasi-Monte Carlo (QMC) methods for high-dimensional integration. We cast two long-standing QMC design problems as program synthesis and solve them with an LLM-guided evolutionary loop that mutates and selects code under task-specific fitness: (i) constructing finite 2D/3D point sets with low star discrepancy, and (ii) choosing Sobol' direction numbers that minimize randomized QMC error on downstream integrands. Our two-phase procedure combines constructive code proposals with iterative numerical refinement. On finite sets, we rediscover known optima in small 2D cases and set new best-known 2D benchmarks for N >= 40, while matching most known 3D optima up to the proven frontier (N <= 8) and reporting improved 3D benchmarks beyond. On digital sequences, evolving Sobol' parameters yields consistent reductions in randomized quasi-Monte Carlo (rQMC) mean-squared error for several 32-dimensional option-pricing tasks relative to widely used Joe--Kuo parameters, while preserving extensibility to any sample size and compatibility with standard randomizations. Taken together, the results demonstrate that LLM-driven evolutionary program synthesis can automate the discovery of high-quality QMC constructions, recovering classical designs where they are optimal and improving them where finite-N structure matters. Data and code are available at https://github.com/hockeyguy123/openevolve-star-discrepancy.git.

Ensuring safety is a foundational requirement for large language models (LLMs). Achieving an appropriate balance between enhancing the utility of model outputs and mitigating their potential for harm is a complex and persistent challenge. Contemporary approaches frequently formalize this problem within the framework of Constrained Markov Decision Processes (CMDPs) and employ established CMDP optimization techniques. However, these methods exhibit two notable limitations. First, their reliance on reward and cost functions renders performance highly sensitive to the underlying scoring mechanism, which must capture semantic meaning rather than being triggered by superficial keywords. Second, CMDP-based training entails tuning dual-variable, a process that is both computationally expensive and does not provide any provable safety guarantee for a fixed dual variable that can be exploitable through adversarial jailbreaks. To overcome these limitations, we introduce Certifiable Safe-RLHF (CS-RLHF) that introduces a cost model trained on a large-scale corpus to assign semantically grounded safety scores. In contrast to the lagrangian-based approach, CS-RLHF adopts a rectified penalty-based formulation. This design draws on the theory of exact penalty functions in constrained optimization, wherein constraint satisfaction is enforced directly through a suitably chosen penalty term. With an appropriately scaled penalty, feasibility of the safety constraints can be guaranteed at the optimizer, eliminating the need for dual-variable updates. Empirical evaluation demonstrates that CS-RLHF outperforms state-of-the-art LLM model responses rendering at-least 5 times efficient against nominal and jail-breaking prompts

We study optimizing a destination-to-chutes task mapping to improve throughput in Robotic Sorting Systems (RSS), where a team of robots sort packages on a sortation floor by transporting them from induct workstations to eject chutes based on their shipping destinations (e.g. Los Angeles or Pittsburgh). The destination-to-chutes task mapping is used to determine which chutes a robot can drop its package. Finding a high-quality task mapping is challenging because of the complexity of a real-world RSS. First, optimizing task mapping is interdependent with robot target assignment and path planning. Second, chutes will be CLOSED for a period of time once they receive sufficient packages to allow for downstream processing. Third, task mapping quality directly impacts the downstream processing, as scattered chutes for the same destination increase package handling time. In this paper, we first formally define task mappings and the problem of Task Mapping Optimization (TMO). We then present a simulator of RSS to evaluate task mappings. We then present a simple TMO method based on the Evolutionary Algorithm and Mixed Integer Linear Programming, demonstrating the advantage of our optimized task mappings over the greedily generated ones in various RSS setups with different map sizes, numbers of chutes, and destinations. Finally, we use Quality Diversity algorithms to analyze the throughput of a diverse set of task mappings. Our code is available online at https://github.com/lunjohnzhang/tmo_public.

Rapid robot motion generation is critical in Human-Robot Collaboration (HRC) systems, as robots need to respond to dynamic environments in real time by continuously observing their surroundings and replanning their motions to ensure both safe interactions and efficient task execution. Current sampling-based motion planners face challenges in scaling to high-dimensional configuration spaces and often require post-processing to interpolate and smooth the generated paths, resulting in time inefficiency in complex environments. Optimization-based planners, on the other hand, can incorporate multiple constraints and generate smooth trajectories directly, making them potentially more time-efficient. However, optimization-based planners are sensitive to initialization and may get stuck in local minima. In this work, we present a novel learning-based method that utilizes a Flow Matching model conditioned on a single-view point cloud to learn near-optimal solutions for optimization initialization. Our method does not require prior knowledge of the environment, such as obstacle locations and geometries, and can generate feasible trajectories directly from single-view depth camera input. Simulation studies on a UR5e robotic manipulator in cluttered workspaces demonstrate that the proposed generative initializer achieves a high success rate on its own, significantly improves the success rate of trajectory optimization compared with traditional and learning-based benchmark initializers, requires fewer optimization iterations, and exhibits strong generalization to unseen environments.

Current quantum computers require algorithms that use limited resources economically. In quantum machine learning, success hinges on quantum feature maps, which embed classical data into the state space of qubits. We introduce Quantum Feature-Map Learning via Analytic Iterative Reconstructions (Q-FLAIR), an algorithm that reduces quantum resource overhead in iterative feature-map circuit construction. It shifts workloads to a classical computer via partial analytic reconstructions of the quantum model, using only a few evaluations. For each probed gate addition to the ansatz, the simultaneous selection and optimization of the data feature and weight parameter is then entirely classical. Integrated into quantum neural network and quantum kernel support vector classifiers, Q-FLAIR shows state-of-the-art benchmark performance. Since resource overhead decouples from feature dimension, we train a quantum model on a real IBM device in only four hours, surpassing 90% accuracy on the full-resolution MNIST dataset (784 features, digits 3 vs 5). Such results were previously unattainable, as the feature dimension prohibitively drives hardware demands for fixed and search costs for adaptive ansätze. By rethinking feature-map learning beyond black-box optimization, this work takes a concrete step toward enabling quantum machine learning for real-world problems and near-term quantum computers.

The scarcity of non-renewable energy sources, geopolitical problems in its supply, increasing prices, and the impact of climate change, force the global economy to develop more energy-efficient solutions for their operations. The Manufacturing sector is not excluded from this challenge as one of the largest consumers of energy. Energy-efficient scheduling is a method that attracts manufacturing companies to reduce their consumption as it can be quickly deployed and can show impact immediately. In this study, the hybrid flow shop scheduling problem with blocking constraint (BHFS) is investigated in which we seek to minimize the latest completion time (i.e. makespan) and overall energy consumption, a typical manufacturing setting across many industries from automotive to pharmaceutical. Energy consumption and the latest completion time of customer orders are usually conflicting objectives. Therefore, we first formulate the problem as a novel multi-objective mixed integer programming (MIP) model and propose an augmented epsilon-constraint method for finding the Pareto-optimal solutions. Also, an effective multi-objective metaheuristic algorithm. Refined Iterated Pareto Greedy (RIPG), is developed to solve large instances in reasonable time. Our proposed methods are benchmarked using small, medium, and large-size instances to evaluate their efficiency. Two well-known algorithms are adopted for comparing our novel approaches. The computational results show the effectiveness of our method.

Conventional passivity-based torque controllers for manipulators are typically unconstrained, which can lead to safety violations under external perturbations. In this paper, we employ viability theory to pre-compute safe sets in the state-space of joint positions and velocities. These viable sets, constructed via data-driven and analytical methods for self-collision avoidance, external object collision avoidance and joint-position and joint-velocity limits, provide constraints on joint accelerations and thus joint torques via the robot dynamics. A quadratic programming-based control framework enforces these constraints on a passive controller tracking a dynamical system, ensuring the robot states remain within the safe set in an infinite time horizon. We validate the proposed approach through simulations and hardware experiments on a 7-DoF Franka Emika manipulator. In comparison to a baseline constrained passive controller, our method operates at higher control-loop rates and yields smoother trajectories.

Pruning is critical for scaling large language models (LLMs). Global pruning achieves strong performance but requires $\mathcal{O}(N)$ memory, which is infeasible for billion-parameter models. Local pruning reduces GPU memory usage to that of a single layer by pruning layers independently, but it neglects inter-layer dependencies and often leads to suboptimal performance in high-sparsity regimes. Unlike unstructured pruning, structured pruning produces regular sparsity patterns that align well with GPU kernels and library optimizations, making it more hardware-efficient. However, structured pruning typically relies on global pruning, since structured patterns are more prone to severe performance degradation under local optimization. To jointly achieve structured pruning and the memory efficiency of local pruning, we propose a divide-and-conquer strategy that decomposes the global pruning problem into coordinated subproblems across different modules, each of which fits within limited GPU memory. Building on this idea, we design \textbf{STRUPRUNE}, an ADMM-based framework that integrates structured sparsity into the pruning process, combining the memory efficiency of local pruning with the hardware compatibility of structured methods. We derive a closed-form analytical solution for structured pruning masks that provides an explicit rule for layer-wise sparsity allocation, and further develop an energy-based asymptotic framework yielding a softmax-form allocation scheme that simplifies optimization while adapting to heterogeneous layer importance. Experiments demonstrate that STRUPRUNE matches the perplexity of global structured pruning while reducing memory cost from $\mathcal{O}(N)$ to $\mathcal{O}(\sqrt{N})$, enabling practical deployment at the billion-parameter scale.

Quadrotors hold significant promise for several applications such as agriculture, search and rescue, and infrastructure inspection. Achieving autonomous operation requires systems to navigate safely through complex and unfamiliar environments. This level of autonomy is particularly challenging due to the complexity of such environments and the need for real-time decision making especially for platforms constrained by size, weight, and power (SWaP), which limits flight time and precludes the use of bulky sensors like Light Detection and Ranging (LiDAR) for mapping. Furthermore, computing globally optimal, collision-free paths and translating them into time-optimized, safe trajectories in real time adds significant computational complexity. To address these challenges, we present a fully onboard, real-time navigation system that relies solely on lightweight onboard sensors. Our system constructs a dense 3D map of the environment using a novel visual depth estimation approach that fuses stereo and monocular learning-based depth, yielding longer-range, denser, and less noisy depth maps than conventional stereo methods. Building on this map, we introduce a novel planning and trajectory generation framework capable of rapidly computing time-optimal global trajectories. As the map is incrementally updated with new depth information, our system continuously refines the trajectory to maintain safety and optimality. Both our planner and trajectory generator outperforms state-of-the-art methods in terms of computational efficiency and guarantee obstacle-free trajectories. We validate our system through robust autonomous flight experiments in diverse indoor and outdoor environments, demonstrating its effectiveness for safe navigation in previously unknown settings.