The estimation of unknown parameters in nonlinear partial differential equations (PDEs) offers valuable insights across a wide range of scientific domains. In this work, we focus on estimating plant root parameters in the Richards equation, which is essential for understanding the soil-plant system in agricultural studies. Since conventional methods are computationally intensive and often yield unstable estimates, we develop a new Gaussian process collocation method for efficient Bayesian inference. Unlike existing Gaussian process-based approaches, our method constructs an approximate posterior distribution using samples drawn from a Gaussian process model fitted to the observed data, which does not require any structural assumption about the underlying PDE. Further, we propose to use an importance sampling procedure to correct for the discrepancy between the approximate and true posterior distributions. As an alternative, we also devise a prior-guided Bayesian optimization algorithm leveraging the approximate posterior. Simulation studies demonstrate that our method yields robust estimates under various settings. Finally, we apply our method on a real agricultural data set and estimate the plant root parameters with uncertainty quantification.

Risk assessment tools in healthcare commonly employ point-based scoring systems that map patients to ordinal risk categories via thresholds. While electronic health record (EHR) data presents opportunities for data-driven optimization of these tools, two fundamental challenges impede standard supervised learning: (1) partial supervision arising from intervention-censored outcomes, where only extreme categories can be reliably labeled, and (2) asymmetric misclassification costs that increase with ordinal distance. We propose a mixed-integer programming (MIP) framework that jointly optimizes scoring weights and category thresholds under these constraints. Our approach handles partial supervision through per-instance feasible label sets, incorporates asymmetric distance-aware objectives, and prevents middle-category collapse via minimum threshold gaps. We further develop a CSO relaxation using softplus losses that preserves the ordinal structure while enabling efficient optimization. The framework supports governance constraints including sign restrictions, sparsity, and minimal modifications to incumbent tools, ensuring practical deployability in clinical workflows.

Resourceful operation and design of robots is key for sustainable industrial automation. This will be enabled by lightweight design along with time and energy optimal control of robotic manipulators. Design and control of such systems is intertwined as the control must take into account inherent mechanical compliance while the design must accommodate the dynamic requirements demanded by the control. As basis for such design optimization, a method for estimating the lifetime of elastic link robotic manipulators is presented. This is applied to the geometry optimization of flexible serial manipulators performing pick-and-place operations, where the optimization objective is a combination of overall weight and vibration amplitudes. The lifetime estimation draws from a fatigue analysis combining the rainflow counting algorithm and the method of critical cutting plane. Tresca hypothesis is used to formulate an equivalent stress, and linear damage accumulation is assumed. The final robot geometry is selected from a Pareto front as a tradeoff of lifetime and vibration characteristic. The method is illustrated for a three degrees of freedom articulated robotic manipulator.

Dynamic algorithm configuration (DAC) is a recent trend in automated machine learning, which can dynamically adjust the algorithm's configuration during the execution process and relieve users from tedious trial-and-error tuning tasks. Recently, multi-agent reinforcement learning (MARL) approaches have improved the configuration of multiple heterogeneous hyperparameters, making various parameter configurations for complex algorithms possible. However, many complex algorithms have inherent inter-dependencies among multiple parameters (e.g., determining the operator type first and then the operator's parameter), which are, however, not considered in previous approaches, thus leading to sub-optimal results. In this paper, we propose the sequential multi-agent DAC (Seq-MADAC) framework to address this issue by considering the inherent inter-dependencies of multiple parameters. Specifically, we propose a sequential advantage decomposition network, which can leverage action-order information through sequential advantage decomposition. Experiments from synthetic functions to the configuration of multi-objective optimization algorithms demonstrate Seq-MADAC's superior performance over state-of-the-art MARL methods and show strong generalization across problem classes. Seq-MADAC establishes a new paradigm for the widespread dependency-aware automated algorithm configuration. Our code is available at https://github.com/lamda-bbo/seq-madac.

Researchers have studied Stewart-Gough platforms, also known as Gough-Stewart platforms or hexapod platforms extensively for their inherent fine control characteristics. Their studies led to the potential deployment opportunities of Stewart-Gough Platforms in many critical applications such as the medical field, engineering machines, space research, electronic chip manufacturing, automobile manufacturing, etc. Some of these applications need micro and nano-level movement control in 3D space for the motions to be precise, complicated, and repeatable; a Stewart-Gough platform fulfills these challenges smartly. For this, the platform must be more accurate than the specified application accuracy level and thus proper calibration for a parallel robot is crucial. Forward kinematics-based calibration for these hexapod machines becomes unnecessarily complex and inverse kinematics complete this task with much ease. To experiment with different calibration techniques, various calibration approaches were implemented by using external instruments, constraining one or more motions of the system, and using extra sensors for auto or self-calibration. This survey paid attention to those key methodologies, their outcome, and important details related to inverse kinematic-based parallel robot calibrations. It was observed during this study that the researchers focused on improving the accuracy of the platform position and orientation considering the errors contributed by one source or multiple sources. The error sources considered are mainly kinematic and structural, in some cases, environmental factors also are reviewed, however, those calibrations are done under no-load conditions. This study aims to review the present state of the art in this field and highlight the processes and errors considered for the calibration of Stewart-Gough platforms.

Recent work on neural scaling laws demonstrates that model performance scales predictably with compute budget, model size, and dataset size. In this work, we develop scaling laws based on problem complexity. We analyze two fundamental complexity measures: solution space size and representation space size. Using the Traveling Salesman Problem (TSP) as a case study, we show that combinatorial optimization promotes smooth cost trends, and therefore meaningful scaling laws can be obtained even in the absence of an interpretable loss. We then show that suboptimality grows predictably for fixed-size models when scaling the number of TSP nodes or spatial dimensions, independent of whether the model was trained with reinforcement learning or supervised fine-tuning on a static dataset. We conclude with an analogy to problem complexity scaling in local search, showing that a much simpler gradient descent of the cost landscape produces similar trends.

Low-rank gradient-based optimization methods have significantly improved memory efficiency during the training of large language models (LLMs), enabling operations within constrained hardware without sacrificing performance. However, these methods primarily emphasize memory savings, often overlooking potential acceleration in convergence due to their reliance on standard isotropic steepest descent techniques, which can perform suboptimally in the highly anisotropic landscapes typical of deep networks, particularly LLMs. In this paper, we propose SUMO (Subspace-Aware Moment-Orthogonalization), an optimizer that employs exact singular value decomposition (SVD) for moment orthogonalization within a dynamically adapted low-dimensional subspace, enabling norm-inducing steepest descent optimization steps. By explicitly aligning optimization steps with the spectral characteristics of the loss landscape, SUMO effectively mitigates approximation errors associated with commonly used methods like Newton-Schulz orthogonalization approximation. We theoretically establish an upper bound on these approximation errors, proving their dependence on the condition numbers of moments, conditions we analytically demonstrate are encountered during LLM training. Furthermore, we both theoretically and empirically illustrate that exact orthogonalization via SVD substantially improves convergence rates while reducing overall complexity. Empirical evaluations confirm that SUMO accelerates convergence, enhances stability, improves performance, and reduces memory requirements by up to 20% compared to state-of-the-art methods.

Developing high-performance software is a complex task that requires specialized expertise. We introduce GSO, a benchmark for evaluating language models' capabilities in developing high-performance software. We develop an automated pipeline that generates and executes performance tests to analyze repository commit histories to identify 102 challenging optimization tasks across 10 codebases, spanning diverse domains and programming languages. An agent is provided with a codebase and performance test as a precise specification, and tasked to improve the runtime efficiency, which is measured against the expert developer optimization. Our quantitative evaluation reveals that leading SWE-Agents struggle significantly, achieving less than 5% success rate, with limited improvements even with inference-time scaling. Our qualitative analysis identifies key failure modes, including difficulties with low-level languages, practicing lazy optimization strategies, and challenges in accurately localizing bottlenecks. We release the code and artifacts of our benchmark along with agent trajectories to enable future research.

Hypothesis ranking is vital for automated scientific discovery, especially in cost-intensive, throughput-limited natural science domains. Current methods focus on pre-experiment ranking, relying solely on language model reasoning without empirical feedback. We introduce experiment-guided ranking, which prioritizes hypotheses based on feedback from prior tests. Due to the impracticality of real experiments, we propose a simulator grounded in domain-specific concepts that models hypothesis performance as a function of similarity to a hidden ground truth, perturbed by noise. Validated against 124 hypotheses with experimentally reported outcomes, the simulator approximates real results with consistent trend alignment. Although deviations exist, they mimic wet-lab noise, promoting more robust ranking strategies. We frame experiment-guided ranking as a sequential decision-making problem and propose an in-context reinforcement learning (ICRL) framework. Our LLM-based policy decomposes hypotheses into functional elements, clusters them by mechanistic roles, and prioritizes recombinations based on feedback. Experiments show our approach significantly outperforms pre-experiment baselines and strong ablations. Our toolkit, comprising the simulator and ICRL framework, enables systematic research on experiment-guided ranking, with the policy serving as a strong proof of concept.

Large Language Models often contain factually incorrect or outdated knowledge, giving rise to model editing methods for precise knowledge updates. However, current mainstream locate-then-edit approaches exhibit a progressive performance decline during sequential editing, due to inadequate mechanisms for long-term knowledge preservation. To tackle this, we model the sequential editing as a constrained stochastic programming. Given the challenges posed by the cumulative preservation error constraint and the gradually revealed editing tasks, \textbf{LyapLock} is proposed. It integrates queuing theory and Lyapunov optimization to decompose the long-term constrained programming into tractable stepwise subproblems for efficient solving. This is the first model editing framework with rigorous theoretical guarantees, achieving asymptotic optimal editing performance while meeting the constraints of long-term knowledge preservation. Experimental results show that our framework scales sequential editing capacity to over 10,000 edits while stabilizing general capabilities and boosting average editing efficacy by 11.89\% over SOTA baselines. Furthermore, it can be leveraged to enhance the performance of baseline methods. Our code is released on https://github.com/caskcsg/LyapLock.