We show that for "any" high-order function that can be minimized in

Abstract-- Multipatterning is an essential decomposition strategy in electronic design automation (EDA) that overcomes lithographic limitations when printing dense circuit layouts. Although heuristic-based backtracking and SA T solvers can address these challenges, they often struggle to simultaneously handle both complex constraints and secondary objectives. In this study, we present a hybrid workflow that casts multipatterning as a variant of a constrained graph coloring problem with the primary objective of minimizing feature violations and a secondary objective of balancing the number of features on each mask. Our pipeline integrates two main components: (1) A GNN-based agent, trained in an unsupervised manner to generate initial color predictions, which are refined by (2) refinement strategies (a GNN-based heuristic and simulated annealing) that together enhance solution quality and balance. Experimental evaluation in both proprietary data sets and publicly available open source layouts demonstrate complete conflict-free decomposition and consistent color balancing. The proposed framework provides a reproducible, data-efficient and deployable baseline for scalable layout decomposition in EDA workflows. As semiconductor technology progresses, the demand for higher circuit densities continues to surpass the limits of conventional lithographic techniques. The ongoing reduction in feature size introduces increasingly complex manufacturing constraints, making it difficult to accurately print intricate patterns on a single mask without defects. To address these challenges, modern electronic design automation (EDA) tools and fabrication processes rely on multipatterning, which is a layout decomposition technique that ensures manufacturability while preserving design integrity. In modern integrated circuit (IC) design, Design Rule Checking (DRC) is a critical step that ensures that the physical layout complies with a set of rules derived from the manufacturing constraints. These rules include the requirements on spacing, width, enclosure, and other geometric and connectivity constraints.

Abstract--In serial batch (s-batch) scheduling, jobs from similar families are grouped into batches and processed sequentially to avoid repetitive setups that are required when processing consecutive jobs of different families. Despite its large success in scheduling, only three Constraint Programming (CP) models have been proposed for this problem considering minimum batch sizes, which is a common requirement in many practical settings, including the ion implantation area in semiconductor manufacturing. These existing CP models rely on a predefined virtual set of possible batches that suffers from the curse of dimensionality and adds complexity to the problem. This paper proposes a novel CP model that does not rely on this virtual set. Instead, it uses key alignment parameters that allow it to reason directly on the sequences of same-family jobs scheduled on the machines, resulting in a more compact formulation. This new model is further improved by exploiting the problem's structure with tailored search phases and strengthened inference levels of the constraint propagators. The extensive computational experiments on nearly five thousand instances compare the proposed models against existing methods in the literature, including mixed-integer programming formulations, tabu search meta-heuristics, and CP approaches. The results demonstrate the superiority of the proposed models on small-to-medium instances with up to 100 jobs, and their ability to find solutions up to 25% better than the ones produces by existing methods on large-scale instances with up to 500 jobs, 10 families, and 10 machines. In the current and highly competitive landscape of the manufacturing industry, companies are under growing pressure to minimize production costs and reduce cycle times. A crucial approach to achieving these goals and boosting production efficiency is processing multiple similar jobs in groups called batches [1]. Two types of batching can be distinguished in the scheduling literature, depending on how the jobs are processed inside their batch: (i) parallel batching (p-batch), where jobs inside a batch are processed in parallel at the same time [2]; and (ii) serial batching (s-batch), where jobs inside a batch are processed sequentially, one after the other [3]. The benefits of p-batching in the manufacturing industry are straightforward due to the parallelized processing of the jobs inside a batch. In contrast, the benefits of s-batching usually come from grouping jobs that require similar machine configurations to avoid repetitive setups [4].

Although Multimodal Large Language Models (MLLMs) have demonstrated remarkable capabilities across diverse tasks, they encounter challenges in terms of reasoning efficiency, large model size and overthinking. However, existing lightweight MLLMs lack the capability to balance high efficiency and performance at a small scale. T o this end, we propose Tiny-R1V, a novel lightweight 3B model that achieves faster inference and higher accuracy via a two-stage optimization, while unifying multimodal reasoning across multiple tasks with fewer inference tokens. In the first stage, Tiny-R1V introduces Length-Informed Relative Policy Optimization (LIPO), a new reinforcement learning method, to train each reasoning model, including mathematical reasoning, chart reasoning, and OCR capability. The LIPO dynamically adjusts the advantages of responses within groups by prioritizing concise yet high-quality responses to encourage the generation of shorter and more accurate responses. In the second stage, we propose Adaptive Model Merging (AMM), a training-free model merging method that merges multiple specialist models into a unified architecture. Specifically, AMM adap-tively adjusts the weights of task vectors via a novel gradient projection regularization loss function, thus mitigating redundant conflicts between them. Extensive evaluations on ten widely-used reasoning benchmarks covering mathematics, structured data (charts, tables, documents), OCR, and general capabilities showcase the superior performance of Tiny-R1V, enabling lightweight models to excel in diverse multimodal reasoning tasks.

Many real-world machine learning tasks require outputs that satisfy hard constraints, such as physical conservation laws, structured dependencies in graphs, or column-level relationships in tabular data. Existing approaches rely either on domain-specific architectures and losses or on strong assumptions on the constraint space, restricting their applicability to linear or convex constraints. We propose a general-purpose framework for constraint-aware refinement that leverages denoising diffusion implicit models (DDIMs). Starting from a coarse prediction, our method iteratively refines it through a deterministic diffusion trajectory guided by a learned prior and augmented by constraint gradient corrections. The approach accommodates a wide class of non-convex and nonlinear equality constraints and can be applied post hoc to any base model. We demonstrate the method in two representative domains: constrained adversarial attack generation on tabular data with column-level dependencies and in AC power flow prediction under Kirchhoff's laws. Across both settings, our diffusion-guided refinement improves both constraint satisfaction and performance while remaining lightweight and model-agnostic.

In this paper we present a hybrid active sampling strategy for pairwise preference aggregation, which aims at recovering the underlying rating of the test candidates from sparse and noisy pairwise labeling. Our method employs Bayesian optimization framework and Bradley-Terry model to construct the utility function, then to obtain the Expected Information Gain (EIG) of each pair. For computational efficiency, Gaussian-Hermite quadrature is used for estimation of EIG. In this work, a hybrid active sampling strategy is proposed, either using Global Maximum (GM) EIG sampling or Minimum Spanning Tree (MST) sampling in each trial, which is determined by the test budget. The proposed method has been validated on both simulated and real-world datasets, where it shows higher preference aggregation ability than the state-of-the-art methods.

We present a new algorithm to generate minimal, stable, and symbolic corrections to an input that will cause a neural network with ReLU activations to change its output. We argue that such a correction is a useful way to provide feedback to a user when the network's output is different from a desired output. Our algorithm generates such a correction by solving a series of linear constraint satisfaction problems. The technique is evaluated on three neural network models: one predicting whether an applicant will pay a mortgage, one predicting whether a first-order theorem can be proved efficiently by a solver using certain heuristics, and the final one judging whether a drawing is an accurate rendition of a canonical drawing of a cat.

Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond to how frequently each variable is set to true among satisfying assignments, and are used to inform branching decisions during search; however, marginal estimates obtained via survey propagation are approximate and can be self-contradictory. We introduce a more general branching strategy based on streamlining constraints, which sidestep hard assignments to variables. We show that streamlined solvers consistently outperform decimation-based solvers on random k-SAT instances for several problem sizes, shrinking the gap between empirical performance and theoretical limits of satisfiability by 16.3% on average for k = 3, 4, 5, 6.

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Crucially, the neural model uses miniKanren's