We present CrochetBench, a benchmark for evaluating the ability of multimodal large language models to perform fine-grained, low-level procedural reasoning in the domain of crochet. Unlike prior benchmarks that focus on high-level description or visual question answering, CrochetBench shifts the emphasis from describing to doing: models are required to recognize stitches, select structurally appropriate instructions, and generate compilable crochet procedures. We adopt the CrochetPARADE DSL as our intermediate representation, enabling structural validation and functional evaluation via execution. The benchmark covers tasks including stitch classification, instruction grounding, and both natural language and image-to-DSL translation. Across all tasks, performance sharply declines as the evaluation shifts from surface-level similarity to executable correctness, exposing limitations in long-range symbolic reasoning and 3D-aware procedural synthesis. CrochetBench offers a new lens for assessing procedural competence in multimodal models and highlights the gap between surface-level understanding and executable precision in real-world creative domains. Code is available at https://github.com/Peiyu-Georgia-Li/crochetBench.

We implement and evaluate different methods for the reconfiguration of a connected arrangement of tiles into a desired target shape, using a single active robot that can move along the tile structure. This robot can pick up, carry, or drop off one tile at a time, but it must maintain a single connected configuration at all times. Becker et al. (CCCG 2025) recently proposed an algorithm that uses histograms as canonical intermediate configurations, guaranteeing performance within a constant factor of the optimal solution if the start and target configuration are well-separated. We implement and evaluate this algorithm, both in a simulated and practical setting, using an inchworm type robot to compare it with two existing heuristic algorithms.

In this paper we provide a novel analytical perspective on the theoretical understanding of gradient-based learning algorithms by interpreting consensus-based optimization (CBO), a recently proposed multi-particle derivative-free optimization method, as a stochastic relaxation of gradient descent. Remarkably, we observe that through communication of the particles, CBO exhibits a stochastic gradient descent (SGD)-like behavior despite solely relying on evaluations of the objective function. The fundamental value of such link between CBO and SGD lies in the fact that CBO is provably globally convergent to global minimizers for ample classes of nonsmooth and nonconvex objective functions, hence, on the one side, offering a novel explanation for the success of stochastic relaxations of gradient descent. On the other side, contrary to the conventional wisdom for which zero-order methods ought to be inefficient or not to possess generalization abilities, our results unveil an intrinsic gradient descent nature of such heuristics. This viewpoint furthermore complements previous insights into the working principles of CBO, which describe the dynamics in the mean-field limit through a nonlinear nonlocal partial differential equation that allows to alleviate complexities of the nonconvex function landscape. Our proofs leverage a completely nonsmooth analysis, which combines a novel quantitative version of the Laplace principle (log-sum-exp trick) and the minimizing movement scheme (proximal iteration). In doing so, we furnish useful and precise insights that explain how stochastic perturbations of gradient descent overcome energy barriers and reach deep levels of nonconvex functions. Instructive numerical illustrations support the provided theoretical insights.

We address the lack of reliability in benchmarking clustering techniques based on labeled datasets. A standard scheme in external clustering validation is to use class labels as ground truth clusters, based on the assumption that each class forms a single, clearly separated cluster. However, as such cluster-label matching (CLM) assumption often breaks, the lack of conducting a sanity check for the CLM of benchmark datasets casts doubt on the validity of external validations. Still, evaluating the degree of CLM is challenging. For example, internal clustering validation measures can be used to quantify CLM within the same dataset to evaluate its different clusterings but are not designed to compare clusterings of different datasets. In this work, we propose a principled way to generate between-dataset internal measures that enable the comparison of CLM across datasets. We first determine four axioms for between-dataset internal measures, complementing Ackerman and Ben-David's within-dataset axioms. We then propose processes to generalize internal measures to fulfill these new axioms, and use them to extend the widely used Calinski-Harabasz index for between-dataset CLM evaluation. Through quantitative experiments, we (1) verify the validity and necessity of the generalization processes and (2) show that the proposed between-dataset Calinski-Harabasz index accurately evaluates CLM across datasets. Finally, we demonstrate the importance of evaluating CLM of benchmark datasets before conducting external validation.

Machine learning (ML) has shown to advance the research field of quantum chemistry in almost any possible direction and has recently also entered the excited states to investigate the multifaceted photochemistry of molecules. In this paper, we pursue two goals: i) We show how ML can be used to model permanent dipole moments for excited states and transition dipole moments by adapting the charge model of [Chem. Sci., 2017, 8, 6924-6935], which was originally proposed for the permanent dipole moment vector of the electronic ground state. ii) We investigate the transferability of our excited-state ML models in chemical space, i.e., whether an ML model can predict properties of molecules that it has never been trained on and whether it can learn the different excited states of two molecules simultaneously. To this aim, we employ and extend our previously reported SchNarc approach for excited-state ML. We calculate UV absorption spectra from excited-state energies and transition dipole moments as well as electrostatic potentials from latent charges inferred by the ML model of the permanent dipole moment vectors. We train our ML models on CH$_2$NH$_2^+$ and C$_2$H$_4$, while predictions are carried out for these molecules and additionally for CHNH$_2$, CH$_2$NH, and C$_2$H$_5^+$. The results indicate that transferability is possible for the excited states.