Cutting-planes are one of the most important building blocks for solving large-scale integer programming (IP) problems to (near) optimality.

Storing and processing of embedding vectors by specialized Vector databases (VDBs) has become the linchpin in building modern AI pipelines. Most current VDBs employ variants of a graph-based ap- proximate nearest-neighbor (ANN) index algorithm, HNSW, to an- swer semantic queries over stored vectors. Inspite of its wide-spread use, the HNSW algorithm suffers from several issues: in-memory design and implementation, random memory accesses leading to degradation in cache behavior, limited acceleration scope due to fine-grained pairwise computations, and support of only semantic similarity queries. In this paper, we present a novel disk-based ANN index, B+ANN, to address these issues: it first partitions input data into blocks containing semantically similar items, then builds an B+ tree variant to store blocks both in-memory and on disks, and finally, enables hybrid edge- and block-based in-memory traversals. As demonstrated by our experimantal evaluation, the proposed B+ANN disk-based index improves both quality (Recall value), and execution performance (Queries per second/QPS) over HNSW, by improving spatial and temporal locality for semantic operations, reducing cache misses (19.23% relative gain), and decreasing the memory consumption and disk-based build time by 24x over the DiskANN algorithm. Finally, it enables dissimilarity queries, which are not supported by similarity-oriented ANN indices.

Shot assembly is a crucial step in film production and video editing, involving the sequencing and arrangement of shots to construct a narrative, convey information, or evoke emotions. Traditionally, this process has been manually executed by experienced editors. While current intelligent video editing technologies can handle some automated video editing tasks, they often fail to capture the creator's unique artistic expression in shot assembly. To address this challenge, we propose an energy-based optimization method for video shot assembly. Specifically, we first perform visual-semantic matching between the script generated by a large language model and a video library to obtain subsets of candidate shots aligned with the script semantics. Next, we segment and label the shots from reference videos, extracting attributes such as shot size, camera motion, and semantics. We then employ energy-based models to learn from these attributes, scoring candidate shot sequences based on their alignment with reference styles. Finally, we achieve shot assembly optimization by combining multiple syntax rules, producing videos that align with the assembly style of the reference videos. Our method not only automates the arrangement and combination of independent shots according to specific logic, narrative requirements, or artistic styles but also learns the assembly style of reference videos, creating a coherent visual sequence or holistic visual expression. With our system, even users with no prior video editing experience can create visually compelling videos. Project page: https://sobeymil.github.io/esa.com

The Combined Algorithm Selection and Hyperparameter optimization (CASH) is a challenging resource allocation problem in the field of AutoML. We propose MaxUCB, a max k-armed bandit method to trade off exploring different model classes and conducting hyperparameter optimization. MaxUCB is specifically designed for the light-tailed and bounded reward distributions arising in this setting and, thus, provides an efficient alternative compared to classic max k-armed bandit methods assuming heavy-tailed reward distributions. We theoretically and empirically evaluate our method on four standard AutoML benchmarks, demonstrating superior performance over prior approaches. We make our code and data available at https://github.com/amirbalef/CASH_with_Bandits

We propose a novel and efficient search algorithm which finds initial centers that can be used subsequently for the local search algorithm.

Logical Credal Networks or LCNs were recently introduced as a powerful probabilistic logic framework for representing and reasoning with imprecise knowledge.

Figure 2: Diffusion modeling for CO solving where the model learns how to gradually denoise from the random noise to predict each step's

Optimisation of functions on graphs is challenging.

Large language models (LLMs) often make reasoning errors when solving mathematical problems, and how to automatically detect and correct these errors has become an important research direction. However, existing approaches \textit{mainly focus on self-correction within the model}, which falls short of the ``teacher-style`` correction required in educational settings, \textit{i.e.}, systematically guiding and revising a student's problem-solving process. To address this gap, we propose \texttt{SMRC} (\textit{\underline{S}tudent \underline{M}athematical \underline{R}easoning \underline{C}orrection}), a novel method that aligns LLMs with student reasoning. Specifically, \texttt{SMRC} formulates student reasoning as a multi-step sequential decision problem and introduces Monte Carlo Tree Search (MCTS) to explore optimal correction paths. To reduce the cost of the annotating process-level rewards, we leverage breadth-first search (BFS) guided by LLMs and final-answer evaluation to generate reward signals, which are then distributed across intermediate reasoning steps via a back-propagation mechanism, enabling fine-grained process supervision. Additionally, we construct a benchmark for high school mathematics, MSEB (Multi-Solution Error Benchmark), consisting of 158 instances that include problem statements, student solutions, and correct reasoning steps. We further propose a dual evaluation protocol centered on \textbf{solution accuracy} and \textbf{correct-step retention}, offering a comprehensive measure of educational applicability. Experiments demonstrate that \texttt{SMRC} significantly outperforms existing methods on two public datasets (ProcessBench and MR-GSM8K) and our MSEB in terms of effectiveness and overall performance. The code and data are available at https://github.com/Mind-Lab-ECNU/SMRC.

Join ordering is the NP-hard problem of selecting the most efficient sequence in which to evaluate joins (conjunctive, binary operators) in a database query. As the performance of query execution critically depends on this choice, join ordering lies at the core of query optimization. Traditional approaches cast this problem as a discrete combinatorial search over binary trees guided by a cost model, but they often suffer from high computational complexity and limited scalability. We show that, when the cost model is differentiable, the query plans can be continuously relaxed into a soft adjacency matrix representing a superposition of plans. This continuous relaxation, together with a Gumbel-Softmax parameterization of the adjacency matrix and differentiable constraints enforcing plan validity, enables gradient-based search for plans within this relaxed space. Using a learned Graph Neural Network as the cost model, we demonstrate that this gradient-based approach can find comparable and even lower-cost plans compared to traditional discrete local search methods on two different graph datasets. Furthermore, we empirically show that the runtime of this approach scales linearly with query size, in contrast to quadratic or exponential runtimes of classical approaches. We believe this first step towards gradient-based join ordering can lead to more effective and efficient query optimizers in the future.