Structured latent variables allow incorporating meaningful prior knowledge into deep learning models. However, learning with such variables remains challenging because of their discrete nature. Nowadays, the standard learning approach is to define a latent variable as a perturbed algorithm output and to use a differentiable surrogate for training. In general, the surrogate puts additional constraints on the model and inevitably leads to biased gradients. To alleviate these shortcomings, we extend the Gumbel-Max trick to define distributions over structured domains. We avoid the differentiable surrogates by leveraging the score function estimators for optimization. In particular, we highlight a family of recursive algorithms with a common feature we call stochastic invariant. The feature allows us to construct reliable gradient estimates and control variates without additional constraints on the model. In our experiments, we consider various structured latent variable models and achieve results competitive with relaxation-based counterparts.

NMF is equivalent to the classical K -means kernel clustering in [11]and it is inherently suitable for clustering nonlinearly separable data from a similarity matrix [10].

One of the long-standing goals in optimisation and constraint programming is to describe a problem in natural language and automatically obtain an executable, efficient model. Large language models appear to bring this vision closer, showing impressive results in automatically generating models for classical benchmarks. However, much of this apparent success may derive from data contamination rather than genuine reasoning: many standard CP problems are likely included in the training data of these models. To examine this hypothesis, we systematically rephrased and perturbed a set of well-known CSPLib problems to preserve their structure while modifying their context and introducing misleading elements. We then compared the models produced by three representative LLMs across original and modified descriptions. Our qualitative analysis shows that while LLMs can produce syntactically valid and semantically plausible models, their performance drops sharply under contextual and linguistic variation, revealing shallow understanding and sensitivity to wording.

We thank all reviewers for their comments and acknowledgement of our contribution. Theorem 3 and Corollary 4, as Reviewer 3 suggested. How to choose the proper Bregman divergence? It is yet unclear whether there exist ways to systematically design the "best Bregman divergence in a (k 1) This is also commonly adopted in the literature. Is continuity of the intensity function restrictive?

Text-to-SQL systems translate natural language questions into SQL queries, providing substantial value for non-expert users. While large language models (LLMs) show promising results for this task, they remain error-prone. Query ambiguity has been recognized as a major obstacle for LLM-based Text-to-SQL systems, leading to misinterpretation of user intent and inaccurate SQL generation. We demonstrate AmbiSQL, an interactive system that automatically detects query ambiguities and guides users through intuitive multiple-choice questions to clarify their intent. Our approach introduces a fine-grained ambiguity taxonomy for identifying ambiguities that affect database element mapping and LLM reasoning, then incorporates user feedback to rewrite ambiguous questions. Evaluation on an ambiguous query dataset shows that AmbiSQL achieves 87.2% precision in ambiguity detection and improves SQL exact match accuracy by 50% when integrated with Text-to-SQL systems. Our demonstration showcases the significant performance gains and highlights the system's practical usability. Code repo and demonstration are available at: https://github.com/JustinzjDing/AmbiSQL.

Multi-Agent Path Finding (MAPF) is a fundamental problem in artificial intelligence and robotics, requiring the computation of collision-free paths for multiple agents navigating from their start locations to designated goals. As autonomous systems become increasingly prevalent in warehouses, urban transportation, and other complex environments, MAPF has evolved from a theoretical challenge to a critical enabler of real-world multi-robot coordination. This comprehensive survey bridges the long-standing divide between classical algorithmic approaches and emerging learning-based methods in MAPF research. We present a unified framework that encompasses search-based methods (including Conflict-Based Search, Priority-Based Search, and Large Neighborhood Search), compilation-based approaches (SAT, SMT, CSP, ASP, and MIP formulations), and data-driven techniques (reinforcement learning, supervised learning, and hybrid strategies). Through systematic analysis of experimental practices across 200+ papers, we uncover significant disparities in evaluation methodologies, with classical methods typically tested on larger-scale instances (up to 200 by 200 grids with 1000+ agents) compared to learning-based approaches (predominantly 10-100 agents). We provide a comprehensive taxonomy of evaluation metrics, environment types, and baseline selections, highlighting the need for standardized benchmarking protocols. Finally, we outline promising future directions including mixed-motive MAPF with game-theoretic considerations, language-grounded planning with large language models, and neural solver architectures that combine the rigor of classical methods with the flexibility of deep learning. This survey serves as both a comprehensive reference for researchers and a practical guide for deploying MAPF solutions in increasingly complex real-world applications.

Structured latent variables allow incorporating meaningful prior knowledge into deep learning models. However, learning with such variables remains challenging because of their discrete nature. Nowadays, the standard learning approach is to define a latent variable as a perturbed algorithm output and to use a differentiable surrogate for training. In general, the surrogate puts additional constraints on the model and inevitably leads to biased gradients. To alleviate these shortcomings, we extend the Gumbel-Max trick to define distributions over structured domains.