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.

Model-based reinforcement learning (RL) methods that leverage search are responsible for many milestone breakthroughs in RL. Sequential Monte Carlo (SMC) recently emerged as an alternative to the Monte Carlo Tree Search (MCTS) algorithm which drove these breakthroughs. SMC is easier to parallelize and more suitable to GPU acceleration. However, it also suffers from large variance and path degeneracy which prevent it from scaling well with increased search depth, i.e., increased sequential compute. To address these problems, we introduce Twice Sequential Monte Carlo Tree Search (TSMCTS). Across discrete and continuous environments TSMCTS outperforms the SMC baseline as well as a popular modern version of MCTS. Through variance reduction and mitigation of path degeneracy, TSMCTS scales favorably with sequential compute while retaining the properties that make SMC natural to parallelize.

This is the accepted author's version of the paper. The final published version is available in the 2015 IEEE 39th Annual Com puter Software and Applications Conference, vol. Abstract -- This paper presents a strategy to allocate services on a Cloud system without overloading nodes and maintaining the system stability with minimum cost. We specify an abstract model of cloud resources utilization, including multiple types of resources as well as consideration s for the service migration costs. A prototype meta - heuristic load balancer is demonstrated and experiment al results are presented and discussed. We also propose a novel genetic algorithm, wher e population is seeded with the outputs of other meta - heuristic algorithms. Modern day applications are often designed in such a way that they can simultaneously use resources from different computer environments. System components are not just properties of individual machines and in many respects they can be viewed as though the y are deployed in a single application environment. Distributed computing differs from traditional computing in many ways.

Retrosynthesis planning aims to decompose target molecules into available building blocks, forming a synthetic tree where each internal node represents an intermediate compound and each leaf ideally corresponds to a purchasable reactant. However, this tree becomes invalid if any leaf node is not a valid building block, making the planning process vulnerable to the "weakest link" in the synthetic route. Existing methods often optimise for average performance across branches, failing to account for this worst-case sensitivity. In this paper, we reframe retrosynthesis as a worst-path optimisation problem within tree-structured Markov Decision Processes (MDPs). We prove that this formulation admits a unique optimal solution and provides monotonic improvement guarantees. Building on this insight, we introduce Interactive Retrosynthesis Planning (InterRetro), a method that interacts with the tree MDP, learns a value function for worst-path outcomes, and improves its policy through self-imitation, preferentially reinforcing past decisions with high estimated advantage. Empirically, InterRetro achieves state-of-the-art results - solving 100% of targets on the Retro*-190 benchmark, shortening synthetic routes by 4.9%, and achieving promising performance using only 10% of the training data.

Originality: The method is relatively new although it is similar to some conditional GAN works in the literature. The main idea is the analysis showing the limitations of prior GAN+SSL work and in proposing a scheme with better chances of succeeding (at least theoretically). Then experiments show that there is an improvement. It would be good to show more the analogies to prior conditional GAN work, and this would not hurt the contribution, rather it would better clarify its context and provide more links to practitioners (who could better understand it). Basically, the minimax game should use the same cost function for the optimization of the discriminator, the generator and the classifier.

NeurIPS 2019 Sun Dec 8th through Sat the 14th, 2019 at Vancouver Convention Center "7259" "Self-supervised GAN: Analysis and Improvement with Multi-class Minimax Game" The paper addresses a problem in self supervised GAN, where the classes strictly have disjoint support. This is mitigated by introducing a new class for generated samples.