The iterative and stochastic nature of diffusion models enables test-time scaling, whereby spending additional compute during denoising generates higher-fidelity samples. Increasing the number of denoising steps is the primary scaling axis, but this yields quickly diminishing returns. Instead, optimizing the noise trajectory--the sequence of injected noise vectors--is promising, as the specific noise realizations critically affect sample quality; but this is challenging due to a high-dimensional search space, complex noise-outcome interactions, and costly trajectory evaluations. We address this by first casting diffusion as a Markov Decision Process (MDP) with a terminal reward, showing tree-search methods such as Monte Carlo tree search (MCTS) to be meaningful but impractical. To balance performance and efficiency, we then resort to a relaxation of MDP, where we view denoising as a sequence of independent contextual bandits. This allows us to introduce an ϵ-greedy search algorithm that globally explores at extreme timesteps and locally exploits during the intermediate steps where de-mixing occurs.

Neural Combinatorial Optimisation (NCO) is a promising learning-based approach for solving Vehicle Routing Problems (VRPs) without extensive manual design. While existing constructive NCO methods typically follow an appending-based paradigm that sequentially adds unvisited nodes to partial solutions, this rigid approach often leads to suboptimal results. To overcome this limitation, we explore the idea of the insertion-based paradigm and propose Learning to Construct with Insertion-based Paradigm (L2C-Insert), a novel learning-based method for constructive NCO. Unlike traditional approaches, L2C-Insert builds solutions by strategically inserting unvisited nodes at any valid position in the current partial solution, which can significantly enhance the flexibility and solution quality. The proposed framework introduces three key components: a novel model architecture for precise insertion position prediction, an efficient training scheme for model optimization, and an advanced inference technique that fully exploits the insertion paradigm's flexibility. Extensive experiments on both synthetic and real-world instances of the Travelling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) demonstrate that L2C-Insert consistently achieves superior performance across various problem sizes.

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.

In this paper, we propose a simple and efficient method for value model training on long-context reasoning traces. Compared to existing process reward models (PRMs), our method does not require a fine-grained notion of "step," which is difficult to define for long-context reasoning models. By collecting a dataset of 2.5 million reasoning traces, we train a 1.5B token-level value model and apply it to DeepSeek models for improved performance with test-time compute scaling. We find that block-wise value-guided search (VGS) with a final weighted majority vote achieves better test-time scaling than standard methods such as majority voting or best-of-n. Moreover, VGS significantly reduces the inference FLOPs required to achieve the same performance of majority voting.

Enhancing large language models by simply scaling up datasets has begun to yield diminishing returns, shifting the spotlight to data quality. Monte Carlo Tree Search (MCTS) has emerged as a powerful technique for generating high-quality chain-of-thought data, yet conventional approaches typically retain only the topscoring trajectory from the search tree, discarding sibling nodes that often contain valuable partial insights, recurrent error patterns, and alternative reasoning strategies. This unconditional rejection of non-optimal reasoning branches may waste vast amounts of informative data in the whole search tree. We propose SIGMA (Sibling Guided Monte Carlo Augmentation), a novel framework that reintegrates these discarded sibling nodes to refine LLM reasoning. SIGMA forges semantic links among sibling nodes along each search path and applies a two-stage refinement: a critique model identifies overlooked strengths and weaknesses across the sibling set, and a revision model conducts text-based backpropagation to refine the top-scoring trajectory in light of this comparative feedback. By recovering and amplifying the underutilized but valuable signals from non-optimal reasoning branches, SIGMA substantially improves reasoning trajectories. On the challenging MATH benchmark, our SIGMA-tuned 7B model achieves 54.92% accuracy using only 30K samples, outperforming state-of-the-art models trained on 590K samples. This result highlights that our sibling-guided optimization not only significantly reduces data usage but also significantly boosts LLM reasoning.

The rise of smart manufacturing under Industry 4.0 introduces mass customization and dynamic production, demanding more advanced and flexible scheduling techniques. The flexible job-shop scheduling problem (FJSP) has attracted significant attention due to its complex constraints and strong alignment with real-world production scenarios. Current deep reinforcement learning (DRL)-based approaches to FJSP predominantly employ constructive methods. While effective, they often fall short of reaching (near-)optimal solutions. In contrast, improvement-based methods iteratively explore the neighborhood of initial solutions and are more effective in approaching optimality.

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Neural Combinatorial Optimization (NCO) has emerged as a promising learningbased paradigm for addressing Vehicle Routing Problems (VRPs) by minimizing the need for extensive manual engineering. While existing NCO methods, trained on small-scale instances (e.g., 100 nodes), have demonstrated considerable success on problems of similar scale, their performance significantly degrades when applied to large-scale scenarios. This degradation arises from the distributional shift between training and testing data, rendering policies learned on small instances ineffective for larger problems. To overcome this limitation, we introduce a novel learning framework driven by Large Language Models (LLMs). This framework learns a projection between the training and testing distributions, which is then deployed to enhance the scalability of the NCO model. Notably, unlike prevailing techniques that necessitate joint training with the neural network, our approach operates exclusively during the inference phase, obviating the need for model retraining. Extensive experiments demonstrate that our method enables a backbone model (trained on 100-node instances) to achieve superior performance on large-scale Traveling Salesman Problems (TSPs) and Capacitated Vehicle Routing Problems (CVRPs) with up to 100K nodes from diverse distributions.

Training-free guidance enables controlled generation in diffusion and flow models, but most methods rely on gradients and assume differentiable objectives. This work focuses on training-free guidance addressing challenges from non-differentiable objectives and discrete data distributions. We propose TreeG: Tree Search-Based Path Steering Guidance, applicable to both continuous and discrete settings in diffusion and flow models. TreeG offers a unified framework for training-free guidance by proposing, evaluating, and selecting candidates at each step, enhanced with tree search over active paths and parallel exploration. We comprehensively investigate the design space of TreeG over the candidate proposal module and the evaluation function, instantiating TreeG into three novel algorithms. Our experiments show that TreeG consistently outperforms top guidance baselines in symbolic music generation, small molecule design, and enhancer DNA design with improvements of 29.01%,26.38%,and

The Time-Dependent Traveling Salesman Problem (TDTSP) extends the classical TSP by allowing dynamic edge weights that vary with departure time, reflecting real-world scenarios such as transportation networks, where travel times fluctuate due to congestion patterns. TDTSP violates symmetry, triangle inequality, and cyclic invariance properties of classical TSP, creating unique computational challenges. In this paper, we propose a neural model that extends MatNet from static asymmetric TSP to time-dependent settings by using an adjacency tensor to capture temporal variations, followed by a time-aware decoder. Our architecture addresses the unique challenge of asymmetry and triangle inequality violations that change dynamically over time. Beyond architectural innovations, our research reveals a critical evaluation insight: many practical TDTSP instances maintain the same optimal solution regardless of time-dependent edge weights.