Dao Tran

Dao Tran, Duc Anh Le, Ngoc Luu et al.

Test-time scaling improves language model reasoning by spending additional compute to explore multiple solution trajectories. The key challenge is to maximize accuracy while minimizing the total number of generated tokens during reasoning. Recent PRM-guided methods score intermediate prefixes to steer this search, but most are frontier-only: they keep only the current active prefixes and irreversibly prune or resample away the rest using noisy PRM scores. This can cause premature commitment, diversity collapse, and the loss of prefixes that still admit correct continuations. We introduce stochastic backtracking over a persistent pool of historical prefixes, allowing test-time compute to revisit previously generated states instead of only expanding the current frontier. To make this efficient, we propose two complementary mechanisms. Subpool Selection strengthens greedy PRM-guided search by applying Top-N selection within random subpools, giving historical prefixes a chance to bypass over-scored frontier candidates. Power Backtrack Sequential Monte Carlo extends SMC-style resampling to the persistent pool using powered PRM scores and mixture-corrected weights. Across mathematical reasoning benchmarks and model scales, our methods consistently achieve higher accuracy per token count, and the same level of accuracy using only a fraction of the token count in comparison to strong PRM-guided baselines, demonstrating that persistent-pool stochastic backtracking provides a simple and effective way to improve the accuracy-token trade-off in test-time scaling.

Minh Hieu Ha, Khanh Ly Ta, Hung Phan et al.

Autonomous path planning requires a synergy between global reasoning and geometric precision, especially in complex or cluttered environments. While classical A* is valued for its optimality, it incurs prohibitive computational and memory costs in large-scale scenarios. Recent attempts to mitigate these limitations by using Large Language Models for waypoint guidance remain insufficient, as they rely only on text-based reasoning without spatial grounding. As a result, such models often produce incorrect waypoints in topologically complex environments with dead ends, and lack the perceptual capacity to interpret ambiguous physical boundaries. These inconsistencies lead to costly corrective expansions and undermine the intended computational efficiency. We introduce MMP-A*, a multimodal framework that integrates the spatial grounding capabilities of vision-language models with a novel adaptive decay mechanism. By anchoring high-level reasoning in physical geometry, the framework produces coherent waypoint guidance that addresses the limitations of text-only planners. The adaptive decay mechanism dynamically regulates the influence of uncertain waypoints within the heuristic, ensuring geometric validity while substantially reducing memory overhead. To evaluate robustness, we test the framework in challenging environments characterized by severe clutter and topological complexity. Experimental results show that MMP-A* achieves near-optimal trajectories with significantly reduced operational costs, demonstrating its potential as a perception-grounded and computationally efficient paradigm for autonomous navigation.

Minh Hieu Ha, Hung Phan, Tung Duy Doan et al.

Multi-objective combinatorial optimization problems (MOCOP) frequently arise in practical applications that require the simultaneous optimization of conflicting objectives. Although traditional evolutionary algorithms can be effective, they typically depend on domain knowledge and repeated parameter tuning, limiting flexibility when applied to unseen MOCOP instances. Recently, integration of Large Language Models (LLMs) into evolutionary computation has opened new avenues for automatic heuristic generation, using their advanced language understanding and code synthesis capabilities. Nevertheless, most existing approaches predominantly focus on single-objective tasks, often neglecting key considerations such as runtime efficiency and heuristic diversity in multi-objective settings. To bridge this gap, we introduce Multi-heuristics for MOCOP via Pareto-Grid-guided Evolution of LLMs (MPaGE), a novel enhancement of the Simple Evolutionary Multiobjective Optimization (SEMO) framework that leverages LLMs and Pareto Front Grid (PFG) technique. By partitioning the objective space into grids and retaining top-performing candidates to guide heuristic generation, MPaGE utilizes LLMs to prioritize heuristics with semantically distinct logical structures during variation, thus promoting diversity and mitigating redundancy within the population. Through extensive evaluations, MPaGE demonstrates superior performance over existing LLM-based frameworks, and achieves competitive results to traditional Multi-objective evolutionary algorithms (MOEAs), with significantly faster runtime. Our code is available at: https://github.com/langkhachhoha/MPaGE.