On the occasion of the 20th Mixed Integer Program Workshop's computational competition, this work introduces a new approach for learning to solve MIPs online. Influence branching, a new graph-oriented variable selection strategy, is applied throughout the first iterations of the branch and bound algorithm. This branching heuristic is optimized online with Thompson sampling, which ranks the best graph representations of MIP's structure according to computational speed up over SCIP. We achieve results comparable to state of the art online learning methods. Moreover, our results indicate that our method generalizes well to more general online frameworks, where variations in constraint matrix, constraint vector and objective coefficients can all occur and where more samples are available.

Approximate Nearest Neighbour (ANN) search is a fundamental problem in information retrieval, underpinning large-scale applications in computer vision, natural language processing, and cross-modal search. Hashing-based methods provide an efficient solution by mapping high-dimensional data into compact binary codes that enable fast similarity computations in Hamming space. Over the past two decades, a substantial body of work has explored learning to hash, where projection and quantisation functions are optimised from data rather than chosen at random. This article offers a foundational survey of early learning-based hashing methods, with an emphasis on the core ideas that shaped the field. We review supervised, unsupervised, and semi-supervised approaches, highlighting how projection functions are designed to generate meaningful embeddings and how quantisation strategies convert these embeddings into binary codes. We also examine extensions to multi-bit and multi-threshold models, as well as early advances in cross-modal retrieval. Rather than providing an exhaustive account of the most recent methods, our goal is to introduce the conceptual foundations of learning-based hashing for ANN search. By situating these early models in their historical context, we aim to equip readers with a structured understanding of the principles, trade-offs, and open challenges that continue to inform current research in this area.

Off-road environments present unique challenges for autonomous navigation due to their complex and unstructured nature. Traditional global path-planning methods, which typically aim to minimize path length and travel time, perform poorly on large-scale maps and fail to account for critical factors such as real-time performance, kinematic feasibility, and memory efficiency. This paper introduces a novel global path-planning method specifically designed for off-road environments, addressing these essential factors. The method begins by constructing an intermediate map within the pixel coordinate system, incorporating geographical features like off-road trails, waterways, restricted and passable areas, and trees. The planning problem is then divided into three sub-problems: graph-based path planning, kinematic feasibility checking, and path smoothing. This approach effectively meets real-time performance requirements while ensuring kinematic feasibility and efficient memory use. The method was tested in various off-road environments with large-scale maps up to several square kilometers in size, successfully identifying feasible paths in an average of 1.5 seconds and utilizing approximately 1.5GB of memory under extreme conditions. The proposed framework is versatile and applicable to a wide range of off-road autonomous navigation tasks, including search and rescue missions and agricultural operations.

Tree search has become as a representative framework for test-time reasoning with large language models (LLMs), exemplified by methods such as Tree-of-Thought and Monte Carlo Tree Search that explore multiple reasoning paths. However, it remains difficult to provide instant and reliable quantitative assessments of intermediate reasoning step quality, and extensive path exploration is computationally costly. To address this, we propose Mutual Information Tree Search (MITS), a novel framework that guides reasoning with information-theoretic principles. MITS introduces an effective scoring function based on pointwise mutual information (PMI), which enables step-wise evaluation of reasoning paths and search tree expansion via beam search without expensive look-ahead simulations, achieving superior reasoning performances while maintaining computational efficiency. The framework is complemented by an entropy-based dynamic sampling strategy that adaptively allocates computational resources to uncertain reasoning steps where exploration is most beneficial. For final prediction, MITS employs a weighted voting scheme that combines PMI scores with prediction consensus. Complex multi-step reasoning remains a fundamental challenge for Large Language Models (LLMs), particularly in tasks that require logical deduction, mathematical computation, or systematic problem-solving (Y ang et al., 2025a; Zhu et al., 2024; Yi et al., 2024). While Chain-of-Thought (CoT) prompting (Wei et al., 2022; Kojima et al., 2022) has emerged as a powerful technique to enhance reasoning by decomposing problems into intermediate steps, it typically generates a single reasoning path, which may lead to incorrect solutions due to error accumulation or the selection of suboptimal reasoning strategies. This limitation becomes particularly pronounced in complex reasoning tasks where multiple valid approaches exist, but only specific paths lead to correct answers.

We introduce CSAR, an algorithm for inducing morphemes from emergent language corpora of parallel utterances and meanings. It is a greedy algorithm that (1) weights morphemes based on mutual information between forms and meanings, (2) selects the highest-weighted pair, (3) removes it from the corpus, and (4) repeats the process to induce further morphemes (i.e., Count, Select, Ablate, Repeat). The effectiveness of CSAR is first validated on procedurally generated datasets and compared against baselines for related tasks. Second, we validate CSAR's performance on human language data to show that the algorithm makes reasonable predictions in adjacent domains. Finally, we analyze a handful of emergent languages, quantifying linguistic characteristics like degree of synonymy and polysemy.

The scarcity of non-renewable energy sources, geopolitical problems in its supply, increasing prices, and the impact of climate change, force the global economy to develop more energy-efficient solutions for their operations. The Manufacturing sector is not excluded from this challenge as one of the largest consumers of energy. Energy-efficient scheduling is a method that attracts manufacturing companies to reduce their consumption as it can be quickly deployed and can show impact immediately. In this study, the hybrid flow shop scheduling problem with blocking constraint (BHFS) is investigated in which we seek to minimize the latest completion time (i.e. makespan) and overall energy consumption, a typical manufacturing setting across many industries from automotive to pharmaceutical. Energy consumption and the latest completion time of customer orders are usually conflicting objectives. Therefore, we first formulate the problem as a novel multi-objective mixed integer programming (MIP) model and propose an augmented epsilon-constraint method for finding the Pareto-optimal solutions. Also, an effective multi-objective metaheuristic algorithm. Refined Iterated Pareto Greedy (RIPG), is developed to solve large instances in reasonable time. Our proposed methods are benchmarked using small, medium, and large-size instances to evaluate their efficiency. Two well-known algorithms are adopted for comparing our novel approaches. The computational results show the effectiveness of our method.

Approximate Nearest Neighbor Search (ANNS), as the core of vector databases (VectorDBs), has become widely used in modern AI and ML systems, powering applications from information retrieval to bio-informatics. While graph-based ANNS methods achieve high query efficiency, their scalability is constrained by the available host memory. Recent disk-based ANNS approaches mitigate memory usage by offloading data to Solid-State Drives (SSDs). However, they still suffer from issues such as long I/O traversal path, misalignment with storage I/O granularity, and high in-memory indexing overhead, leading to significant I/O latency and ultimately limiting scalability for large-scale vector search. In this paper, we propose PageANN, a disk-based approximate nearest neighbor search (ANNS) framework designed for high performance and scalability. PageANN introduces a page-node graph structure that aligns logical graph nodes with physical SSD pages, thereby shortening I/O traversal paths and reducing I/O operations. Specifically, similar vectors are clustered into page nodes, and a co-designed disk data layout leverages this structure with a merging technique to store only representative vectors and topology information, avoiding unnecessary reads. To further improve efficiency, we design a memory management strategy that combines lightweight indexing with coordinated memory-disk data allocation, maximizing host memory utilization while minimizing query latency and storage overhead. Experimental results show that PageANN significantly outperforms state-of-the-art (SOTA) disk-based ANNS methods, achieving 1.85x-10.83x higher throughput and 51.7%-91.9% lower latency across different datasets and memory budgets, while maintaining comparable high recall accuracy.

Quadrotors hold significant promise for several applications such as agriculture, search and rescue, and infrastructure inspection. Achieving autonomous operation requires systems to navigate safely through complex and unfamiliar environments. This level of autonomy is particularly challenging due to the complexity of such environments and the need for real-time decision making especially for platforms constrained by size, weight, and power (SWaP), which limits flight time and precludes the use of bulky sensors like Light Detection and Ranging (LiDAR) for mapping. Furthermore, computing globally optimal, collision-free paths and translating them into time-optimized, safe trajectories in real time adds significant computational complexity. To address these challenges, we present a fully onboard, real-time navigation system that relies solely on lightweight onboard sensors. Our system constructs a dense 3D map of the environment using a novel visual depth estimation approach that fuses stereo and monocular learning-based depth, yielding longer-range, denser, and less noisy depth maps than conventional stereo methods. Building on this map, we introduce a novel planning and trajectory generation framework capable of rapidly computing time-optimal global trajectories. As the map is incrementally updated with new depth information, our system continuously refines the trajectory to maintain safety and optimality. Both our planner and trajectory generator outperforms state-of-the-art methods in terms of computational efficiency and guarantee obstacle-free trajectories. We validate our system through robust autonomous flight experiments in diverse indoor and outdoor environments, demonstrating its effectiveness for safe navigation in previously unknown settings.

LLM inference often generates a batch of candidates for a prompt and selects one via strategies like majority voting or Best-of- N (BoN). For difficult tasks, this single-shot selection often underperforms. Consequently, evaluations commonly report Pass@$k$: the agent may submit up to $k$ responses, and only the best of them is used when computing regret. Motivated by this, we study inference scaling in the more general Pass@$k$ inference setting, and prove that neither majority voting nor BoN exhibits the desirable scaling with $k$ and the sampling budget $N$. Combining the advantages of majority voting and BoN, we propose a new inference strategy called Best-of-Majority (BoM), with a pivotal step that restricts the candidates to the responses with high frequency in the $N$ samples before selecting the top-$k$ rewards. We prove that when the sampling budget is $N=\tildeΩ(C^*)$, the regret of BoM is $O(ε_{\mathrm{opt}}+\sqrt{ε_{\mathrm{RM}}^2C^*/k})$, where $C^*$ is the coverage coefficient, $ε_{\mathrm{RM}}$ is the estimation error of the reward model, and $ε_{\mathrm{opt}}$ is the estimation error of reward at the optimal response. We further establish a matching lower bound, certifying that our algorithm is minimax optimal. Beyond optimality, BoM has a key advantage: unlike majority voting and BoN, its performance does not degrade when increasing $N$. Experimental results of inference on math problems show BoM outperforming both majority voting and BoN.

Hyperparameters greatly impact models' capabilities; however, modern models are too large for extensive search. Instead, researchers design recipes that train well across scales based on their understanding of the hyperparameters. Despite this importance, few tools exist for understanding the hyperparameter loss surface. We discover novel structure in it and propose a new theory yielding such tools. The loss surface is complex, but as you approach the optimum simple structure emerges. It becomes characterized by a few basic features, like its effective dimension and the best possible loss. To uncover this asymptotic regime, we develop a novel technique based on random search. Within this regime, the best scores from random search take on a new distribution we discover. Its parameters are exactly the features defining the loss surface in the asymptotic regime. From these features, we derive a new asymptotic law for random search that can explain and extrapolate its convergence. These new tools enable new analyses, such as confidence intervals for the best possible performance or determining the effective number of hyperparameters. We make these tools available at https://github.com/nicholaslourie/opda .