Autonomous navigation in mobile robots, reliant on perception and planning, faces major hurdles in large-scale, complex environments. These include heavy computational burdens for mapping, sensor occlusion failures for UAVs, and traversal challenges on irregular terrain for UGVs, all compounded by a lack of perception-aware strategies. To address these challenges, we introduce Random Mapping and Random Projection (RMRP). This method constructs a lightweight linear parametric map by first mapping data to a high-dimensional space, followed by a sparse random projection for dimensionality reduction. Our novel Residual Energy Preservation Theorem provides theoretical guarantees for this process, ensuring critical geometric properties are preserved. Based on this map, we propose the RPATR (Robust Perception-Aware Trajectory Planner) framework. For UAVs, our method unifies grid and Euclidean Signed Distance Field (ESDF) maps. The front-end uses an analytical occupancy gradient to refine initial paths for safety and smoothness, while the back-end uses a closed-form ESDF for trajectory optimization. Leveraging the trained RMRP model's generalization, the planner predicts unobserved areas for proactive navigation. For UGVs, the model characterizes terrain and provides closed-form gradients, enabling online planning to circumvent large holes. Validated in diverse scenarios, our framework demonstrates superior mapping performance in time, memory, and accuracy, and enables computationally efficient, safe navigation for high-speed UAVs and UGVs. The code will be released to foster community collaboration.

Mixed-precision quantization (MPQ) is crucial for deploying deep neural networks on resource-constrained devices, but finding the optimal bit-width for each layer represents a complex combinatorial optimization problem. Current state-of-the-art methods rely on computationally expensive search algorithms or local sensitivity heuristic proxies like the Hessian, which fail to capture the cascading global effects of quantization error. In this work, we argue that the quantization sensitivity of a layer should not be measured by its local properties, but by its impact on the information flow throughout the entire network. We introduce InfoQ, a novel framework for MPQ that is training-free in the bit-width search phase. InfoQ assesses layer sensitivity by quantizing each layer at different bit-widths and measuring, through a single forward pass, the resulting change in mutual information in the subsequent layers. This quantifies how much each layer quantization impacts the network information flow. The resulting scores are used to formulate bit-width allocation as an integer linear programming problem, which is solved efficiently to minimize total sensitivity under a given budget (e.g., model size or BitOps). Our retraining-free search phase provides a superior search-time/accuracy trade-off (using two orders of magnitude less data compared to state-of-the-art methods such as LIMPQ), while yielding up to a 1% accuracy improvement for MobileNetV2 and ResNet18 on ImageNet at high compression rates (14X and 10.66X).

We propose a generative, end-to-end solver for black-box combinatorial optimization that emphasizes both sample efficiency and solution quality on NP problems. Drawing inspiration from annealing-based algorithms, we treat the black-box objective as an energy function and train a neural network to model the associated Boltzmann distribution. By conditioning on temperature, the network captures a continuum of distributions--from near-uniform at high temperatures to sharply peaked around global optima at low temperatures--thereby learning the structure of the energy landscape and facilitating global optimization. When queries are expensive, the temperature-dependent distributions naturally enable data augmentation and improve sample efficiency. When queries are cheap but the problem remains hard, the model learns implicit variable interactions, effectively "opening" the black box. We validate our approach on challenging combinatorial tasks under both limited and unlimited query budgets, showing competitive performance against state-of-the-art black-box optimizers.

The performance of Bayesian optimization (BO), a highly sample-efficient method for expensive black-box problems, is critically governed by the selection of its hyperparameters, including the kernel and acquisition functions. This presents a challenge: an inappropriate combination of these can lead to poor performance and wasted evaluations. While individual improvements to kernel functions (e.g., tree-based kernels, deep kernel learning) and acquisition functions (e.g., multi-step lookahead, tree-based planning) have been explored, the joint and autonomous selection of the best pair of these fundamental hyperparameters has been overlooked. This forces practitioners to rely on heuristics or costly manual training. We propose a simple yet effective framework, BOOST (Bayesian Optimization with Optimal Kernel and Acquisition Function Selection Technique), that automates this selection. BOOST utilizes a lightweight, offline evaluation stage to predict the performance of various kernel-acquisition function pairs and identify the most suitable configuration before expensive evaluations. BOOST partitions data-in-hand into two subsets: a reference subset and a query subset, and it prepares all possible kernel-acquisition pairs from the user's chosen candidates. For each configuration, BOOST conducts internal BO runs using the reference subset, evaluating how effectively each pair guides the search toward the optimum in the unknown query subset, thereby identifying the configuration with the best retrospective performance for future optimization. Experiments on both synthetic benchmark functions and real-world hyperparameter optimization tasks demonstrate that BOOST consistently outperforms standard BO approaches with fixed hyperparameters, highlighting its effectiveness and robustness in diverse problem landscapes.

The Elementary Shortest-Path Problem(ESPP) seeks a minimum cost path from s to t that visits each vertex at most once. The presence of negative-cost cycles renders the problem NP-hard. We present a probabilistic method for finding near-optimal ESPP, enabled by an unsupervised graph neural network that jointly learns node value estimates and edge-selection probabilities via a surrogate loss function. The loss provides a high probability certificate of finding near-optimal ESPP solutions by simultaneously reducing negative-cost cycles and embedding the desired algorithmic alignment. At inference time, a decoding algorithm transforms the learned edge probabilities into an elementary path. Experiments on graphs of up to 100 nodes show that the proposed method surpasses both unsupervised baselines and classical heuristics, while exhibiting high performance in cross-size and cross-topology generalization on unseen synthetic graphs.

Randomized methods such as PRM and RRT are widely used in motion planning. However, in some cases, their running-time suffers from inherent instability, leading to ``catastrophic'' performance even for relatively simple instances. We apply stochastic restart techniques, some of them new, for speeding up Las Vegas algorithms, that provide dramatic speedups in practice (a factor of $3$ [or larger] in many cases). Our experiments demonstrate that the new algorithms have faster runtimes, shorter paths, and greater gains from multi-threading (when compared with straightforward parallel implementation). We prove the optimality of the new variants. Our implementation is open source, available on github, and is easy to deploy and use.

AI-based computer-aided synthesis planning (CASP) systems are in demand as components of AI-driven drug discovery workflows. However, the high latency of such CASP systems limits their utility for high-throughput synthesizability screening in de novo drug design. We propose a method for accelerating multi-step synthesis planning systems that rely on SMILES-to-SMILES transformers as single-step retrosynthesis models. Our approach reduces the latency of SMILES-to-SMILES transformers powering multi-step synthesis planning in AiZynthFinder through speculative beam search combined with a scalable drafting strategy called Medusa. Replacing standard beam search with our approach allows the CASP system to solve 26\% to 86\% more molecules under the same time constraints of several seconds. Our method brings AI-based CASP systems closer to meeting the strict latency requirements of high-throughput synthesizability screening and improving general user experience.

Neural Combinatorial Optimization aims to learn to solve a class of combinatorial problems through data-driven methods and notably through employing neural networks by learning the underlying distribution of problem instances. While, so far neural methods struggle to outperform highly engineered problem specific meta-heuristics, this work explores a novel approach to formulate the distribution of problem instances to learn from and, more importantly, plant a structure in the sampled problem instances. In application to routing problems, we generate large problem instances that represent custom base problem instance distributions from which training instances are sampled. The test instances to evaluate the methods on the routing task consist of unseen problems sampled from the underlying large problem instance. We evaluate representative NCO methods and specialized Operation Research meta heuristics on this novel task and demonstrate that the performance gap between neural routing solvers and highly specialized meta-heuristics decreases when learning from sub-samples drawn from a fixed base node distribution.

Diffusion models have demonstrated remarkable success in generative tasks, including audio super-resolution (SR). In many applications like movie post-production and album mastering, substantial computational budgets are available for achieving superior audio quality. However, while existing diffusion approaches typically increase sampling steps to improve quality, the performance remains fundamentally limited by the stochastic nature of the sampling process, leading to high-variance and quality-limited outputs. Here, rather than simply increasing the number of sampling steps, we propose a different paradigm through inference-time scaling for SR, which explores multiple solution trajectories during the sampling process. Different task-specific verifiers are developed, and two search algorithms, including the random search and zero-order search for SR, are introduced. By actively guiding the exploration of the high-dimensional solution space through verifier-algorithm combinations, we enable more robust and higher-quality outputs. Through extensive validation across diverse audio domains (speech, music, sound effects) and frequency ranges, we demonstrate consistent performance gains, achieving improvements of up to 9.70% in aesthetics, 5.88% in speaker similarity, 15.20% in word error rate, and 46.98% in spectral distance for speech SR from 4kHz to 24kHz, showcasing the effectiveness of our approach. Audio samples are available at: https://racerk.github.io/tt-scale-audiosr/.

Shortest path search is a core operation in graph-based applications, yet existing methods face important limitations. Classical algorithms such as Dijkstra's and A* become inefficient as graphs grow more complex, while index-based techniques often require substantial preprocessing and storage. Recent learning-based approaches typically focus on spatial graphs and rely on context-specific features like geographic coordinates, limiting their general applicability. We propose a versatile learning-based framework for shortest path search on generic graphs, without requiring domain-specific features. At the core of our approach is the construction of a skeleton graph that captures multi-level distance and hop information in a compact form. A Skeleton Graph Neural Network (SGNN) operates on this structure to learn node embeddings and predict distances and hop lengths between node pairs. These predictions support LSearch, a guided search algorithm that uses model-driven pruning to reduce the search space while preserving accuracy. To handle larger graphs, we introduce a hierarchical training strategy that partitions the graph into subgraphs with individually trained SGNNs. This structure enables HLSearch, an extension of our method for efficient path search across graph partitions. Experiments on five diverse real-world graphs demonstrate that our framework achieves strong performance across graph types, offering a flexible and effective solution for learning-based shortest path search.