Cone Beam Computed Tomography (CBCT) is widely used in medical imaging. However, the limited number and intensity of X-ray projections make reconstruction an ill-posed problem with severe artifacts. NeRF-based methods have achieved great success in this task. However, they suffer from a local-global training mismatch between their two key components: the hash encoder and the neural network. Specifically, in each training step, only a subset of the hash encoder's parameters is used (local sparse), whereas all parameters in the neural network participate (global dense). Consequently, hash features generated in each step are highly misaligned, as they come from different subsets of the hash encoder. These misalignments from different training steps are then fed into the neural network, causing repeated inconsistent global updates in training, which leads to unstable training, slower convergence, and degraded reconstruction quality. Aiming to alleviate the impact of this local-global optimization mismatch, we introduce a Normalized Hash Encoder, which enhances feature consistency and mitigates the mismatch. Additionally, we propose a Mapping Consistency Initialization(MCI) strategy that initializes the neural network before training by leveraging the global mapping property from a well-trained model. The initialized neural network exhibits improved stability during early training, enabling faster convergence and enhanced reconstruction performance. Our method is simple yet effective, requiring only a few lines of code while substantially improving training efficiency on 128 CT cases collected from 4 different datasets, covering 7 distinct anatomical regions.
GA LLM is a hybrid framework that combines Genetic Algorithms with Large Language Models to handle structured generation tasks under strict constraints. Each output, such as a plan or report, is treated as a gene, and evolutionary operations like selection, crossover, and mutation are guided by the language model to iteratively improve solutions. The language model provides domain knowledge and creative variation, while the genetic algorithm ensures structural integrity and global optimization. GA LLM has proven effective in tasks such as itinerary planning, academic outlining, and business reporting, consistently producing well structured and requirement satisfying results. Its modular design also makes it easy to adapt to new tasks. Compared to using a language model alone, GA LLM achieves better constraint satisfaction and higher quality solutions by combining the strengths of both components.
Large Language Models (LLMs) have recently emerged as effective surrogate models and candidate generators within global optimization frameworks for expensive blackbox functions. Despite promising results, LLM-based methods often struggle in high-dimensional search spaces or when lacking domain-specific priors, leading to sparse or uninformative suggestions. To overcome these limitations, we propose HOLLM, a novel global optimization algorithm that enhances LLM-driven sampling by partitioning the search space into promising subregions. Each subregion acts as a ``meta-arm'' selected via a bandit-inspired scoring mechanism that effectively balances exploration and exploitation. Within each selected subregion, an LLM then proposes high-quality candidate points, without any explicit domain knowledge. Empirical evaluation on standard optimization benchmarks shows that HOLLM consistently matches or surpasses leading Bayesian optimization and trust-region methods, while substantially outperforming global LLM-based sampling strategies.
Orienting point clouds is a fundamental problem in computer graphics and 3D vision, with applications in reconstruction, segmentation, and analysis. While significant progress has been made, existing approaches mainly focus on watertight, object-level 3D models. The orientation of large-scale, non-watertight 3D scenes remains an underexplored challenge. To address this gap, we propose DACPO (Divide-And-Conquer Point Orientation), a novel framework that leverages a divide-and-conquer strategy for scalable and robust point cloud orientation. Rather than attempting to orient an unbounded scene at once, DACPO segments the input point cloud into smaller, manageable blocks, processes each block independently, and integrates the results through a global optimization stage. For each block, we introduce a two-step process: estimating initial normal orientations by a randomized greedy method and refining them by an adapted iterative Poisson surface reconstruction. To achieve consistency across blocks, we model inter-block relationships using an an undirected graph, where nodes represent blocks and edges connect spatially adjacent blocks. To reliably evaluate orientation consistency between adjacent blocks, we introduce the concept of the visible connected region, which defines the region over which visibility-based assessments are performed. The global integration is then formulated as a 0-1 integer-constrained optimization problem, with block flip states as binary variables. Despite the combinatorial nature of the problem, DACPO remains scalable by limiting the number of blocks (typically a few hundred for 3D scenes) involved in the optimization. Experiments on benchmark datasets demonstrate DACPO's strong performance, particularly in challenging large-scale, non-watertight scenarios where existing methods often fail. The source code is available at https://github.com/zd-lee/DACPO.
Designing free-form photonic devices is fundamentally challenging due to the vast number of possible geometries and the complex requirements of fabrication constraints. Traditional inverse-design approaches--whether driven by human intuition, global optimization, or adjoint-based gradient methods--often involve intricate binarization and filtering steps, while recent deep learning strategies demand prohibitively large numbers of simulations (10^5 to 10^6). To overcome these limitations, we present AdjointDiffusion, a physics-guided framework that integrates adjoint sensitivity gradients into the sampling process of diffusion models. AdjointDiffusion begins by training a diffusion network on a synthetic, fabrication-aware dataset of binary masks. During inference, we compute the adjoint gradient of a candidate structure and inject this physics-based guidance at each denoising step, steering the generative process toward high figure-of-merit (FoM) solutions without additional post-processing. We demonstrate our method on two canonical photonic design problems--a bent waveguide and a CMOS image sensor color router--and show that our method consistently outperforms state-of-the-art nonlinear optimizers (such as MMA and SLSQP) in both efficiency and manufacturability, while using orders of magnitude fewer simulations (approximately 2 x 10^2) than pure deep learning approaches (approximately 10^5 to 10^6). By eliminating complex binarization schedules and minimizing simulation overhead, AdjointDiffusion offers a streamlined, simulation-efficient, and fabrication-aware pipeline for next-generation photonic device design. Our open-source implementation is available at https://github.com/dongjin-seo2020/AdjointDiffusion.
Previous text-to-image diffusion models typically employ supervised fine-tuning (SFT) to enhance pre-trained base models. However, this approach primarily minimizes the loss of mean squared error (MSE) at the pixel level, neglecting the need for global optimization at the image level, which is crucial for achieving high perceptual quality and structural coherence. In this paper, we introduce Self-sUpervised Direct preference Optimization (SUDO), a novel paradigm that optimizes both fine-grained details at the pixel level and global image quality. By integrating direct preference optimization into the model, SUDO generates preference image pairs in a self-supervised manner, enabling the model to prioritize global-level learning while complementing the pixel-level MSE loss. As an effective alternative to supervised fine-tuning, SUDO can be seamlessly applied to any text-to-image diffusion model. Importantly, it eliminates the need for costly data collection and annotation efforts typically associated with traditional direct preference optimization methods. Through extensive experiments on widely-used models, including Stable Diffusion 1.5 and XL, we demonstrate that SUDO significantly enhances both global and local image quality. The codes are provided at \href{https://github.com/SPengLiang/SUDO}{this link}.
To address the challenges of limited Battery Swap Stations datasets, high operational costs, and fluctuating user charging demand, this research proposes a probability estimation model based on charging pile data and constructs nine scenario-specific battery swap demand datasets. In addition, this study combines Least Recently Used strategy with Genetic Algorithm and incorporates a guided search mechanism, which effectively enhances the global optimization capability. Thus, a dual-factor decision-making based charging schedule optimization system is constructed. Experimental results show that the constructed datasets exhibit stable trend characteristics, adhering to 24-hour and 168-hour periodicity patterns, with outlier ratios consistently below 3.26%, confirming data validity. Compared to baseline, the improved algorithm achieves better fitness individuals in 80% of test regions under the same iterations. When benchmarked against immediate swap-and-charge strategy, our algorithm achieves a peak cost reduction of 13.96%. Moreover, peak user satisfaction reaches 98.57%, while the average iteration time remains below 0.6 seconds, demonstrating good computational efficiency. The complete datasets and optimization algorithm are open-sourced at https://github.com/qingshufan/GA-EVLRU.
In recent years, there has been a growing interest in data-driven evolutionary algorithms (DDEAs) employing surrogate models to approximate the objective functions with limited data. However, current DDEAs are primarily designed for lower-dimensional problems and their performance drops significantly when applied to large-scale optimization problems (LSOPs). To address the challenge, this paper proposes an offline DDEA named DSKT-DDEA. DSKT-DDEA leverages multiple islands that utilize different data to establish diverse surrogate models, fostering diverse subpopulations and mitigating the risk of premature convergence. In the intra-island optimization phase, a semi-supervised learning method is devised to fine-tune the surrogates. It not only facilitates data argumentation, but also incorporates the distribution information gathered during the search process to align the surrogates with the evolving local landscapes. Then, in the inter-island knowledge transfer phase, the algorithm incorporates an adaptive strategy that periodically transfers individual information and evaluates the transfer effectiveness in the new environment, facilitating global optimization efficacy. Experimental results demonstrate that our algorithm is competitive with state-of-the-art DDEAs on problems with up to 1000 dimensions, while also exhibiting decent parallelism and scalability. Our DSKT-DDEA is open-source and accessible at: https://github.com/LabGong/DSKT-DDEA.
The indicator matrix plays an important role in machine learning, but optimizing it is an NP-hard problem. We propose a new relaxation of the indicator matrix and prove that this relaxation forms a manifold, which we call the Relaxed Indicator Matrix Manifold (RIM manifold). Based on Riemannian geometry, we develop a Riemannian toolbox for optimization on the RIM manifold. Specifically, we provide several methods of Retraction, including a fast Retraction method to obtain geodesics. We point out that the RIM manifold is a generalization of the double stochastic manifold, and it is much faster than existing methods on the double stochastic manifold, which has a complexity of \( \mathcal{O}(n^3) \), while RIM manifold optimization is \( \mathcal{O}(n) \) and often yields better results. We conducted extensive experiments, including image denoising, with millions of variables to support our conclusion, and applied the RIM manifold to Ratio Cut, we provide a rigorous convergence proof and achieve clustering results that outperform the state-of-the-art methods. Our Code in \href{https://github.com/Yuan-Jinghui/Riemannian-Optimization-on-Relaxed-Indicator-Matrix-Manifold}{here}.
Federated Learning (FL) has emerged as a promising framework for distributed machine learning, enabling collaborative model training without sharing local data, thereby preserving privacy and enhancing security. However, data heterogeneity resulting from differences across user behaviors, preferences, and device characteristics poses a significant challenge for federated learning. Most previous works overlook the adjustment of aggregation weights, relying solely on dataset size for weight assignment, which often leads to unstable convergence and reduced model performance. Recently, several studies have sought to refine aggregation strategies by incorporating dataset characteristics and model alignment. However, adaptively adjusting aggregation weights while ensuring data security-without requiring additional proxy data-remains a significant challenge. In this work, we propose Federated learning with Adaptive Weight Aggregation (FedAWA), a novel method that adaptively adjusts aggregation weights based on client vectors during the learning process. The client vector captures the direction of model updates, reflecting local data variations, and is used to optimize the aggregation weight without requiring additional datasets or violating privacy. By assigning higher aggregation weights to local models whose updates align closely with the global optimization direction, FedAWA enhances the stability and generalization of the global model. Extensive experiments under diverse scenarios demonstrate the superiority of our method, providing a promising solution to the challenges of data heterogeneity in federated learning.
The hierarchical structure of 3D scene graphs shows a high relevance for representations purposes, as it fits common patterns from man-made environments. But, additionally, the semantic and geometric information in such hierarchical representations could be leveraged to speed up the optimization and management of map elements and robot poses. In this direction, we present our work Situational Graphs 2.0 (S-Graphs 2.0), which leverages the hierarchical structure of indoor scenes for efficient data management and optimization. Our algorithm begins by constructing a situational graph that represents the environment into four layers: Keyframes, Walls, Rooms, and Floors. Our first novelty lies in the front-end, which includes a floor detection module capable of identifying stairways and assigning floor-level semantic relations to the underlying layers. Floor-level semantics allows us to propose a floor-based loop closure strategy, that effectively rejects false positive closures that typically appear due to aliasing between different floors of a building. Our second novelty lies in leveraging our representation hierarchy in the optimization. Our proposal consists of: (1) local optimization over a window of recent keyframes and their connected components across the four representation layers, (2) floor-level global optimization, which focuses only on keyframes and their connections within the current floor during loop closures, and (3) room-level local optimization, marginalizing redundant keyframes that share observations within the room, which reduces the computational footprint. We validate our algorithm extensively in different real multi-floor environments. Our approach shows state-of-art-art accuracy metrics in large-scale multi-floor environments, estimating hierarchical representations up to 10x faster, in average, than competing baselines
Optimizing expensive, non-convex, black-box Lipschitz continuous functions presents significant challenges, particularly when the Lipschitz constant of the underlying function is unknown. Such problems often demand numerous function evaluations to approximate the global optimum, which can be prohibitive in terms of time, energy, or resources. In this work, we introduce Every Call is Precious (ECP), a novel global optimization algorithm that minimizes unpromising evaluations by strategically focusing on potentially optimal regions. Unlike previous approaches, ECP eliminates the need to estimate the Lipschitz constant, thereby avoiding additional function evaluations. ECP guarantees no-regret performance for infinite evaluation budgets and achieves minimax-optimal regret bounds within finite budgets. Extensive ablation studies validate the algorithm's robustness, while empirical evaluations show that ECP outperforms 10 benchmark algorithms including Lipschitz, Bayesian, bandits, and evolutionary methods across 30 multi-dimensional non-convex synthetic and real-world optimization problems, which positions ECP as a competitive approach for global optimization.
Typical LiDAR SLAM architectures feature a front-end for odometry estimation and a back-end for refining and optimizing the trajectory and map, commonly through loop closures. However, loop closure detection in large-scale missions presents significant computational challenges due to the need to identify, verify, and process numerous candidate pairs for pose graph optimization. Keyframe sampling bridges the front-end and back-end by selecting frames for storing and processing during global optimization. This article proposes an online keyframe sampling approach that constructs the pose graph using the most impactful keyframes for loop closure. We introduce the Minimal Subset Approach (MSA), which optimizes two key objectives: redundancy minimization and information preservation, implemented within a sliding window framework. By operating in the feature space rather than 3-D space, MSA efficiently reduces redundant keyframes while retaining essential information. In sum, evaluations on diverse public datasets show that the proposed approach outperforms naive methods in reducing false positive rates in place recognition, while delivering superior ATE and RPE in metric localization, without the need for manual parameter tuning. Additionally, MSA demonstrates efficiency and scalability by reducing memory usage and computational overhead during loop closure detection and pose graph optimization.
Graduated optimization is a global optimization technique that is used to minimize a multimodal nonconvex function by smoothing the objective function with noise and gradually refining the solution. This paper experimentally evaluates the performance of the explicit graduated optimization algorithm with an optimal noise scheduling derived from a previous study and discusses its limitations. It uses traditional benchmark functions and empirical loss functions for modern neural network architectures for evaluating. In addition, this paper extends the implicit graduated optimization algorithm, which is based on the fact that stochastic noise in the optimization process of SGD implicitly smooths the objective function, to SGD with momentum, analyzes its convergence, and demonstrates its effectiveness through experiments on image classification tasks with ResNet architectures.
We propose a novel method that solves global optimization problems in two steps: (1) perform a (exponential) power-$N$ transformation to the not-necessarily differentiable objective function $f$ and get $f_N$, and (2) optimize the Gaussian-smoothed $f_N$ with stochastic approximations. Under mild conditions on $f$, for any $\delta>0$, we prove that with a sufficiently large power $N_\delta$, this method converges to a solution in the $\delta$-neighborhood of $f$'s global optimum point. The convergence rate is $O(d^2\sigma^4\varepsilon^{-2})$, which is faster than both the standard and single-loop homotopy methods if $\sigma$ is pre-selected to be in $(0,1)$. In most of the experiments performed, our method produces better solutions than other algorithms that also apply smoothing techniques.
In modern deep neural networks, the learning dynamics of the individual neurons is often obscure, as the networks are trained via global optimization. Conversely, biological systems build on self-organized, local learning, achieving robustness and efficiency with limited global information. We here show how self-organization between individual artificial neurons can be achieved by designing abstract bio-inspired local learning goals. These goals are parameterized using a recent extension of information theory, Partial Information Decomposition (PID), which decomposes the information that a set of information sources holds about an outcome into unique, redundant and synergistic contributions. Our framework enables neurons to locally shape the integration of information from various input classes, i.e. feedforward, feedback, and lateral, by selecting which of the three inputs should contribute uniquely, redundantly or synergistically to the output. This selection is expressed as a weighted sum of PID terms, which, for a given problem, can be directly derived from intuitive reasoning or via numerical optimization, offering a window into understanding task-relevant local information processing. Achieving neuron-level interpretability while enabling strong performance using local learning, our work advances a principled information-theoretic foundation for local learning strategies.
Bayesian optimization devolves the global optimization of a costly objective function to the global optimization of a sequence of acquisition functions. This inner-loop optimization can be catastrophically difficult if it involves posterior sample paths, especially in higher dimensions. We introduce an efficient global optimization strategy for posterior samples based on global rootfinding. It provides gradient-based optimizers with two sets of judiciously selected starting points, designed to combine exploration and exploitation. The number of starting points can be kept small without sacrificing optimization quality. Remarkably, even with just one point from each set, the global optimum is discovered most of the time. The algorithm scales practically linearly to high dimensions, breaking the curse of dimensionality. For Gaussian process Thompson sampling (GP-TS), we demonstrate remarkable improvement in both inner- and outer-loop optimization, surprisingly outperforming alternatives like EI and GP-UCB in most cases. Our approach also improves the performance of other posterior sample-based acquisition functions, such as variants of entropy search. Furthermore, we propose a sample-average formulation of GP-TS, which has a parameter to explicitly control exploitation and can be computed at the cost of one posterior sample. Our implementation is available at https://github.com/UQUH/TSRoots .
Bayesian optimization (BO) is an attractive machine learning framework for performing sample-efficient global optimization of black-box functions. The optimization process is guided by an acquisition function that selects points to acquire in each round of BO. In batched BO, when multiple points are acquired in parallel, commonly used acquisition functions are often high-dimensional and intractable, leading to the use of sampling-based alternatives. We propose a statistical physics inspired acquisition function for BO with Gaussian processes that can natively handle batches. Batched Energy-Entropy acquisition for BO (BEEBO) enables tight control of the explore-exploit trade-off of the optimization process and generalizes to heteroskedastic black-box problems. We demonstrate the applicability of BEEBO on a range of problems, showing competitive performance to existing methods.
Surgical navigation based on multimodal image registration has played a significant role in providing intraoperative guidance to surgeons by showing the relative position of the target area to critical anatomical structures during surgery. However, due to the differences between multimodal images and intraoperative image deformation caused by tissue displacement and removal during surgery, effective registration of preoperative and intraoperative multimodal images faces significant challenges. To address the multimodal image registration challenges in Learn2Reg 2024, an unsupervised multimodal medical image registration method based on multilevel correlation balanced optimization (MCBO) is designed to solve these problems. First, the features of each modality are extracted based on the modality independent neighborhood descriptor, and the multimodal images are mapped to the feature space. Second, a multilevel pyramidal fusion optimization mechanism is designed to achieve global optimization and local detail complementation of the deformation field through dense correlation analysis and weight-balanced coupled convex optimization for input features at different scales. For preoperative medical images in different modalities, the alignment and stacking of valid information between different modalities is achieved by the maximum fusion between deformation fields. Our method focuses on the ReMIND2Reg task in Learn2Reg 2024, and to verify the generality of the method, we also tested it on the COMULIS3DCLEM task. Based on the results, our method achieved second place in the validation of both two tasks. The code is available at https://github.com/wjiazheng/MCBO.
Data augmentation has become an integral part of deep learning, as it is known to improve the generalization capabilities of neural networks. Since the most effective set of image transformations differs between tasks and domains, automatic data augmentation search aims to alleviate the extreme burden of manually finding the optimal image transformations. However, current methods are not able to jointly optimize all degrees of freedom: (1) the number of transformations to be applied, their (2) types, (3) order, and (4) magnitudes. Many existing methods risk picking the same transformation more than once, limit the search to two transformations only, or search for the number of transformations exhaustively or iteratively in a myopic manner. Our approach, FreeAugment, is the first to achieve global optimization of all four degrees of freedom simultaneously, using a fully differentiable method. It efficiently learns the number of transformations and a probability distribution over their permutations, inherently refraining from redundant repetition while sampling. Our experiments demonstrate that this joint learning of all degrees of freedom significantly improves performance, achieving state-of-the-art results on various natural image benchmarks and beyond across other domains. Project page at https://tombekor.github.io/FreeAugment-web