Localization Methods

{Closed-loop inverse source localization and characterization (ISLC) requires a mobile agent to select measurements that localize sources and infer latent field parameters under strict time constraints.} {The core challenge lies in the belief-space objective: valid uncertainty estimation requires expensive Bayesian inference, whereas using fast learned belief model leads to reward hacking, in which the policy exploits approximation errors rather than actually reducing uncertainty.} {We propose \textbf{Distill-Belief}, a teacher--student framework that decouples correctness from efficiency. A Bayes-correct particle-filter teacher maintains the posterior and supplies a dense information-gain signal, while a compact student distills the posterior into belief statistics for control and an uncertainty certificate for stopping. At deployment, only the student is used, yielding constant per-step cost.} {Experiments on seven field modalities and two stress tests show that Distill-Belief consistently reduces sensing cost and improves success, posterior contraction, and estimation accuracy over baselines, while mitigating reward hacking.}

Graph-based representations such as Scene Graphs enable localization in structured indoor environments by matching a locally observed graph, constructed from sensor data, to a prior map. This process is particularly challenging in environments with repetitive or symmetric layouts, where structural cues alone are often insufficient to resolve ambiguities. We propose a semantic-enhanced graph matching approach that explicitly models relations between detected objects and structural elements, such as rooms and wall planes. Objects are detected from RGB-D data and integrated into the graph, and their relations to structural elements are exploited to filter candidate correspondences prior to geometric verification, significantly reducing ambiguity and search complexity. The proposed method is integrated within the iS-Graphs framework and evaluated in synthetic and simulated environments. Results show that semantic relations significantly reduce the number of candidate matches, improve computational efficiency, and enable faster convergence, particularly in symmetric scenarios where purely geometric approaches fail.

Architectural floor plans are widely available priors which contain not only geometry but also the semantic information of the environment, yet existing localization methods largely ignore this semantic information. To address this, we present COMPASS, an algorithm that exploits both geometric and semantic priors from floor plans to estimate the pose of a robot equipped with dual fisheye cameras. Inspired by scan context descriptor from LiDAR-based place recognition, we design a multi-channel radial descriptor that encodes the geometric layout surrounding a position. From the floor plan, rays are cast in 360 azimuth bins and the results are encoded into five channels: normalized range, structural hit type (wall, window, or opening), range gradient, inverse range, and local range variance. From the image side, the same descriptor structure is populated by detecting structural elements in the fisheye imagery. As a first step toward full cross-modal matching, we present a window detection algorithm for fisheye images that uses a line segment detector to identify window frames via vertical edge clustering and brightness verification. Detected windows are projected to azimuthal bearings through the fisheye camera model, producing the hit-type channel of the visual descriptor. As a proof of concept, we generate both descriptors at a single known pose from the Hilti-Trimble SLAM Challenge 2026 dataset and demonstrate that the wall-window pattern extracted from the first frame of each camera closely matches the floor plan descriptor, validating the feasibility of cross-modal structural matching.

Proactive watermarking offers a promising approach for deepfake tamper detection and localization in short-form videos. However, existing methods often decouple audio and visual evidence and assume that watermark signals remain reliable under real-world degradations, making tamper localization vulnerable to multimodal misalignment and compression distortions. Moreover, existing semi-fragile visual watermarking methods often degrade significantly under codec compression because their embedding bands overlap with compression-sensitive frequency regions. To address these limitations, we propose Layered Audio-Visual Anti-tampering Watermarking (LAVA), a calibration-aware audio-visual watermark fusion framework for deepfake tamper detection and localization. LAVA leverages cross-modal watermark fusion and calibration-aware alignment to preserve consistent and reliable tamper evidence under compression and audio-visual asynchrony, enabling robust tamper localization. Extensive experiments demonstrate that LAVA achieves near-perfect detection performance (AP = 0.999), remains robust to compression and multimodal misalignment, and significantly improves tamper localization reliability over existing audio-visual fusion baselines.

Wireless localization of permanent magnets enables occlusion-free guidance for medical interventions, yet its practical accuracy is fundamentally limited by two coupled challenges: the poor observability of conventional planar sensor arrays and the simulation-to-reality (Sim-to-Real) gap of learning-based estimators. To address these issues, this article presents a unified framework that combines information-theoretic sensor geometry optimization with physics-aware deep learning. First, a rigorous Fisher Information Matrix (FIM)-based evaluation framework is established to quantify geometry-induced observability limitations. The results show that a staggered split-array topology provides a substantially stronger observability foundation for localization while remaining compatible with practical external deployment. Second, building on this optimized sensing configuration, we propose Phy-GAANet, a calibration-free estimator trained entirely on hardware-aware synthetic data. By incorporating Physics-Informed Features (PIF) for saturation modeling and Geometry-Aware Attention (GAA) for preserving cross-layer vector structure, the network effectively bridges the Sim-to-Real gap. Extensive real-world experiments demonstrate state-of-the-art performance, achieving a position error of 1.84 mm and an orientation error of 3.18 degrees at a refresh rate exceeding 270 Hz. The proposed method consistently outperforms classical Levenberg--Marquardt solvers and generic convolutional baselines, particularly in suppressing catastrophic outliers and maintaining robustness in challenging near-field boundary regions. Beyond the proposed network, the FIM-guided analysis also provides a framework for sensor geometry design in magnetic localization systems under practical deployment constraints.

Indoor positioning is an essential technology for a wide range of applications in GNSS-denied environments, including indoor navigation and IoT systems. Combining convolutional neural networks (CNNs) and magnetic field-based features offers a low-cost, infrastructure-free solution for precise positioning. While magnetic fingerprints are a promising approach for indoor positioning, models trained on raw 3D magnetometer data are highly sensitive to device orientation. We address this by using two rotation invariant features derived from the 3D magnetic field: the norm (Mn) and the projection onto the gravity axis (Mg). We train a lightweight 7-layer dilated CNN (MagNetS/XL) on magnetic sequences to directly regress (x, y) positions. Using the MagPie dataset (three buildings, handheld trajectories), we systematically evaluate fixed and random rotations of test and/or train data. Raw 3D inputs (Mx, My , Mz) exhibit isotropic error increases under fixed 90° rotations and further degrade with growing random rotations. In contrast, 2D (Mn, Mg) inputs maintain rotation invariant accuracy and surpass the 3D inputs once rotation exceeds building-specific thresholds for three reference buildings: 0° for Loomis (large), 5° for Talbot (medium), and 6° for CSL (small). MagNetXL achieves or exceeds state-of-the-art accuracy on the MagPie dataset, and MagNetS delivers similar performance with roughly one third of the parameters, favoring mobile deployment. These results show that the robustness gained from rotation invariant inputs outweighs the loss of input dimensionality in realistic usage, allowing mapping and localization without orientation alignment or added infrastructure.

Reliable automated analysis of Optical Coherence Tomography (OCT) imaging is crucial for diagnosing retinal disorders but faces a critical barrier: the need for expensive, labor-intensive expert annotations. Supervised deep learning models struggle to generalize across diverse pathologies, imaging devices, and patient populations due to their restricted vocabulary of annotated abnormalities. We propose an unsupervised anomaly detection framework that learns the normative distribution of healthy retinal anatomy without lesion annotations, directly addressing annotation efficiency challenges in clinical deployment. Our approach leverages a discrete latent model trained on normal B-scans to capture OCT-specific structural patterns. To enhance clinical robustness, we incorporate retinal layer-aware supervision and structured triplet learning to separate healthy from pathological representations, improving model reliability across varied imaging conditions. During inference, anomalies are detected and localized via reconstruction discrepancies, enabling both image and pixel-level identification without requiring disease-specific labels. On the Kermany dataset (AUROC: 0.799), our method substantially outperforms VAE, VQVAE, VQGAN, and f-AnoGAN baselines. Critically, cross-dataset evaluation on Srinivasan achieves AUROC 0.884 with superior generalization, demonstrating robust domain adaptation. On the external RETOUCH benchmark, unsupervised anomaly segmentation achieves competitive Dice (0.200) and mIoU (0.117) scores, validating reproducibility across institutions.

Instruction-based image editing (IIE) aims to modify images according to textual instructions while preserving irrelevant content. Despite recent advances in diffusion transformers, existing methods often suffer from over-editing, introducing unintended changes to regions unrelated to the desired edit. We identify that this limitation arises from the lack of an explicit mechanism for edit localization. In particular, different editing operations (e.g., addition, removal and replacement) induce distinct spatial patterns, yet current IIE models typically treat localization in a task-agnostic manner. To address this limitation, we propose a training-free, task-aware edit localization framework that exploits the intrinsic source and target image streams within IIE models. For each image stream, We first obtain attention-based edit cues, and then construct feature centroids based on these attentive cues to partition tokens into edit and non-edit regions. Based on the observation that optimal localization is inherently task-dependent, we further introduce a unified mask construction strategy that selectively leverages source and target image streams for different editing tasks. We provide a systematic analysis for our proposed insights and approaches. Extensive experiments on EdiVal-Bench demonstrate our framework consistently improves non-edit region consistency while maintaining strong instruction-following performance on top of powerful recent image editing backbones, including Step1X-Edit and Qwen-Image-Edit.

We present a system for automated detection, localization, and scoring of arrow punctures on 40,cm indoor archery target faces, trained on only 48 annotated photographs (5{,}084 punctures). Our pipeline combines three components: a color-based canonical rectification stage that maps perspective-distorted photographs into a standardized coordinate system where pixel distances correspond to known physical measurements; a frozen self-supervised vision transformer (DINOv3 ViT-L/16) paired with AnyUp guided feature upsampling to recover sub-millimeter spatial precision from $32 \times 32$ patch tokens; and lightweight CenterNet-style detection heads for arrow-center heatmap prediction. Only 3.8,M of 308,M total parameters are trainable. Across three cross-validation folds, we achieve a mean F1 score of $0.893 \pm 0.011$ and a mean localization error of $1.41 \pm 0.06$,mm, comparable to or better than prior fully-supervised approaches that require substantially more training data. An ablation study shows that the CenterNet offset regression head, typically essential for sub-pixel refinement, provides negligible detection improvement while degrading localization in our setting. This suggests that guided feature upsampling already resolves the spatial precision lost through patch tokenization. On downstream archery metrics, the system recovers per-image average arrow scores with a median error of 1.8% and group centroid positions to within a median of 4.00,mm. These results demonstrate that frozen foundation models with minimal task-specific adaptation offer a practical paradigm for dense prediction in small-data regimes.

With the rapid advancement of deep generative models, realistic fake images have become increasingly accessible, yet existing localization methods rely on complex designs and still struggle to generalize across manipulation types and imaging conditions. We present a simple but strong baseline based on DINOv3 with LoRA adaptation and a lightweight convolutional decoder. Under the CAT-Net protocol, our best model improves average pixel-level F1 by 17.0 points over the previous state of the art on four standard benchmarks using only 9.1,M trainable parameters on top of a frozen ViT-L backbone, and even our smallest variant surpasses all prior specialized methods. LoRA consistently outperforms full fine-tuning across all backbone scales. Under the data-scarce MVSS-Net protocol, LoRA reaches an average F1 of 0.774 versus 0.530 for the strongest prior method, while full fine-tuning becomes highly unstable, suggesting that pre-trained representations encode forensic information that is better preserved than overwritten. The baseline also exhibits strong robustness to Gaussian noise, JPEG re-compression, and Gaussian blur. We hope this work can serve as a reliable baseline for the research community and a practical starting point for future image-forensic applications. Code is available at https://github.com/Irennnne/DINOv3-IML.

Code localization is a cornerstone of autonomous software engineering. Recent advancements have achieved impressive performance on real-world issue benchmarks. However, we identify a critical yet overlooked bias: these benchmarks are saturated with keyword references (e.g. file paths, function names), encouraging models to rely on superficial lexical matching rather than genuine structural reasoning. We term this phenomenon the Keyword Shortcut. To address this, we formalize the challenge of Keyword-Agnostic Logical Code Localization (KA-LCL) and introduce KA-LogicQuery, a diagnostic benchmark requiring structural reasoning without any naming hints. Our evaluation reveals a catastrophic performance drop of state-of-the-art approaches on KA-LogicQuery, exposing their lack of deterministic reasoning capabilities. We propose LogicLoc, a novel agentic framework that combines large language models with the rigorous logical reasoning of Datalog for precise localization. LogicLoc extracts program facts from the codebase and leverages an LLM to synthesize Datalog programs, with parser-gated validation and mutation-based intermediate-rule diagnostic feedback to ensure correctness and efficiency. The validated programs are executed by a high-performance inference engine, enabling accurate and verifiable localization in a fully automated, closed-loop workflow. Experimental results demonstrate that LogicLoc significantly outperforms SOTA methods on KA-LogicQuery while maintaining competitive performance on popular issue-driven benchmarks. Notably, LogicLoc attains superior performance with significantly lower token consumption and faster execution by offloading structural traversal to a deterministic engine, reducing the overhead of iterative LLM inference.

Autonomous drone racing demands robust real-time localization under extreme conditions: high-speed flight, aggressive maneuvers, and payload-constrained platforms that often rely on a single camera for perception. Existing visual SLAM systems, while effective in general scenarios, struggle with motion blur and feature instability inherent to racing dynamics, and do not exploit the structured nature of racing environments. In this work, we present a dual pose-graph architecture that fuses odometry with semantic detections for robust localization. A temporary graph accumulates multiple gate observations between keyframes and optimizes them into a single refined constraint per landmark, which is then promoted to a persistent main graph. This design preserves the information richness of frequent detections while preventing graph growth from degrading real-time performance. The system is designed to be sensor-agnostic, although in this work we validate it using monocular visual-inertial odometry and visual gate detections. Experimental evaluation on the TII-RATM dataset shows a 56% to 74% reduction in ATE compared to standalone VIO, while an ablation study confirms that the dual-graph architecture achieves 10% to 12% higher accuracy than a single-graph baseline at identical computational cost. Deployment in the A2RL competition demonstrated that the system performs real-time onboard localization during flight, reducing the drift of the odometry baseline by up to 4.2 m per lap.

Precise and real-time visual localization is critical for applications like AR/VR and robotics, especially on resource-constrained edge devices such as smart glasses, where battery life and heat dissipation can be a primary concerns. While many efficient models exist, further reducing compute without sacrificing accuracy is essential for practical deployment. To address this, we propose asymmetric visual localization: a large Teacher model processes pre-mapped database images offline, while a lightweight Student model processes the query image online. This creates a challenge in matching features from two different models without resorting to heavy, learned matchers. We introduce AsymLoc, a novel distillation framework that aligns a Student to its Teacher through a combination of a geometry-driven matching objective and a joint detector-descriptor distillation objective, enabling fast, parameter-less nearest-neighbor matching. Extensive experiments on HPatches, ScanNet, IMC2022, and Aachen show that AsymLoc achieves up to 95% of the teacher's localization accuracy using an order of magnitude smaller models, significantly outperforming existing baselines and establishing a new state-of-the-art efficiency-accuracy trade-off.

We localize the policy routing mechanism in alignment-trained language models. An intermediate-layer attention gate reads detected content and triggers deeper amplifier heads that boost the signal toward refusal. In smaller models the gate and amplifier are single heads; at larger scale they become bands of heads across adjacent layers. The gate contributes under 1% of output DLA, yet interchange testing (p < 0.001) and knockout cascade confirm it is causally necessary. Interchange screening at n >= 120 detects the same motif in twelve models from six labs (2B to 72B), though specific heads differ by lab. Per-head ablation weakens up to 58x at 72B and misses gates that interchange identifies; at scale, interchange is the only reliable audit. Modulating the detection-layer signal continuously controls policy from hard refusal through evasion to factual answering. On safety prompts the same intervention turns refusal into harmful guidance, showing that the safety-trained capability is gated by routing, not removed. Thresholds vary by topic and by input language, and the circuit relocates across generations within a family even while behavioral benchmarks register no change. Routing is early-commitment: the gate fires at its own layer before deeper layers finish processing the input. An in-context substitution cipher collapses gate interchange necessity by 70 to 99% across three models, and the model switches to puzzle-solving rather than refusal. Injecting the plaintext gate activation into the cipher forward pass restores 48% of refusals in Phi-4-mini, localizing the bypass to the routing interface. A second method, cipher contrast analysis, uses plain/cipher DLA differences to map the full cipher-sensitive routing circuit in O(3n) forward passes. Any encoding that defeats detection-layer pattern matching bypasses the policy regardless of whether deeper layers reconstruct the content.

Recently, visual localization has become an important supplement to improve localization reliability, and cross-view approaches can greatly enhance coverage and adaptability. Meanwhile, future 6G will enable a globally covered mobile communication system, with a space-air-ground integrated network (SAGIN) serving as key supporting architecture. Inspired by this, we explore an integration of cross-view localization (CVL) with 6G SAGIN, thereby enhancing its performance in latency, energy consumption, and privacy protection. First, we provide a comprehensive review of CVL and SAGIN, highlighting their capabilities, integration opportunities, and potential applications. Benefiting from the fast and extensive image collection and transmission capabilities of the 6G SAGIN architecture, CVL achieves higher localization accuracy and faster processing speed. Then, we propose a split-inference framework for implementing CVL, which fully leverages the distributed communication and computing resources of the 6G SAGIN architecture. Subsequently, we conduct joint optimization of communication, computation, and confidentiality within the proposed split-inference framework, aiming to provide a paradigm and a direction for making CVL efficient. Experimental results validate the effectiveness of the proposed framework and provide solutions to the optimization problem. Finally, we discuss potential research directions for 6G SAGIN-enabled CVL.

Recent advances in imaging technologies, deep learning and numerical performance have enabled non-invasive detailed analysis of artworks, supporting their documentation and conservation. In particular, automated detection of craquelure in digitized paintings is crucial for assessing degradation and guiding restoration, yet remains challenging due to the possibly complex scenery and the visual similarity between cracks and crack-like artistic features such as brush strokes or hair. We propose a hybrid approach that models crack detection as an inverse problem, decomposing an observed image into a crack-free painting and a crack component. A deep generative model is employed as powerful prior for the underlying artwork, while crack structures are captured using a Mumford--Shah-type variational functional together with a crack prior. Joint optimization yields a pixel-level map of crack localizations in the painting.

Topological mapping offers a compact and robust representation for navigation, but progress in the field is hindered by the lack of standardized evaluation metrics, datasets, and protocols. Existing systems are assessed using different environments and criteria, preventing fair and reproducible comparisons. Moreover, a key challenge - perceptual aliasing - remains under-quantified, despite its strong influence on system performance. We address these gaps by (1) formalizing topological consistency as the fundamental property of topological maps and showing that localization accuracy provides an efficient and interpretable surrogate metric, and (2) proposing the first quantitative measure of dataset ambiguity to enable fair comparisons across environments. To support this protocol, we curate a diverse benchmark dataset with calibrated ambiguity levels, implement and release deep-learned baseline systems, and evaluate them alongside classical methods. Our experiments and analysis yield new insights into the limitations of current approaches under perceptual aliasing. All datasets, baselines, and evaluation tools are fully open-sourced to foster consistent and reproducible research in topological mapping.

This letter presents a CWT-enhanced vibration sensing framework for bearing fault monitoring through localized time-frequency region detection on continuous wavelet transform (CWT) spectrograms. Vibration signals are transformed into CWT spectrograms to improve the observability of weak and non-stationary fault signatures, and YOLOv9, YOLOv10, and YOLOv11 are employed to detect and identify localized fault-related energy regions in the time-frequency domain. Experiments on the CWRU, PU, and IMS datasets show that the proposed framework improves the detectability and robustness of fault-related sensing patterns compared with conventional time-series models, modern vision backbones, and short-time Fourier transform (STFT)-based representations, achieving mean average precision (mAP) values up to 99.4%, 97.8%, and 99.5%, respectively. In addition, the localized region detection framework provides a more interpretable relationship between time-frequency energy distributions and characteristic bearing fault frequencies. These results demonstrate an effective and generalizable approach for interpretable vibration sensing in noisy industrial environments.

We introduce GSVisLoc, a visual localization method designed for 3D Gaussian Splatting (3DGS) scene representations. Given a 3DGS model of a scene and a query image, our goal is to estimate the camera's position and orientation. We accomplish this by robustly matching scene features to image features. Scene features are produced by downsampling and encoding the 3D Gaussians while image features are obtained by encoding image patches. Our algorithm proceeds in three steps, starting with coarse matching, then fine matching, and finally by applying pose refinement for an accurate final estimate. Importantly, our method leverages the explicit 3DGS scene representation for visual localization without requiring modifications, retraining, or additional reference images. We evaluate GSVisLoc on both indoor and outdoor scenes, demonstrating competitive localization performance on standard benchmarks while outperforming existing 3DGS-based baselines. Moreover, our approach generalizes effectively to novel scenes without additional training.

Attention is the critical component of a transformer. Yet the quadratic computational complexity of vanilla full attention in the input size and the inability of its linear attention variant to focus have been challenges for computer vision tasks. We provide a mathematical definition of generalized attention and formulate both vanilla softmax attention and linear attention within the general framework. We prove that generalized attention disperses, that is, as the number of keys tends to infinity, the query assigns equal weights to all keys. Motivated by the dispersion property and recent development of Mamba form of attention, we design Scalable and Efficient Mamba like Attention (SEMA) which utilizes token localization to avoid dispersion and maintain focusing, complemented by theoretically consistent arithmetic averaging to capture global aspect of attention. We support our approach on Imagenet-1k where classification results show that SEMA is a scalable and effective alternative beyond linear attention, outperforming recent vision Mamba models on increasingly larger scales of images at similar model parameter sizes.

The advances in Vision-Language models (VLMs) offer exciting opportunities for robotic applications involving image geo-localization - the problem of identifying the geo-coordinates of a place based on visual data only. In robotics, such capabilities are particularly relevant to the global re-localization stage of the kidnapped robot problem, where a robot must recover its pose without prior knowledge of its location. Recent work has focused on using a VLM as embedding extractor for geo-localization. However, the most sophisticated VLMs may only be available as black boxes that are accessible through an API, and come with a number of limitations: there is no access to training data, model features and gradients; retraining is not possible; and the number of predictions may be limited by the API. The potential of state-of-the-art VLMs as a stand-alone, zero-shot geo-localization systems at planet scale using a single text-based prompt is largely unexplored. To bridge this gap, this paper undertakes the first systematic study, to the best of our knowledge, to investigate state-of-the-art generative VLMs as stand-alone, zero-shot geo-localization systems in a black-box setting with realistic constraints. We consider three main scenarios for this thorough investigation: a) fixed text-based prompt; b) semantically-equivalent text-based prompts; and c) semantically-equivalent query images. Beyond standard accuracy, we introduce model consistency as a metric to account for the auto-regressive and probabilistic nature of generative VLMs. Our findings reveal that while VLMs demonstrate strong coarse-level localization and navigation priors, fine-grained localization degrades significantly under realistic variations, highlighting reliability challenges for deploying generative VLMs in robust, open-world robotic navigation systems.

This paper introduces 2Fast-2Lamaa, a lidar-inertial state estimation framework for odometry, mapping, and localization. Its first key component is the optimization-based undistortion of lidar scans, which uses continuous IMU preintegration to model the system's pose at every lidar point timestamp. The continuous trajectory over 100-200ms is parameterized only by the initial scan conditions (linear velocity and gravity orientation) and IMU biases, yielding eleven state variables. These are estimated by minimizing point-to-line and point-to-plane distances between lidar-extracted features without relying on previous estimates, resulting in a prior-less motion-distortion correction strategy. Because the method performs local state estimation, it directly provides scan-to-scan odometry. To maintain geometric consistency over longer periods, undistorted scans are used for scan-to-map registration. The map representation employs Gaussian Processes to form a continuous distance field, enabling point-to-surface distance queries anywhere in space. Poses of the undistorted scans are refined by minimizing these distances through non-linear least-squares optimization. For odometry and mapping, the map is built incrementally in real time; for pure localization, existing maps are reused. The incremental map construction also includes mechanisms for removing dynamic objects. We benchmark 2Fast-2Lamaa on over 750km of public and self-collected datasets from both automotive and handheld systems. The framework achieves state-of-the-art performance across diverse and challenging scenarios, reaching odometry and localization errors as low as 0.22% and 0.06 m, respectively. The real-time implementation is publicly available at https://github.com/clegenti/2fast2lamaa.

Weakly Supervised Object Localization (WSOL) allows training deep learning models for classification and localization (LOC) using only global class-level labels. The absence of bounding box (bbox) supervision during training raises challenges in the literature for hyper-parameter tuning, model selection, and evaluation. WSOL methods rely on a validation set with bbox annotations for model selection, and a test set with bbox annotations for threshold estimation for producing bboxes from localization maps. This approach, however, is not aligned with the WSOL setting as these annotations are typically unavailable in real-world scenarios. Our initial empirical analysis shows a significant decline in LOC performance when model selection and threshold estimation rely solely on class labels and the image itself, respectively, compared to using manual bbox annotations. This highlights the importance of incorporating bbox labels for optimal model performance. In this paper,a new WSOL evaluation protocol is proposed that provides LOC information without the need for manual bbox annotations. In particular, we generated noisy pseudo-boxes from a pretrained off-the-shelf region proposal method such as Selective Search, CLIP, and RPN for model selection. These bboxes are also employed to estimate the threshold from LOC maps, circumventing the need for test-set bbox annotations. Our experiments with several WSOL methods on challenging natural and medical image datasets show that using the proposed pseudo-bboxes for validation facilitates the model selection and threshold estimation, with LOC performance comparable to models selected using GT bboxes on the validation set and threshold estimation on the test set. It also outperforms models selected using class-level labels, and then dynamically thresholded with only LOC maps.

Assessing the spatial fairness of predictive models involves establishing whether they are statistically penalizing (favoring) individuals associated with certain geographical locations. Literature on this topic makes the fundamental assumption that each individual is assigned to a single geographical location (e.g., place of residence). However, fairness with respect to the set of regions where one regularly spends time, i.e., the individual's activity space, also matters when fairness is considered. Consequently, we argue that it is necessary to generalize the notion of spatial fairness to also account for such activity-space patterns, leading to the novel problem of assessing predictive models for fairness relative to the movements of individuals. To deal with this problem, we propose an approach that first associates individuals with geographic regions relevant to their activity spaces, considering multiple spatial partitions with different resolutions and alignments, and then employs a suitable spatial scan statistic to assess whether a predictive model is fair based on activity-space patterns. In the experimental evaluation, we study the performance of our approach over thousands of synthetic unfair datasets, showing that it is effective at detecting this new type of unfairness and at retrieving the set of objects treated unfairly, while localization performance exhibits a consistent multi-resolution trade-off.

This paper proposes a general machine learning framework called the localization method, which is fundamentally built on two core concepts: localization kernels and local means -- key components that underpin the self-attention mechanism. To establish a rigorous theoretical foundation, the framework is formally defined through two essential pillars: the formulation of the local(-ized) model and the localization trick. We systematically investigate the connections between the localization method and a wide range of existing machine learning models/methods, including (but not limited to) kernel methods, lazy learning, the MeanShift algorithm, relaxation labeling, Hopfield networks, local linear embedding (LLE), fuzzy inference, and denoising autoencoders (DAEs). By dissecting these relationships, we clarify the broader theoretical significance of the localization method and demonstrate its practical applicability across diverse machine learning tasks. Furthermore, we explore advanced extensions of the framework, such as adaptive kernels, hierarchical local models, and non-local models. Notably, we show that the Transformer -- a cornerstone of modern sequence modeling -- can be constructed using hierarchical local models, revealing the ability of the localization method to unify and generalize state-of-the-art architectures. This work not only provides a unified theoretical lens to reinterpret existing models but also offers new methodological tools for designing flexible, data-adaptive learning systems.