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.

Visual localization is a fundamental task in computer vision and robotics. Training existing visual localization methods requires a large number of posed images to generalize to novel views, while state-of-the-art methods generally require ground truth 3D labels for supervision. However, acquiring a large number of posed images and 3D labels in the real world is challenging and costly. In this paper, we present a novel visual localization method that achieves accurate localization while using only a few posed images compared to other localization methods. To achieve this, we first use a few posed images with coarse pseudo-3D labels provided by NeRF to train a coordinate regression network.

While performing abest-first search, compilation errors constitute 88.7% ofprogramfailures.

A challenge in mobile sensing is to overcome the location uncertainty of its sensors.

Visual localization is a fundamental task in computer vision and robotics.

Visual localization is a fundamental task in computer vision and robotics. Training existing visual localization methods requires a large number of posed images to generalize to novel views, while state-of-the-art methods generally require dense ground truth 3D labels for supervision. However, acquiring a large number of posed images and dense 3D labels in the real world is challenging and costly. In this paper, we present a novel visual localization method that achieves accurate localization while using only a few posed images compared to other localization methods. To achieve this, we first use a few posed images with coarse pseudo-3D labels provided by NeRF to train a coordinate regression network.

Abstract--Received signal strength indicator (RSSI) is the primary representation of Wi-Fi fingerprints and serves as a crucial tool for indoor localization. However, existing RSSI-based positioning methods often suffer from reduced accuracy due to environmental complexity and challenges in processing multi-source information. T o address these issues, we propose a novel multi-graph heterogeneous GNN framework (MG-HGNN) to enhance spatial awareness and improve positioning performance. In this framework, two graph construction branches perform node and edge embedding, respectively, to generate informative graphs. Subsequently, a heterogeneous graph neural network is employed for graph representation learning, enabling accurate positioning. The MG-HGNN framework introduces the following key innovations: 1) multi-type task-directed graph construction that combines label estimation and feature encoding for richer graph information; 2) a heterogeneous GNN structure that enhances the performance of conventional GNN models. Evaluations on the UJIIndoorLoc and UTSIndoorLoc public datasets demonstrate that MG-HGNN not only achieves superior performance compared to several state-of-the-art methods, but also provides a novel perspective for enhancing GNN-based localization methods. Ablation studies further confirm the rationality and effectiveness of the proposed framework. Index T erms--Fingerprint-based localization, graph neural network, heterogeneous network, received signal strength indicator (RSSI). NDOOR localization technologies aim to estimate the position of mobile users or devices in indoor environments where satellite-based systems such as GPS are ineffective [1]. Over the past decade, a variety of wireless indoor localization techniques have been developed based on different sensing modalities, including Bluetooth Low Energy (BLE) [2], Ultra Wideband (UWB) [3], Radio Frequency Identification (RFID) [4], magnetic field sensing [5], and Wi-Fi [6], [7]. Among them, Wi-Fi based localization has attracted a lot of attention due to the ubiquity of Wi-Fi infrastructure, low deployment cost, and compatibility with existing mobile devices without requiring additional hardware [1]. This work has been submitted to the IEEE for possible publication. This work is supported by the National Key Research and Development Program of China [Grant No. 2024QY1103], the Shandong Provincial Natural Science Foundation, China [Grant No. ZR2024QF138].(Corresponding Yibu Wang, Zhaoxin Zhang, Ning Li, and Tianzi Zhao are with the School of Computer Science and Technology, Harbin Institute of Technology, China (e-mail: 24b903081@stu.hit.edu.cn; Xinlong Zhao is with the China Mineral Resources Group Big Data Co., Ltd, China (e-mail: xinlong.zhao@qq.com).