map representation learning

Standard position encodings in natural language processing exhibit limited effectiveness for the Vehicle Routing Problem (VRP) due to their neglect of the problem’s geometric and topological structure. This work proposes a geometry-guided hierarchical anisotropic position encoding that explicitly models VRP’s cyclic directionality, anisotropic distances, and depot-centered hierarchical organization by integrating intra-route distance-based cyclic consistency with inter-route angular information anchored at the depot. The proposed encoding unifies insights from natural language processing, graph Transformers, and route planning, significantly outperforming conventional index-based encodings across multiple VRP variants. Moreover, it demonstrates strong generalization capabilities across diverse model architectures, problem types, and distribution shifts.

This work addresses the challenge of precisely removing specific visual concepts while preserving both unrelated and semantically proximate concepts in concept erasure tasks. Building upon the Stable Diffusion v1.4 framework, the authors propose a method that integrates a semantic routing mechanism with a proxy-guided strategy. By incorporating task-specific training objectives, enhanced concept representations, and a dynamic mapper selection scheme, the approach achieves fine-grained and high-fidelity concept forgetting. Evaluated on the official Genμ 2.0 Challenge benchmark, the method outperforms the current state-of-the-art baseline by an average of 12.1% in terms of the ERR metric, demonstrating consistent and significant improvements across all five concept categories.

This work addresses the limitation of standard Transformers in team orienteering problems, where the lack of explicit spatial relationship modeling hinders performance. To overcome this, the authors propose incorporating relative positional encoding as an additive bias within the attention mechanism, thereby explicitly embedding geometric distances between nodes into the graph representation for the first time. This enhancement significantly improves the model’s spatial awareness and path decoding quality. Evaluated on instances with up to 100 nodes, the proposed Transformer-based encoder-decoder architecture consistently outperforms existing methods, achieving notable gains in both collected reward and optimality gap metrics. The approach effectively enhances the model’s scalability and generalization capability for complex combinatorial optimization problems.

Multimodal large language models (MLLMs) exhibit limited performance on fine-grained spatial understanding tasks—such as map-based path tracing—due to scarce and costly pixel-level ground-truth annotations. Method: This paper introduces the first synthetic data generation paradigm specifically designed for path tracing, leveraging controllable map rendering and automated pixel-level path parsing to construct a large-scale, pixel-accurate synthetic training set comprising 23K samples. We perform supervised fine-tuning of MLLMs on this dataset and propose MapBench, a dedicated evaluation framework for systematic assessment. Contribution/Results: Experimental results demonstrate that our approach improves path tracing success rate by up to 6.4 points and significantly reduces Normalized Dynamic Time Warping (NDTW) error. To our knowledge, this is the first work to empirically validate that synthetic supervision can effectively enhance MLLMs’ fine-grained spatial reasoning capabilities.

To address the limited generalization capability of neural motion planners in autonomous driving—particularly their difficulty adapting to diverse road topologies and dynamic environments—this paper proposes an isometric road network embedding method based on Multidimensional Scaling (MDS). We are the first to apply classical MDS to road graph modeling, constructing a low-dimensional continuous feature space that preserves global geometric structure. Additionally, we introduce a graph node embedding paradigm tailored for autonomous driving, balancing topological fidelity with learning scalability. Experimental results demonstrate a 12.7% improvement in motion planning success rate on cross-regional complex road networks. Moreover, even when compressed to a 16-dimensional embedding space, the representation retains 98.3% structural similarity to the original graph, substantially enhancing model generalization to unseen scenarios.

Traditional visual navigation struggles to balance global geometric consistency with topological generalization, limiting its performance in complex environments. This work proposes a novel map representation based on pixel-level relative 3D connectivity, which constructs a pixel correspondence graph in a relative coordinate frame from image sequences and generates a “WayPixel Costmap” for planning and control. By preserving high-fidelity geometric information without requiring global geometric consistency, the approach overcomes the limitations of conventional topological graphs and dense reconstructions. Experimental results demonstrate that the method significantly outperforms image-level and object-level representations across four simulated tasks and real-world scenarios, validating its accuracy and practicality for visual navigation.

Current AI systems lack biologically inspired cognitive map capabilities, hindering strong out-of-distribution (OOD) generalization and flexible path integration. To address this, we propose MapFormers: a Transformer-based self-supervised framework for cognitive map modeling. Its core innovation is input-dependent dynamic positional encoding, which naturally disentangles spatial structure from semantic content while unifying absolute (episodic) and relative (working) positional representations. This design enables parallel path integration and faithful simulation of memory systems. Evaluated on 2D navigation tasks, MapFormers achieves near-perfect OOD generalization—substantially outperforming state-of-the-art methods—and empirically validates the critical role of structural priors in cognitive map learning.

This work addresses the challenge of optimizing last-mile delivery routes in highly asymmetric road networks—such as those with one-way streets or severe congestion—where conventional heuristics struggle to perform effectively. To tackle this, the authors propose a geography-aware training strategy that partitions the service area into balanced subregions using a Discrete Global Grid System (DGGS). Within each subregion, an encoder-decoder model composed of a Graph Neural Network (GNN) and a Pointer Network is independently trained to generate optimal stop sequences. By tailoring the model to local spatial characteristics, this approach significantly enhances route prediction performance in high-stop-density scenarios. Experiments on the 2021 Amazon Los Angeles dataset demonstrate that the partitioning strategy yields shorter average predicted route lengths compared to global training, with performance gains becoming more pronounced as the number of stops increases.

Existing trajectory representation learning methods coarsely map GPS trajectories onto grids or road segments, resulting in significant loss of fine-grained spatiotemporal information. To address this, we propose BLUE—a multi-scale trajectory block construction method based on fuzzy encoding—that hierarchically represents trajectories via progressive coordinate precision decay. BLUE employs an encoder-decoder pyramid architecture integrating Transformers with upsampling and downsampling modules, jointly optimizing local geometric details and global mobility patterns under an unsupervised trajectory reconstruction objective. The model is trained end-to-end using mean squared error as the loss function. Evaluated on three downstream tasks—including trajectory classification, clustering, and next-location prediction—BLUE outperforms eight state-of-the-art methods, achieving an average accuracy improvement of 30.90%. It effectively alleviates the representational imbalance between fine-grained spatial details and high-level semantic patterns in trajectory modeling.

This work investigates the geospatial reasoning capabilities of large language models (LLMs), specifically their ability to perform navigation solely from textual representations of road networks. To address this, we propose a novel trajectory recovery paradigm, introduce GLOBALTRACE—a benchmark dataset comprising over 4,000 real-world trajectories—and design a zero-shot prompting framework that natively integrates road network topology, coordinate systems, and multimodal traffic semantics without external tools, enabling cross-regional, multi-modal route generation. Experiments demonstrate that our framework significantly outperforms existing baselines and specialized trajectory models under zero-shot settings; it also supports flexible incorporation of user preferences to enhance navigational plausibility and practicality. Our core contributions are: (1) the first systematic evaluation of LLMs’ intrinsic geospatial reasoning capacity, and (2) a scalable, tool-free, end-to-end trajectory generation methodology.