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PlatonicNav: Unveiling Semantic Correspondence in Navigation with Platonic Topological Maps

Junlin Long, Zeyu Zhang, Xu Deng, Yiran Wang, Yue Yang, Luke Borgnolo, Maxwell Twelftree, Yang Zhao

arXiv:2606.01788v1cs.CV

TL;DR

Whether independently trained vision and language encoders share semantic structure remains open, and language grounding in object-centric maps still commonly uses cross-modal supervision. PlatonicNav uses blind matching to ground language goals in a vision-built topological map, and experiments report generalization across tasks, modalities, and embodiments without explicit cross-modal training.

  • Problem

    It remains open whether independently trained vision and language encoders share common semantic structure, despite efforts to unify VLN and ObjNav through model fusion and mixed-task training.

    Source: §1 · p. 2

  • Method

    PlatonicNav is a training-free framework that fuses geometric and semantic distances in a vision-built topological map and grounds language goals by blind matching independent encoders without paired vision-language data.

    Source: §1 · p. 2

  • Results

    Experiments on HM3D-IIN, OVON, R2R-CE on MP3D, and Unitree Go2 show cross-task, cross-modality, and cross-embodiment generalization without explicit cross-modal training.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The results suggest that some cross-modal alignment is already latent in independently trained vision and language encoders.

    Source: §1 · p. 2

    Trajectory overlap may partly reflect environmental constraints, and cross-modal target correspondence relies on human annotation, which is explicit cross-modal supervision.

    Source: §3.2 · p. 5

Abstract

from arXiv · show

Embodied visual navigation, where an agent perceives a complex environment and acts to reach a goal from raw sensory input, underpins a wide range of applications such as household service robotics, assistive robotics, and large-scale autonomous exploration. However, recent attempts to unify vision-and-language navigation (VLN) and object goal navigation (ObjNav) remain at the level of architectural fusion, mixed-task training, and large vision-language pretraining, without examining whether independently trained vision and language encoders may already share a common semantic structure. Moreover, even object-centric topological maps still ground language goals through explicit cross-modal supervision such as CLIP or large vision-language models, leaving open whether such grounding is possible from a purely vision-built map. To address these challenges, we extend the Platonic Representation Hypothesis to embodied navigation and recast vision-only ObjNav, cross-modal ObjNav, and VLN as three different interfaces to the same object-centric semantic manifold. We further introduce PlatonicNav, a training-free framework whose Platonic Topological Map fuses geometric and semantic node distances from a self-supervised visual encoder, and grounds language goals via blind matching without any paired vision-language data. Extensive experiments on simulation benchmarks including HM3D-IIN, OVON, and R2R-CE on MP3D, together with deployment on Unitree Go2, demonstrate that PlatonicNav generalizes across tasks, modalities, and embodiments without explicit cross-modal training. Code: https://github.com/AIGeeksGroup/PlatonicNav. Website: https://aigeeksgroup.github.io/PlatonicNav.

1 Introduction

PlatonicNav frames vision-only ObjNav, cross-modal ObjNav, and VLN as different interfaces to one object-centric semantic structure. It proposes that independently trained vision and language encoders can support this unification through a vision-built map, without paired vision-language data.

Motivation

  • The paper argues that unified navigation models still rely on architectural fusion, mixed-task training, or large vision-language pretraining, while object-centric maps still use explicit cross-modal grounding [22] [21] [47] [6].These approaches leave open whether independently trained vision and language encoders already share semantic structure, making some cross-modal supervision potentially redundant [40] [72] [20].Source: §1 · p. 2
  • If the Platonic Representation Hypothesis [30] extends to navigation, vision-only ObjNav, cross-modal ObjNav, and VLN should produce closely related trajectories for the same scene and target.The proposed mechanism is that object-centric map nodes from a self-supervised visual encoder [60] encode pairwise visual semantics, enabling blind matching [57] to language without paired data, contrastive pretraining, or VLM supervision.Source: §1 · p. 2

PlatonicNav

  • PlatonicNav is a training-free framework that grounds language goals in a vision-built Platonic Topological Map via blind matching, treating three navigation tasks as queries to one semantic manifold.Its map edges fuse geometric and Platonic semantic distances; matching uses independently trained vision [60] and language [43] encoders without paired vision-language data [57].Source: §1 · p. 2

Contributions

  • The paper formulates embodied navigation through the Platonic Representation Hypothesis [30] and proposes a falsifiable two-step thought experiment to test task unification on real navigation trajectories.Source: §1 · p. 2

Evaluation and takeaway

  • PlatonicNav is evaluated on HM3D-IIN, OVON, R2R-CE on MP3D, and Unitree Go2, with reported cross-task, cross-modality, and cross-embodiment generalization without explicit cross-modal training.The authors suggest that alignment often engineered with paired data, contrastive learning, or VLM supervision is partly latent in independently trained encoders, and that ObjNav and VLN share an object-centric semantic structure.Source: §1 · pp. 2–3

2 Related Work

The literature develops ObjNav and VLN largely on parallel tracks, while language grounding typically uses paired supervision; related work also identifies sparse topological mapping and relational blind matching as alternatives.

2.1 Embodied Visual Navigation

  • ObjNav moved from Habitat-trained agents and semantic maps [56] [10] toward foundation-model-guided open-vocabulary methods [42] [19] [69], while VLN evolved separately from R2R and RxR [39] to VLM policies [74] [18] [76] [13].A nascent unification line pursues shared backbones through mixed-task training, large-scale vision-language pretraining, or 3D-grounded reasoning [72] [20] [40] [29] [78].Source: §2.1 · p. 3

2.2 Representation-Level Grounding for Navigation

  • Language-vision grounding is dominated by paired image-text supervision, whose joint embeddings are also lifted into open-vocabulary 3D representations.A separate lineage favors sparse graphs over dense metric reconstruction, progressing from semi-parametric memory and Neural Topological SLAM to RoboHop and ObjectReact.Source: §2.2 · p. 3
  • The Platonic Representation Hypothesis [30] proposes cross-modal convergence; blind matching [57] recovers correspondence from pairwise relations without parallel data, alongside self-supervised vision and dense text encoders.The hypothesis has been critiqued for naive isotropy [24], re-examined for scaling behavior [34], and extended by work arguing residual misalignment can be closed post-hoc [68].Source: §2.2 · p. 3

3 Method

PlatonicNav frames vision-only ObjNav, cross-modal ObjNav, and VLN as interfaces to shared semantic structure, then builds a semantic topological map and grounds language goals through relational blind matching without paired vision-language data.

3.1 Overview

  • The method combines representation-level framing, a semantic topological map with blind language grounding, and real-world deployment on a Unitree Go2 Air quadruped.The pipeline constructs the map, matches language goals to visual clusters, then plans paths and assigns path lengths to segmentation masks for control prediction.Source: §3.1 · pp. 3–4, Figure 2 · p. 4

3.2 Platonic Representation Hypothesis in Embodied Navigation

  • Vision-only ObjNav, cross-modal ObjNav, and VLN are framed as distinct goal interfaces over a shared semantic manifold, based on relational structure preserved across independently trained modalities.Double-centering removes modality-specific row, column, and global means to isolate each concept’s relational position.Source: §3.2 · pp. 4–5
  • Trajectory overlap motivates the hypothesis, but floor-plan constraints and human-annotated target correspondence limit that evidence; PlatonicNav’s non-trivial OVON performance without cross-modal training provides a direct test.The thought experiment compares vision-only ObjNav and VLN in the same scene and target setting; trajectory similarity uses visited nodes, semantic categories, and landmark intersections rather than pixel-level paths.Source: §3.2 · pp. 5–6, Figure 3 · p. 5

3.3 Platonic Topological Maps

  • Platonic Topological Maps represent object segments as a graph whose edges combine geometric distance with semantic distance from self-supervised visual embeddings.The semantic distance is calibrated to geometry’s meter scale, and the edge weights trade off the two distances.Source: §3.3 · p. 6
  • Blind matching assigns category labels to clustered visual prototypes by aligning relational structure from independently pretrained encoders, without paired vision-language data or VLM supervision.Visual nodes are clustered with K-means, and a quadratic-assignment formulation matches visual and language pairwise relations.Source: §3.3 · p. 7
  • Dijkstra selects the minimum hybrid-cost path to any admissible instance of the grounded goal category, favoring semantically meaningful transitions while retaining geometric grounding.When several instances match the query, they are treated as admissible goals.Source: Figure 2 · p. 4, §3.3 · p. 7

4 Experiments

Experiments evaluate PlatonicNav on vision-only ObjNav, open-vocabulary ObjNav, and VLN benchmarks, and include qualitative ObjectNav and VLN executions on a Unitree Go2. Results show competitive navigation across these settings without explicit vision-language supervision.

4.1 Benchmarks and Metrics

  • PlatonicNav achieves higher SPL and SSPL than ObjectReact on HM3D-IIN, outperforms most cross-modal ObjNav methods on HM3D-OVON, and exceeds many VLN baselines on R2R-CE.The R2R-CE comparison also notes that some VLN methods remain ahead.Source: Table 1 · p. 8, §4.1 · pp. 8–9, Table 2 · p. 8
  • Evaluation spans HM3D-IIN instance goals, HM3D-OVON open-vocabulary object categories, and R2R-CE natural-language routes in unseen MP3D environments.IIN reports SPL and SSPL; OVON and R2R-CE report SR and SPL.Source: §4.1 · p. 8
  • Semantic distances from a self-supervised visual encoder improve the topological map’s object-relation reasoning, while blind matching supports language-specified goals without explicit vision-language supervision.The IIN comparison isolates the map’s contribution using purely visual goal selection; OVON and R2R-CE use the full pipeline, including blind-match goal selection.Source: §4.1 · pp. 8–9

4.2 Real-World Evaluation

  • On the Unitree Go2 Air, real-world evaluation includes three ObjectNav teach-and-repeat tasks and VLN executions for instructions to find a lamp, plant, or chair.The map is built offline from a human-guided teaching trajectory and reused during repeat execution; the goal is its terminal topological node, avoiding simulator-only ground-truth masks.Source: §4.2 · p. 9

5 Conclusion … B Meter-scale calibration of Platonic distance

PlatonicNav treats vision-only object navigation, cross-modal object navigation, and vision-language navigation as interfaces to one semantic manifold, using Platonic topological maps to support navigation without explicit cross-modal supervision. The accompanying preliminaries explain blind matching and topological-map representations, while the calibration section puts semantic edge costs on a meter scale.

5 Conclusion

  • PlatonicNav unifies object- and language-driven navigation through intrinsic semantic alignment between independently trained encoders and geodesic traversal over a learned semantic manifold.The conclusion reports generalization across tasks, modalities, sensing configurations, and real-world robot platforms.Source: §5 · p. 9

A.1 Platonic Representation Hypothesis

  • After modality-specific scale normalization, independently trained visual and language encoders preserve relative concept geometry without cross-modal supervision.The hypothesis is framed through pairwise distances between visual and language embeddings.Source: §A.1 · p. 15
  • Blind matching grounds language goals in a vision-only map by aligning visual and language pairwise-distance matrices without paired data or contrastive training.The paper uses this property for language-goal grounding in its topological map.Source: §A.1 · p. 15

A.2 Topological Map for Embodied Navigation

  • Topological maps trade dense mapping’s global geometric consistency for sparse, structure-aware graphs; RoboHop plans through image-segment nodes and spatial-relation edges.Navigation becomes a sequence of segment-level hops.Source: §A.2 · p. 15, Figure 4 · p. 15
  • ObjectReact links object-centric image segments through intra-image 3D distances and cross-view associations, then uses goal-mask overlap and graph shortest paths to produce a dense costmap.A downstream control policy consumes the WayObject Costmap projected onto the input image.Source: §A.2 · p. 15

B Meter-scale calibration of Platonic distance

  • Platonic cosine distance is dimensionless while ObjectReact edge cost is measured in meters, so episode-specific 95th-percentile calibration converts eligible navigation-edge distances before hybrid weighting.Inter-image and same-object association edges are excluded from scale estimation and retain their original geometric costs.Source: B Meter-scale calibration of Platonic… · pp. 15–16
  • The experiments use c = 2.0 to limit outlier influence; calibrated distances keep hybrid weights on a meter scale, and λg = 1 recovers ObjectReact’s geometric graph.If the scale estimate is non-finite or degenerate, the method uses a positive default scale and records the fallback in graph metadata.Source: B Meter-scale calibration of Platonic… · p. 16

C Top-down Trajectory Comparison

PlatonicNav’s trajectories are generally similar in shape to vision-only ObjNav’s, but are more straightforward and efficient in most scenes, consistent with language-level semantic information making actions more meaningful.

C Top-down Trajectory Comparison

  • PlatonicNav’s trajectories are generally similar in shape to vision-only ObjNav’s, but appear more straightforward.Figure 5 compares PlatonicNav with vision-only ObjectReact on HM3D-IIN.Source: Figure 5 · p. 16
  • In most scenes, PlatonicNav acts more efficiently; the authors relate this to language-level semantic information making actions more meaningful.This interpretation is reported as aligning with the main IIN experiment.Source: C Top-down Trajectory Comparison · p. 16

D Real-world Implementation Platform

PlatonicNav is evaluated on a Unitree Go2 quadruped using onboard sensory inputs to build topological maps. The real-world protocol tests object-goal and language-conditioned navigation under noisy observations and limited sensing.

D Real-world Implementation Platform

  • PlatonicNav is deployed on a quadruped Unitree Go2 robot for real-world evaluation.The platform is described as providing robust perception and locomotion.Source: Figure 6 · p. 17
  • Topological maps are constructed from onboard sensory inputs for object-goal and language-conditioned navigation evaluation.The protocol applies to both platforms.Source: D Real-world Implementation Platform · p. 17
  • The experiments test whether semantic distances in representation space guide navigation under noisy observations and limited sensing.Source: D Real-world Implementation Platform · p. 17

E Limitation and future work · F Ablation Study

PlatonicNav is an initial test of the Platonic Representation Hypothesis in embodied navigation, not a fully optimized end-to-end system. Its limitations motivate work on more robust matching, instruction handling, long-distance control, and open-vocabulary navigation.

E Limitation and future work

  • PlatonicNav’s performance is bounded by segmentation, blind matching, language-encoder expressiveness, and the long-distance capability of its ObjectReact-style controller [21].R2R-CE results indicate that handling long natural-language instructions remains challenging.Source: E Limitation and future work · p. 17
  • Future work targets more robust vision-language matching, stronger goal extraction from complex instructions, controller post-training for long-distance navigation, and architecture optimization for open-vocabulary, long-context navigation.Source: E Limitation and future work · p. 17

F.1 Selection of metric for Platonic distance … G Additional Real-world Qualitative Results

The ablations identify L2-normalized cosine distance and a geometry-heavy edge-weight balance as effective choices for Platonic distance and map construction. They also show that segmentation quality substantially affects navigation performance.

F.1 Selection of metric for Platonic distance

  • L2-normalized cosine distance outperforms L2-normalized Euclidean distance on HM3D-IIN, and is selected to compute Platonic distance.The passage attributes the advantage to better capture of semantic information from visual embeddings; L2 normalization removes feature-norm effects so distance reflects semantic direction similarity.Source: §F.1 · pp. 17–18, Table 3 · p. 18

F.2 Selection of (λg, λs)

  • On HM3D-IIN, Platonic Topological Map achieves its best performance with (λg, λs) = (0.8, 0.2).The comparison indicates that adding semantic information to pure geometric edge weights improves navigation efficiency.Source: Table 4 · p. 18, §F.2 · p. 18

F.3 Comparison of Segmentation

  • FastSAM segmentation reduces SPL and SSPL for both ObjectReact and PlatonicNav severely, to nearly half their performance with ground-truth segmentation.Both methods achieve relatively high performance with ground-truth segmentation, according to the comparison.Source: Table 5 · p. 18, §F.3 · p. 18
  • 10 percentage points in SPL and SSPL from 41.1 to 46.6: PlatonicNav improves with SAM2 segmentation.The passage attributes these reported gains to the comparison of segmentation configurations.Source: Table 5 · p. 18, §F.3 · p. 18

F.2 Selection of (λg, λs)

  • With (λg, λs) = (0.8, 0.2), both reported metrics are lower than for the pure geometric topological map, suggesting excess semantic weight may harm navigation.Source: §F.2 · p. 18

F.3 Comparison of Segmentation

  • PlatonicNav’s advantage with both ground-truth and FastSAM segmentation supports the claim that semantic information improves the Platonic Topological Map.Source: §F.3 · p. 18

G.1 ObjectNav Qualitative Results · G.2 VLN Qualitative Results · H Additional Simulation Results

The supplementary qualitative results show ObjectNav visualizations across three tasks’ teach and repeat phases, alongside VLN visualizations for teaching and three repeat-phase goals.

G.1 ObjectNav Qualitative Results

G.2 VLN Qualitative Results

  • VLN has a qualitative visualization for the teach phase.Source: Figure 13 · p. 20
  • VLN repeat-phase qualitative results include the goal “go to the lamp.”Source: Figure 14 · p. 20
  • VLN repeat-phase qualitative results include the goal “find the plant.”Source: Figure 15 · p. 20
  • VLN repeat-phase qualitative results include the goal “go to the chair.”Source: Figure 16 · p. 21

H.1 VLN Simulation Results … J Compute Resources

The supplementary sections show qualitative VLN and ObjNav simulation examples, list external assets with versions and licenses, and report the compute used for experiments.

H.1 VLN Simulation Results

H.2 ObjNav Simulation Results

I External Assets

  • The asset inventory covers HM3D, HM3D-IIN, HM3D-OVON, Matterport3D, R2R-CE/VLN-CE, ETPNav trajectories, Habitat-Sim, and Habitat-Lab.It lists versions or identifiers and license terms; HM3D-derived data are governed by Matterport terms, while several code releases are MIT-licensed.Source: I External Assets · p. 26
  • The inventory also records ETPNav trajectories, Habitat-Sim and Habitat-Lab versions, and licenses or availability notes for ObjectReact, It’s a Match, DINOv3, SAM2, and GTR-T5-base.ObjectReact lacks an upstream license file; DINOv3 uses its own license, while It’s a Match is MIT-licensed and SAM2 is Apache-2.0.Source: I External Assets · p. 26

J Compute Resources

  • Each PlatonicNav run used one NVIDIA H100 GPU, 4–8 CPU cores, and up to 64 GB RAM; mapping and feature caching used one NVIDIA L40 GPU.Four reported experiments consumed roughly 100–150 H100-hours, with a comparable amount spent on earlier method iterations omitted from the paper.Source: J Compute Resources · p. 26

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