Relative Position Matters: Trajectory Prediction and Planning with Polar Representation

Bingzhao Gao; Bozhou Zhang; Li Zhang; Nan Song

REVIEW 3 major objections 3 minor 32 references

Relative Position Matters: Trajectory Prediction and Planning with Polar Representation

T0 review · 3 major / 3 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper claims that representing the entire driving scene in polar coordinates rather than Cartesian yields state-of-the-art trajectory prediction and planning.

desk verdict The supplied full text is a different arXiv paper, so Polaris is an abstract-only submission; the SOTA claim is unverifiable. read the letter →

arxiv 2508.11492 v1 pith:QLGAMQEU submitted 2025-08-15 cs.RO cs.CV

Bozhou Zhang , Nan Song , Bingzhao Gao , Li Zhang This is my paper

classification cs.ROcs.CV

keywords trajectorypredictionautonomousdrivingpolarcoordinatesmotionplanningArgoverse2nuPlanrelativepositionspatialrepresentation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that the polar coordinate system, in which positions are encoded by radius and angle, is a better representational frame for trajectory prediction and planning in autonomous driving than the standard Cartesian frame. It proposes Polaris, a method that keeps all inputs, internal computations, and decoded trajectories in polar coordinates, with dedicated modules that model how other traffic elements influence the ego vehicle through explicit distance and direction relationships. The authors report that Polaris achieves state-of-the-art performance on the Argoverse 2 prediction benchmark and the nuPlan planning benchmark. If correct, this suggests that a carefully chosen coordinate frame can embed spatial inductive biases directly into a network architecture, improving behavior without requiring new sensors or more data.

What carries the argument

The central object is the polar coordinate representation (r, θ) applied uniformly to agent histories, map elements, and headings, with a corresponding polar-space decoding of future trajectories. This representation explicitly models distance variation along the radius and direction variation along the angle, so the network can weight nearby versus distant and same-direction versus crossing elements in a geometrically natural way. Dedicated encoding and refinement modules are designed to capture relative relationships within this polar frame, and the whole pipeline stays in polar coordinates rather than converting back to Cartesian.

What would settle it

A controlled experiment in which a Cartesian coordinate model with the same encoder and decoder architecture, same parameter count, and same training schedule matches or beats Polaris on the Argoverse 2 validation set would directly falsify the claim that the polar representation is the cause of the improvement.

Watch

Extended reading notes

Core claim

Polaris is a trajectory prediction and planning method that operates entirely in polar coordinates. Unlike conventional Cartesian-based approaches that encode agent positions, map geometry, and headings in x-y space, Polaris represents every element relative to the ego vehicle as a radius and an angle. The paper argues that this representation naturally captures the varying influence of surrounding elements based on their relative distances and directions, and that dedicated encoding and refinement modules in polar space preserve this structure through to the final trajectory output. On the Argoverse 2 and nuPlan benchmarks, Polaris is reported to achieve state-of-the-art performance, suppor

Load-bearing premise

The load-bearing premise is that converting all scene information into polar coordinates preserves enough global context while making relative distance and direction easier to model, and that the reported performance gains come from this representation rather than from the added modules or benchmark-specific tuning.

Editorial extensions

If this is right

If Polaris is correct, coordinate-frame choice becomes a first-order design decision for trajectory prediction and planning, not a preprocessing detail.
A polar representation provides a built-in inductive bias for egocentric driving tasks, where the ego vehicle's own frame is the natural reference for nearby obstacles and lane geometry.
The reported state-of-the-art results on both prediction and planning suggest that a single unified polar pipeline can serve both tasks, potentially reducing the need for task-specific architectures.
The approach implies that distance and direction influence can be modeled explicitly, rather than learned implicitly, which may improve interpretability of motion forecasts.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's central claim would be strengthened by a controlled comparison against a Cartesian model with equivalent architecture, parameter count, and training budget; the reported experiments were not available in the review, so this isolation of the polar effect remains unverified.
Polar coordinates may combine naturally with attention mechanisms that already weight by relative position, suggesting a testable extension where polar position encodings replace or augment learned attention biases.
The same polar framing could extend to other egocentric prediction problems, such as pedestrian intent estimation or robot arm motion planning, where relative direction and distance are also decisive.
A potential risk is that the polar transformation loses global spatial context, so a practical extension would be to test whether adding a coarse Cartesian global feature, while retaining polar local features, improves robustness.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's the thing: the manuscript body for 2508.11492 is not the Polaris paper. It's the full text of KV-Auditor, an unrelated LDP auditing paper (arXiv:2508.11495). So as reviewed, Polaris consists of an abstract and nothing else. Your UNVERDICTED call is the right one; I can't add anything beyond that.

What the abstract does suggest: switching from Cartesian to polar coordinates for vehicle interaction modeling is a plausible, low-cost change that could be layered onto existing prediction and planning stacks. The claim to operate entirely in polar coordinates with dedicated encoding and refinement modules is a concrete architectural statement, and if the experiments bear it out, it would be a useful engineering contribution on Argoverse 2 and nuPlan. The motivating idea—that relative distance and direction matter in driving contexts—is reasonable; there's no obvious conceptual flaw there.

The problem is that every load-bearing part is missing. No method details, no ablations, no metrics, no error bars, no comparison protocol. The SOTA claim is literally just the abstract. The premise that a polar representation preserves the necessary Cartesian information is an empirical question, and there's no evidence here. The novelty claim about being the first fully polar method also needs a careful check against prior work on polar and relative representations, and we can't do that check. We also can't comment on whether the experiments are tuned to the test benchmarks—that risk is unaddressed.

I should say: this looks like a pipeline error, not necessarily a bad paper. The authors may have a complete paper under that arXiv ID. But as reviewers we can only assess what's in front of us, and this package has no substance.

My recommendation: don't send this to referees in its current form. Flag the metadata mismatch, retrieve the actual Polaris PDF, and then evaluate that. If the real paper has the experiments and ablations the abstract implies, it could well deserve a serious review. Based on this package, it's unverdictable.

Referee Report

3 major / 3 minor

Summary. The submission is for arXiv:2508.11492, titled "Relative Position Matters: Trajectory Prediction and Planning with Polar Representation," but the supplied full text is an unrelated paper, "KV-Auditor: Auditing Local Differential Privacy for Correlated Key-Value Estimation" (arXiv:2508.11495v1 [cs.CR]), by different authors. The only content belonging to the claimed paper is the abstract, which proposes 'Polaris,' an architecture operating entirely in polar coordinates for trajectory prediction and planning, and asserts state-of-the-art results on Argoverse 2 and nuPlan. No methods, equations, experimental setup, results tables, ablations, error bars, or code are present. Treating the provided full text as the manuscript under review, the manuscript does not contain the paper it claims to be, and none of the central claims can be verified.

Significance. If the Polaris method exists and performs as the abstract claims, the idea of replacing Cartesian representations with a fully polar coordinate system for trajectory prediction and planning could be a useful contribution to autonomous driving research. However, as submitted, there is no evidence to evaluate: no architecture description, no theoretical justification beyond the intuition stated in the abstract, no benchmark comparisons, and no reproducibility artifacts. The potential significance is entirely conditional on content that is absent from the manuscript.

major comments (3)

[Full Text] The full text supplied is the KV-Auditor paper (arXiv:2508.11495v1 [cs.CR]), not the Polaris paper under review. This is not a minor formatting issue: every load-bearing claim in the abstract—the polar-coordinate encoding, the dedicated refinement modules, the Argoverse 2 and nuPlan results—is unsupported by any in-scope body text. I treat this as a missing-support flag, as instructed.
[Abstract, 'Extensive experiments ... demonstrate that Polaris achieves state-of-the-art performance'] The abstract reports no quantitative results, no comparison baselines, no ablations, no error bars, and no statistical significance tests. Even if the correct full text were present, this sentence alone is insufficient to substantiate a state-of-the-art claim; as submitted, no experiments are visible at all.
[Abstract, 'operates entirely in Polar coordinates'] The central architectural premise—that converting all inputs to polar coordinates preserves the information needed for prediction and planning while better capturing relative distance and direction—is not demonstrated or even described. There is no account of how map geometry, agent headings, or global context are encoded, nor any analysis of potential information loss or degeneracy at the origin. This premise is load-bearing and cannot be assessed.

minor comments (3)

[Overall submission] The title, abstract, and full text describe entirely different papers. A complete, self-contained manuscript for the Polaris work is required before any meaningful review can occur.
[References] The reference list is exclusively from the KV-Auditor paper and is therefore irrelevant to the claimed Polaris work. This further confirms that the wrong full text was included.
[Authorship] The full text lists authors and affiliations for KV-Auditor, not for the Polaris submission. The submitted record needs to identify the correct authors and affiliations for the paper under review.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity identified: the provided text contains only the abstract of Polaris and an unrelated full paper, so no derivation chain exists to be circular.

full rationale

The submitted manuscript content for arXiv:2508.11492 is incomplete: the abstract describes Polaris, a polar-coordinate trajectory prediction and planning method, but the full text supplied is actually the unrelated KV-Auditor paper (arXiv:2508.11495). The only Polaris content available is the abstract. The abstract makes two kinds of claims: (1) a representational motivation—that Cartesian coordinates do not naturally capture relative distance/direction influence, and polar coordinates do; and (2) an empirical claim—that Polaris achieves state-of-the-art performance on Argoverse 2 and nuPlan. There are no equations, no fitted parameters, no self-citations, no imported uniqueness theorems, and no ansatz smuggling evident in this abstract. The performance claim is evaluated against external public benchmarks and therefore is not defined in terms of the method's own outputs. The representational claim is a design premise, not a derived result; it does not reduce to a fitted input or a renamed known result. Because the full derivation/experimental section is missing, no circular step can be exhibited, and no speculation about hidden circularity is warranted. The verifiability concern—that the body text is absent—is a correctness/reproducibility issue, not a circularity issue. Consistent with the default expectation and the proportional scoring rule, the circularity score is 0.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The ledger is minimal because the review is abstract-only. Polaris introduces an architecture, not a new physical entity, force, or conserved quantity. The only free parameter class is the undisclosed polar encoding and network design; the axioms are the representational premise of the abstract plus two unstated assumptions about information preservation and benchmark validity. All entries would need revision once the actual manuscript is available.

free parameters (1)

Polar encoding hyperparameters and architecture choices = not disclosed in abstract
A polar representation requires choices for radius and angle ranges, discretization, the depth of the encoding and refinement modules, and loss weights. These are typically tuned per benchmark. The abstract does not report them and the full text is unavailable.

assumptions (3)

domain assumption Relative influence of traffic elements is better captured by distance and direction than by Cartesian offsets.
Motivating premise of the method, stated in the abstract: Cartesian space 'does not naturally capture the varying influence of different elements based on their relative distances and directions'. If false, the polar architecture has no expected advantage.
domain assumption All inputs (agent histories, map geometry, headings, velocities) can be converted to polar coordinates without loss of information that matters for prediction and planning.
Unstated but load-bearing: a fully polar pipeline must encode curved map lanes and global context through angles and radii; the abstract does not address how orientation or global consistency is preserved. The missing full text would contain this design.
domain assumption Benchmark metrics on Argoverse 2 and nuPlan are a valid proxy for the claimed improvement.
The empirical claim is a state-of-the-art benchmark statement; if the benchmarks fail to capture the polar advantage, the claim loses its supporting evidence.

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Cite this review

Pith. "Pith review of Relative Position Matters: Trajectory Prediction and Planning with Polar Representation." pith.science (2026). https://pith.science/paper/QLGAMQEU

@misc{pith2026250811492,
  author       = {Pith},
  title        = {Pith review of: Relative Position Matters: Trajectory Prediction and Planning with Polar Representation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QLGAMQEU}},
  note         = {Machine review of arXiv:2508.11492}
}

read the original abstract

Trajectory prediction and planning in autonomous driving are highly challenging due to the complexity of predicting surrounding agents' movements and planning the ego agent's actions in dynamic environments. Existing methods encode map and agent positions and decode future trajectories in Cartesian coordinates. However, modeling the relationships between the ego vehicle and surrounding traffic elements in Cartesian space can be suboptimal, as it does not naturally capture the varying influence of different elements based on their relative distances and directions. To address this limitation, we adopt the Polar coordinate system, where positions are represented by radius and angle. This representation provides a more intuitive and effective way to model spatial changes and relative relationships, especially in terms of distance and directional influence. Based on this insight, we propose Polaris, a novel method that operates entirely in Polar coordinates, distinguishing itself from conventional Cartesian-based approaches. By leveraging the Polar representation, this method explicitly models distance and direction variations and captures relative relationships through dedicated encoding and refinement modules, enabling more structured and spatially aware trajectory prediction and planning. Extensive experiments on the challenging prediction (Argoverse 2) and planning benchmarks (nuPlan) demonstrate that Polaris achieves state-of-the-art performance.

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Reference graph

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

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Arcolezi, Sébastien Gambs, Jean-François Couchot, and Catuscia Palamidessi

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work page arXiv 2023

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John C Duchi, Michael I Jordan, and Martin J Wainwright. 2013. Local privacy and statistical minimax rates. In 2013 IEEE 54th annual symposium on foundations of computer science. IEEE, 429–438

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