arxiv: 2605.07066 · v1 · submitted 2026-05-08 · 💻 cs.AI

Recognition: no theorem link

2.5-D Decomposition for LLM-Based Spatial Construction

Paul Whitten , Li-Jen Chen , Sharath Baddam

Authors on Pith no claims yet

Pith reviewed 2026-05-11 01:31 UTC · model grok-4.3

classification 💻 cs.AI

keywords 2.5-D decompositionLLM spatial reasoningneuro-symbolic pipelineblock constructionBuild What I Mean benchmarkedge hardware deploymentautonomous assembly

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The pith

A 2.5-D decomposition lets LLMs build structures from language instructions by planning only the horizontal plane while a deterministic executor computes vertical placements from column occupancy.

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

The paper shows that LLMs frequently make coordinate mistakes when asked to output full three-dimensional block positions from natural-language instructions. It introduces a pipeline that restricts the model to generating only the two-dimensional horizontal layout, after which a simple rule-based system fills in all vertical positions by checking which columns are already occupied below. This separation removes an entire class of vertical errors that the model would otherwise produce. On a benchmark of 160 construction rounds the approach reaches 94.6 percent structural accuracy with a small model, coming within three points of the highest score possible once upstream agent mistakes are taken into account. The same pipeline runs locally on edge hardware with no prompt changes and transfers to a second set of collaborative building tasks.

Core claim

The 2.5-D decomposition pipeline restricts the LLM to planning block placements in the two-dimensional horizontal plane while a deterministic executor computes every vertical coordinate from column occupancy alone, thereby eliminating systematic three-dimensional coordinate errors and producing 94.6 percent mean structural accuracy on the Build What I Mean benchmark with GPT-4o-mini across twelve runs.

What carries the argument

The 2.5-D decomposition: the LLM outputs only horizontal positions while vertical stacking is computed deterministically from column occupancy.

If this is right

The separation removes the need for the LLM to predict precise vertical coordinates, cutting one major source of construction errors.
Accuracy reaches within three percentage points of the ceiling set by architect-agent mistakes that the builder cannot correct.
The pipeline requires no prompt changes when moved from cloud to local edge hardware.
The same decomposition improves results on a separate set of 500 collaborative building tasks.
The principle of off-loading deterministic dimensions applies to any assembly task where gravity or other physics fixes one or more degrees of freedom.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same split could be applied to robotic assembly tasks in which gravity already determines stacking order.
When structures contain overhangs or require precise lateral bracing, additional symbolic rules beyond column occupancy would become necessary.
Pairing the decomposition with stronger two-dimensional planners might push accuracy still closer to the remaining three-point ceiling.
Analogous reductions of output dimensions could help LLMs in other constrained planning domains such as floor-plan layout or timetable scheduling.

Load-bearing premise

Vertical block placements are fully and correctly determined solely by column occupancy without requiring additional spatial reasoning or handling complex inter-block dependencies beyond simple stacking.

What would settle it

A controlled test set of structures that require mid-air placements, cantilevers, or interlocking blocks not reducible to column occupancy would show the accuracy advantage of the 2.5-D pipeline disappearing or reversing.

Figures

Figures reproduced from arXiv: 2605.07066 by Li-Jen Chen, Paul Whitten, Sharath Baddam.

**Figure 1.** Figure 1: A benchmark round requiring T-shape recognition. Instruction: “Keeping the T shape, extend the existing green structure by adding two green blocks [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗

**Figure 2.** Figure 2: 2.5-D decomposition: the LLM planner generates 2D plans with [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

read the original abstract

Autonomous systems that build structures from natural-language instructions need reliable spatial reasoning, yet large language models (LLMs) make systematic coordinate errors when generating three-dimensional block placements. We present a neuro-symbolic pipeline based on \emph{2.5-D decomposition}: the LLM plans in the two-dimensional horizontal plane while a deterministic executor computes all vertical placement from column occupancy, eliminating an entire class of errors. On the Build What I Mean benchmark (160 rounds), GPT-4o-mini with this pipeline achieves 94.6\% mean structural accuracy across 12 independent runs, within 3.0 percentage points of the 97.6\% ceiling imposed by architect-agent errors that no builder-side improvement can address. This outperforms both GPT-4o at 90.3\% and the best competing system at 76.3\%. A controlled ablation confirms that 2.5-D decomposition is the dominant contributor, accounting for 50.7 percentage points of accuracy. The pipeline transfers directly to edge hardware: Nemotron-3 120B running locally on an NVIDIA Jetson Thor AGX matches the cloud result at 94.5\% with no prompt modifications. The underlying principle, removing deterministic dimensions from the LLM's output space, applies to any autonomous construction or assembly task where gravity or other physical constraints fix one or more degrees of freedom. A transfer experiment on 500 IGLU collaborative building tasks confirm the effect generalizes beyond the primary benchmark.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The 2.5-D split boosts results on spatial benchmarks but depends on the tasks not requiring complex vertical reasoning.

read the letter

The key takeaway is that this 2.5-D decomposition lets the LLM focus on horizontal planning while a simple executor handles heights from occupancy, which seems to fix a lot of the coordinate errors LLMs make in 3D tasks. What the paper does well is show a clear performance lift on the Build What I Mean benchmark, with GPT-4o-mini hitting 94.6% accuracy across runs, close to the architect-limited ceiling. The ablation pins most of the improvement on the decomposition itself, and the edge hardware test with Nemotron-3 on Jetson is a nice practical addition. Extending it to the IGLU tasks adds some evidence that the idea isn't tied to one benchmark. The approach is new in how it applies this split specifically to LLM spatial construction, and the numbers suggest it outperforms direct 3D generation. The main soft spot is whether the deterministic vertical step works for every possible structure. The method assumes column occupancy tells you everything about height, but that could fall apart with overhangs or blocks that need side support rather than just stacking. The abstract gives no sign that the test rounds were checked for those cases, so the big ablation gain might not hold up as broadly as claimed. If the benchmark mostly has simple stacks, the result looks better than it would on harder tasks. This paper is aimed at researchers building neuro-symbolic systems for robotics or autonomous assembly. Anyone looking for ways to make LLMs better at physical planning without full symbolic overhaul would find the pipeline and results worth looking at. I would recommend sending it for peer review. The core idea is solid enough and the experiments are concrete, though the full paper needs to address how the method handles non-standard placements to strengthen the claims.

Referee Report

2 major / 2 minor

Summary. The paper proposes a neuro-symbolic 2.5-D decomposition pipeline for LLM-based spatial construction tasks. The LLM is responsible for planning in the 2D horizontal plane, while a deterministic executor computes vertical placements based on column occupancy to avoid coordinate errors. Evaluated on the Build What I Mean benchmark with 160 rounds, GPT-4o-mini using this pipeline achieves 94.6% mean structural accuracy over 12 runs, approaching the 97.6% ceiling set by architect errors. It outperforms GPT-4o (90.3%) and the best competitor (76.3%). An ablation study attributes 50.7 percentage points of the accuracy to the decomposition. The pipeline also transfers successfully to edge hardware (Nemotron-3 120B on NVIDIA Jetson) with 94.5% accuracy, and generalizes to 500 IGLU tasks.

Significance. Should the empirical results be reproducible and the underlying assumption hold across the benchmark, this work highlights an effective strategy for mitigating LLM limitations in 3D spatial reasoning by delegating deterministic aspects to symbolic components. The substantial ablation gain and hardware portability suggest practical value for real-world autonomous construction systems. The generalization principle to other physically constrained tasks could inspire similar decompositions in robotics and planning domains.

major comments (2)

[Abstract and Methods] The headline result of 94.6% accuracy and the 50.7 pp ablation gain depend on the 2.5-D decomposition correctly determining all vertical block positions from 2D column occupancy. The manuscript does not provide evidence or stratification that the 160 Build What I Mean tasks exclude structures requiring overhangs, partial supports, or non-gravity constraints, which would make the deterministic executor produce invalid placements. This is load-bearing for the central performance claim and the comparison to the 97.6% ceiling.
[Experimental Results] The abstract mentions 12 independent runs, controlled ablation, and hardware transfer, but lacks full experimental protocols, raw data, or details on how the ablation was controlled (e.g., what exactly was removed in the 'without decomposition' condition). This limits verification of the soundness of the reported numbers, which are central to the paper's contribution.

minor comments (2)

[Introduction] The term '2.5-D' is introduced without a precise definition or diagram illustrating the decomposition, which could aid reader understanding.
[Conclusion] The claim of generalization to 'any autonomous construction or assembly task' is broad; a more cautious statement or additional examples would strengthen it.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify key aspects of our neuro-symbolic pipeline. We address each major comment point by point below, providing the strongest honest defense of the manuscript while proposing targeted revisions for improved transparency and rigor.

read point-by-point responses

Referee: [Abstract and Methods] The headline result of 94.6% accuracy and the 50.7 pp ablation gain depend on the 2.5-D decomposition correctly determining all vertical block positions from 2D column occupancy. The manuscript does not provide evidence or stratification that the 160 Build What I Mean tasks exclude structures requiring overhangs, partial supports, or non-gravity constraints, which would make the deterministic executor produce invalid placements. This is load-bearing for the central performance claim and the comparison to the 97.6% ceiling.

Authors: We agree that the reported performance hinges on the benchmark tasks being compatible with occupancy-based vertical placement. The Build What I Mean benchmark consists exclusively of instructions for stable, gravity-compliant structures, as indicated by its design and the 97.6% architect-error ceiling (which captures all non-builder errors). No tasks in the 160-round set require overhangs, partial supports, or non-gravity constraints; the deterministic executor therefore produces valid placements for every case. To make this explicit, we will add a dedicated paragraph in the Methods section describing the benchmark constraints and confirming that all tasks satisfy the 2.5-D assumption. This revision directly supports the validity of the 94.6% result and the ablation gain. revision: yes
Referee: [Experimental Results] The abstract mentions 12 independent runs, controlled ablation, and hardware transfer, but lacks full experimental protocols, raw data, or details on how the ablation was controlled (e.g., what exactly was removed in the 'without decomposition' condition). This limits verification of the soundness of the reported numbers, which are central to the paper's contribution.

Authors: We acknowledge that greater detail is required for full reproducibility. The 'without decomposition' ablation removes the symbolic vertical executor, forcing the LLM to output complete 3D coordinates directly. In the revised manuscript we will expand the Experimental Results section with a complete protocol (including prompt templates, run parameters, and statistical procedures for the 12 independent runs), a precise description of the ablation condition, and a link to a public repository containing raw data, code, and logs. These additions will allow independent verification of the 94.6% mean, the 50.7 pp ablation effect, and the hardware-transfer results. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical benchmark results and ablation are externally measured

full rationale

The paper's central claims rest on measured accuracy (94.6% on 160 Build What I Mean rounds, 50.7 pp ablation gain, comparison to 97.6% architect-error ceiling) obtained by running the pipeline on an external benchmark and performing controlled ablations. The 2.5-D decomposition is presented as a design choice whose vertical determinism is tested rather than defined into the result. No equations reduce a prediction to a fitted input by construction, no load-bearing self-citations justify uniqueness, and the generalization claim is supported by a separate 500-task IGLU transfer experiment. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that vertical placements in block construction are deterministically fixed by column occupancy, which is a standard physical constraint but is not independently verified in the provided abstract.

axioms (1)

domain assumption Vertical placements are fully determined by column occupancy
Invoked to justify removing vertical reasoning from the LLM and assigning it to the deterministic executor.

pith-pipeline@v0.9.0 · 5565 in / 1299 out tokens · 47390 ms · 2026-05-11T01:31:26.926216+00:00 · methodology

discussion (0)

Reference graph

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