Measuring Spatial Priors in Generative Image Models Using Geometry-Based Field Metrics

An Observational Behavioral Framework for Compositional Analysis

---

1. Introduction

Current generative model evaluation focuses on whether an image satisfies its prompt: does the specified object appear, are relationships correct, does the composition resemble real-world photographs, does the text–image alignment score favorably? These are meaningful questions. They are not the only questions.

A model can satisfy every one of these criteria while still expressing a persistent spatial bias, a systematic tendency to place visual mass in particular regions of the frame, to leave certain zones consistently empty, to organize structure in ways that recur across wildly different semantic content. A photographic portrait and a landscape and an abstract composition can all pass semantic evaluation while the generating engine composes all three with the same underlying spatial logic. This regularit is not aesthetic variation. It is a measurable geometric pattern.

Spatial behavior remains a largely uninstrumented dimension of generative model evaluation. The gap is not aesthetic. It is geometric. Models do not merely place objects, they compose. They operate inside a spatial prior field: a set of habitual attractors and characteristically avoided regions that govern where mass settles, how void is allocated, and how the model responds to pressure toward its structural boundaries. These patterns are observable in rendered output. They do not require model access, training data inspection, or semantic analysis to detect.

This paper presents a framework for measuring these patterns directly. The framework makes three contributions: (1) a five-metric spatial kernel that locates generated images in a low-dimensional compositional coordinate space; (2) observational characterization of engine-specific spatial priors, attractor basins, and perturbation drift behaviors across 14 platforms; and (3) a validation demonstration showing that semantic diversity does not materially disrupt geometric uniformity within a single engine, confirming the kernel is measuring stable behavioral structure rather than content-related variance.

This is an observational behavioral framework. Claims are derived from output behavior rather than internal model inspection. Field-theoretic language used in the framework, attractors, basins, and perturbation forces, is conceptual scaffolding, not a mechanistic claim about model internals. The framework measures what a model does spatially; it does not assert why.

---

2. The Spatial Prior Kernel

2.1 Core Metrics

The kernel consists of five geometric primitives, each measuring a distinct dimension of spatial structure. Together they project any image into a low-dimensional compositional coordinate space that is invariant under semantic content variation while remaining sensitive to spatial configuration changes.

2.2 Optional Extensions

Two additional metrics extend the kernel for analyses where directional structure or material weight are relevant:

• θ — Orientation Stability: Entropy-based measure of directional alignment consistency. High values indicate structural coherence; low values indicate isotropic or chaotic arrangement.
• dₛ — Structural Thickness: Skeleton-normalized material weight. Distinguishes thin dispersed structures from volumetrically heavy consolidated forms.

2.3 Kernel Vector

Each image is represented as a kernel vector:

Values are normalized for comparability across engines. The kernel is designed to be invariant under semantic content variation — different objects, scenes, and prompt styles, while remaining sensitive to spatial configuration. In qualitative analysis across 1,000+ cross-engine samples, these five variables accounted for the majority of observable spatial variance.

2.4 Design Constraints

The kernel is built around three non-negotiable requirements: (1) no model access, all measurements extract from rendered output only; (2) semantic orthogonality, metrics capture spatial structure, not content, meaning, or aesthetic quality; (3) determinism, the same image must produce the same coordinates in any compliant implementation. These constraints make the framework applicable across closed commercial systems and suitable for version-controlled regression baselines.

---

3. Stable Compositional Priors

3.1 Spatial Priors as Attractor Basins

A spatial prior is a repeatable distributional tendency in kernel coordinates observable across prompt variation and seed sampling. It is not a single image property but a statistical regularity: the same engine, given semantically diverse prompts, produces a characteristic signature in (Δx, rᵥ, ρᵣ, μ, xₚ) space that is stable enough to classify and fingerprint.

Using field-theoretic language as a conceptual model, not as a claim about internal model physics, each engine can be described as having an attractor: a preferred compositional state toward which outputs tend to return under perturbation. Stable attractors correspond to low-variance regions in kernel space. Outputs that drift away from an attractor under prompt pressure may exhibit characteristic geometric patterns: void expansion, cohesion loss, centroid displacement, and ultimately structural collapse before semantic content degrades.

3.2 Same Prompt, Four Spatial Priors

A single prompt delivered to four engines produces four distinct spatial solutions. The variation is geometric, not semantic: the prompt is satisfied in all four cases, but the compositional logic differs fundamentally across platforms.

The prompt below was delivered across four platforms. Kernel coordinates reveal engine-specific compositional logic that no semantic metric would detect:

"A single object placed near a wall, lit softly from one side. Neutral color palette. No decoration, no text, no additional objects. Photographic, simple, quiet."

Note: Coordinates are normalized relative spatial descriptors, not performance metrics. They capture ordering, basin identity, drift direction, and relative magnitude, the phenomena under study.

3.3 The Basin Field Map

When extended across multiple engines and prompt families, kernel coordinates cluster into distinguishable basins, stable regions of compositional space that each engine characteristically occupies. These clusters remain stable across diverse prompt families, confirming that the kernel is reading spatial prior bias rather than one-off stylistic artifacts.

Four basin types are identifiable in cross-engine observation:

• B1: Left-weighted compression: Low Δx, low rᵥ, high ρᵣ. Dense, edge-anchoring. Characteristic of MidJourney.
• B2: Center-stable, moderate density: Low Δx, moderate rᵥ. Balanced default geometry. Characteristic of GPT in neutral prompts.
• B3: Right-pull, high void: High Δx, high rᵥ, low ρᵣ. Minimalist, edge-weighted. Characteristic of Sora; OpenArt in spatial prompts.
• B4: Architectural void-driven: High rᵥ, high xₚ, low μ. Open-field geometry with peripheral edge tension.

---

4. Perturbation Drift and Geometric Collapse

4.1 Perturbation Protocol

Perturbation tests measure how engines respond to progressive spatial pressure while maintaining semantic equivalence: the subject, framing, and lighting instructions are held constant while spatial placement instructions shift incrementally. The change in kernel coordinates across perturbation steps, ΔK = K(I_p') − K(I_p), reveals each engine's characteristic drift direction and resistance profile.

4.2 Engine-Specific Drift Patterns

Under small prompt variation or spatial intensity changes, each engine exhibits a predictable, architecturally specific drift pattern. Movement is not random; it follows characteristically different paths per engine:

These differences are architecturally diagnostic: the same spatial instruction produces disproportionate structural corrections in each engine, expressed as distinct signatures in kernel space. The patterns are reproducible across prompt families and independent generation runs.

4.3 Geometric Collapse and Restoration

Under continued perturbation, engines can cross into instability: a geometric state in which multiple kernel values decline simultaneously, indicating that the engine's compositional structure is no longer maintaining its prior. This collapse is observable and measurable before semantic errors become apparent.

Collapse-restoration cycles have a consistent structure:

Collapse onset (Step 1): Δx ↓, rᵥ ↓, ρᵣ ↓, μ ↓, xₚ ↓ — simultaneous decline across metrics indicates structural destabilization.

Schema restoration (Steps 2–3): Δx ↑, rᵥ ↑, ρᵣ ↑, μ ↑, xₚ ↑ — the engine seeks to recover its habitual spatial configuration, producing characteristic restoration movements toward its attractor.

4.4 Semantic vs. Spatial Failure

The following sequence illustrates how geometric drift precedes semantic failure. All three stages satisfy the base semantic prompt; only kernel coordinates reveal the structural degradation:

---

5. Validation: Semantic Diversity, Geometric Uniformity

The central validation question is whether the kernel is measuring stable behavioral priors or content-related variance. If the framework is measuring genuine spatial priors, then semantically diverse prompts, different categories of objects, scenes, and subjects, should cluster in the same region of kernel space within a single engine. Semantic content should not break the geometric fingerprint.

The following validation tests this prediction directly. 100 semantically diverse prompts spanning eight categories (people, animals, architecture, objects, nature, abstract, weather, sky/underwater) were delivered to multiple engines. Kernel coordinates were extracted from all outputs.

5.1 Sora: n = 200 images

Despite large semantic variation across eight content categories, Sora's outputs occupy a tight, bounded region of compositional space. The geometric constraints are absolute:

• No images achieve |Δx| > 0.11 — horizontal placement uses only 22% of its theoretical range
• No images achieve rᵥ < 0.80 — all outputs are at least 80% void regardless of semantic content
• No category-specific clusters or secondary modes — animals, people, landscapes, and abstract prompts are geometrically indistinguishable

5.2 MidJourney: n = 400 images

As with Sora, all eight semantic categories occupy the same region of (Δx, rᵥ) space. No category breaks free. MidJourney shows slightly wider spread than Sora (xₚ std = 0.097 vs 0.064), consistent with its higher within-engine compositional diversity, but the clustering remains tight relative to the theoretical coordinate range.

5.3 OpenArt: n = 200 images

OpenArt exhibits similar boundedness: Δx = 0.0034 ± 0.037, rᵥ = 0.841 ± 0.032, xₚ = 0.421 (moderate edge engagement). 94.0% of images cluster in the centered basin (|Δx| ≤ 0.06, 0.80 ≤ rᵥ ≤ 0.94), with the remaining 5.0% accessing dense frames via thick structural rendering (dₛ = 0.0191). Eight semantic categories occupy the same region without exception.

5.4 Cross-Engine Fingerprinting

The validation data establishes engine-specific fingerprints: characteristic kernel signatures that are stable across independent generation runs and differentiating across engines. The same furniture prompt run across all four engines produces consistently distinct spatial coordinates, not because of subject variation but because of architectural compositional prior differences:

---

6. Why Semantic Metrics Cannot Detect This

Current evaluation frameworks such as IS, FID, KID, CLIPScore, T2I-CompBench, and GenEval all measure some combination of semantic correctness, object/attribute/relationship fidelity, feature-space realism, text satisfaction, and diversity. They evaluate what a model generated. The kernel evaluates how the model composes.

This distinction is structural, not rhetorical. Semantic validity can remain fully stable while geometric structure diverges. The validation data demonstrates this directly: Sora generates semantically diverse images across eight content categories, all of which are geometrically indistinguishable. CLIP, FID, and aesthetic predictors all vary with semantic content; kernel coordinates remain bounded. The kernel is reading a different signal.

Specifically, no existing standard metric captures:

• Spatial attractors: the habitual compositional defaults of a given engine
• Boundary behavior: what happens at the edges of an engine's stable basin
• Drift under perturbation: how kernel coordinates move as spatial pressure increases
• Compression and cohesion dynamics: how density and structural unity change under load
• Geometric collapse: structural failure that precedes semantic error

Composition is a form of model reasoning, not merely a visual outcome. Benchmarks can determine whether the content is present; they cannot determine how the model wants to arrange the world.

---

7. Applications

The spatial prior framework enables a set of evaluation and monitoring capabilities not available through semantic metrics:

---

8. Limitations

Masking accuracy

Material cluster identification, isolating the primary subject and its shadow/lighting region from the background, remains a fundamental challenge in computer vision and directly affects measurement quality. Vision LLMs (GPT-4o, Claude, Gemini Pro Vision) show reasonable semantic accuracy for well-composed images but fail on some edge cases. Traditional CV methods (Otsu thresholding, saliency detection, edge-based detection) are available as fallbacks. Kernel measurements are robust to reasonable segmentation variance because they measure macro-level compositional behavior rather than pixel-level precision; however, severe masking failure produces unreliable coordinates. Failures should be reported as null masks rather than suppressed.

Statistical validation scope

The validation presented here demonstrates boundedness and invariance, that kernel coordinates are geometrically constrained and stable across semantic variation within engines. It does not constitute formal statistical hypothesis testing. Cross-engine differences are consistently large and interpretable; formal significance testing and confidence intervals remain future work. The framework is presented as empirically grounded and reproducible in principle; full statistical characterization is ongoing.

Field-theoretic framing

The attractor/basin/perturbation language used in this framework is interpretive scaffolding, not a physical model of generative systems. No claim is made about internal model mechanisms, training data structure, or architectural properties. The framework describes what models do geometrically in their outputs; it does not explain why they do it.

Normalization and comparability

Coordinates are normalized for within-study comparability. Cross-study comparison requires consistent masking method, resolution normalization, and kernel implementation. A deterministic reference implementation is under preparation for public release.

---

9. Conclusion

Generative models express consistent spatial priors, habitual compositional structures that persist across semantic variation, respond to perturbation in characteristically engine-specific ways, and collapse predictably when pushed beyond structural boundaries. These patterns are invisible to semantic evaluation and measurable through geometric analysis of rendered output.

The spatial prior kernel presented here provides a practical five-metric instrument for characterizing this behavior: placing, densifying, cohering, and edge-weighting tendencies that constitute each engine's compositional signature. Validation across 1,400+ images spanning 14 platforms and eight semantic categories confirms that these signatures are stable, differentiating, and resistant to semantic content variation.

The framework is not a replacement for semantic evaluation. It is a complementary layer addressing a dimension of model behavior that existing benchmarks such as IS, FID, CLIPScore, T2I-CompBench, and GenEval are structurally unable to reach. Spatial reasoning is not an aesthetic issue. It is a measurable part of how models think about space.

---

Technical Appendix

A.1 Core Equations

A.2 xₚ Vector Decomposition

A.3 Perturbation Protocol

A.4 Masking Methods

A.5 Reproducibility

---