Architectural Reasoning in Complex Systems

• Architectural reasoning is a multidisciplinary approach that links visible forms to underlying structural, environmental, and functional logics across diverse domains.
• It integrates surface recognition with process-level understanding, supporting evaluations in built environments, AI floor plans, software architecture, and formal proof synthesis.
• This paradigm enhances model performance by enforcing explicit structure representation, thereby improving design coherence, evaluative accuracy, and optimization in complex systems.

Architectural reasoning is a family of related capacities concerned with relating observable organization to the constraints, functions, and consequences that make that organization intelligible. Across current research, the term names different but structurally comparable activities: connecting built form to material, environmental, and cultural logic; reasoning over geometry, semantics, and spatial hierarchy in floor plans; synthesizing proofs from local axioms in an alien formal theory; evaluating software systems against quality attributes, design patterns, and recorded decisions; and designing AI systems whose internal routing, memory, and planning architectures support more reliable reasoning (Pishahang et al., 29 Dec 2025, Li, 1 May 2026, Santilli et al., 28 Jun 2026, Liang et al., 28 Jun 2026).

1. Conceptual scope

Across these literatures, a common distinction separates surface recognition from process-level understanding. In vernacular architecture, the distinction is between reproducing a recognizable silhouette and understanding why a form exists; in theorem proving, between exploiting semantic cues and reasoning from local formal structure alone; in software engineering, between passing tests and respecting module boundaries, abstractions, and decision rationale (Pishahang et al., 29 Dec 2025, Li, 1 May 2026, Vasilevski et al., 12 Jun 2026). A plausible implication is that architectural reasoning is best understood not as raw problem-solving ability, but as the capacity to infer and preserve the latent organization that makes a system work.

Domain	Operational meaning	Representative work
Built environment	“connect what a building looks like to how and why it works—structurally, environmentally, materially, programmatically, and culturally”	(Pishahang et al., 29 Dec 2025)
Floor-plan AI	“joint reasoning over geometry, semantics, and spatial hierarchy”	(Qin et al., 12 Mar 2026)
Theorem proving	“synthesize formal proofs using exclusively local definitions, axioms, theorems, and limited tactics within a closed theory”	(Li, 1 May 2026)
Software architecture	reasoning over “quality attribute trade-offs, design patterns, and system-level constraints”	(Santilli et al., 28 Jun 2026)
Code patch generation	respecting “module and layer boundaries,” abstractions, and extension mechanisms	(Vasilevski et al., 12 Jun 2026)

This breadth matters because the phrase does not denote a single benchmarkable faculty. In some papers it names reasoning about architectures; in others it names reasoning enabled by architectural organization; and in still others it refers to the architecture of the reasoner itself. The shared denominator is relationality: parts are interpreted through the whole, and local decisions are judged by their consistency with broader structural invariants.

2. Built form, vernacular intelligence, and spatial organization

In architectural design research, architectural reasoning is defined most explicitly in the study of Iranian pigeon towers. There it is framed as the capacity to connect appearance to structural, environmental, material, programmatic, and cultural operation. Vernacular architecture is treated not as style but as environmental intelligence embodied in form: earthen walls storing and releasing heat, aperture rhythms regulating ventilation and nesting, and clustered cylindrical massing participating in a larger ecology of birds, guano collection, agriculture, maintenance, and tradition. The paper formalizes this through five aligned dimensions—Typology & Form, Materiality, Context & Environment, Realism & Representation, and Cultural Specificity—and argues that reasoning is present only when these dimensions cohere with the building’s ecological function (Pishahang et al., 29 Dec 2025).

The same shift from image to system appears in floor-plan research. HouseMind treats floor plans as a “language of space” and recasts architectural reasoning as explicit control over geometry, semantics, and topology. Its central representation decomposes a plan into outline tokens, room-category tokens, and room-instance tokens, yielding a unified sequence

$$Z = [\boldsymbol{z}_o,\; \ell_{r_1},\; \boldsymbol{z}_{r_1},\; \dots,\; \ell_{r_N},\; \boldsymbol{z}_{r_N}],$$

so that understanding, generation, and editing all become autoregressive operations in one token space. In this formulation, adjacency, zoning, and circulation are not post hoc annotations but properties recoverable from the sequence itself. Reported results show strong structural fidelity, including Macro IoU $\approx 0.653$–$0.654$, Node F1 $\approx 0.994$, and Edge Overlap $\approx 0.88$ for generation, together with substantially stronger editing locality than image-based editors (Qin et al., 12 Mar 2026).

ArchSIBench extends this line into evaluation of Vision-LLMs by defining architectural spatial intelligence as “the ability to recognize and infer the scale, layout, and configuration of architectural space.” Its five dimensions—perception, reasoning, navigation, transformation, and configuration—span 17 subtasks, including Room-to-Room, Route-Planning, Drawing-to-Real-Scene, Grouping-by-Use, Composition-Completion, and Topological-Depth. The benchmark shows that some state-of-the-art models approach human evaluators without architectural training, but a clear gap remains to human evaluators with architectural training, especially in spatial transformation and configuration reasoning (Shen et al., 20 May 2026). This suggests that higher-level layout understanding, circulation, and functional zoning remain materially harder than object-centric spatial relations.

3. From visual resemblance to computable judgment

A recurring methodological theme is the conversion of architectural reasoning into explicit evaluation frameworks. In the pigeon-tower study, three diffusion systems—Midjourney v6, DALL·E 3, and DreamStudio / SDXL—are tested through referential, adaptive, and speculative prompts, each run with and without a reference image. The analysis shows that models reliably reconstruct typological cues such as cylindrical towers, aperture bands, and roof turrets, but systematically misread material and climatic reasoning. Reference imagery improves realism and proportional fidelity, yet narrows speculative range; removing the reference increases invention but often collapses cultural specificity into generic “desert adobe” or “sci-fi desert” imagery. The paper therefore defines a boundary between resemblance and reasoning: current models “reconstruct what a form looks like without understanding why it exists” (Pishahang et al., 29 Dec 2025).

ArchShapeNet pushes evaluation into 3D geometry. It builds ArchForms-4000, voxelizes human-designed and EvoMass-generated massings into $128 \times 128 \times 128$ grids, and trains a 3D-CNN with saliency analysis to classify design origin. The model achieves 94.29% accuracy, 96.2% precision, and 98.51% recall, outperforming human experts on the same discrimination task. More important than classification is what the saliency reveals: architectural “intelligence” concentrates at edges, corners, concave–convex transitions, courtyards, setbacks, and other feature-dense regions where hierarchy, articulation, and solid–void reasoning are encoded, while large regular surfaces are comparatively low-saliency (Yin et al., 14 Jun 2025). In this usage, architectural reasoning becomes an interpretable evaluative function over 3D massing.

Research on abstract visual reasoning reinforces that the surrounding reasoning architecture also matters. A systematic benchmark on RAVEN-FAIR compares single-shot prompting, embedding-controlled repetition, self-reflection, and feature-based multi-agent reasoning across GPT-4.1-Mini, Claude-3.5-Haiku, Gemini-1.5-Flash, and Llama-3.3-70B. GPT-4.1-Mini achieves the highest overall accuracy across architectures, but the gains from architectural intervention are model-specific: embedding-controlled repetition improves GPT-4.1-Mini substantially, multi-agent reasoning benefits Llama-3.3-70B most, and self-reflection often degrades accuracy or coverage. The paper also finds that changes in architecture can alter the balance between semantic hallucination and numeric misperception without producing uniformly better reasoning (Urgun et al., 14 Nov 2025). This suggests that reasoning quality is not determined by model scale alone, but by the interaction between base model and inference architecture.

4. Formal systems and reasoning architectures

In formal mathematics, “Architectural Reasoning” is given an unusually strict definition. The Obfuscated Natural Number Game paper defines it as the ability to synthesize formal proofs using only local axioms, definitions, and previously proved theorems within a closed theory, while excluding semantic knowledge, external libraries, and high-level automated tactics. The benchmark is constructed by obfuscating identifiers in Lean 4, with a noise parameter $\lambda \in [0,1]$ mapped to perturbation probability by

$P = 1 - 2^{-5\lambda}.$

Across 68 problems, all models incur a universal latency tax under obfuscation, but only reasoning-oriented systems—DeepSeek-R1, GPT-5, and DeepSeek-Prover-V2—maintain statistically stable accuracy as semantic cues disappear; GPT-4o and Claude-Sonnet-4.5 degrade significantly (Li, 1 May 2026). In this formulation, architectural reasoning means robustness to the logical architecture of a domain when names, notation, and prior lexical cues are removed.

A related diagnosis appears in work on symbolic computation, which argues that current transformer LLMs exhibit “comprehension without competence.” They can often state the correct algorithmic principle yet fail to execute it reliably, a dissociation described as a computational “split-brain syndrome” between instruction and action pathways. The paper argues that the standard transformer trained by next-token prediction remains a powerful pattern completion engine but lacks the architectural scaffolding for principled, compositional reasoning, especially in arithmetic, symbolic manipulation, and logical consistency (Zhang, 14 Jul 2025). This diagnosis sharpens the distinction made elsewhere between verbalized rationale and executable structural understanding.

Other papers shift the term from the object of reasoning to the design of the reasoner. A review of Case-Based Reasoning for LLM agents presents a memory-centric architecture in which a case is a tuple $c = (P, S, O, M)$ of problem, solution, outcome, and metadata, and reasoning is organized as retrieve, adapt, revise, and retain. The proposed combined reasoning function

$$f_{\text{reasoning}}(q) = \omega_1 f_{\text{CBR}}(q) + \omega_2 f_{\text{CoT}}(q) + \omega_3 f_{\text{parametric}}(q)$$

treats architectural design as the composition of memory, retrieval, and generation rather than as monolithic inference (Hatalis et al., 9 Apr 2025). Mixture of Debaters makes a similar move internally: debate is realized through dual-routing, momentum switching, and unified self-debate inside a single MoE-style model, yielding reported gains with 3.7x lower latency and 87% reduction in token consumption relative to conventional multi-agent systems (Liang et al., 28 Jun 2026). In both cases, architectural reasoning becomes inseparable from architectural arrangement.

AgentDSE offers a practical systems analogue. It reframes design space exploration from black-box optimization over a simulator into iterative architectural reasoning with the simulator in the loop: the agent reads task files, forms hypotheses about bottlenecks and constraints, proposes candidate configurations, runs the simulator, and updates notes and search state. Across DNN accelerator mapping, hardware/software co-design, and CPU cache hierarchy optimization, AgentDSE achieves competitive or better design quality with up to two orders of magnitude fewer evaluations, while exposing the hypotheses, performance cliffs, and simulator artifacts that drove each step (Wang et al., 20 Jun 2026). Here the term designates a hypothesis–test–refine loop grounded in structure rather than scalar objective values alone.

5. Software architecture: rationale, bias, formality, and conformance

In software architecture, architectural reasoning is closely tied to decision-making. An empirical inquiry into architectural decision rationales found that the most frequently cited motivations are Ease of use for development, Maintainability, Performance, Prior knowledge/experience, and Time/deadline, with mid-career architects more open to new solutions than both beginners and experienced practitioners. The study also found that Compatibility and Portability are rarely explicit concerns, often because standards and virtualization/containerization are taken to have moved those issues into lower infrastructural layers (Borowa et al., 2023). This literature locates architectural reasoning not only in abstract trade-off analysis but in the concrete rationales, heuristics, and experience gradients that shape choices in practice.

A complementary experimental study treats architectural reasoning as observable argumentation around alternatives and shows that debiasing can measurably improve it. A workshop teaching three techniques—generate multiple solution options, list at least one drawback of each alternative, and list at least one risk for each alternative—reduced occurrences of anchoring and optimism bias, increased counterarguments, and lowered the percentage of biased statements from 49.90% to 23.13%. Practitioners were found to be more susceptible to cognitive biases than students, and the intervention had a more substantial impact on practitioners (Borowa et al., 6 Feb 2025). A plausible implication is that architectural reasoning is not exhausted by formal method; it also depends on disciplined argumentation against predictable distortions in judgment.

At the formal end of the spectrum, neurosymbolic architectural reasoning proposes a pipeline in which neural models infer formal software-architecture descriptions from code, documentation, traces, and diagrams, and symbolic methods then reason over those models. The target representation is a first-order $\approx 0.653$0 structure with predicates such as Package, Component, Interface, Layer, containsComponent, requiresInterface, mapsToPackage, and isAllowedToUse. Architectural rules such as layerConsistent are then checked as logical satisfaction claims of the form $\approx 0.653$1 (Herbold et al., 20 Mar 2025). This work does not present a finished toolchain, but it provides a rigorous account of what it would mean to connect inferred architectural facts with formal conformance checking.

Benchmarking studies expose what current LLMs know and where they fail. SAKE introduces 2,154 expert-curated multiple-choice questions across eight architectural categories and four context-length levels. Overall accuracy is high across 11 models, but performance varies sharply by category: Quality Attributes and Creational Patterns are easiest, while Architectural Solutions is hardest, especially as contextual detail grows (Santilli et al., 28 Jun 2026). A separate study of ADR compliance analyzes 980 ADRs across 109 GitHub repositories and 1,317 accepted decisions, using one primary LLM and three validators. It reports substantial inter-model agreement with Fleiss’ $\approx 0.653$2, together with strong accuracy for explicit, code-inferable decisions, but markedly weaker performance for implicit or deployment-oriented decisions that depend on configuration or organizational knowledge (Su et al., 7 Feb 2026). Together these results show that software-architectural reasoning remains uneven: explicit code-visible constraints are tractable, while context-heavy intent and system-wide trade-offs are not.

Recent work on code LLM training pushes from judgment into optimization. “Beyond Correctness” introduces an agentic judging pipeline with the Architecture Complexity Judge (ACJ), which estimates how much codebase-specific architectural understanding a task demands, and the Architecture Quality Judge (AQJ), which evaluates patch conformance to repository-specific architectural conventions through source-grounded rubrics. Fine-tuning Qwen3-8B/14B/32B on 3,360 curated instances yields resolved rates of up to 27.2% on SWE-bench Verified, alongside consistent gains in architectural patch quality and cross-language generalization (Vasilevski et al., 12 Jun 2026). This places architectural reasoning not only in evaluation but in dataset construction itself: the target is no longer merely a patch that passes tests, but one that respects structure.

6. Limits, common patterns, and future directions

Across domains, the most consistent result is that present systems are stronger at recognizing or restating structure than at inhabiting the constraints that structure encodes. In vernacular-image generation, models reproduce typological outline but not climatic or material logic; in symbolic reasoning, they can articulate rules without executing them; in software engineering, they often satisfy tests or identify explicit code evidence while missing deployment, organizational, or cross-boundary implications (Pishahang et al., 29 Dec 2025, Zhang, 14 Jul 2025, Su et al., 7 Feb 2026). This suggests that current models frequently operate at the level of correlational proxy rather than process-level architectural understanding.

A second pattern is that architectural reasoning becomes more reliable when latent structure is made explicit in the representation or the loop around the model. HouseMind uses room-instance tokens and structured JSON descriptions to couple geometry with semantics; ArchShapeNet uses voxel grids and saliency to make geometric judgment inspectable; ArchSIBench decomposes spatial intelligence into navigation, transformation, and configuration; AgentDSE externalizes hypotheses, constraints, and simulator feedback; ACJ and AQJ turn repository-specific architectural expectations into explicit rubrics (Qin et al., 12 Mar 2026, Yin et al., 14 Jun 2025, Shen et al., 20 May 2026, Wang et al., 20 Jun 2026, Vasilevski et al., 12 Jun 2026). A plausible implication is that architectural reasoning improves when a system is forced to represent intermediate structure rather than merely optimize end outputs.

The research agenda that follows is convergent. Built-environment work calls for richer datasets containing material properties, climate data, historical and cultural annotations, and for multi-modal or physics-aware models coupled to energy simulation, structural analysis, and agent-based behavioral models (Pishahang et al., 29 Dec 2025). Spatial-layout work points toward more detailed interior representations, regulatory constraints, architecture–structure co-design, and stronger 2D–3D integration (Qin et al., 12 Mar 2026, Shen et al., 20 May 2026). Software-architecture research points toward richer ADRs, human-in-the-loop validation, hybrid static-analysis-plus-LLM pipelines, and formal or probabilistic reasoning over inferred models (Herbold et al., 20 Mar 2025, Su et al., 7 Feb 2026). Formal reasoning work points toward training regimes that reward zero-knowledge proof synthesis and architectures with metacognitive control, principle lifting, and structurally grounded execution (Li, 1 May 2026, Zhang, 14 Jul 2025).

Taken together, these lines of work portray architectural reasoning as a test of whether a system can preserve the relation between structure, constraint, and consequence. Whether the object is a pigeon tower, a floor plan, a proof, a software repository, or an agent stack, the decisive question is the same: can the model move from pattern to process, from visible arrangement to the latent organization that gives that arrangement necessity?