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Knossos and Ariadne: Benchmarking and Learning Complete Diagram Topology Extraction with Vision-Language Models
Bangwei Guo, Xujiang Zhao, Shengyu Chen, Yanchi Liu, Wei Cheng, Xi Zhu, Guoning Zhang, Dimitris N. Metaxas, Haifeng Chen
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Abstract:Structural diagrams are widely used to represent complex systems and relational information across scientific, engineering, procedural, and spatial domains. Recent vision-language models (VLMs) have become increasingly capable of recognizing diagram elements and reasoning about their content, while complete diagram topology extraction remains comparatively underexplored. In this paper, we study diagram-to-graph topology extraction: extracting all diagram entities and the complete relations among them. To enable large-scale supervised training and systematic evaluation of this task, we introduce Knossos, a benchmark of 19,200 diagrams across six diverse domains, with 245,179 nodes and 439,740 edges. Its symbolic generation process provides exact alignment between rendered diagrams and annotations of complete topology, relation types, and connector geometry. To address the modeling challenge of complete topology extraction, we also present Ariadne, a structured framework that decomposes the task into node inventory extraction and source-conditioned edge prediction. Extensive experiments show that training on Knossos substantially improves complete topology extraction in smaller open-source VLMs. Ariadne further improves over one-step extraction under matched supervision, demonstrating the additional benefit of structured decomposition. It achieves the highest average Edge F1 among the evaluated methods on Knossos, while both backbone variants also improve over their unadapted counterparts on the real-world external benchmark. Code and benchmark are available at this https URL.
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Under review KNOSSOS AND ARIADNE:BENCHMARKING AND LEARNING COMPLETE DIAGRAM TOPOLOGY EX- TRACTION WITH VISION–LANGUAGE MODELS Bangwei Guo 1 , Xujiang Zhao 2 , Shengyu Chen 3 Yanchi Liu 3 , Wei Cheng 3 , Xi Zhu 1 Guoning Zhang 1 , Dimitris N. Metaxas 1 , Haifeng Chen 3 1 Rutgers University 2 Meta 3 NEC Labs America ABSTRACT Structural diagrams are widely used to represent complex systems and relational information across scientific, engineering, procedural, and spatial domains. Re- cent vision–language models (VLMs) have become increasingly capable of rec- ognizing diagram elements and reasoning about their content, while complete di- agram topology extraction remains comparatively underexplored. In this paper, we study diagram-to-graph topology extraction: extracting all diagram enti- ties and the complete relations among them. To enable large-scale supervised training and systematic evaluation of this task, we introduce Knossos, a bench- mark of 19,200 diagrams across six diverse domains, with 245,179 nodes and 439,740 edges. Its symbolic generation process provides exact alignment be- tween rendered diagrams and annotations of complete topology, relation types, and connector geometry. To address the modeling challenge of complete topol- ogy extraction, we also present Ariadne, a structured framework that decomposes the task into node inventory extraction and source-conditioned edge prediction. Extensive experiments show that training on Knossos substantially improves com- plete topology extraction in smaller open-source VLMs. Ariadne further improves over one-step extraction under matched supervision, demonstrating the additional benefit of structured decomposition. It achieves the highest average Edge F1 among the evaluated methods on Knossos, while both backbone variants also im- prove over their unadapted counterparts on the real-world external benchmark. Code and benchmark are available at https://github.com/bangwayne/ knossos_Ariadne_Public. 1INTRODUCTION Structural diagrams are essential for representing complex structured and relational information across science, engineering, education, and technical domains. Recent advances in large vision– language models (VLMs) have broadened the scope of diagram understanding, spanning scientific and chart question answering, visual-graph reasoning, and specialized engineering-diagram anal- ysis (Masry et al., 2022; Zhu et al., 2025; Zhao et al., 2025; Li et al., 2025a). These advances have improved the ability of VLMs to recognize diagram elements and reason about their content. However, structural diagrams often contain many interacting entities and densely routed relations, making complete structural understanding substantially more challenging than recognizing individ- ual elements (Hou et al., 2024; Hu et al., 2026). Despite this progress, existing diagram-understanding tasks typically evaluate only selected enti- ties and relations, for example through question answering or localized reasoning (Lu et al., 2022; Li et al., 2024b). Such evaluations do not require extracting the complete topology: a model may answer individual questions correctly while still omitting, reversing, or hallucinating other rela- tions (Zhu et al., 2025; Hu et al., 2026). We therefore study diagram-to-graph topology extraction, which aims to extract the complete graph topology encoded in a diagram, where diagram entities correspond to nodes and their relations to edges. Once the complete topology is available, many 1 arXiv:2610.04721v1 [cs.CV] 3 Oct 2026 Under review structure-centric question answering and reasoning tasks become simpler by directly analyzing the extracted textual graph representation. Complete diagram-to-graph topology extraction, however, faces two key challenges: the scarcity of large-scale benchmarks that support both training and evaluation, and the difficulty of modeling complete diagram topology. On the data side, constructing complete topology supervision requires exhaustively labeling all diagram entities and relations, making large-scale dataset construction far more demanding than question-answer supervision (Guo et al., 2026; Hu et al., 2026). On the modeling side, VLMs must identify all relevant entities and extract their complete relations from potentially dense diagrams. As diagram complexity grows, the resulting graph serialization becomes longer and harder to generate consistently, increasing the likelihood of omissions, hallucinations, and structural inconsistencies (Jiang et al., 2026; Zheng et al., 2025). To address these challenges, we introduce two complementary contributions: Knossos, a large-scale benchmark for supervised topology learning and evaluation, and Ariadne, a structured framework for complete topology extraction 1 . Knossos is generated from symbolic topology specifications, ensuring exact alignment between rendered diagrams and complete topology annotations by con- struction. This pipeline scales to 19,200 diagrams across six domains while varying topology struc- tures, layouts, connector routes, and visual assets. Ariadne addresses the modeling challenge by first extracting a complete node inventory and then decomposing topology extraction into source-group edge predictions, replacing a single long graph serialization with shorter structured generations that are deterministically assembled into the complete topology. We train Ariadne on the Knossos train- ing split using its complete topology annotations as supervision. Extensive experiments show that Knossos provides effective large-scale supervision for complete topology extraction, while Ariadne further improves over matched one-step models through structured source-conditioned prediction. Evaluation on an external real-world benchmark further demonstrates cross-domain generalization beyond the synthetic training distribution. Our contributions are summarized as follows: • We establish a large-scale supervised setting for diagram-to-graph topology extraction, moving beyond isolated entities or relations toward complete diagram topology extraction with vision–language models. • We introduce Knossos, a large-scale benchmark containing 19,200 diagrams across six diverse domains, with complete annotations of nodes, directed and typed relations, and connector geometry for both training and evaluation. • We present Ariadne, a structured framework that decomposes complete topology extraction into node inventory construction and short source-conditioned edge predictions. • We conduct extensive experiments across Knossos and an external real-world benchmark, demonstrating the effectiveness of large-scale topology supervision, the benefit of struc- tured decomposition, and cross-domain generalization. 2TASK FORMULATION AND THE KNOSSOS BENCHMARK 2.1DIAGRAM-TO-GRAPH TOPOLOGY EXTRACTION Given a diagram image I , the task is to extract its topology G = (V,E), where V is the set of diagram nodes and E is a multiset of directed edges. Each node v i ∈ V has a diagram-local identifier and a visible text label, and each edge e = (s,t) ∈ E connects source node s to target node t. When relation semantics are defined, an edge is additionally assigned a type r, yielding a typed edge (s,t,r). Multiple typed edges may share the same endpoint pair, allowing distinct relations between the same two nodes to be preserved. 2.2KNOSSOS: MULTI-DOMAIN SYNTHETIC DIAGRAM BENCHMARK We introduce Knossos, a large-scale synthetic diagram benchmark for supervised topology extrac- tion. Knossos contains 19,200 diagrams spanning six complementary domains: Food Web, Net- 1 The names draw from the Greek myth of the Labyrinth at Knossos, where Ariadne gave Theseus a thread to navigate its passages. Here, Knossos evokes the benchmark’s intricate structures, while Ariadne provides the thread for extracting their underlying topology. 2 Under review Food WebNetworkNatural ProcessWorkflowCircuitMap Route 1. Generation controls Domain Difficulty Template Orientation Domain grammar 2. Symbolic topology Nodes Edges Grass Rabbit Bird Insect Snake Plant ... ... 3. Layout & routing n1 n1 n2 n3 n4 n5 n3 n4 n4 n5 n6 n6 Fixed positions and connectors Rendered diagramComplete annotations 4. Rendering & annotation Icon pool 5. Screening & release Structural checks VLM screening Frozen release 18K train + 1.2K test Dataset profile 19.2K diagrams | 245K nodes | 439K edges (a) (b) (c) Figure 1: Overview of the Knossos benchmark. (a) Representative diagrams from the six do- mains. (b) The generation pipeline samples generation controls, instantiates a symbolic topology, places nodes and routes edges, and renders the diagram together with aligned node, typed-edge, and geometry annotations. Structural validation and VLM-based screening produce the frozen training and test release. (c) Dataset statistics summarize difficulty, topology scale, edge directionality, and multi-link prevalence across 19,200 diagrams, 245,179 nodes, and 439,740 typed edges. work, Workflow, Natural Process, Circuit, and Map Route, with representative examples shown in Figure 1(a). Together, these domains cover scientific, engineering, procedural, and spatial structures while introducing diverse extraction challenges, including dense directed connectivity, unarrowed connections, branching and merging structures, legend-defined relation types, and multiple typed edges between common endpoint pairs. The dataset contains 245,179 node instances and 439,740 edge instances, with the nodes drawn from 310 domain-specific canonical concepts. The frozen re- lease is divided into 18,000 training images and 1,200 held-out test images. Each diagram is paired with its complete graph topology, relation types when defined by the diagram, and geometric an- notations for both nodes and edges, including node bounding boxes and connector paths. These annotations support both topology extraction and geometric grounding. 2.3SYMBOLIC GENERATION PIPELINE Figure 1(b) summarizes the Knossos generation pipeline. The generator samples the domain, dif- ficulty, structural template, and orientation, instantiates nodes from the corresponding domain vo- cabulary, and constructs edges using the domain-specific grammar and selected template. Once the topology is fixed, the layout stage assigns node positions and bounding boxes, after which connec- tors are routed between the corresponding node boundaries. Depending on the domain and template, connectors may follow direct, bent, or orthogonal paths, and the routed connector paths are retained as geometric traces associated with the corresponding edges. Finally, the renderer combines the fixed topology, layout, connector geometry, and visual assets to produce the diagram image. Com- plete annotations are serialized from the same finalized node and edge objects, including node labels and bounding boxes, graph topology, relation types when defined, and connector traces. This shared representation keeps the rendered diagram and its annotations aligned by construction. Detailed domain grammars and rendering configurations are provided in Appendix B. 3 Under review Input diagram Diagram image I Stage 1: Node inventoryStage 2: Source-group edge extractionComplete topology Predicted inventory! " Active source 1 2 3 n n n 3,4 4,7 5,6 n n n 4 5 6 n n n 7 8 9 n n n 6,8 6,9 9 n n n 8 9 n n Æ # " !" ! " !" ! " !# Validate & merge Node Predicator N q ! Edge Predicator $ # ! Edge Predicator $ # ! Edge Predicator $ # ! % " =(1,(2,(3 Input: .,!, / % $ =(4,(5,(6 % % =(7,(8,(9 Input: .,!, / Input: .,!, / Trace Predicator $ & ! Connector geometric grounding 6(!,#∣.)=6 ' ! (!∣.):6 ' " ( (# ! # ∣.,!,% ( ) Node-to-edge topology extraction Trace(e) = [# $ ,# " ,# # ,# % ,# & ] ! " =(% " ,' " ) Figure 2: Overview of Ariadne. Ariadne decomposes topology extraction into node inventory prediction and source-group edge extraction. Edge prediction is restricted to active sources within each group while retaining all predicted nodes as candidate targets. The group-wise edge multisets are validated and merged into the final graph, with node bounding boxes and separately predicted connector traces providing auxiliary geometric grounding. 2.4STRUCTURAL AND VISUAL DIVERSITY Structural diversity is introduced through parameterized, domain-specific template families rather than unconstrained graph sampling. These templates cover hierarchical, clustered, branching, lay- ered, and spatial structures. Seeded rules vary graph size, density, depth, branching, cross-links, relation types, and parallel edges within each grammar. Difficulty controls both topology and pre- sentation: harder samples generally contain more nodes and edges, more layers and cross-links, and longer, more intersecting connector paths. Training and test instances are generated with disjoint random seeds for template instantiation, topology sampling, and layout variation. Visual diversity is introduced through offline-prepared, label-matched asset pools, with each eligible canonical concept associated with multiple visual styles and variants; nodes without image assets are rendered programmatically using role-specific shapes. At rendering time, assets are sampled only from the pool corresponding to the selected node concept. Seeded presentation choices further vary, where applicable, orientation, label casing, background, connector appearance, arrowhead size, and legend placement. Visible labels are drawn by the renderer rather than by the asset-generation model, so visual variation does not alter the underlying node identity or graph topology. Implementation details are provided in Appendix B.3. 2.5QUALITY CONTROL AND DATASET RELEASE As summarized in Figure 1(b), each generated sample undergoes structural validation followed by VLM-based visual screening. Structural checks focus on basic annotation and graph consistency, including format validity, completeness, and duplicate detection. A separate VLM-based screening step filters out samples with clearly unreadable text or visually unclear diagram elements. The final release is constructed by stratified selection across domains and difficulty levels, replacing failed samples with valid candidates from the same stratum. The frozen benchmark contains 18,000 train- ing images and 1,200 held-out test images, with 3,000 training and 200 test examples per domain. Figure 1(c) summarizes the resulting benchmark statistics. Additional screening and release details are provided in Appendix B.5. 3ARIADNE 3.1NODE-TO-EDGE TOPOLOGY EXTRACTION Figure 2 illustrates the overall framework. Following the topology formulation in Section 2.1, Ari- adne decomposes topology extraction into node inventory prediction followed by source-conditioned edge prediction. The predicted node inventory provides a fixed reference vocabulary and is parti- tioned into K source groupsS(V ) =S 1 ,...,S K with target group size g. For each S i , the edge 4 Under review predictor outputs only the typed edges originating from nodes in S i . The group-wise edge multisets are then merged deterministically to form the complete graph. We model this decomposition as p θ (V,E | I) = p θ N (V | I) K Y i=1 p θ E (E S i | I,V,S i ),(1) where E S i is the multiset of directed edges originating from sources in S i . At inference, the pre- dicted group-wise edge multisets are merged as ˆ E = K ] i=1 ˆ E S i , ˆ G = ( ˆ V , ˆ E).(2) This decomposition replaces a single long graph serialization with shorter, source-conditioned gen- erations and, under our serialization setting, removes cross-group ordering ambiguity. Under a position-sensitive decoding assumption, the shorter generation horizon may also reduce error ac- cumulation at later output positions. We formalize these properties and their assumptions in Ap- pendix C. 3.2TWO-STAGE TOPOLOGY PREDICTION Stage 1: Node inventory. The node predictor first identifies the diagram nodes and their visible text labels, producing the predicted node inventory ˆ V . Each node is localized with a bounding box b v = [x 1 ,y 1 ,x 2 ,y 2 ] for geometric grounding, while a diagram-local identifier is included only to provide a stable reference in later stages. The output contains only node records and no edge or connector predictions. At test time, the predicted node inventory, rather than the ground-truth inventory, is passed to the next stage. Stage 2: Source-group edge extraction. Given ˆ V , Ariadne processes the source groupsS i K i=1 independently. Each query contains the diagram, the complete predicted node inventory, and the active sources in S i . The edge predictor may emit relations only from these active sources, while any node in ˆ V remains available as a target. For each active source, it emits one CHECK NODE block: Example Stage 2 output for one active source <CHECK_NODE id="n4" name="Sensor"> <EDGE source="n4" source_name="Sensor" target="n6" target_name="Controller" type="signal"/> <EDGE source="n4" source_name="Sensor" target="n8" target_name="Ground" type="ground"/> </CHECK_NODE> Relation types are predicted only when defined by the diagram legend; otherwise the type is left empty. Directionality is encoded by the ordered source–target pair, with undirected or bidirectional connectors represented by reciprocal edges. Multiple typed relations between the same endpoints remain distinct multiset elements, and an empty CHECKNODE block denotes a source with no outgoing edge. Finally, all source-group predictions are validated and merged into ˆ E. 3.3GEOMETRIC GROUNDING Beyond symbolic topology, Ariadne associates each graph primitive with explicit geometric evi- dence. Nodes are localized by the bounding boxes predicted in Stage 1, while each predicted edge is grounded by an ordered connector trace generated after the Stage 2 edge set is fixed. For each edge, the trace predictor outputs five points sampled along its visible connector from source to tar- get. Training targets are obtained by uniformly sampling the final rendered connector path by arc 5 Under review length, so the endpoints localize the connector boundaries and the intermediate points capture its routed geometry. Reciprocal edges use the same connector path in reverse order. The trace serves only as auxiliary geometric grounding and does not modify the predicted graph topology. Detailed results are provided in Appendix D.2. 4EXPERIMENTS 4.1EXPERIMENTAL SETUP Implementation and evaluation protocol. We instantiate Ariadne with GLM-4.6V-Flash (Hong et al., 2025) and Qwen3-VL-8B (Bai et al., 2025) as two vision–language backbones, each using sep- arate adapters for the node, edge, and trace predictors. All main Knossos results are evaluated on the frozen 1,200-image held-out test set, with 200 images from each of the six domains. At inference, the predicted node inventory is partitioned into source groups of target size 3 for edge extraction, while the trace predictor is applied only after the symbolic edge set is fixed. Complete training and decoding details are provided in Appendix E.1, with prompt templates in Appendix E.2. We use macro-averaged Node F1 and Edge F1 scores as the primary topology metrics. Node F1 measures node identification after matching predictions to reference nodes, while Edge F1 evaluates directed source–target connectivity between matched nodes. Scores are averaged across images within each domain, and the overall Knossos score is the mean across the six domains. Additional relation-type and connector-grounding metrics are reported in ablation analyses and appendix. We additionally evaluate generalization on a 162-image subset of the external TopoBench-180 test set (Guo et al., 2026), with preprocessing details provided in Appendix B.6. We report only Node F1 and Edge F1 on this benchmark. Baselines. We organize the baselines into three groups. Open-source VLMs include Qwen3-VL- 32B and Qwen3-VL-8B (Bai et al., 2025), GLM-4.6V-Flash (Hong et al., 2025), MiMo-VL-7B- RL (Yue et al., 2025), Keye-VL-1.5-8B (Yang et al., 2025), InternVL3.5-8B (Wang et al., 2025), and Ovis2.5-9B (Lu et al., 2025). Closed-source VLMs include GPT-4o (Hurst et al., 2024), GPT- 5.6 (Singh et al., 2025), and Claude Opus 5 (Anthropic, 2026). For all open- and closed-source VLM baselines, we use direct full-graph generation, requiring the model to produce all diagram nodes and edges in a single response. This setting provides a direct comparison with Ariadne’s decomposed node-to-edge prediction strategy. Structured visual-reasoning methods include Pixel Reasoner (Su et al., 2026a), Chain of Region (Li et al., 2025b), Speculative Verdict (Liu et al., 2026), and TopoAgent (Guo et al., 2026). We instantiate Ariadne with two backbone configurations, GLM- 4.6V-Flash (9B) and Qwen3-VL-8B, allowing us to evaluate the proposed decomposition across two different open-source VLM families. 4.2NODE EXTRACTION Figure 3 compares node extraction results on the internal and external test sets. Node extraction is highly reliable on the Knossos internal test set: Ariadne achieves a macro-average Node F1 of 97.8% with both the GLM- and Qwen3-based variants, while strong open-source VLMs also generally ex- ceed 95%. Recent closed-source VLMs are already close to this ceiling, with Opus 5 reaching 97.4% and GPT-5.6 reaching 96.8%. Together, these results suggest that current multimodal models already provide strong OCR and visual-semantic recognition for identifying diagram entities. Performance decreases on TopoBench-180, suggesting that additional node-specific training may introduce some distribution specialization. Given the already strong node recognition capabilities of modern VLMs, a separately trained node predictor may therefore not always be necessary. This further motivates focusing model capacity and evaluation on relation and topology extraction, where the performance gap remains substantially larger. Detailed domain-level results and additional analysis are provided in Appendix D.3. 4.3EDGE EXTRACTION Table 1 compares Ariadne with a broad set of baselines on Edge F1. On Knossos, recent closed- source VLMs already show strong direct topology-extraction capability: GPT-5.6 reaches 81.1% average Edge F1, substantially outperforming all direct open-source VLMs. Ariadne improves 6 Under review 889092949698100 Node F1 (%) ↑ Ariadne-Qwen Ariadne-GLM Opus 5 GPT-5.6 GPT-4o TopoAgent Qwen3-32B Spec. Verdict Chain of Region Qwen3-8B GLM-4.6V InternVL-8B Ovis-9B Pixel Reasoner Keye-8B MiMo-7B 97.8 97.8 97.4 96.8 96.6 96.4 96.3 95.7 95.6 95.2 95.1 93.9 93.8 93.7 92.1 90.0 (a) Knossos internal test set 707580859095100 Node F1 (%) ↑ Qwen3-8B GPT-5.6 Qwen3-32B TopoAgent Chain of Region Opus 5 InternVL-8B GLM-4.6V Ariadne-GLM GPT-4o Spec. Verdict Ariadne-Qwen Keye-8B Ovis-9B MiMo-7B Pixel Reasoner 92.2 92.0 91.9 91.3 91.2 90.8 90.6 90.3 88.8 88.7 88.4 85.8 85.3 79.3 77.5 73.3 (b) TopoBench-180 external test set Open-source VLMsClosed-source VLMsVisual reasoning methodsAriadne (ours) Figure 3: Node extraction results on the internal and external test sets. Panel (a) reports the un- weighted mean Node F1 across the six Knossos domains. Panel (b) reports the unweighted mean across the Web-style and Network-style subsets of TopoBench-180. Colors distinguish open-source VLMs, closed-source VLMs, visual reasoning methods, and our Ariadne models. Full model names are listed in Table 1. further, reaching 91.6% with the Qwen3-based variant and 88.8% with the GLM-based variant. Ariadne-Qwen uses an 8B backbone yet substantially exceeds the 32B Qwen3-VL model under direct extraction (91.6% vs. 54.7%). Relative to the corresponding direct backbones, Ariadne im- proves Qwen3-VL-8B from 46.1% to 91.6% and GLM-4.6V-Flash from 38.9% to 88.8%, reflecting the combined effects of task adaptation and the proposed structured decomposition. On TopoBench-180, closed-source VLMs show the strongest generalization, with Claude Opus 5 reaching 81.2% on Web-style diagrams and GPT-5.6 reaching 68.7% on Network-style diagrams. This suggests that broad multimodal pretraining provides strong out-of-distribution topology un- derstanding without task-specific adaptation. Ariadne nevertheless substantially improves over its corresponding backbones: the GLM-based variant increases from 55.2% to 73.4% on Web-style diagrams and from 45.1% to 55.6% on Network-style diagrams, while the Qwen3-based variant im- proves from 44.1% to 68.6% and from 49.8% to 53.2%, respectively. The GLM-based variant also generalizes better than the Qwen3-based variant despite its lower in-domain score, highlighting the distinction between in-distribution performance and external generalization. Edge F1 evaluates whether the two endpoints are correctly recovered, but does not require the pre- dicted relation type to be correct. Typed-Edge F1 is stricter: a prediction is counted as correct only when both endpoints match and the edge type indicated by the diagram legend is also extracted correctly. Figure 4 summarizes relation-type prediction by averaging Typed-Edge F1 over Natural Process, Circuit, and Map Route, the three domains with explicit relation semantics. Ariadne-Qwen ranks first at 90.4%, followed by Ariadne-GLM at 88.9%. Both outperform the strongest baseline, GPT-5.6 at 84.0%, by 6.4 and 4.9 points, respectively. The gap is substantially larger relative to direct open-source VLMs: the strongest of these, Qwen3-VL-32B, reaches 49.8%. This aggregate comparison indicates that Ariadne’s gains extend beyond identifying the correct endpoints to ex- tracting the semantics of their relations. Complete domain-level results are provided in Appendix Table 5. 4.4ANALYSIS AND ABLATIONS When does staged topology extraction help? Table 2a compares one-step and staged topology extraction across models with different capacities and training settings. Staging does not improve GPT-5.6 and instead reduces its Edge F1, suggesting that frontier models may already have sufficient capacity for joint entity and relation extraction. In contrast, decomposition provides a modest gain for the base Qwen3-VL-8B model and a much larger gain after task-specific adaptation: Ariadne- Qwen improves from 80.0% to 91.6% Edge F1. Node F1 changes only marginally, indicating that the improvement primarily comes from more reliable edge extraction. Overall, our results suggest 7 Under review Table 1: Edge extraction results across six Knossos domains and two external TopoBench-180 do- mains, measured by Edge F1 scores (%). KnossosTopoBench-180 MethodFood WebNetworkWorkflowNatural ProcessCircuitMap RouteAvg.Web-styleNetwork-style Open-source VLMs Qwen3-VL-32B28.848.776.465.836.771.954.754.752.3 Qwen3-VL-8B27.547.059.949.531.661.146.144.149.8 GLM-4.6V-Flash30.025.046.348.427.356.338.955.245.1 MiMo-VL-7B-RL24.737.154.340.226.161.740.742.246.5 Keye-VL-1.5-8B30.736.751.144.322.049.239.047.945.5 InternVL3.5-8B22.846.052.544.828.050.340.741.946.2 Ovis2.5-9B25.837.556.739.025.245.838.342.148.8 Closed-source VLMs GPT-4o16.843.346.843.130.567.041.232.854.1 GPT-5.661.991.080.589.677.086.681.180.368.7 Opus 554.751.185.696.556.977.570.481.251.8 Visual reasoning methods Pixel Reasoner23.031.435.431.224.345.631.832.635.3 Chain of Region18.240.645.640.228.357.138.335.051.8 Speculative Verdict23.436.864.250.928.959.443.942.847.4 TopoAgent28.451.654.541.437.665.546.545.856.8 Ours Ariadne (GLM-based)80.488.594.396.784.388.388.873.455.6 Ariadne (Qwen3-based)87.293.595.597.886.489.391.668.653.2 that staged decomposition is particularly beneficial for smaller task-adapted models, while larger frontier models benefit less from explicitly separating the two steps. 020406080100 Average Typed-Edge Macro F1 (%) ↑ Ariadne-Qwen Ariadne-GLM GPT-5.6 Opus 5 Qwen3-32B GPT-4o Spec. Verdict Qwen3-8B TopoAgent MiMo-7B InternVL-8B Chain of Region GLM-4.6V Ovis-9B Keye-8B Pixel Reasoner 90.4 88.9 84.0 76.5 49.8 41.7 40.5 40.5 39.8 37.7 34.7 34.6 34.3 28.4 23.8 16.4 Relation-Type Prediction on Knossos Open-source VLMs Closed-source VLMs Visual reasoning Ariadne Figure 4: Average Typed-Edge F1 scores across Natural Process, Circuit, and Map Route. Each bar is the arithmetic mean of the three domain- level Macro F1 scores reported in Appendix Ta- ble 5. What limits Ariadne’s external generaliza- tion? Table 2b examines why the large gains observed on the internal test set generalize only partially to the external test set. We keep the trained Qwen3 edge predictor fixed and vary only the upstream node inventory.Replac- ing Ariadne’s task-adapted node predictions with those from the base Qwen3-VL-8B raises Node F1 from 85.8% to 92.2% and Edge F1 from 60.9% to 67.3%. This indicates that the more limited external improvement is driven in substantial part by weaker node generaliza- tion under distribution shift, which constrains the downstream edge predictor. Meanwhile, general-purpose VLMs already show strong node-recognition generalization on the external data, suggesting that additional node-specific adaptation may be less necessary in this set- ting. With oracle nodes, the frozen edge predic- tor reaches 78.2% macro-F1, 10.9 points above the strongest predicted-node source, confirming substantial error propagation from node extrac- tion while also revealing remaining limitations in edge reasoning even when node uncertainty is removed. What diagram structures remain challenging? Table 3 examines how diagram structure affects topology prediction. Performance decreases consistently as diagram difficulty increases, showing that overall diagram complexity remains a primary source of error. Harder diagrams typically con- tain denser connectivity, more cross-links, and more intersecting connector paths, increasing the difficulty of assigning relations to the correct endpoints. Multi-link diagrams are also more challeng- ing, likely because multiple relations must be visually disentangled and preserved separately rather than collapsed into a single connection. In contrast, performance remains relatively stable across di- 8 Under review (a) One-step vs. staged topology extraction on the Knossos test set. Node and Edge F1 are macro- averaged across the six domains (%). ModelProtocolNode F1↑Edge F1↑ GPT-5.6 One-step96.881.1 Staged extraction97.077.1 Qwen3-VL-8B (base) One-step95.246.1 Staged extraction95.149.3 Ariadne-Qwen One-step97.180.0 Staged extraction97.891.6 (b) Node-source ablation on the external TopoBench test set with a fixed trained Qwen3 edge predictor. Node source Average Node F1↑ Average Edge F1↑ Web-style Edge F1↑ Network-style Edge F1↑ Ariadne node predictor85.860.968.653.2 Qwen3-VL-8B (base)92.267.371.762.9 GPT-5.692.067.175.059.2 Oracle nodes100.078.278.378.1 Table 2: Ablations on staged topology extraction and external generalization. (a) compares one-step and staged extraction across model and training settings. (b) varies the upstream node inventory while keeping the trained Qwen3 edge predictor fixed on the public TopoBench subset. rected, bidirectional, and mixed settings, suggesting that relation direction itself is no longer a major bottleneck for current models. Overall, topology extraction is affected more by diagram complexity and visually entangled connectivity than by directionality. 5DISCUSSION AND CONCLUSION Table 3: Edge F1 (%) across structural subsets. N denotes the number of images. To better iso- late each structural factor while reducing variation from other domain-specific properties, difficulty is averaged across all six Knossos domains, di- rectionality is evaluated within Map Route, and multi-link effects are evaluated across Circuit, Map Route, and Natural Process. FactorSubsetN GPT-5.6 Ariadne-Qwen Difficulty Simple16494.496.5 Medium57184.994.7 Difficult46576.889.0 Direction Directed13286.789.0 Bidirectional3786.788.6 Mixed3186.291.0 Multi-link Absent38486.092.0 Present21682.189.6 We studied complete diagram-to-graph topol- ogy extraction, where a model must extract both the visible entities and the directed rela- tions connecting them in the diagram. To sup- port this task, we introduced Knossos, a bench- mark of 19,200 diagrams across six domains with aligned node, edge, relation-type, and con- nector annotations, and Ariadne, which sepa- rates node inventory prediction from source- conditioned edge extraction.On the 1,200- image Knossos test set, Ariadne-Qwen reaches 91.6% Edge F1, compared with 81.1% for GPT-5.6, with the margin increasing from 2.0 points on simple diagrams to 12.2 points on dif- ficult diagrams. On the external TopoBench- 180 test set, Ariadne substantially improves over its direct open-source backbones, although the strongest closed-source VLMs remain more competitive. Limitations and outlook. First, Knossos re- mains synthetic, and its assets, layouts, connec- tor styles, and rendering patterns cannot capture the full diversity of real-world diagrams. Results on the external TopoBench-180 test set show generalization beyond the synthetic distribution, but a synthetic-to-real gap remains. Second, Knossos relies on finite domain-specific vocabularies and predefined graph grammars, limiting the semantic and structural diversity seen during training. Gen- eralization to unseen entity types, relation semantics, and topology patterns therefore remains open. Third, Ariadne is sequential: node errors can propagate to edge extraction, while source grouping requires multiple model calls per image. Finally, structured decomposition benefits smaller task- adapted VLMs most, whereas recent closed-source models already show strong direct topology- extraction capability. Whether these gains persist with stronger and larger backbones remains to be studied. Broader real-world evaluation, more efficient decoding, and stronger open-source back- bones are important directions for future work. Conclusion. Our results show that complete diagram topology extraction can be substantially improved through large-scale supervision and structured prediction. Knossos provides a large- scale benchmark for training and controlled evaluation, while Ariadne demonstrates that source- 9 Under review conditioned decomposition can effectively improve topology extraction, particularly for smaller task-adapted VLMs. Together, they provide a practical framework for studying diagram-to-graph topology extraction. We hope Knossos and Ariadne support further progress toward reliable topol- ogy extraction across increasingly diverse real-world diagrams. AI USE STATEMENT Generative AI and agentic AI tools were used to assist with code implementation, debugging, code execution, and experiment workflows, as well as synthetic visual asset generation, the creation and editing of figures and other visual elements, and language editing of the manuscript. AI agents were also used to execute and inspect computational workflows under author supervision. All AI-assisted code, experimental outputs, data-processing results, figures, and text were reviewed and verified by the authors. The authors take full responsibility for the final code, data, experiments, analyses, claims, figures, and manuscript. REPRODUCIBILITY STATEMENT The benchmark construction rules, asset-generation and sampling policies, annotation schema, val- idation procedure, training stages, and evaluation metrics are documented in the main paper and appendix. The complete benchmark, including 18,000 training images and 1,200 test images, an- notations, and visual assets, is publicly available at https://huggingface.co/datasets/ WayneGuo0011/Knossos. Generation code, training recipes, and evaluation scripts are avail- able at https://github.com/bangwayne/knossos_Ariadne_Public. REFERENCES Qihang Ai, Ruizhou Li, Menghui Wang, and Haiyun Jiang. Graph-to-vision: Multi-graph under- standing and reasoning using vision-language models. arXiv preprint arXiv:2503.21435, 2025. 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In Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), p. 30678–30701, 2025. ARELATED WORK Benchmarks for structural diagram understanding. Existing multimodal and diagram- understanding benchmarks largely formulate structured visual understanding as question answer- ing or reasoning over selected visual content. Representative examples include AI2D (Kembhavi 12 Under review et al., 2016), ChartQA (Masry et al., 2022), MMBench (Liu et al., 2024), MMMU (Yue et al., 2024), and ChartMuseum (Tang et al., 2026). More recent work moves toward graph-centric vi- sual reasoning: VisionGraph (Li et al., 2024a), VGCURE (Zhu et al., 2025), and Graph-to-Vision (Ai et al., 2025) evaluate structural and relational reasoning over visually rendered graphs, while domain-specific benchmarks study structured understanding and extraction in software architecture, engineering, and other specialized diagrams (Ouyang et al., 2026; Kumar et al., 2026; Su et al., 2026b). Synthetic data has also been used to scale structured diagram supervision. SSVC (Sch ̈ olch et al., 2022) provides synthetic structured-visual-content images with bounding-box and graph an- notations, while FlowLearn (Pan et al., 2024) and FlowGen (Shi et al., 2026) use simulated or controllably generated flowcharts for structured understanding and evaluation. Most closely related, TopoBench-180 (Guo et al., 2026) provides a human-verified real-world evaluation set with canoni- cal graph annotations for diagram-to-graph topology extraction. In contrast, Knossos provides large- scale fully supervised training and controlled evaluation across six domains, with complete topology annotations and systematic variation in topology, layout, connector routing, and visual appearance. Structure-aware diagram understanding and topology extraction. Recent work on diagram understanding has increasingly moved from localized visual evidence toward explicit structural rep- resentations. Chain-of-Region decomposes scientific diagrams into semantically meaningful re- gions for fine-grained reasoning (Li et al., 2025b), while related visual-reasoning methods such as Pixel Reasoner (Su et al., 2026a) and Speculative Verdict (Liu et al., 2026) improve detailed per- ception through pixel-space reasoning and speculative visual inference. Moving beyond localized evidence, TextFlow (Ye et al., 2025) converts flowcharts into textual graph representations before downstream reasoning, Diagram2Structure (Hu et al., 2026) reconstructs raster diagrams into stan- dardized structured representations, and DaVinci (Zeng et al., 2026) learns diagram structure from visual primitives and their relations. More directly related, TopoAgent (Guo et al., 2026) targets diagram-to-graph topology extraction through grounded structural prediction. Ariadne builds on this direction through supervised complete-topology training and source-group decomposition, with local predictions deterministically assembled into the final graph. BDETAILED BENCHMARK CONSTRUCTION This appendix describes the benchmark construction pipeline in sufficient detail for reproduction. We first introduce the domain-specific node vocabularies and graph grammars used to generate valid symbolic topologies. We then describe visual-asset generation and sampling, layout and connector routing, annotation derivation, quality control, and the final balancing and release procedure. We ad- ditionally specify the boundary between the released synthetic benchmark and the separately curated real-diagram evaluation set. B.1CANONICAL VOCABULARIES AND NODE INSTANCES Each domain is defined by a version-controlled JSON vocabulary of canonical node entries. An entry separates a stable key and base display name from the attributes used by generation, including a broader semantic category and, when applicable, a structural role, preferred shape, render mode, or symbol. For example, one Circuit entry is label: ground, display: Ground, category: reference, role: ground, symbol: ground. The graph gram- mar uses its category and role to place the node in a valid topology, while the renderer uses its display name and symbol to construct its appearance. Keeping these vocabularies with the released generator fixes the available node semantics for a dataset version and makes later vocabulary changes explicit. Instantiating a vocabulary entry creates a diagram-specific node. To avoid repeating a small closed set of labels verbatim, the renderer may append a domain-specific suffix sampled from letters, num- bers, or location terms, as in Server 03 or Server West. If the same base label occurs more than once in a diagram, distinct suffixes are assigned to disambiguate the instances, as in Ground X and Ground 2. Capitalization may also vary independently. Every instance stores the exact label drawn in the image, a unique diagram-local ID, and a bounding box; these surface variations do not change its underlying vocabulary entry or structural role. 13 Under review The frozen release contains 310 domain-local canonical labels across the six domains. Table 4 summarizes their coverage and the resulting node counts. Table 4: Canonical vocabulary and node-occurrence statistics in the frozen release. Domain iden- tifies the six diagram domains; Canonical labels is the number of domain-local vocabulary entries represented in that domain; Node instances is the total number of node occurrences across its 3,200 diagrams; Avg./image is the mean number of nodes per diagram; and Min–max is the observed per- diagram node-count range. The total row aggregates all 19,200 diagrams, counting a shared label separately in each domain. DomainCanonical labelsNode instancesAvg./imageMin–max Food Web3138,58512.066–17 Network4044,31513.858–17 Workflow6047,74614.928–20 Natural Process5940,52712.667–18 Circuit6045,14214.117–23 Map Route6028,8649.026–15 Total310245,17912.776–23 Food Web (31 names; three trophic tiers). Producer (8): Grass, Berries, Algae, Leaves, Acorn, Flowering Plant, Plankton, Seaweed. Intermediate consumer (12): Rabbit, Mouse, Squirrel, Deer, Caribou, Moose, Caterpillar, Grasshopper, Dragonfly, Butterfly, Frog, Fish. Higher consumer (11): Bobcat, Fox, Hawk, Owl, Gray Wolf, Black Bear, Snake, Eagle, Shark, Seal, Killer Whale. The FoodWeb appearance pool also contains assets for Mushroom, Coral, Shrimp, Clam, Snail, Spruce Tree, Evergreen Tree, Oak Tree, and Pine Tree. These nine candidate labels are not sampled by the frozen graph generator and therefore are not counted in the 31-name benchmark vocabulary. Network (40 names; 15 categories). Compute (1): Server. Endpoint (7): Client, Workstation, Laptop, Desktop, Phone, Tablet, Terminal. Infrastructure (1): Data Center. IoT (3): Sensor, Con- troller, IoT Device. Network device (4): Repeater, Bridge, Modem, Relay. Network group (2): Subnet, Cluster. Network node (2): Edge Node, Core Node. Peripheral (2): Printer, Camera. Rout- ing (2): Router, Gateway. Security (4): Firewall, VPN, IDS, IPS. Service (2): DNS Server, Cloud. Storage (3): Database, Storage, NAS. Switching (2): Switch, Hub. Traffic (2): Load Balancer, Proxy. Wireless (3): Access Point, Base Station, Satellite. Workflow (60 names; 10 categories). Terminal (2): Start, End. Intake (3): Receive Request, Submit Form, Capture Input. Validation (7): Validate Input, Check Completeness, Verify Iden- tity, Check Eligibility, Check Inventory, Quality Check, Run Test. Data pipeline (8): Extract Data, Transform Data, Load Data, Query Database, Update Database, Sync Records, Generate Report, Export File. Automation (8): Run Model, Score Result, Classify Item, Route Task, Enqueue Job, Process Job, Retry Step, Handle Error. Approval (7): Manual Review, Review Result, Approve Request, Reject Request, Escalate Case, Assign Owner, Sign Off. Communication (6): Send Notifi- cation, Send Email, Create Ticket, Update Status, Notify Customer, Schedule Meeting. Operations (6): Pack Item, Ship Order, Receive Shipment, Inspect Item, Repair Item, Close Case. Storage (4): Archive Record, Store Document, Retrieve Record, Backup Data. Control flow (9): Merge Branches, Split Path, Wait for Event, Timer Expires, Parallel Tasks, Join Tasks, Decision Point, Condition Met?, Fallback Path. Natural Process (59 realized names; nine categories). Energy (2): Sunlight, Heat. Climate (2): Wind, Cloud. Water (8): Rain, Snow, River, Stream, Lake, Ocean, Groundwater, Glacier. Earth (6): Soil, Sand, Clay, Rock, Mineral, Sediment. Organic (4): Leaf Litter, Organic Matter, Dead Wood, Compost. Organism (14): Plant, Grass, Tree, Algae, Moss, Fungi, Bacteria, Microbe, Pollinator, Insect, Worm, Fish, Bird, Small Animal. Role (1): Decomposer. Chemical (8): Carbon Dioxide, Oxygen, Nitrogen, Phosphate, Nitrate, Ammonium, Nutrient, Toxin. Process (14): Photosynthe- sis, Respiration, Decomposition, Evaporation, Condensation, Runoff, Infiltration, Sedimentation, Erosion, Absorption, Fixation, Mineralization, Uptake, Release. The candidate configuration also 14 Under review contains the human–nature label Pollution, but it is not selected by the frozen layer pools and does not occur in the 19,200 released annotations. Circuit (60 names; 11 categories). Power source (5): Battery, Power Supply, USB Power, Solar Cell, AC Adapter. Power conditioning (3): Voltage Regulator, Buck Converter, Boost Converter. Protection (1): Fuse. Passive (7): Resistor, Variable Resistor, Capacitor, Polarized Capacitor, In- ductor, Transformer, Crystal Oscillator. Passive sensor (2): Thermistor, Photoresistor. Active (10): Diode, LED, Zener Diode, Transistor, MOSFET, Op Amp, Comparator, Logic Gate, Integrated Circuit, Driver Chip. Control (6): Switch, Push Button, Toggle Switch, Relay, Microcontroller, Ar- duino Board. Connector (6): DC Jack, Jumper, GPIO Pin, Terminal Block, Header Connector, Test Point. Sensor (10): Temperature Sensor, Light Sensor, Motion Sensor, Pressure Sensor, Humidity Sensor, Current Sensor, Voltage Sensor, Hall Sensor, Microphone, Photodiode. Load (9): Motor, Servo Motor, Speaker, Buzzer, Lamp, Heater, Display, Fan, Pump. Reference (1): Ground. Map Route (60 names; six categories). Transit (10): Station, Platform, Terminal, Transfer Hub, Depot, Bus Stop, Train Stop, Tram Stop, Ferry Pier, Taxi Stand. Indoor (10): Lobby, Office, Lab- oratory, Storage Room, Elevator, Stairwell, Hallway, Conference Room, Reception, Server Room. Campus (10): Main Gate, Library, Dormitory, Cafeteria, Parking Lot, Auditorium, Gymnasium, Courtyard, Admin Building, Lecture Hall. Warehouse (10): Loading Dock, Packing Area, Shelf Zone, Conveyor, Sorting Area, Cold Storage, Forklift Bay, Inventory Desk, Dispatch Gate, Return Station. Landmark (10): Bridge, Park, Tower, Plaza, Checkpoint, Fountain, Museum, Monument, Tunnel Entrance, Overlook. Utility (10): Junction, Entrance, Exit, Security Post, Control Room, Service Gate, Emergency Exit, Information Desk, Rest Area, Access Point. B.2DOMAIN GRAPH GRAMMARS Each domain grammar begins from semantic node roles and a collection of valid structural motifs rather than sampling unconstrained random graphs. Difficulty then changes graph scale, density, and geometric ambiguity in ways appropriate to that domain. The statistics below are measured from the frozen release. Across domains, generation follows the same high-level procedure: sample difficulty-conditioned grammar parameters and role slots, instantiate a symbolic graph satisfying the resulting structural constraints, and only then assign layout, connector routing, and visual assets. Figure 5 illustrates this procedure with the layered Natural Process grammar. Let L k denote the nodes sampled for process stage k. For every adjacent pair L k ,L k+1 , the generator gives each node in L k at least one outgoing edge into L k+1 and each node in L k+1 at least one incoming edge from L k , before adding difficulty-dependent adjacent-stage and intra-stage relations. The example demonstrates how difficulty modifies the grammar—the number and cardinality of stages, relation density, and routing complexity— rather than merely enlarging an otherwise fixed graph. Food Web. The grammar samples producer, intermediate-consumer, and higher-consumer tiers and arranges them in one of four orientations. In the frozen release, simple images contain 6–8 nodes and 5–9 edges, medium images contain 9–13 nodes and 7–15 edges, and difficult images contain 16–17 nodes and 14–22 edges. Most relations follow plausible trophic direction between adjacent tiers, while denser examples add long-range links and directed, bidirectional, or unarrowed connector variants. Medium and difficult cases may also contain close visual alternatives and con- nector crossings that do not denote additional relations. Node, label, and arrow sizes are reduced together in dense layouts so that difficulty is not produced by simply adding edges to an unchanged canvas. Network. Network diagrams combine hub–spoke, layered infrastructure, tiered, and cluster- bridge structures, with device roles constraining plausible connections. Simple examples contain 8–10 nodes and 8–12 edges, medium examples 12–15 nodes and 13–21 edges, and difficult ex- amples 14–17 nodes and 23–31 edges. Increasing difficulty introduces multiple hubs or clusters, shorter distances between candidate endpoints, and more links sharing the same devices or bridge regions. Connectors primarily express unarrowed structural connectivity, with routing adjusted in denser cases to keep connectivity visually traceable. 15 Under review Figure 5: Difficulty-conditioned Natural Process grammar and three frozen instantiations. Left: the executable constraints used at each difficulty. Here L k is the node set at process stage k, K is the number of stages, and the two coverage constraints require every node in adjacent stages to participate in at least one forward relation. The listed ranges are grammar-level cardinality ranges, while “shown instance” gives the realized cardinalities in that row. Middle: the exact symbolic nodes and edge multiset of the selected example, with geometry regularized only for legibility. Right: the corresponding unmodified rendered image and its relation-type legend. From top to bottom, the examples contain 9/9, 11/14, and 14/18 nodes/relations. All three are drawn directly from the frozen test set; no topology, annotation, or rendered connector was edited for the figure. Workflow. Workflow templates encode three control-flow families used in the frozen release: staged grids, ladder-feedback workflows, and swimlanes. Each template defines role slots and a backbone that preserves the functions of terminals, processes, decisions, splits, and merges. Simple, medium, and difficult examples contain 8–9, 13–14, and 20 nodes, respectively, with 10–11, 18, and 29–32 directed edges. Harder cases increase the number of stages or parallel lanes and may intro- duce skip or feedback relations. Role-specific shapes are rendered locally, while typed connector styles are assigned after topology creation and communicated through a matching legend. Natural Process. Natural Process diagrams organize sources, carriers, reservoirs, flows, organ- isms, and materials into layered transformation or transport structures. Simple and medium cases use four layers with 7–9 and 10–14 nodes, while difficult cases use five layers with 13–18 nodes. Their corresponding edge ranges are 6–13, 10–23, and 15–33. The grammar first establishes progression between adjacent layers, ensures that nodes participate in the process, and then adds difficulty- dependent cross-layer or reversible within-layer links. An image may use one or several semantic relation types and may contain multiple typed relations between the same endpoint pair. Parallel connectors are visually separated and distinguished through the legend. Circuit. Circuit diagrams use layered functional structures that progress from power, sensing, or passive components through control and active components to loads and grounds. Simple and 16 Under review Figure 6: Representative visual-appearance pools in Knossos. Each row is a domain, each column is an appearance family, and each cell shows the two candidate variants available for one representative vocabulary entry. Workflow appearances are rendered programmatically rather than generated. The figure shows the candidate pool; the frozen renderer uses the domain-specific subset and sampling policy described below. medium diagrams use four layers, whereas difficult diagrams use five; the frozen ranges are 7– 10, 10–14, and 16–23 nodes and 6–12, 9–22, and 18–35 edges. Endpoint roles determine whether a relation is rendered as wire, power, ground, or signal: links to ground use the ground relation, power- source links favor power, and control, sensor, or active components favor signal or wire. Harder diagrams add denser inter-layer and parallel typed connections. Shared endpoints and parallel links are visually separated and identified in a legend. Map Route. Map Route diagrams cover city and campus grids, indoor corridors, transit networks, subway-like lines, floorplans, warehouse routes, cluster bridges, and free spatial maps. Simple ex- amples contain 6–8 nodes and 4–7 edges, medium examples contain 8–12 nodes and 6–16 edges, and difficult examples contain 8–15 nodes and 8–25 edges. Difficulty additionally increases inter- sections, shared corridors, and alternative paths between nearby destinations. Routes may be direct, softly bent, or orthogonal and may be directed or unarrowed. Overlapping routes and parallel links are visually separated, while route types and direction conventions are indicated by the legend. B.3VISUAL ASSET PIPELINE Visual appearance is sampled only after the symbolic graph has been fixed. The graph generator de- termines node identities and roles, typed relations, and layout constraints; the asset pipeline supplies alternative appearances for the resulting nodes. Consequently, changing an asset cannot change the graph or any evaluation target. 17 Under review Asset construction. For each image-eligible vocabulary entry, the pipeline constructs label–style– variant generation jobs from its canonical label, semantic role, and requested visual style. Prompts request a single centered subject in a square composition and explicitly exclude text, arrows, diagram lines, brands, borders, and watermarks. Two independent candidates are generated for each label– style pair and screened for recognizability, unwanted text, and visual quality. Assets are generated with the OpenAI Images API using gpt-image-1-mini at 1024× 1024 resolution, medium quality, and PNG output. Visible node labels are rendered separately from the symbolic annotations using Pillow rather than by the image model, ensuring exact agreement between displayed text and stored ground truth. The 1024× 1024 resolution above refers only to source assets before they are fitted into diagram nodes, not to the resolution of the rendered diagrams. Domain-specific visual pools. Food Web uses three appearance families over 40 candidate labels, of which 31 occur in the frozen graph vocabulary. Network uses textbook-icon and realistic-device assets. Natural Process combines two generated icon families for image-eligible concepts with locally rendered text cards for abstract process nodes. Circuit and Map Route each use three vi- sual families over their 60-category vocabularies. Workflow does not use generated image assets; its nodes are rendered programmatically using role-specific shapes. Representative examples are shown in Figure 6. The resulting candidate pools contain 240 Food Web, 240 Network, 212 Natural Process, 360 Circuit, and 360 Map Route assets. Sampling in the frozen renderer. Asset sampling is domain-specific and seeded for reproducibil- ity. Food Web samples independently from label-matched visual candidates for each node, whereas Network selects a consistent visual style at the image level. Natural Process, Circuit, and Map Route alternate between fixed-style and mixed-style rendering to increase visual diversity. Map Route ad- ditionally includes locally rendered text-only nodes. The selected asset identity is stored with each node annotation to support exact replay. B.4GEOMETRY AND ANNOTATION DERIVATION Let B i denote the finalized bounding box of node v i , and let e = (s,t) denote a directed edge, optionally associated with a relation type r. The renderer obtains source and target anchors by in- tersecting the center-to-center ray with the boundaries of B s and B t . It then constructs a logical connector polyline P e using the routing family associated with the sampled domain and template: direct, softly bent, or orthogonal. When obstacle-aware routing is used, candidate detours are se- lected according to their interference with non-endpoint nodes and path length. Terminal clearance and arrow placement may slightly shorten the path actually drawn. We therefore store both the logical polyline P e and the rendered polyline e P e (visible path). Arrowheads are derived from the terminal direction of e P e , and reciprocal directions use the same path in re- verse. Any image-resizing transform is applied consistently to node boxes, centers, path vertices, and arrowheads, preserving image–annotation alignment. A five-point trace is derived deterministically from the rendered path. Let ep e : [0, 1] →R 2 denote its normalized arc-length parameterization in the final image coordinate system. The parameter t ∈ [0, 1] specifies relative traversal distance along the connector, while ep e (t) remains an (x,y) location on the resized image canvas. The geometric target is τ e = ep e (j/4) 4 j=0 .(3) The sampled coordinates are rounded to the nearest integer pixel. For the reciprocal direction, the five trace points are stored in reverse order. Node records, edges, relation types when present, connector geometry, and training targets are all serialized from the same finalized objects; none is recovered from rendered pixels or entered manually. Figure 7 visualizes these annotations on a released Food Web sample. Every node is overlaid with its finalized bounding box, and every connector with its five sampled trace points. B.5QUALITY CONTROL AND RELEASE CONSTRUCTION Before large-scale generation, human researchers inspect preview batches from each domain to ver- ify that the generated diagrams are visually coherent and semantically plausible. The review focuses 18 Under review Figure 7: Geometry annotations on a released Food Web sample. Teal dashed boxes denote finalized node bounding boxes. Gold polylines denote rendered connector paths (visiblepath), and the five circular markers on each path are trace points sampled at equal arc-length intervals in source- to-target order. All coordinates are stored in pixels on the final image canvas. on overall image quality, node and connector readability, layout and routing plausibility, consis- tency with the intended domain structure, and whether increasing difficulty produces meaningfully more challenging yet still interpretable diagrams. Generation rules and rendering configurations are refined when systematic issues are identified. After the generation templates and rendering rules are validated through human inspection, the pipeline performs large-scale generation, producing 24,000 candidate diagrams across the six do- mains, with 4,000 candidates generated for each domain. Visual screening is then applied directly to the rendered images using GPT-4o with temperature zero. The binary screening criteria cover over- all clarity, text readability, node and connector visibility, arrow and legend clarity, and excessive overlap. Dense layouts, crossings, and mild local clutter are allowed as long as the diagram remains visually interpretable, preventing difficult examples from being systematically filtered out. Visual screening continued until all release quotas were filled. In total, GPT-4o evaluated 19,223 candidate diagrams, of which 19,200 passed and 23 failed. For release construction, candidates are deterministically shuffled within each domain and difficulty level and assigned to training and test pools before screening. The selected release contains 3,000 training and 200 test images per domain, yielding 18,000 training images and 1,200 held-out test images in total, with matching JSON annotations and manifest entries. Released diagrams use one of two fixed resolutions: 900× 630 pixels for landscape layouts and 630× 900 pixels for portrait layouts. Of the released images, 14,318 (74.6%) use the landscape resolution and 4,882 (25.4%) use the portrait resolution. The canvas dimensions are stored in every annotation, and all node boxes, connector paths, arrowheads, and trace points are defined in this final pixel coordinate system. An audit of the complete release found exact agreement between the recorded canvas dimensions and the actual PNG resolutions. B.6TOPOBENCH-180 EVALUATION SUBSET We evaluate on a 162-image subset of TopoBench-180 (Guo et al., 2026), comprising 54 AI2D/Web and 108 Network diagrams. Relative to the original 180-image collection, we exclude 16 internal Network diagrams and two Network diagrams with unresolved edge references. These exclusions reflect data availability and annotation integrity, rather than model performance. We convert name- keyed annotations to stable node-instance IDs and remove annotation-only naming suffixes while preserving visible labels and distinct repeated-label instances. All evaluation images are obtained from the released files or their provided source links. The resulting annotations contain 1,786 nodes and 3,063 ordered relations. We use this subset exclusively for external evaluation and report Node F1 and Edge F1. 19 Under review CTHEORETICAL DERIVATION OF SOURCE-GROUP DECOMPOSITION Prior work has observed that longer vision–language generations can be more susceptible to hallu- cination and semantic drift (Zheng et al., 2025; Jiang et al., 2026). These observations motivate examining how Ariadne’s source-group decomposition changes both the output representation and the autoregressive decoding process by replacing one long graph serialization with multiple shorter generations. We condition throughout on a fixed node inventory and isolate the edge-decoding stage; errors in- troduced by upstream node prediction are outside the scope of the derivation. Our analysis pro- ceeds from representation to decoding. We first establish that source grouping preserves the target edge multiset, quantify the cross-group ordering freedom in a one-shot representation, and examine its implications for sequence supervision. We then bound the edge-decoding horizon and, under an explicit position-sensitive error model, derive bounds on the reduction in cumulative position- dependent error. C.1LOSSLESS DECOMPOSITION AND SERIALIZATION AMBIGUITY We begin by separating the target topology from the order in which its edges are serialized. Let S(V ) =S 1 ,...,S K be a partition of the node inventory, and let E S i denote the multiset of directed edges whose sources belong to S i . Since every directed edge has a unique source and therefore belongs to exactly one source group, E = K ] i=1 E S i .(4) Thus, source grouping is lossless with respect to graph topology: it changes the decoding represen- tation without restricting the set of edge multisets that can be represented. Although the target topology is unchanged, its serialization may still admit multiple equivalent or- derings. Let m i =|E S i |, m =|E| = K X i=1 m i .(5) Fix the within-group edge orders, denoted by O, and consider a flat one-shot representation that permits arbitrary cross-group interleavings. All other serialization choices are held fixed. An inter- leaving is determined by assigning m i of the m output positions to each group; the fixed within- group orders then determine which edge occupies each assigned position. The number of equivalent interleavings is therefore N interleave = m m 1 ,...,m K = m! Q K i=1 m i ! .(6) For this one-shot representation, we quantify cross-group ordering freedom by its log-cardinality, A one = logN interleave = logm!− K X i=1 logm i !,(7) where log denotes the natural logarithm. This quantity measures the size of the equivalence class, not the entropy of a particular model distribution. Ariadne instead decodes each E S i in a separate call and combines the results by multiset union. Since edges from different groups are not interleaved within a shared output sequence, its corresponding cross-group ambiguity is A group = 0,(8) giving ∆A = A one − A group = log m! Q K i=1 m i ! .(9) 20 Under review Possible ordering choices within each group remain unchanged. This comparison establishes a difference in representation, rather than a difference in prediction er- ror. Its relevance to training arises when supervision specifies a single reference sequence: multiple orderings may encode the same topology, but the sequence-level objective evaluates the probability of the particular reference ordering. We next make this distinction explicit. Implication for sequence supervision. Fix the input X = (I,V ) and retain the within-group orders O defined above. Let Σ O (E) denote the set of N interleave equivalent interleavings. For a sequence model p θ , define their total probability mass and the conditional distribution within this class as q = X y∈Σ O (E) p θ (y | X), π θ (y | E,O,X) = p θ (y | X) q , y ∈ Σ O (E), (10) assuming q > 0. Because the within-group orders are fixed, q is the probability assigned to this interleaving class, not necessarily to all serializations of the target graph. For a reference sequence y ⋆ ∈ Σ O (E) with positive probability, its negative log-likelihood decom- poses exactly as − logp θ (y ⋆ | X) =− logq− logπ θ (y ⋆ | E,O,X).(11) The first term evaluates the total probability assigned to the equivalent interleavings. The second is the additional loss incurred by specifying one reference ordering rather than marginalizing over this class. In the idealized uniform case, π θ (y ⋆ | E,O,X) = 1/N interleave , so the additional term equals logN interleave = A one . Otherwise, it depends on the probability assigned to the particular reference. This decomposition connects the ordering freedom counted above to an ordering-dependent com- ponent of sequence supervision. Source-group decoding removes the need to choose a cross-group interleaving, while leaving possible within-group ordering choices intact. It does not, however, guar- antee a lower total training loss or graph-prediction error, because the grouped model may assign different probabilities to the target outputs. The comparison also depends on the one-shot format: enforcing a unique cross-group order removes this particular ordering freedom, whereas canonically ordered training targets alone do not constrain the model’s output support. The analysis so far con- cerns how topology is represented and supervised. The following subsections examine a separate consequence of source grouping—a shorter decoding horizon—and its implications for position- dependent error. C.2BOUND ON THE DECODING HORIZON Source grouping also shortens the maximum edge-decoding horizon of each autoregressive genera- tion. A one-shot representation predicts all m =|E| edges in a single sequence, L one = m,(12) whereas source-group decoding requires at most L group = max i m i ≤ m,(13) where m i =|E S i |. The inequality is strict whenever at least two source groups contain edges. Thus, source grouping preserves the complete edge set while replacing one global decoding horizon with multiple shorter local ones. This reduction motivates the position-sensitive error analysis below. C.3POSITION-SENSITIVE DECODING MODEL Empirical studies of LVLM generation have reported greater hallucination risk and semantic drift in longer responses, including increased error toward later decoding positions (Zheng et al., 2025; Jiang et al., 2026). Motivated by this behavior, we consider a stylized position-sensitive decoding model. 21 Under review Let ε j denote the expected error associated with an edge-level decision made at position j within one autoregressive generation. For this stylized comparison, we assume that ε j captures the position- dependent component of edge-level error and is shared between the one-shot and grouped decoding processes. We first assume only monotonicity: ε j+1 ≥ ε j .(14) This assumption does not assert that output position itself causes error. Rather, it models a regime in which later decisions are no easier on average than earlier ones, potentially reflecting accumulated uncertainty, semantic drift, or increasing dependence on previously generated context. For the comparison below, consider a one-shot serialization in which the source groups are written as contiguous blocks in the order S 1 ,...,S K . Define the cumulative number of edges preceding group i as M i−1 = i−1 X h=1 m h , M 0 = 0.(15) Under one-shot decoding, the edges of group i therefore occupy positions M i−1 +1,...,M i−1 +m i , giving E one = K X i=1 m i X j=1 ε M i−1 +j .(16) Under source-group decoding, each group starts a new autoregressive generation, so that E group = K X i=1 m i X j=1 ε j .(17) Since M i−1 + j ≥ j, monotonicity in Eq. 14 immediately gives E group ≤E one .(18) Hence, in the position-sensitive regime, restarting autoregressive decoding across source groups weakly reduces the cumulative error component associated with output position. C.4BOUND ON POSITION-DEPENDENT ERROR REDUCTION We now strengthen the monotonicity assumption by bounding the growth of the position-dependent error. Let 0≤ α≤ ε j+1 − ε j ≤ β(19) for all relevant decoding positions j. Here, α and β bound the per-position increase in expected edge-level error. Define the reduction induced by source grouping as ∆E =E one −E group .(20) Using Eqs. 16 and 17, ∆E = K X i=1 m i X j=1 ε M i−1 +j − ε j .(21) For every term, ε M i−1 +j − ε j = M i−1 +j−1 X r=j (ε r+1 − ε r ).(22) Applying Eq. 19 yields αM i−1 ≤ ε M i−1 +j − ε j ≤ βM i−1 .(23) Summing over all m i edges in group i gives αm i M i−1 ≤ m i X j=1 ε M i−1 +j − ε j ≤ βm i M i−1 .(24) 22 Under review Summing again over all source groups, α K X i=1 m i M i−1 ≤ ∆E ≤ β K X i=1 m i M i−1 .(25) Because K X i=1 m i M i−1 = X h<i m h m i = 1 2 m 2 − K X i=1 m 2 i ! ,(26) we obtain α 2 m 2 − K X i=1 m 2 i ! ≤ ∆E ≤ β 2 m 2 − K X i=1 m 2 i ! (27) with ∆E =E one −E group . Equation 27 makes explicit how the benefit of restarting decoding depends on the edge distribution across source groups. If K = 1, then P i m 2 i = m 2 and the bound correctly gives zero reduction. For a fixed total number of edges m, the quantity m 2 − X i m 2 i (28) is larger when edges are distributed more evenly across groups, indicating a larger potential reduc- tion in position-dependent error. For approximately balanced groups, m i ≈ m/K, giving K X i=1 m 2 i ≈ m 2 K .(29) The lower bound then becomes ∆E≳ αm 2 2 1− 1 K .(30) Under this stylized regime, the potential benefit of source-group restarting therefore increases with graph size and with the extent to which the full edge set is distributed across multiple decoding groups. Scope of the analysis. The analysis separates model-independent structural guarantees from model-dependent conclusions. The first two results are deterministic under the serialization setting defined above. Source grouping preserves the complete target topology while removing cross-group serialization ambiguity, and it strictly shortens the maximum decoding horizon whenever multiple nonempty source groups are present. These properties do not depend on any assumption about VLM error behavior. The subsequent error analysis is conditional on the position-sensitive decoding model. In particular, the inequalityE group ≤ E one requires the assumption that expected edge-level error is nondecreas- ing with decoding position, while the quantitative error-reduction bound further assumes bounded per-position error growth. Prior work provides empirical motivation for this regime by showing increased hallucination and semantic drift in longer LVLM generations (Zheng et al., 2025; Jiang et al., 2026), but these observations do not imply that every VLM follows such an error profile. Our derivation therefore provides unconditional guarantees about representation and decoding length, together with conditional guarantees about error reduction when longer autoregressive generations become progressively harder to maintain consistently. DADDITIONAL EXPERIMENTAL RESULTS D.1RELATION-TYPE PREDICTION BY DOMAIN Table 5 reports domain-level Typed-Edge F1 on the three Knossos domains with explicit relation semantics. Across all three typed domains, both Ariadne variants consistently outperform their cor- responding direct backbones. Ariadne-Qwen achieves the highest Typed-Edge F1 in each domain, 23 Under review Table 5: Typed-Edge F1 (%) on the three Knossos domains with explicit relation semantics. MethodNatural Process Circuit Map Route Open-source VLMs Qwen3-VL-32B49.530.769.3 Qwen3-VL-8B41.824.055.8 GLM-4.6V-Flash34.919.848.3 MiMo-VL-7B-RL34.521.357.4 Keye-VL-1.5-8B31.611.528.2 InternVL3.5-8B38.921.244.1 Ovis2.5-9B24.917.143.1 Closed-source VLMs GPT-4o38.526.660.1 GPT-5.688.976.686.5 Opus 596.356.177.1 Visual reasoning methods Pixel Reasoner16.311.721.2 Chain of Region29.822.951.2 Speculative Verdict43.120.358.2 TopoAgent36.329.653.4 Ours Ariadne (GLM-based)95.982.987.8 Ariadne (Qwen3-based)97.385.089.0 Table 6: Geometric grounding on the fixed 120-image Knossos subset. Box mIoU and R@0.5 are percentages; connector L2 is measured in original-image pixels. MethodBox mIoU↑R@0.5↑Connector L2↓ GPT-5.681.8193.7311.34 Ariadne-GLM86.4296.966.14 Ariadne-Qwen396.5997.554.13 with Ariadne-GLM close behind. Circuit remains the most challenging domain for most methods, while Natural Process generally shows the strongest performance. The large variation of several closed-source models across domains further suggests that relation-type prediction remains sensi- tive to domain-specific semantics. D.2BOUNDING-BOX AND CONNECTOR LOCALIZATION We evaluate geometric grounding on a fixed 120-image subset of the Knossos test set, with 20 im- ages per domain and difficulty proportions approximately preserved. The subset contains 1,548 reference nodes and 2,759 connector instances corresponding to typed edges. Bounding-box evalu- ation uses each model’s predicted nodes, whereas connector localization is conditioned on reference nodes and edges to isolate geometric localization quality from topology errors. For bounding boxes, predictions are matched to reference nodes by normalized visible names using one-to-one maximum-IoU assignment. We report mean IoU (mIoU) over matched nodes and recall at IoU≥ 0.5 (R@0.5). Connector localization is evaluated using the mean L2 distance between the five predicted and reference points along each connector. All distances are measured in the original image coordinate system. Table 6 shows that both Ariadne variants improve geometric grounding over GPT-5.6, with Ariadne- Qwen3 performing best overall. Its box mIoU increases from 81.81% to 96.59%, while connector localization error decreases from 11.34 to 4.13 pixels. Ariadne-GLM also substantially reduces connector localization error while improving bounding-box localization. The domain-level results in Table 7 show that the gains are broadly consistent across diagram types. Ariadne-Qwen3 achieves the highest box mIoU in all six domains and lower connector localization error than GPT-5.6 throughout. The largest reductions in connector error occur on Food Web and Circuit, which are also among the most challenging domains for connector localization. Figure 8 provides qualitative examples of the same comparison. 24 Under review Table 7: Per-domain geometric grounding on the same 120-image subset. Box mIoU is reported in percent and connector L2 in pixels. Box mIoU↑Connector L2↓ DomainGPT-5.6 Ariadne-GLM Ariadne-Qwen3 GPT-5.6 Ariadne-GLM Ariadne-Qwen3 Food Web88.7186.2096.0617.546.805.74 Network91.7892.9198.557.514.074.14 Workflow95.1584.6297.756.804.782.86 Natural Process67.7485.7894.946.686.093.37 Circuit69.1282.9893.4920.248.364.67 Map Route69.3785.2999.198.278.114.00 Natural Process | 900 x 630 pixels Reference Matched-node IoU 0.742 | Shown TRACE error 7.5 px GPT-5.6 Matched-node IoU 0.973 | Shown TRACE error 4.6 px Ariadne (Qwen3) Workflow | 900 x 630 pixels Matched-node IoU 0.937 | Shown TRACE error 3.8 pxMatched-node IoU 0.997 | Shown TRACE error 1.5 px Node bounding boxes Connector 1: five sampled points Connector 2: five sampled points Connector 3: five sampled points Figure 8: Geometric grounding examples on two original Knossos test images. Boxes show node localization, while colored polylines and markers show reference-conditioned connector predictions. No predicted coordinates are manually adjusted. D.3NODE EXTRACTION BY DOMAIN Table 8 reports the complete domain-level Node F1 results underlying the macro-averages summa- rized in the main paper, together with results on the external TopoBench-180 test set. The Knossos average gives equal weight to all six domains. Across Knossos, node extraction is consistently strong for most models, with Food Web, Network, Workflow, and Natural Process generally ap- proaching ceiling performance. Circuit is noticeably more challenging, producing the largest drop in Node F1 for many baselines, while Map Route also shows somewhat greater variation. Both Ariadne variants remain stable across domains and achieve the highest Knossos average of 97.8%. On TopoBench-180, however, general-purpose VLMs often retain stronger node-level generaliza- tion than the task-adapted Ariadne node predictors. This domain-level breakdown further supports the observation that node-specific adaptation improves in-domain accuracy but may introduce some specialization to the synthetic training distribution. D.4PROTOCOL EFFICIENCY ABLATION We compare the inference cost of one-step generation and staged decomposition on the same 30 Knossos test images, with 10 images from each difficulty level. For each backbone, both proto- cols use the same model configuration. One-step generation requires a single model invocation per 25 Under review Table 8: Node F1 (%) across the frozen KNOSSOS internal test set and TopoBench-180. Avg. is the unweighted macro-average of the six KNOSSOS domain-level scores. Dashes indicate results that are not available. KNOSSOSTopoBench-180 MethodFood WebNetworkWorkflowNatural ProcessCircuitMap RouteAvg.Web-styleNetwork-style Open-source VLMs Qwen3-VL-32B99.399.599.497.987.893.996.396.387.5 Qwen3-VL-8B99.399.699.496.086.390.995.295.488.9 GLM-4.6V-Flash98.998.799.098.085.490.895.194.386.3 MiMo-VL-7B-RL87.098.692.388.783.390.490.073.781.2 Keye-VL-1.5-8B97.098.496.492.580.887.592.186.783.9 InternVL3.5-8B99.299.098.596.780.689.293.994.786.4 Ovis2.5-9B96.799.198.697.380.290.993.880.178.6 Closed-source VLMs GPT-4o99.999.199.498.989.293.096.693.384.1 GPT-5.699.999.299.298.888.994.796.896.487.5 Opus 599.999.999.999.290.595.197.493.688.1 Visual reasoning methods Pixel Reasoner99.899.899.291.082.390.093.775.271.4 Chain of Region99.898.699.599.287.589.295.695.686.8 Speculative Verdict99.699.899.399.285.591.095.793.683.2 TopoAgent99.999.699.098.488.892.496.495.687.0 Ours Ariadne (GLM-based)99.799.599.899.293.495.097.894.682.9 Ariadne (Qwen3-based)99.799.799.999.293.694.997.892.279.3 Table 9: Inference efficiency on the same 30-image test slice (10 simple, 10 medium, and 10 diffi- cult). S/M/D denote mean latency (seconds per image) by difficulty; Overall is the mean across all 30 images. BackboneProtocolCalls/imgAPI calls/imgSMDOverallTokens/imgCost/img ($) GLM-4.6V-FlashOne-step1.000.0061.81106.00153.92107.24–0.000 GLM-4.6V-FlashStaged5.230.0083.39126.86204.33138.19–0.000 GPT-5.6One-step1.001.0013.8926.9828.9023.263,8430.052 GPT-5.6Staged5.235.2321.9934.5554.8137.1210,7470.147 image, whereas staged inference performs one node-prediction call followed by one call for each active source group. Table 9 reports mean per-image inference cost. GPT-5.6 latency, token usage, and API cost are obtained directly from archived request metadata. For GLM-4.6V-Flash, latency is reconstructed from consecutive completion timestamps within each continuously running GPU shard, excluding model loading. The comparison is therefore paired within each backbone; ab- solute latency between local GLM inference and the GPT-5.6 API should not be interpreted as a hardware-versus-service benchmark. Staged inference uses 5.23× as many model invocations on this slice. Relative to one-step genera- tion, mean latency increases by 28.9% for GLM-4.6V-Flash and 59.6% for GPT-5.6. For GPT-5.6, token usage increases by 2.80×, with a comparable increase in estimated API cost. The overhead also grows with diagram difficulty because larger node inventories induce more source-group calls. These results quantify the main efficiency trade-off of staged decomposition alongside its accuracy gains reported in the main ablation. 26 Under review Table 10: Stage-specific supervised-training configuration. “Initialization” denotes the adapter state from which each specialist is trained. Steps are optimizer steps after gradient accumulation. StageEpochs Steps Learning rate Initialization NODE1 1,125 5×10 −5 Pretrained VLM EDGE1 5,960 1×10 −5 Node predictor adapter TRACE1 5,801 1×10 −5 Node predictor adapter EADDITIONAL REPRODUCIBILITY MATERIAL E.1TRAINING AND INFERENCE CONFIGURATION Both Ariadne instantiations use the same data, optimization protocol, prompts, and output schemas. Table 10 summarizes the stage-specific training hyperparameters and adapter initialization. Edge and trace predictors each initialize from the completed node adapter but are trained independently. All trainable Ariadne predictors and same-backbone direct full-graph baselines are trained with QLoRA using 4-bit NF4 quantization, double quantization, and bfloat16 computation. We use LoRA rank r = 16, scaling factor α = 32, and dropout 0.05. Adapters are applied to the language atten- tion and MLP projections, the corresponding vision projections, and the vision–language merger. Training optimizes assistant-response tokens only, while image, system, and user-prompt tokens are masked from the supervised cross-entropy loss. We use paged 8-bit AdamW with zero weight decay, gradient clipping at 1.0, cosine learning-rate decay, 3% linear warmup, and random seed 7. Gradient checkpointing is enabled. The effective batch size is 16 with a per-device batch size of one. All Ariadne predictors and direct full-graph baselines are trained on four NVIDIA A100 GPUs with four gradient-accumulation steps. We train direct full-graph baselines using GLM-4.6V-Flash (9B) and Qwen3-VL-8B with the same corresponding backbones, training data, and backbone-specific optimization settings as their Ariadne counterparts. Model evaluation is performed after training on the frozen evaluation splits rather than during the training loop. Inference uses deterministic greedy decoding with one beam. For Ariadne, the node and edge pre- dictors use maximum generation budgets of 2,048 tokens, while the trace predictor uses 1,024 tokens. Generation terminates early upon producing the corresponding closing tag (</NODES>, </EDGE GRAPH>, or </TRACES>). The predicted node inventory is partitioned into source groups of target size three, while every group retains the complete predicted inventory as its candidate target set. The direct full-graph baselines instead generate the complete node inventory and edge structure within a single response. Evaluation loads model weights in 4-bit mode, and identical frozen test examples are used for the GLM- and Qwen3-based Ariadne variants and their corresponding direct full-graph baselines. E.2PROMPTS FOR TOPOLOGY EXTRACTION Ariadne separates topology extraction into a node-inventory predictor followed by a source-group edge predictor. The two predictors are trained with separate objectives and independent QLoRA adapters. In particular, edge prediction does not consume or produce connector traces; the symbolic topology is complete once the source-group edge predictions are merged. During edge training, the complete reference node inventory is provided as input, whereas end-to-end inference uses the inventory predicted by Stage 1. Text enclosed in square brackets below denotes per-example content inserted by the data or evaluation pipeline and is not literal prompt text. Node inventory prompt. The node predictor is restricted to node discovery and geometric local- ization. Its output contains visible node labels, diagram-local identifiers, and bounding boxes, but no relations or connector predictions. 27 Under review NODE system prompt You are the Node Inventory Predictor. Given a topology diagram image, detect only the visible nodes and return their ids, names, and bounding boxes. Do not extract edges, traces, legends, or final graphs. NODE user prompt Extract only the visible node inventory from this diagram. Return only a <NODES> block. Do not output edges or traces. Rules: - List every visible node exactly once. - Use node ids n1, n2, ... in reading order. - Preserve the visible label text as the node name. - Each box covers the full visible node region, including its symbol and text label. - Use integer coordinates in [x1,y1,x2,y2] format. NODE response schema <NODES> <NODE id="n1" name="Grass" box="[120,40,200,120]"/> <NODE id="n2" name="Rabbit" box="[320,220,410,350]"/> </NODES> Source-group edge prompt. The edge predictor receives the complete node inventory as target context but may emit outgoing relations only for the active source group. Because the source groups partition the predicted node inventory, the resulting edge multisets can be merged deterministically after independent decoding. EDGE system prompt You are the Edge Predictor. Extract typed topology relations for the selected source nodes and output EDGE elements only. 28 Under review EDGE user prompt template Extract typed topology relations for the selected source nodes. You are given: 1. the diagram image; 2. the complete fixed node list with id, name, and box; and 3. the current source node group. Use only the provided node ids and names. Output only relations whose source is in the current source group. For every positive relation, output EDGE directly; do not output TRACE. Preserve the visible target and exact relation type. If one source-target pair has multiple types, output one EDGE per type and do not merge them. If an active source has no outgoing relation, output an empty CHECK_NODE. Use sparse NO_EDGE only for hard negatives such as a near miss, a crossing without connection, or the wrong direction. Return only <EDGE_GRAPH> and do not explain. Complete node list: [NODE_INVENTORY] Current source node group: [ACTIVE_SOURCES] Rules: - Put each relation under its source CHECK_NODE. - Emit every active source CHECK_NODE exactly once. - EDGE carries source, target, their names, and the typed label. - Never output TRACE or repeat node boxes in the response. EDGE response schema <EDGE_GRAPH> <CHECK_NODE id="n4" name="Sensor"> <EDGE source="n4" source_name="Sensor" target="n6" target_name="Controller" type="signal"/> <EDGE source="n4" source_name="Sensor" target="n8" target_name="Ground" type="ground"/> </CHECK_NODE> </EDGE_GRAPH> Direction is represented by the ordered source–target pair. When a diagram legend defines semantic relation types, type stores the corresponding relation label; otherwise, it is left empty. Undirected and bidirectional connectors are represented by reciprocal ordered edges, while multiple typed re- lations sharing the same endpoints remain distinct multiset elements. NO EDGE provides sparse hard-negative supervision and is never inserted into the predicted topology. E.3INDEPENDENT GEOMETRIC GROUNDING PROMPT Connector geometry is predicted only after the symbolic edge set has been fixed. A third, inde- pendently trained QLoRA adapter receives the diagram, node inventory, and already-decided edges and predicts a five-point trace for each relation. The trace predictor cannot add, remove, redirect, or retype an edge. Each input edge is assigned an immutable edge id, which links the predicted geometry back to its corresponding symbolic relation. 29 Under review For the geometric-grounding evaluation reported in this paper, the trace predictor is conditioned on reference nodes and reference edges, isolating connector-localization quality from upstream topol- ogy errors. TRACE system prompt You are the Ariadne Trace Predictor. Given a diagram, fixed nodes, and already-decided typed edges, localize each edge with exactly five source-to-target coordinates. Never revise or emit an EDGE. TRACE user prompt template Localize the already-decided typed edges in the diagram. The EDGE decisions are fixed. Do not add, remove, rename, retype, or emit an EDGE. For each input edge, output exactly one TRACE with the same edge_id. Each TRACE must contain exactly five points ordered from the source boundary to the target boundary. Intermediate points must follow the visible connector rather than a straight-line guess. Return only <TRACES> and stop after </TRACES>. Complete fixed node list: [NODE_INVENTORY] Already-decided typed edges: [EDGE_LIST_WITH_EDGE_IDS] TRACE response schema <TRACES> <TRACE edge_id="e1" points="[[180,100],[220,145],[260,190],[300,235],[340,280]]"/> </TRACES> E.4DIRECT FULL-GRAPH BASELINE PROMPT For the general-purpose open- and closed-source VLM baselines, we use direct full-graph genera- tion. Each model receives the diagram and produces the complete node inventory and edge set in a single response, using the same node and edge output conventions as Ariadne. 30 Under review Direct full-graph user prompt Extract the complete typed topology graph from this diagram in one response. First output a <NODES> inventory, then an <EDGE_GRAPH>. Do not explain. Rules: - List every visible node exactly once using ids n1, n2, ... in from reading order; preserve its visible name and integer box. - For every positive relation, output an EDGE with the correct source, target, and relation type when defined. - Inspect every connector separately and determine direction only from visible arrowheads, never from layout or semantics. - Preserve the exact domain-specific relation type and all multiple types between the same endpoint pair. - Put each relation under its source CHECK_NODE and cover every visible connector. - Encode a one-arrow connector as one ordered relation. - Encode a two-arrow or no-arrow connector as two reciprocal ordered relations; do not confuse bidirectional and undirected. - Return only the structured <NODES> and <EDGE_GRAPH> blocks. 31