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CircuitSense: A Hierarchical Circuit System Benchmark Bridging Visual Comprehension and Symbolic Reasoning in Engineering Design Process

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Mathematical Reasoning BenchmarkCircuit BenchmarkSymbolic Reasoning
Abstract:

Engineering design operates through hierarchical abstraction from system specifications to component implementations, requiring visual understanding coupled with mathematical reasoning at each level. While Multi-modal Large Language Models (MLLMs) excel at natural image tasks, their ability to extract mathematical models from technical diagrams remains unexplored. We present \textbf{CircuitSense}, a comprehensive benchmark evaluating circuit understanding across this hierarchy through 8,006+ problems spanning component-level schematics to system-level block diagrams. Our benchmark uniquely examines the complete engineering workflow: Perception, Analysis, and Design, with a particular emphasis on the critical but underexplored capability of deriving symbolic equations from visual inputs. We introduce a hierarchical synthetic generation pipeline consisting of a grid-based schematic generator and a block diagram generator with auto-derived symbolic equation labels. Comprehensive evaluation of eight state-of-the-art MLLMs, including both closed-source and open-source models, reveals fundamental limitations in visual-to-mathematical reasoning. Closed-source models achieve over 85% accuracy on perception tasks involving component recognition and topology identification, yet their performance on symbolic derivation and analytical reasoning falls below 19%, exposing a critical gap between visual parsing and symbolic reasoning. Models with stronger symbolic reasoning capabilities consistently achieve higher design task accuracy, confirming the fundamental role of mathematical understanding in circuit synthesis and establishing symbolic reasoning as the key metric for engineering competence. Our synthetic pipeline code is available at \href{https://anonymous.4open.science/r/CircuitSense-8AC7/README.md}{URL}.

Disclaimer
This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

CircuitSense introduces a benchmark for evaluating visual-to-mathematical reasoning in circuit understanding, spanning component-level schematics to system-level block diagrams with over 8,000 problems. The paper resides in the Circuit and Diagram Visual Parsing leaf, which contains only three papers total, including two siblings. This represents a relatively sparse research direction within the broader taxonomy of sixteen papers across ten leaf nodes, suggesting the specific focus on hierarchical circuit understanding with mathematical derivation is not yet densely populated.

The taxonomy reveals neighboring work in Symbolic and Geometric Primitive Extraction and Visual-to-Symbolic Equation Derivation, which address related but distinct challenges. While sibling papers like Neural Circuit Diagrams and CircInspect focus on diagram interpretation, they do not emphasize the complete engineering workflow from perception through symbolic equation derivation. The Mathematical Reasoning branch contains only two papers, indicating that visual-to-symbolic translation remains underexplored compared to pure visual parsing or hierarchical modeling approaches found in other branches.

Among twenty-eight candidates examined, the benchmark contribution and synthetic generation pipeline show no clear refutation across eighteen examined candidates. However, the systematic evaluation contribution encountered two refutable candidates among ten examined, suggesting prior work has explored MLLM limitations in technical reasoning tasks. The limited search scope means these findings reflect top-K semantic matches rather than exhaustive coverage, and the sparse refutation pattern indicates the specific combination of hierarchical circuit understanding with mathematical derivation may offer incremental novelty over existing evaluation frameworks.

The analysis suggests moderate novelty given the sparse taxonomy leaf and limited prior work on complete visual-to-mathematical workflows in circuits. However, the evaluation component overlaps with existing MLLM capability studies, and the twenty-eight candidate scope leaves open questions about broader literature coverage. The hierarchical emphasis and symbolic equation focus appear to differentiate this work within the constrained search space examined.

Taxonomy

Core-task Taxonomy Papers
16
3
Claimed Contributions
28
Contribution Candidate Papers Compared
2
Refutable Paper

Research Landscape Overview

Core task: visual-to-mathematical reasoning in circuit understanding across hierarchical abstraction levels. The field structure suggested by the taxonomy reflects a multifaceted challenge that spans visual perception, symbolic reasoning, hierarchical modeling, and pedagogical applications. The first branch, Visual Perception and Structural Parsing in Technical Domains, encompasses methods that extract structured representations from diagrams and schematics, often drawing on insights from neuroscience and computer vision to parse complex visual layouts. The second branch, Mathematical Reasoning and Symbolic Derivation, focuses on translating parsed structures into formal equations and constraint systems, bridging perceptual input with symbolic computation. The third branch, Hierarchical Abstraction Frameworks and Architectures, addresses the need to reason at multiple levels of granularity—from low-level component interactions to high-level system behavior—often leveraging hierarchical Bayesian models or reinforcement learning strategies. Finally, the fourth branch, Pedagogical and Multimodal Visualization Systems, explores interactive tools that support learning and explanation, making abstract circuit concepts accessible through dynamic visual feedback. A particularly active line of work centers on integrating visual parsing with hierarchical reasoning, where methods must simultaneously recognize circuit topology and infer mathematical relationships at varying abstraction levels. CircuitSense[0] sits squarely within the Circuit and Diagram Visual Parsing cluster, emphasizing the extraction of structured circuit representations from visual input. It shares common ground with Neural Circuit Diagrams[6] and CircInspect[7], both of which tackle diagram interpretation, yet CircuitSense[0] places stronger emphasis on bridging visual parsing with mathematical derivation across hierarchical layers. This contrasts with works like Hierarchical Quantum Circuits[1] or Hierarchical Process Rewards[10], which prioritize abstraction mechanisms over the initial visual-to-symbolic translation. The interplay between perceptual fidelity and symbolic rigor remains an open question, as does the scalability of these approaches to real-world circuit complexity and diverse abstraction schemes.

Claimed Contributions

CircuitSense benchmark for hierarchical visual-to-mathematical reasoning

The authors introduce CircuitSense, a benchmark comprising over 8,006 problems organized across six hierarchy levels (from resistor networks to system-level block diagrams) and three task categories (Perception, Analysis, and Design). The benchmark uniquely emphasizes symbolic equation derivation from visual circuit representations, combining curated problems from textbooks with synthetically generated circuits.

8 retrieved papers
Hierarchical synthetic generation pipeline with ground-truth symbolic equations

The authors develop a two-part synthetic generation pipeline: a grid-based circuit schematic generator that produces component-level circuits with guaranteed symbolic ground-truth equations, and a block diagram generator for system-level architectures with transfer function ground-truth. This pipeline enables unbiased evaluation while preventing dataset contamination.

10 retrieved papers
Systematic evaluation revealing visual-to-mathematical reasoning gap in MLLMs

Through extensive experiments on eight state-of-the-art MLLMs, the authors demonstrate that while models excel at visual perception tasks (over 85% accuracy for closed-source models), they catastrophically fail at symbolic equation derivation (below 19% accuracy). The study establishes that stronger symbolic reasoning capabilities correlate with better design task performance, confirming mathematical understanding as prerequisite for engineering competence.

10 retrieved papers
Can Refute

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

CircuitSense benchmark for hierarchical visual-to-mathematical reasoning

The authors introduce CircuitSense, a benchmark comprising over 8,006 problems organized across six hierarchy levels (from resistor networks to system-level block diagrams) and three task categories (Perception, Analysis, and Design). The benchmark uniquely emphasizes symbolic equation derivation from visual circuit representations, combining curated problems from textbooks with synthetically generated circuits.

Contribution

Hierarchical synthetic generation pipeline with ground-truth symbolic equations

The authors develop a two-part synthetic generation pipeline: a grid-based circuit schematic generator that produces component-level circuits with guaranteed symbolic ground-truth equations, and a block diagram generator for system-level architectures with transfer function ground-truth. This pipeline enables unbiased evaluation while preventing dataset contamination.

Contribution

Systematic evaluation revealing visual-to-mathematical reasoning gap in MLLMs

Through extensive experiments on eight state-of-the-art MLLMs, the authors demonstrate that while models excel at visual perception tasks (over 85% accuracy for closed-source models), they catastrophically fail at symbolic equation derivation (below 19% accuracy). The study establishes that stronger symbolic reasoning capabilities correlate with better design task performance, confirming mathematical understanding as prerequisite for engineering competence.

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