Explainable Error Detection in Integrated Circuits Image Segmentation via Graph Neural Networks
Authors: MA XIAOYU
Jingyang Dai
Feng Ji
Deruo Cheng
Yiqiong Shi
Bah-Hwee Gwee
Venue: Accepted by TMLR ()

Abstract: Automated segmentation of integrated circuit (IC) images plays a critical role in hardware assurance, yet remains challenging due to nanoscale structural complexity, extremely low error tolerance, and the limited interpretability of existing deep learning–based approaches. Most convolutional neural network (CNN)–based error detection methods operate at the whole-image level, making it difficult to localize specific faults or explain their structural causes. In this work, we propose an explainable graph neural network (GNN) framework for component-level error detection in IC segmentation masks. Each connected component in the binary mask is converted into a feature-annotated graph that captures both topological connectivity and geometric properties. Error detection is then formulated as graph-based classification, enabling the identification of anomalous components and precise localization of erroneous regions. Experiments on multiple IC layouts under diverse imaging conditions demonstrate that the proposed method achieves robust and generalizable performance. In addition to accurate detection, the graph-based formulation provides improved interpretability by explicitly linking predictions to structural deviations at the component level.

Published in Transactions on Machine Learning Research (04/2026)
Explainable Error Detection in Integrated Circuits Image Segmentation via Graph Neural Networks
Xiaoyu Ma
MA0009YUGe.ntuu wtw.eee.en.u.u.......
College of Computing and Data Science, Nanyang Technologioal University
Jingyang Dai
jingyyang, dawiantt.eeduu...
School of Electrical and Electronic Engineering, Nangang Technological University
Feng Ji
jifeng@ntu.. edu.sg
School of Electricol and Electronic Engineering, Nonyang Technological University
Deruo Cheng
deruo.cheng cet.tttuu.......... edu.sg
School of Electrical and Electronic Engineering, Nanyang Technological University
Yiqiong Shi
YQSHI@nnt.edu...
School of Electricol and Electronic Engineering, Nanyang Technological University
Bah Hwee Gwee
eblgwee@ntu.cde edu.sg
School of Electrical and Electronic Engineering, Nanyang Technological University
Reviewed on OpenReview: https: // http://pppere...ee/// net/ pdfp id- 96889mTom5
Abstract
Automated segmentation of integrated circuit (IC) images plays critical role in hardware assurance, yet remains challenging due to nanoscale structural complexity, extremely low error tolerance, and the limited interpretability of existing deep learning- approaches. Most convolutional neural network (CNN)-based error detection methods operate at the whole-image level, making it difficult to localize specific faults or explain their structural causes. this work, we propose an explainable graph neural network (GNN) framework for component-leved error detection in IC segmentation masks. Each connected component in the binary mask is converted into featuro-amnotated graph that captures both topological connectivily and geometric properties. Error detection is then formulated graph-based classification, enabling the identification of anomalous components and precise localization of erroncous regions. Experiments on multiple IC layouts under diverse imaging conditions demonstrate that the proposed method achieves robust and generalizable performance. In addition to accurate detection, the graph-based formulation provides improved interpretability by explicitly linking predictions structural deviations the component level.
1 Introduction
The rapid advancement of semiconductor technology has led to increasingly complex integrated circuit (IC) designs with smaller feature sizes and higher integration density (Mack 2011). Accurate segmentation of IC structures from scanning electron microscope (SEM) images essential for applications such as failure analysis and hardware assurance (Huang Jing 2007 Cai al. 2018 Wilson et al. 2022).
However, segmentation algorithms often produce errors that significantly impact downstream function-
level analysis, which relies accurately segmented circuit structures [Zang et al.) 2016). The complex
*Corresponding Ji and D. Cheng.

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(a) Input IC image
(b) Ground-truth
(c) Predicted mask
Figure 1: For the IC image (a), its ground-truth segmentation mask is (b). The segmentation task is challenging due to noise and imaging artifacts, which may result in short or open circuits. Notably, the predicted mask (cf. (c)) often appears visually coherent, even when errors (highlighted in red bounding boxes) are present, making them difficult to detect through direct visual means. To address this, we propose a graph-based approach to identify local topological anomalies.
structures of modern ICs, including multi-level interconnects, varying material contrasts, and noise artifacts during SEM imaging, make accurate segmentation difficult (see Fig, | for examples). Moreover, segmentation errors, such as short and open circuits, can have subtle visual manifestations that are challenging to detect
using conventional image analysis techniques (Doudkin et al. 2005 Lee & Yoo 2008 Cheng et al. 2018
2019a Hong et al. 2019 Wilson et al. 2020 Yu et al. 2022
Therefore, the detection of such segmentation
errors is a crucial task.
Correcting such errors typically requires manual visual inspection by experts. However, a single IC chip could have millions of SEM images, making manual review impractical, posing major bottleneck for largo-scale industrial deployment. In this paper, our main objective is to perform:
Error Detection in (given) IC image segmentation.
In contrast to IC image segmentation, the problem of error detection less studied. Zhang et al. (2023) has proposed a CNN-based automatic error detection. Such an approach is holistic nature, i.e., full images are used for both training and testing. A decision made on the feature representation of the whole image.
However, like the "spot the difference" game segmentation errors in IC images typically local in nature (ef. Fig. D. while holistic approaches offer limited explainability regarding which specific circuit elements are erroncous. Furthermore, unlike natural images, the foreground components, such metal lines (i.c., conductive metal pathways that interconnect transistors and other components on a chip), exhibit minimal variation in appearance features like color, intensity, texture, or shape. Instead, they are primarily defined by their structural topology and spatial arrangement. This observation motivates a graph-based approach to error detection, which naturally aligns with the structural charactoristics of IC images.
For the high-level idea, encode each (metal-line) component C in an IC image or binary mask using graph G, which is 1-dimensional skeleton of the component (see Fig, 2 and Fig. 4 below). The functionality of the component C is fully determined by its connectivity, and hence captured by the topology of G. We encode other information, such as position, thickness, and orientation, as features of G. Therefore, the error detection problem can be re-interpreted as a graph classification or outlier detection problem, for which we can employ Graph Neural Network (GNN) models (Defferrard et al. 2016 Kipl & Welling 2017).
The proposed graph-based method offers several advantages. It provides inherent explainability by operating individual connccted components, allowing precise localization of segmentation errors. When an error is detected, the method can identily the specific nodes and edges in the graph that contribute to the classification decision. Moreover, it demonstrates superior generalization capability by focusing on topological features rather than image-level characteristics. This allows the method to handle datasets with varying image complexity and different numbers of connected components without requiring retraining. The graph-based
http://wwwk.pccia..oo/tt//t////s the_ difference
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representation is more robust (Hamilton et al. 2017 to variations in imaging conditions and noise artifacts that commonly affect SEM images.
Notice the problem is inherently supervised, despite the limited labeled defect images. Unlike open-set anomaly detection, hardware assurance involves defects arising from a small number of recurring, well- understood mechanisms (e.g., opens and shorts), resulting this assumption, supervised classification is appropriate, as the defect distribution can be estimated from reprosentative labeled data. While this may not capture entirely unseen defects, it aligns with the practical goal of reliably detecting known high-risk faults.
structured and constrained error space. Under
Our contributions can be summarized as follows:
Our work offers a novel graph-based perspective on IC image analysis, polentially paving the way for future research in this direction.
We propose an efficient pipeline for converting a segmentation mask (for an IC) into a set of graphs We describe how the mask information can be encoded with node and edge features.
We design tailored GNN model for our specific task. In particular, it leverages edge features for message passing in usual GNN models.
We discuss why our approach "explainable" and demonstrate that our approach can applied in conjunction with computer vision (CV) models for the detection task.
2 Preliminaries
2.1
Problem: error detection in IC image segmentation
Given an IC image I, a segmentation model generates a binary mask of the foreground components, most notably metal lines (see Fig. [ left panel). For the error detection problem, we want decide whether there is error in the given binary mask M, without accessing I. Moreover, is preferably able pinpoint the error component/locatte /location with minimal human intervention. We refer readers more detailed discussions "explainability" below.
As we have highlighted in Section ! unlike natural images, the correctness of structural topology is a more important aspect for the functionality of an IC. Therefore, we proposc to use graph-based methods, which are well-suited for such a need.
Explainability Our approach offers more than a binary image classification. In our context, explainability refers to the ability to identify the specific metal-line component where an error occurs, rather than producing only a binary docision at the image level. This component-level localization is important for downstream hardware assurance lasks, such as targeted inspection or correction.
In contrast, conventional CV-based approaches typically output single prediction for the entire image. Even when image is flagged as abnormal, additional processing is still required to determine which circuit element is responsible for the error. In this sense, their explainability is limited to image-level classification and does not directly provide structural attribution.
2.2 Graph neural networks
As outlined in Section D we shall encode foreground components as graphs with features, which can be further processed with graph neural works (GNNs). In this subsection, we give a brief overview of GNNs.
Graph neural networks (GNNs) have emergod as powerful tools for analyzing structured data with complex relationships and topological properties (Defferrard al. 2016 Veličković al. (017)), which is particularly helpful for setting. At the high level, many GNN models consist of layers of message-passing and feature
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G1
22
Gi
M
M
Figure 2: these examples, we have graphs the components of the masks. a short circuit occurs for the segmentation mask M', then the graph G₁ is not comparable to any graph derived from M.
aggregation [u et al. 2019 More specifically, given a graph G = (V, E) and initial node features represented (0) for each V. the node features can then be updated in the 1-th layer as follows:
by z+
a a (WOAGG(((2 (1-1) I [mE(()))))
(1)
where a is an activation function, ( are the learnable weights in the (-th layer and ((v) is the neighbor set of v. AGGR is message aggregation function, such as weighted average (Kipf & Welling, 2017) or a weighted sum (Xu et. al. 2019). The latter is the backbone of the graph isomorphism network (GIN). For a graph-level task, one may retrieve a graph feature by applying a global pooling function (e.g., summation, averago) to the output node features of the last layer.
As preview, in the context of IC images, graph edges approximate metal lines and possess inherent attributes. To accommodate this, we refine the general formulation in (I) by integrating edge features, thereby constructing model specifically tailored to the IC image analysis task.
3
Methodology
3.1
Why the graph approach: an overview
In this subscction, outline the motivation for adopting graph-based approach and provide high-level overview of our model. To maintain clarity and avoid delving into technical concepts from metric geomelry [Bridson & Haefliger 1999) and algebraic topology (Hatcher 2001), we keep the discussion informal here. A detailed and rigorous thcoretical treatment provided in Appendix
Recall that a primary objective of this work to detect topological anomalies, such as opens and shorts, that are critical circuit functionality and hardware assurance. These defects directly affect connectivity and are thus naturally captured by graph-based representation. The following problem sctup reflects this objective.
For mask M of an IC image, a (metal-line) component is usually regular in shape. Therefore, many of its essential functionalities, such as connectivity, can be captured with an embedded 1-dimensional metrical graph (i.e., graph with a metric) G C C. To more specific, for a small e > O, we call an e-approzimation of (a) points on are within 6 distance to points in 9; (b) C can be continuously deformed to g without. breaking (see Fig. 2
Therefore, if we approximate each component in ground-truth mask M by metrical graph, obtain arrangement of collection of graphs 9M {G, 1 S c), where is the number of components of M. Intuitively, consider a segmentation mask M' and let 9M' [G] i d') be the collection of graphs similarly derived from M. If M' contains errors such as open or short circuits, then some graph G', E GM does not have a comparable counterpart in 9M (see Fig. 2), i.e., being outliers in reference to GM-
In other words, suppose M' is the segmentation mask and M is the ground-truth mask. A graph G¹ in the graph collection GM is comparable to Gj in the ground-truth graph collection 9M if the following holds:
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(a) G and G5 located close to each other.
(b) G2 and G3 are similar as both topological spaces and metric spaces.
If we do not have a oue-to-one correspondence between 9M and GM of comparable graph pairs, then M' is likely have errors such as open or short circuits. A more rigorous formulation and its proof are provided in Appendix B
The upshot is that if no errors (e.g., open short circuits) are present, then the graphs in the mask M' are likely to have been "seen before". If, across dataset, graphs derived from ground-truth masks of different images follow a similar distribution, error detection can then be framed as identifying "unseen graphs", effectively roducing the task to a two-class classification problem.
To encode the "comparability" conditions defined above, the following features component graphs are potentially useful for classification:
locations (for positional proximity),
lengths of edges and turning angles (for similarity in topology and geometric shape).
Additional visual information can be helpful, and more details are given in the next subsection.
+
Input Mask
Components
Skeletons
Graphs/ features
GNN
Figure An input mask is converted into graphs with features, which are fed into a GNN. The figure summarizes the pipeline. An explicit example is given in Fig.
The above discussions inspire us to adopt a graph-based based strategy for error detection by framing the task classification problem over feature-annotated graphs, each derived from connected component of the binary mask. It offers expleinability by directly indicating anomalous components. This approach naturally decomposes into two core modules: (a) image-to-graph conversion, and (b) graph classification via. GNNs, which we detail in the following subsections. A visual summary of our model pipeline is in Fig. 3
3.2 Image-to toaeetto-eee to-graph conversion
For an overview, in our application domain, metal lines in IC layouts typically exhibit simple and highly regular geometric structures, consisting primarily of straight segments with right-angle junctions. Because of this constrained geometry, a deterministic and hand-crafted procedure is sufficient to reliably capture the essential structural information needed for graph construction. We next provide the details.
Suppose I is an IC image of dimension x W. Given a binary segmentation mask M E {0. HXW we extract individual connected components using 8-connectivity analysis. This means that two pixels P1.P2
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are adjacent if P2 is one of the 8 neighbors (including 4 diagonal neighbors) of p1. They belong to the same component if there is sequential path of pixels from p1 to p2 consisting of adjacent pixels.
Each component C represents distinct metal-line structure. We apply the morphological thinning operation with the skeletonization algorithm in Zhang & Suen [984), to reduce each component C to hinle-pixel-widee medial axis representations S while preserving topological connectivity (see Fig.
However, each skeleton S usually consists of large collection of pixels, which does not represent a proper graph structure. To better represent the rectilinear nature of integrated circuit layouts, convert the skeletons S into a graph G = (V, E)) with small node set V as follows.
Figure 4: In the example, given the binary segmentation mask M (left panel), Skeletonization generates the skelctons of the components (middle pancl), cach of which contains excessive number of nodes. The refinement greatly reduces the number of nodes and yields the final graph structures (red nodes, blue edges in the right panel).
The node set We categorize V into three sub-types:
End points. These are pixels with exactly one neighbor belonging to the skeleton S (among 8-neighbors). Intuitively, they represent the end points of the graph G.
Junctions. These are pixels with three or more neighbors belonging to S. Intuitively, they are connection points for different branches.
Corerss. These are pixels with two neighbors where the path direction makes significant turn (see details below). Intuitively, they represent the turning corner locations of the metal line (see Fig. right panel).
More on corners. For a pixel po with two neighbors, let M be the x g neighborhood grid of pn- The skeleton S intersects the boundary of / at two pixels P1.P2. P2. We compute the angle between the vectors popi and pop2. The pixel po a corner if within 90" = A Large indicates that there is no directional change, while a very small 0 is unlikely, as meta-lines rarely reverse direction abruptly. Our implementation chooses g and A 30.
The edge set E Edges are constructed by tracing paths between nodes in V using breadth-first search on the skeleton S. This prevents the connection of far-away nodes and thus faithfully captures the topology of the component.
The edge construction skips many lopologically unimporlant pixels. To compensate, we encode their informa- tion as features, which we discuss next.
Node and edge features For each node V, we concatenate the following mumerical information as node feature vector (0) [Te, yos 20, 0.]:
Uo) is the coordinate of the pixel location, normalized with the image dimension.

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2v is the one-hot encoding of node type: end point, junction, corner.
The angles between edges incident at are recorded in a clockwise direction as vector 0, of dimension d. Here, d is prescribed upper bound on the number of incident edges (usually d = 4 is sufficient). We use 0 padding if the number of incident edges at v is less than
As have pointed out, it is crucial use edge features compensate for the information loss in graph conversion. For an edge (vt, 02) E, its feature vector
eij Li Maj Uij. Mij. mayl
(2)
encodes geomctric and width information as follows:
Eg is the Euclidean distance between the pixels for Ua Vy-
For number k we identify equally spaced k-points P= (pI..... p&} on the edge (y), The width of the binary mask perpendicular to (1))2)) and passing through each E P is recorded as vector Wiy (wI,..., wp) (see Fig. 5 for an example). Then Mij. Vij, Mij, mij are the average, variance, max and min Way, respectively.
Intuitively, these features encode visual information of the original binary mask.
Remark 1. The converled graphs may have small artifacts, e.g., small addendum edges, inheriled from skeletonization. However, as such an edge has a short length, its contribution during feature aggregation almost vanished due to the continuous nature of the GNN. Therefore, such an artifact does not pose serious challenge.
In the next subsection, we describe how incorporate node and edge features into GNN for the error detection task.
W1 W2
Wk
Figure 5: As shown in the example, the perpendicular width wi.... wh of different locations on the skeleton (red) are used to form edge features.
3.3 Edge-aware graph isomorphism network
As in the "overview" subsection, we cast the explainable error detection problem as a classification problem of feature-annotated graphs with two types, either normal or abnormal. This is slightly different from the 1-class classification for anomaly detection (Zhao & Akoglu 2021 Qiu et. al. 2022), we have both positive and negative training samples.
The GIN model is proven to be a powerful model for graph classification with node features. Our tailor-made model in the style of GIN. To highlight the incorporation of edge features, we call our model Edge-aware Graph Tsomorphism Network (FA-GIN).
FFor each sampled point p P along edge (on the skeleton), first estimate the local tangent direction of the edge and compute the corresponding normal direction using standard linear algebra. Let Lp denote the line passing through p and perpendicular the edge direction. We then compute the interscction points between Lp and the boundary of the binary segmentation mask, denoted by dr and v The perpendicular width is defined the Euclidean distance between vi.p and p2 This procedure ensures that the width measured directly from the segmentation mask rather than from the skeleton representation.

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An essential design requirement is to incorporate the edge features ezj into the model. A natural idea is to convert. them into attention weights for node leature aggregation in message passing. Therefore, the I-th EA-GIN layer performs the following updates for the node uy:
o (MLL(((e.))
(3)
4
D 1/2 Of Dj1 1/2
(4)
h (1+1) = MIPP(+1)
(1+1)
(1 (1+600n +
E JEN(()
(5)
In the model, we use two learnable multilayer perceptrons (with ReLU activation): MT.P converts edge features into attention weights d'j and MLP((+1) updates node representations. The parameter e()) is
(1) learnable in GIN. The weights aij normalized by the diagonal entries of the degree matrix D of the graph. As usual, the aggregation is performed in the 1-hop neighbor M(ii of oe-
For a graph-level downstream task, a READOUT function (e.g., summation or another pooling function Ying
et al. 2018)) aggregates node features of the last layer (L) Us E V) to generate the graph representation:
hg (E) (L) |u E)).
In our case, bg is used for two-class classification. It is passed through an MLP to generate the probability weights for the classes. The predictions are further used in the standard cross-entropy loss or weighted cross-entropy loss (when there is label imbalance) for training.
Although the model not equipped with a complex mochanism, scamlessly integrates all koy clements. Its effectiveness is demonstrated through numerical results in the next section.
4 Experimental results
4.1 Datasets and experiment overview
Our model is evaluated across four IC image datasets: A1, A2, S1, and S2 Each dataset contains binary segmentation masks, ground-truth masks, and ground-truth labels for crror detection. The datascts exhibit varying design characteristies in terms of circuit lopology, feature density, and error types. In Table D we show the size of positive (i.e., with errors) and negative samples in each dataset. We notice that all datasets are highly class-imbalanced, and we evaluate model performance with the F Fi-score.
Table 1: Sizes of positive (i.e., with errors) and negative samples in each IC image dataset (img.) and the converted graph (graph) dataset.
+ve img.
-ve img.
+ve graph
-ve graph
A11
190
31197
921
170609
A2
102
29277
721
116602
10526
22643
22310
376329
S2
2575
37269
6822
144335
We perform the following studies the subsections below:
TThe datasets are proprietary. Interested readers may Cheng; access requests will be considered on
casee basis.
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We combine graph conversion and EA-GIN full-fledged error detection model in IC image segmentation. We evaluate its performance on error detection by comparing it with several similarly constructed GNN-based detection models. Specifically, they apply the same graph constructions, feature definitions, training splits, and evaluation metrics to ensure a fair comparison
We compare the performance of EA-GIN with CV (Zhang al. 2023) and dedicated anomaly detection models (Qiu et al. 2022), and study their ability for cross- data generalization (i.e., training and testing performed different datasets).
We study the explainability of EA-GIN by analyzing its ability to pinpoint error locations, and explore the possibility of using EA-GIN to assist a CV-based model, by localizing the exact abnormal region for images flagged by a CV-based model.
Ablation studies and computation cost reported in Appendix
4.2 Error detection IC image segmentation: GNN models
Details for EA-GIN For our model, we use EA-GIN layers 13 (3-15) for feature aggregation. In the edge encoder 3 MLP, has one hidden layer with hidden units (and ReLU activation). On the other hand, MLP₂ in (5) has one hidden layer with 64 hidden units. The "Summation" function used as the READOUT function in 6 Finally, due to label imbalance, we use the weighted cross-entropy for training (Ling & Sheng 2011 ie., weights are inversely proportional to the nunber of training samples in each class.
Experimental setting and evaluation protocol A dataset consists of multiple images with a segmented binary mask, and we retrieve multiple graphs from each mask. As described earlier, each graph is converted from a connected component in the segmentation mask. We obtain the ground-trute tonnht label for the graphs from the ground-truth segmentation mask.
For the downstream error detection task in IC image segmentation, all (component) graphs for a single image should be collectively used either for training, validation or testing. Therefore, for each dataset (i.e., A1, A2, S1, 52), split all images into training/ validationn/////a /tessingg sets such that the corresponding split of graphs is approcimately 70%/20% 200222%%/19 110%
We train EA-GIN and tune hyperparameters with the training/validattonn /validation set. For testing, given a test image I with segmentation mask M, we apply EA-GIN to the set GM of component graphs of M. The sogmentation is deemed erroneous if there is at least one graph in GM of error type. The resulting model is also called F.AGINN. The F1-score on the testing set is used as the evaluation metric.
The experiments are performed on server with GPU: NVIDIA RTX A5000, 24GB memory.
Results We compare EA-GIN with our backbone model GIN [Xu et al. 2019), and GNN models using edge information: GINE [Brossard et al. 2020), EGAT (Wang et al. 2021). and CensNet (Jiang et al.) 2019 For any benchmark GNN model, the same procedure described above is applied for the downstream error detection task.
The results are shown in Table 2 We see that the models generally perform better on the A1 and A2 datasets. The IC structures in these two datasets are simpler with less variety. It is observed that our EA-GIN performs much better than its backbone GIN. Morcover, GINE also has a relatively good performance. Therefore, is beneficial incorporate edge features into the models.
EA-GIN generally outperforms benchmarks by clear margin, and in the following subsection, we study other aspects of the model as outlined in Section 4.1
4.3 Cross-data generalization: CV and anomaly detection models
Cross-data generalization plays key role in hardware assurance, as ground-truth is often obtained from different batches of data in practice. This underscores the need for robust models. For the study, compare
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Table 2: Results (Fl-score) on error detection image segmentation. The best performance is boldfaced and the 2nd best is underlined.
A1
A2
S1
S2
GIN
0.6274
0.8089
0.7316
0.6853
GINE
0.9356
0.9498
0.7825
0.7614
EGAT
0.4316
0.7503
0.4591
0.4401
CensNet
0.6458
0.8551
0.7189
0.6243
EA-GIN
0.9884
0.9953
0.9183
0.8990
T
Figure 6: Examples of segmentation missed by ED-ResNet, while identified by EA-GIN. Left panels: ground- truth, right panels: segmentation mask, and error locations detected by EA-GIN are boxed.
with the CV benchmark ED-ResNef dedicated to the error detection problem Zhang et al. 2023 As the
problem is closely related to anomaly detection, we also compare it with the graph anomaly detection model OCGTL 'Quu et al. 2022 We show test results and cross-data generalization results in Table 3
From the results, we see that the CV-approach ED-ResNet and our graph approach EA-GIN have their respective advantages. F.D-ResNet. performs well when trained on larger and more complex datasets, whereas EA-GIN demonstrates strong generalization even when trained on smaller datasets, for example, when trained Al A2 and evaluated on the larger dataset S1. This may be because the number of metal-line connection structures/pattee patterns is limited, and hence, small dataset may have given enough component graphs to capture fcasible metal-line topologies. On the other hand, CV model that requires a large amount of visual information may need more training data to identify essential features for detection.
For EA-GIN, is interesting to notice that to test on S2, training on Al or A2 yields a better result than training on $2 itself. This suggests that sufficiently many positive and negative patterns may be seen in A1 A2, while training on the much larger S2 may overfit the model to certain extent.
For illustration, show examples of segmentation missed by ED-ResNet, while identified by EA-GIN in Fig. 0 It is observed that EA-GIN can capture small errors resembling noise, and this may be duc to the local nature of the graph approach. For the statistics, we compute the percentage of error images that were misclassified by ED-ResNet but correctly identified by the proposed EA-GIN. For example, for the A1 dataset, = 34.55% and for the A2 dataset, p = 63.16%. These results suggest that EA-GIN can complement
We call it error detoction with ResNet, abbreviated ED-ResNer for convenience. See details in Appendix SEA-GIN and ED- ResNet have slight edge over OCGTL, anomaly detection one-class classification utilize the small positive samples.
does
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Table 3: Comparison error detection models for 1C image segmentation. The performance measured by the Fl-score. Cross-data generalization results are also reported.
Train.
Test.
ED-ResNet
OCGTL
EA-GIN
A1
A1
0.9823
0.9877
0.9884
A2
0.9956
0.9961
0.9962
S1
0.6598
0.8699
0.9070
S2
0.9118
0.8762
0.9369
A2
A1
0.9534
0.8979
0.9827
A2
0.9872
0.9270
0.9953
S1
0.6543
0.8505
0.9396
0.9261 S2
0.8650
0.9385
S1
A1
0.9726
0.9093
0.9580
A2
0.9936
0.9950
0.9775
S1
0.9795
0.8615
0.9183
S2
0.9732
0.8805
0.9155
S2
A1
0.9666
0.7640
0.8951
A2
0.9939
0.9273
0.9887
S1
0.7657
0.8516
0.8230
S2
0.9951
0.8842
0.8990
the CV-based approach not only for post-hoc localization of erroneous components (cf. Section 4.4 but also the image level by recovering substantial fraction of detection failures from ED-ResNet.
The CV and graph approaches potentially contribute to the detection problem in different ways, supplementing each other. Therefore, it can be beneficial to combine them, and the details shall be given in the next subsection.
4.4 Explainability
An important feature of the graph-based based approach is its inherent explainability. This is particularly useful in practice to assist manual checking. In this study, we consider the following sequential merging of the CV and graph-based models. Specifically, for a dataset, we consider the set S of all test images correctly predicted to be erroneous by the CV model NetResNet. For each image in S+, we use EA-GIN to generate the probability score of a component being abnormal. The components with the top-x highest scores are flagged for further manual chocking.
Table Fl-scores for the detection of error components with varying R.
K
A1
A2
S1
S2
1
1.00
1.00
0.92419
0.9187
2
1.00
1.00
0.9492
0.9774
3
1.00
1.00
0.9724
0.9911
In Table 4 show the results, measured by Fl-scores, for whether the above procedure correctly identify the error components when the budget 1,2 or 3. We see that for A1 and A2, the graph approach can always correctly identify the error components, conditioned on knowing that the image contains errors. While for S1 and S2, increasing x to 3 yields reasonably good detection performance.
We show examples of the error localization Fig. 7 in which the error components are correctly identified. In conclusion, our grsph-based approach can be used as stand-alone model or together with CV tools for automated error detection.
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Figure We show error localization of the examples in Fig. 1 The (highlightod) error components in the segmentation mask can be identified via their converted graphs. Left panels: ground-truie masks, middle panels: segmentation masks, right panels: skeletons of detected error components.
To make the study more complete, we also include in Table 5 the results corresponding to Table for images outside S+, i.e, those mis-classified by ED-ResNet. These results show that even when the CV model fails to detect an error at the image level, EA-GIN can still identify the erroneous component with high probability by examining small set of top-ranked candidates. This supports the claim that EA-GIN provides effective component-level localization and can complement CV-based detection methods.
Table 5: Fl-scores for the detection of error components with varying for images outside S+
K
A1
A2
S1
$2
0.9667
1.00
0.8333
0.8961
2
0.9836
1.00
0.8333
0.9555
3
1.00
1.00
0.8800
0.9868
5 Conclusions
We propose explainable traph-based framework for error detection in IC images segmentation, addressing key limitations of prior methods. Our approach introduces (i) mask-to-graph conversion pipcline that encodes topological and geometric information into Teature-annotated graphs, and (ii) a tailored EA-GIN model that incorporates edge features into the powerful GIN model for accurate graph classification. The method achieves strong cross-dataset performance and precise component-level error localization, offering scalability, robustness, and interpretability.
Future work includes enhancing graph representations with hierarchical semantic information, exploring graph transformers, and integrating spatial cues from raw images, Real-time inference, uncertainty quantifica- tion, and adaptation to domains such as biological or road networks present promising directions, as does the development of interactive tools for quality assurance in manufacturing.
References
M. Bridson and A. Haefliger. Metric Spaces of Non-Positive Curvature. Springer, 1999.
Remy Brossard, Oriel Frigo, and David Dehaene. Deep graph anomaly detection: A survey and new perspectives. arXit:2011.1506; 2020.
Yiqing Cai, Natasha Ostrouchov, Ankur Jain, Sonali Purohit, Stefanie Schulze, and Jie Zhang. Automated defect inspection of patterned thin films using image processing. IEEE Transactions on Semiconductor Manufacturing, 31(3):385-39) 2018.
Deruo Cheng, Yiqiong Shi, Tong Lin, Bah Hwee Gwee, and Kar-Ann Toh. Hybrid k-mcans clustering and support vector machine method for via and metal line detections in delayered IC images. IEEE Thans. Circuits Syst. II: Fapress Br., 65:1849-188 1853, 2018.
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Deruo Cheng, Yiqiong Shi, Bah Hwee Gwee, Kar-Ann Toh, and Tong Lin. A hierarchical multiclassifier system for automated analysis of delayered IC images. IEEE Intell. Syst., 34:36-43, 2019a.
Deruo Cheng, Yiqiong Shi, Tong Lin, Bah Hwee Gwee, and Kar-Ann Toh. Global template projection and matching method for training-free analysis of delayered IC images. In ISCAS, 2019b.
Michaël Defferrard, Xavier Bresson, and Pierre Vandergheynst. Convolutional neural networks on graphs with fast localized spectral filtering. In NewrIPS, pp. 3844 3852, 2016.
Alexander A. Doudkin, Alexander Inyutin, and Maksim Vatkin. Objects identification on the color layout images of the integrated circuit layers. In IDAACS, pp. 610-614, 2005.
Will Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning on large graphs. In NewrIPS, pp. 1024-1034, 2017.
A. Hatcher. Algerbraic Topology. Cambridge University Press, 2001.
Xiaoxiao Hong et al. Deep learning for automatic ic image analysis. In IEEE 23rd International Conference on Computer Supported Cooperative Work in Design, pp. 234-239, 2019.
Wei Huang and Ning Jing. Automatic optical inspection in the semiconductor industry. Machine Vision and Applications, 18(5):279 292, 2007.
Xiaodong Jiang, Pengsheng Ji, and Sheng Li. CensNet: Convolution with edge-node switching in graph neural networks. In IJCAT, 2019.
Thomas N Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. In ICLR, 2017.
Janghee Lee and Suk In Yoo. An effective image segmentation technique for the SEM image. In ICIT, pp. 1-5, 2008.
Charles X Ling and Victor S Sheng. Cost-sensitive learning. In Encyclopedia of machine learning, pp. 231-235. Springer, 2011.
Chris Mack. Fifty years of moore's law. IEEE Transactions on Semiconductor Manafacttrring, 24(2):202-25) 2011.
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Alexey A. Tuchilin. Lectures on hausdorff and gromov-hausdorff distance geometry. arXiv:2012.00756 2020.
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Zifan Yu, Bruno Machado Trindade, Michael Green, Zhikang Zhang, Pullela Sncha, Erfan Bank Tavakoli, Christopher Pawlowicz, and Fengbo Ren. A data driven approach for automated integrated circuit. segmentation of scan electron microscopy images. In ICIP, pp. 2851 2855, 2022.
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A Further results and analysis
A.1 Ablation studies
Consider the key node features as the node type and angles, and key edge features as the width information. To inspect the contributions of node and odge features in EA-GIN, we perform the following ablation study by disregarding either the node features edge features. The results shown in Table
Table 6: Ablation study: w.o. node foat.: without using node type and angles, and w.o. edge feat.: without
using edge width information.
Train.
Test.
w.o. node feat.
edge feat.
full EA-GIN
A1
A1
0.9276
0.8760
0.9884
A2
0.9255
0.8695
0.9962
A2
A1
0.9328
0.8979 0.8647
0.9827
A2
0.8675
0.9953
The results suggest that the features indeed contribute to the overall performance of the model, and the edge width information is more important.
A.2 Computation and memory cost
In this subsection, we provide overall computation and memory cost of our model. For preprocessing, the average time required to convert an IC image into a set of graphs is 7.48 seconds, with a memory consumption of 536.65 MB on an NVIDIA A5000 GPU. In practical industrial settings, the preprocessing of multiple images can be accelerated through distributed or parallelizod computation, as the conversion of different. images independent.
For training on 10,000 graphs, the average runtime per epoch is 5.72 seconds, with peak GPU memory usage of 37.48 MB.
During testing, the average runtime of a graph is 0.000932 seconds, and the peak GPU memory usage is 14.49 MB.
Overall, these results demonstrate that the proposed method computationally efficient and scalable, making it suitable for deployment. in industrial-scale applications.
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B Theoretical framework
In this appendix, we establish a theoretical framework for the study of IC segmentation masks. We employ formal mathematical concepts, enabling us to study IC segmentatioon-rellted problems rigorously and systematically.
B.1
Geometry and topology for IC segmentation masks
For an IC image I of size H x W, we model a segmentation mask M as a binary function (on the continuous domain):
M: (0, HJ x [] + 1)
such that the following holds: M (1) has finitely many compact connected components, each with continuous boundaries.
We use Cm = (Ci,...,Cm, to denote the set of components of M-) They correspond to the set of metal-line components of the image.
To procood, need few important concepts from metrical geometry Bridson & Haefliger (1999
Definition In metric space (X,d), the Hausdorff distance between two subsets S S2 is
(s1. maxf sup d(r1, S2), sup d(S) s,ES,
22ES;
For two metric spaces (X1,d1) and (X2, d2), their Gromov-Hausdon distance is defined as:
dGH (x), = inf du (f(())))g(Xx))
f.g.M
where the infomum is laken over isometric embeddings of X1, X2 inlo the same metric space M as: J Xi - M and X2 + M.
For O call M Cm c-seporated if for i S m, (C, Cj) Intuitively, the conditions imply that the metal-line components on the segmentation mask are well-separated without ambiguity.
For each component C₁, an embedded subgraph G; C C (i.e., a subset homeomorphic to graph) is an c-approrimation for some (small) c > 0 if the following holds:
Consider G,, C subsets of j0, W] [0, H] with the Euclidean metric:
( C.) Se
G; is a homotopy retract of C (Hatcher 2001
Intuitively, the two conditions ensure the metrical and topological fidelity of G;-
Fix 6 >> For each C₁ let the graph G, be an e-approximation. We use 9M to denote the set (GI,..., Gm We next formalize open and short circuits. For this, we assume M is the ground-truth mask and M' is a segmentation mask (to be tested). Accordingly, have CM which are defined similarly.
C,yy and GM .G'...., G' }
Fix a small threshold > 0. We say that M' does not have open or short circwits if the following holds: for any C, E Car and C₁ E CMr such that C, n C + 0, then each connected component of their symmetric difference C,AC/ = (C, CJ) U (C)AC)) has diameter bounded by e.
Notice that for different concepts, the "error parameter e" used independently in the respective definition. However, they may be related each other if we bring all the concepts together.
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Regarding open and short circuits, intuitively, the masks e-separated, large component in the symmetric difference can only occur if there are open or short circuits.
Aside from the above common errors affecting IC functionality, there are other types of errors, likely to be caused by image artifacts: a component Cj E Car' is a noise if Cj n = for every Cu CM. Moreover, CJ E Cyr contains a hole if it contains component of (0) within its interior, while none of C, E Cm does so.
Intuitively, noise corresponds to small additional artifacts in the IC images, e-g., caused by dust. Holes the segmentation can result from lighting conditions, where parts of metal line appear dark during image caplure
In summary, we consider 4 main error types:
open circuits
short circuits
noise
holes.
For the ground-truth mask M, a graph G3 IM usually has tree structure, it is the homotopy retract of metal-line component, which by design, is unlikely to have holes inside. If this is true for cach G3 9M, call Gm consists of lrees. Such property is topological. In general, the 1sl Belli number (Hatcher 2001 | is sufficient to encode such property for graph. For the simplified definition in the case of graphs, the 1st Betti number by (G) counts the number of (closed) loops a graph G. For example, by = 0 if G is tree.
B.2 Analysis of Segmentation Errors
In this subsection, discuss result that gives conditions on segmentation errors, using the above theoretical framework. We keep the notations and assumptions of the previous subsection. For error, assume that it belongs to one of the types described in the previous section, which most commonly occurs in 1C image segmentation.
Theorem 1. If any of the below holds, then there is error in the segmentation mask M:
(a) The namber of components m + m'.
(b) Gm consists of trees and for some C. Con + 0, (1.))) + bi()))
(c) Let K be an upper bound on the namber of components for any symmetric differences, and assume the largest diameter of any component is bounded by <ec. e. For some C,n.' + 0, there does not exist any construction of G such that dGH(G,, GJ)) S Ke//2.
Notice that the three conditions arranged in order of increasing difficulty of verification. (a) can be interpreted matching the 0th Betti number of the segmentation mask, while (b) is the matching of the 1st Betti number of each graph component. Both of them are topological in nature, which are coarser. On the other hand, (c) matches the graph components metrically, which is a more refined condition.
Proof. Suppose m + m' and there no noise, then for each Cj there a C₁ such that C. + As m 4 m', we have either of the following cases:
For ji * j2, C2 n C²2, 00 and C. Canc, C2 #
For i + i2, C₁ n C and C₁ nc 00
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C
C
Gi
C
Figure 8: Due to possible small perturbations of C₁ we modify G; accordingly depending on the perturbation type.
The former corresponds to an open circuit, as the diameter some components of C,YC,, is > e by the e-separability of M'. Similarly, for the latter case, there is a closed circuit, as the diameter of some components of C'AC,, is e by the e-separability of M'. Hence, there always an error if # m'. This handles (a).
For the rest of the proof, we assume that m = m'. Consider condition (b). Re-order the indices if necessary, we assume that C. C C * 0 for any i S m and for some i S b (G.) * by (G)). As G; and G¹ are the respective homotopy retracts of C; and C₁ the 1st Betti numbers of by (G.) & bj (G) by the assumption, so are (C,), and b (C)) (Hatcher 2001). Therefore, as G, is a tree and thus the b1(C,) = 0, we have by (C₁) > 0. Hence, there at least. an error type of a hole in C₁.
For (c), suppose the condition holds for an index i S m. We assume that there is no noise or holes in the segmentation mask M'. We claim that there is an open short circuit. The strategy is to modify G, to construct an e-approximation G2 of C₁ such that de (G G)) S 6. This will contradict the assumption.
For this, we need an equivalent definition of the Gromov-Hauee Hausdofff distance Tuzhilin 2020 For two metric spaces, a correspondence is a relation R C X x Y such that the projections (from R to X or Y) Px,Pr Py satisfy: (X) = X and py (R) = Y. The distortion of the correspondence R is defined as:
8(I)= sup(id(z, x') d(y, 3/) (z, v), (a', v²) E R}..
(7)
Then, don = in 8(R)22, where the infimum is taken over all correspondences R. In particular, if for some R, 6(R) < 2e, then (x, S.
If there is no open or short circuit, then the symmetric difference C,AC₁ has at most components, each with diameter bounded by e'. For each such component, we construct an e-approximation G¹ of C2 by modifying a small segment of G. by one of the following two ways (see Fig. g for an illustration):
Replace by a union l' of small segments whose total length is within e' of L, and set the linear correspondence between E and L'
Add a small linear segment ll of length at most e' to be point un on Gj. Let every point e' correspond to
Now, for any pair of corresponding points (u, v) and (u, e²) on G. x G¹, the geodesic path (i.e., shortest path) connecting u, u' differs from that v, v' by crossing at most K modifications. Therefore, [d(u, u'),,")) d(v, o'| < Ké', By (7) and its consoquence, we have that deu (G, G²) < Ké/2, which contradicts the assumption.
The practical implication of the result is that errors can be detected if we identify closely located components in M and M', while their corresponding graphs (i.e., approximations) are either topologically or metrically dissimilar. This prompts the use of GNN for error detection.
Correspondingly, failures may occur when practical conditions deviate significantly from the theoretical assumptions. For example, severe over- or under-segmentatton distort graph topology; noisy masks may
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introduce spurious branches remove critical connections during skcletonization; and components with inherently ambiguous topology may not deviate sufficiently from learned normal patterns. Additionally, if the training distribution contains systematic errors or biases, the learned decision boundary may be misaligned, leading to degraded performance.
C Related works
To the best, of our knowledge, IC segmentation error detection, particularly for conneciivity-related faults, is relatively underexplored in the literature. The image-based method ED-ResNet Zhang et al. (2023) represents the most recent and relevant approach for this specific problem sctting. For each pixel the segmentation mask, ED-ResNet computes its distance the nearest mask boundaries and use the values a feature vector, resulting in distance-transsormed feature map. The entire preprocessed image then fed into ResNet-based classifier, where error detection is formulated level. On the other hand, our work is the first method at the object level error detection for IC image segmentation.
binary classification problem at the image
18


Reviews:
[{"review_id": "a9WFGtOKpx", "reviewer": "Reviewer_gygf", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper proposes an edge-aware Graph Isomorphism Network (EA-GIN) for error detection in IC image segmentation. The approach is well motivated for this specific application, where the types of segmentation errors are relatively constrained. Experiments are conducted on four proprietary datasets (A1, A2, S1, and S2). While the method shows strong performance within datasets, its reliance on supervised error labels and segmentation masks raises concerns about generalization and its positioning relative to anomaly detection literature.", "claims_and_evidence_yn": "Yes", "claims_explanation": "1. Table 4 demonstrates that the proposed approach provides explainable predictions by localizing erroneous components.\n\n2. Tables 1 and 2 show that GINs achieve high accuracy for in-domain error detection in IC images.\n\n3. The structured connectivity of IC layouts and dataset characteristics make GINs a suitable modeling choice for this task.", "audience_yn": "Yes", "audience_explanation": "1.  The use of Graph Isomorphism Networks for modeling IC topology is well motivated and appropriate for segmentation error detection.\n    \n2.  The overall approach is simple, and clear. But, the paper could still be improved with some additional details. \n    \n3.  Incorporating edge features into GIN is novel and empirically effective.\n    \n4.  The method demonstrates strong within-dataset performance.", "requested_changes": "1. The method relies on labeled erroneous and normal regions and is trained using weighted binary cross-entropy. This deviates from standard anomaly detection assumptions, where anomalies are rare, random, and typically unlabeled. Although the paper argues that error types are limited in this domain, the supervised formulation restricts the method’s applicability to known and recurring error patterns. (which might have be the case for S1/S2)\n    \n2. While cross-dataset experiments are included, performance drops noticeably when transferring models trained on A1/A2 to S1/S2. This suggests that component structures or error distributions differ across datasets. A deeper analysis is needed to clarify whether these datasets share common topological patterns and to explain the observed performance degradation.\n    \n3. The paper does not sufficiently discuss or compare how the proposed method relates to unsupervised or reconstruction-based anomaly detection approaches, which are common. Why it is not useful to train them? Despite this, the method ultimately trains a supervised classifier, creating a mismatch between framing and methodology.\n    \n4.   The paper lacks a clear description of the four datasets (A1, A2, S1, S2). Since the datasets appear to be private and the codebase is not publicly available, reproducibility and broader applicability of the method are limited.\n    \n5. The paper states that weighted cross-entropy is used to address class imbalance, but does not explain how the class weights are computed. This information is important for reproducibility and fair comparison.\n    \n6. The paper claims that EA-GIN is complementary to CV-based approaches such as ED-ResNet. However, no hybrid or joint model is evaluated, and no improvement in end-to-end detection performance is demonstrated. As a result, this claim remains largely speculative.\n    \n7. In the explainability study, Top-K components are evaluated only for images where ED-ResNet successfully detects errors. Consequently, all cases missed by ED-ResNet are excluded from the EA-GIN evaluation, preventing an assessment of whether EA-GIN can recover detection failures of the CV model. The explainability claim is therefore limited to post-hoc localization rather than improving detection robustness.", "broader_impact_concerns": "There are no broader impact concerns associated with this work.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "KAl6DYzEyx", "reviewer": "Reviewer_qsdo", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper addresses the problem of error detection in integrated circuit (IC) image segmentation, focusing on identifying local topological errors such as open circuits, short circuits, noise artifacts, and holes in segmentation masks. Unlike prior CNN-based approaches that operate holistically at the image level, the authors propose an explainable, graph-based framework that converts each connected component of a segmentation mask into a feature-annotated graph. The approach is evaluated on four IC datasets with varying complexity. Results show strong performance, especially in cross-dataset generalization, and the model demonstrates the ability to localize error-causing components, supporting its explainability claims.\n\nKey Strengths:\n \n1.) Reframing IC segmentation error detection as a graph classification problem is well motivated and technically sound. The component-level graph representation naturally supports error localization, which is valuable for hardware assurance workflows.\n\n2.) The ability to pinpoint which specific component is erroneous, moving beyond a binary image-level error flag. This is crucial for practical debugging and hardware assurance.\n\n3.) EA-GIN consistently outperforms baseline GNNs and compares favorably with CNN-based detectors, particularly in cross-dataset generalization, a critical requirement for industrial deployment where training data may be limited or varied.\n\n4.) The skeleton-based graph extraction and the use of both node and edge features are carefully justified.\n\n5.) The inclusion of a theoretical appendix (Appendix A) formalizing errors (open/short circuits, noise, holes) using metric and topological concepts supports the intuition behind the method.\n\n\nKey Weaknesses:\n\n1.) The authors should have discussed computational overhead. Like, the pipeline involves skeletonization, graph construction, and per-component GNN inference. A discussion of the runtime or computational cost compared to an end-to-end CNN would be useful for assessing practical deployment trade-offs.\n\n2.) The method assumes reasonably accurate segmentation masks; failure modes under poor segmentation are not fully explored. Also, the contribution of individual node and edge features is not systematically evaluated.\n\n3.) The graph conversion relies heavily on the quality of the morphological skeletonization step. The paper briefly mentions artifacts (Remark 1) but does not deeply analyze failure cases or robustness limits when skeletons are noisy or incorrectly extracted.\n\n4.) The method is primarily validated on detecting topological anomalies (shorts/opens) and noise. Its effectiveness on other semantic error types (e.g., minor width variations, material misclassifications) is less clear.\n\n5.) While justified, the node and edge features are hand-crafted. An ablation study or discussion on the necessity and contribution of each feature type would strengthen the methodology section.\n\n6.) The description of edge feature construction (Equation 2, Fig. 5) could be slightly clearer. Specifically, how the perpendicular width is calculated from the binary mask (not the skeleton) at the k sample points could be elaborated.\n\n7.) In Section 4.3, the intriguing result that training on smaller datasets (A1/A2) sometimes generalizes better to S2 than training on S2 itself is noted but not deeply analyzed. A brief hypothesis on why this occurs (e.g., overfitting on larger, noisier datasets; limited topological vocabulary) would enhance the discussion.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The paper's main claims-: improved error detection accuracy, strong generalization, and enhanced explainability are largely supported by empirical evidence:\n\n1.) The experimental design is substantial. The use of four distinct datasets (A1, A2, S1, S2) with varying complexity demonstrates robustness. Quantitative results (Tables 2 & 3) show EA-GIN's superior F1-scores against strong baselines (GIN, GINE, EGAT, CensNet, ED-ResNet, OCGTI). The cross-dataset generalization tests are particularly compelling evidence of the method's strength and practicality. Qualitative results (Figs. 6 & 7) effectively visualize the explainability claim, showing precise error localization.\n\n2.) The methodology is explained step-by-step, from high-level motivation (Section 3.1) to detailed graph construction (Section 3.2) and model architecture (Section 3.3). Figures 3, 4, and 5 are helpful in visualizing the pipeline.\n\n3.) The localization capability is demonstrated through component-level detection results and visual examples (Figures 6 and 7), which align well with the explainability claims.", "audience_yn": "Yes", "audience_explanation": "Yes, the paper is clearly relevant to TMLR's audience and broader ML community. \n\n1.) It presents a novel application of GNNs (with a tailored architecture, EA-GIN) to a structured, non-social, industrial domain. The focus on edge features and explainability is relevant to ongoing GNN research.\n\n2.) The work provides a concrete case study in inherently explainable model design for a critical task, moving beyond post-hoc explanations. This is a valuable contribution to the XAI literature.\n\n3.) It addresses a real, economically significant problem in semiconductor manufacturing and hardware assurance. Demonstrating robust cross-dataset performance is key for industrial relevance.\n\n4.) The framing of the problem as graph-level classification or outlier detection connects to active research in anomaly detection on non-Euclidean data.\n\n5.) The findings offer both a practical solution to an important problem and methodological insights (graph representation, edge-feature integration, explainable design) that can inspire researchers in related fields (e.g., circuit verification, biomedical image analysis).", "requested_changes": "1.) The paper should include an ablation analysis isolating:\n    a) Node features vs edge features\n    b) Width statistics vs geometric features\n    c) Positional features vs purely topological features\n\nThis is essential to validate the design choices and confirm that performance gains are not incidental.\n\n2.) The authors should have reported the average graph construction time per image, inference time per graph/image, and memory footprint trends with increasing component count. This is critical for assessing industrial applicability.\n\n3.) The paper should explicitly discuss scenarios where the method may fail, such as severe over-segmentation or under-segmentation, skeletonization errors in noisy masks, and components with ambiguous topology.\n\n4.) Metrics such as top-k localization accuracy (beyond F1) or component-level precision/recall would strengthen the explainability claims.", "broader_impact_concerns": "The work has primarily positive implications for improving the efficiency, accuracy, and automation of hardware assurance in the semiconductor industry, which is critical for technological advancement and supply chain security. Potential broader impacts include:\n\n1.) While the paper focuses on error detection for quality assurance, similar techniques for analyzing IC layouts could potentially be repurposed for reverse engineering or identifying hardware vulnerabilities (e.g., Trojans). This is a common concern in hardware security research.\n\n2.) As an automation tool, it could reduce the need for manual visual inspection by experts. However, this is a standard effect of industrial automation and is likely to be offset by creating new roles in ML system maintenance and data analysis.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "W3Jp431DZl", "reviewer": "Reviewer_2R5b", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "- The authors present a new method for error detection in integrated circuits image segmentation via graph neural networks. \n- This is supported by a theoretical framework for the study of IC segmentation masks as well as experiments.\n- This is an industry-related application, somewhat niche, but quite interesting and relevant. The method seems to be well thought out and explicitly tailored to this application.\n- The study results demonstrate that the method produces good results.\n\n- The method presented is based on image segmentation. There is no analysis of how different segmentation methods affect the performance of the method presented. \n- I am missing a related work section that specifically addresses similar work (graph-based approaches) and other image analysis methods. The baselines seems outdated. \n- The authors argue that precise segmentation of IC structures is important for failure analysis, which, as I understand it, refers to chip defects. However, the method deals exclusively with segmentation errors. A segmentation error can look like a chip defect, or a real defect can be overlooked due to poor segmentation. The distinction between these two types of errors is not highlighted.", "claims_and_evidence_yn": "No", "claims_explanation": "Some claims are made, but in my opinion they are not really proven, e.g.: \n- \"Moreover, segmentation errors, such as short and open circuits, can have subtle visual manifestations that are challenging to detect using conventional image analysis techniques\" - This was not explained further, but only older sources were cited, and only two baselines were used in the experiments.\n- \"segmentation errors in IC images are typically local in nature (cf. Fig. 1), while holistic approaches offer limited explainability regarding which specific circuit elements are erroneous.\" - On the one hand, I find that the concept of explainability is only vaguely explained at the beginning, as it is a question of pointing out specific components that have errors and not just pure binary classification at image level. On the other hand, limited explainability is mentioned in relation to other methods, but there is no explanation of what this looks like. \n- \"As we have highlighted in Section 1, unlike natural images, the correctness of structural topology is a more important aspect for the functionality of an IC.\" - I don't think this was emphasized in the introduction, nor do the experiments show this, since CV and anomaly detection models partly perform better than the graph-based method.", "audience_yn": "Yes", "audience_explanation": "The authors present a different approach to error detection in IC image segmentation that yields good results, so the work could be of interest to certain scientific fields. However, the work seems a little outdated, as no references from the last two years are cited.", "requested_changes": "Critical changes:\n- I find the abstract very concise and difficult to understand. In addition, several abbreviations are used without being introduced. \n- Conventional image analysis techniques are mentioned, but not explained in detail. \n- Wikipedia should not be used as a reference. \n- Figure 1 is intended to highlight segmentation errors, so these should also be visually emphasized.\n- \"For the high-level idea, we encode each...\" - The notation belongs in the method or preliminaries, but not really in the introduction - here, high-level explanations and, in particular, motivation should be provided. \n- I don't think section 2 is integrated in a meaningful way. Section 2.1 consists only of a very short section, which could be included in the method. And section 2.2 is illogical in terms of order, as GNNs are introduced briefly at the beginning, but are the last step in the pipeline.\n- \"the following features of component graphs are potentially useful for classification:\" - Only potentially? It is only briefly mentioned, but not further explained or elaborated on. \n- The datasets should be described in more detail, especially with regard to the differences between them (apart from the number of images). Are they proprietary datasets or freely available? \n- A related work section is missing. \n- \"We evaluate its performance on error detection by comparing it with several similarly constructed GNN-based detection models.\" - The methodological differences should be highlighted. \n- The citations are inaccurate, often only abbreviations of the conference are used. In addition, for example, the “Graph attention networks” paper was accepted at ICLR 2018.\n\n\nMinor:\n- \"Error Detection in (given) IC image segmentation.\" - Only one bullet point looks out of place; I would adjust the layout.\n- \"and M is the ground-truth mask M\"", "broader_impact_concerns": "NA", "additional_comments": "Questions:\n- The image-to-graph conversion is very hand-crafted. Why was this approach chosen and not, for example, a keypoint/skeleton neural network trained on this data? \n- \"It is passed through an MLP to generate two probability weights for the classes.\" - It is a binary classification, so one output value is sufficient. Why are two probabilities needed? \n- How are the (predicted) binary segmentation masks obtained? \n- The class imbalance is very large. Is the use of weighted cross-entropy loss sufficient? \n- Was the architecture of the EA-GIN obtained through ablation, or why this number of layers/neurons?\n- Is this the first method that works also at the object level and not just at the image level?", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)