Morphology-Aware Ambiguity Learning for Wafer Defect Decision Support

Seungjun Chu; Seokhyun Chung

cs.CVSep 18, 2026

Morphology-Aware Ambiguity Learning for Wafer Defect Decision Support

Authors: Seungjun Chu, Seokhyun Chung

Organizations: School of Industrial and Management Engineering, Korea University, Seoul 02841, Republic of Korea

Abstract

Wafer map defect recognition is commonly formulated as a fixed-taxonomy classification problem that assigns each wafer to a single defect class. However, some wafers exhibit morphologies near class boundaries, for which forcing a single prediction may be less informative than providing plausible diagnostic alternatives. This paper proposes a morphology-aware ambiguity learning framework that supports three diagnostic actions: automatic single-class diagnosis, assisted diagnosis with two plausible defect classes, and full review. Using the radial, angular, and geometric characteristics of training wafer maps, the framework constructs a class-level ambiguity matrix representing defect-class pairs with similar morphology and plausible diagnostic alternatives. It guides the model to learn plausible alternative classes rather than treating all incorrect classes equally. During inference, the matrix determines whether an uncertain prediction can be represented by a meaningful two-class diagnostic set or should be escalated for full review. Experiments on WM-811K show that the proposed framework outperforms conventional approaches in defect recognition and diagnostic decision support, providing meaningful two-class alternatives while reserving full review for cases with unresolved ambiguity. Illustrative cost analyses further show the potential cost advantage of the proposed routing strategy. The diagnostic behavior of the framework remains consistent across different backbone architectures.

Figures & tables

Panel of Figure 1 — Figure 1: Representative wafer maps illustrating class taxonomy and boundary ambiguity. (a) Examples of the nine WM-811K classes; no class has a single canonical morphology. (b) Wafers from different annotated classes with visually similar defect morphologies.

$y$	Class name	Diagnostic role
0	Nonpattern	No identifiable failure pattern
1	Center	Defect concentrated at wafer center
2	Donut	Ring-shaped defect around the center
3	Edge-Loc	Localized cluster on the wafer edge
4	Edge-Ring	Full peripheral ring
5	Loc	Localized cluster away from the edge

Table 1: Fixed class indexing used throughout the paper. Labels

1

–

8

constitute the defect block

\mathcal{Y}_{d}

Figure 2: Overview of the proposed framework. The ambiguity matrix $\mathbf{A}^{\mathrm{morph}}$ derived from wafer morphology plays a key role in both training and inference. During training, it defines morphology-aware soft targets. During inference, it determines whether the top-2 predictions form a plausible two-class diagnostic set.

Figure 3: The morphology descriptor

\boldsymbol{\phi}(x)

on an Edge-Loc wafer. (a) Radial defect profile over ten concentric bins. (b) Defect density over twelve peripheral sectors and its rotation-invariant angular spectrum; shaded bars are not part of the descriptor. (c) The seven scalar shape cues, each with the geometry it measures overlaid.

Method	Target structure	Macro-F1	Defect macro-F1	Defect bal. acc.
CE	Hard one-hot	0.9154 $\pm$ 0.0059	0.9176 $\pm$ 0.0049	0.8934 $\pm$ 0.0060
LS	Uniform across all classes	0.9109 $\pm$ 0.0063	0.9174 $\pm$ 0.0074	0.8914 $\pm$ 0.0142
$\mathbf{A}^{\mathrm{uniform}}$	Uniform across defect classes	0.9093 $\pm$ 0.0090	0.9120 $\pm$ 0.0097	0.8863 $\pm$ 0.0112
$\mathbf{A}^{\mathrm{pixel}}$	Raw-pixel-derived	0.9114 $\pm$ 0.0043	0.9138 $\pm$ 0.0038	0.8855 $\pm$ 0.0095
$\mathbf{A}^{\mathrm{morph}}$	Morphology-derived	0.9201 $\pm$ 0.0076	0.9245 $\pm$ 0.0082	0.9009 $\pm$ 0.0153

Table 2: Classification performance and structural ablation on WM-811K using ResNet-34.

Class	Samples	$\mathbf{A}^{\mathrm{morph}}$	$\mathbf{A}^{\mathrm{uniform}}$	$\Delta$ F1
Center	859	0.9512 $\pm$ 0.0015	0.9493 $\pm$ 0.0060	+0.0020
Donut	111	0.8915 $\pm$ 0.0100	0.8781 $\pm$ 0.0307	+0.0134
Edge-Loc	1,038	0.8777 $\pm$ 0.0154	0.8600 $\pm$ 0.0101	+0.0177
Edge-Ring	1,936	0.9840 $\pm$ 0.0038	0.9801 $\pm$ 0.0049	+0.0038
Loc	718	0.8431 $\pm$ 0.0085	0.8195 $\pm$ 0.0122	+0.0236
Near-full	30	0.9583 $\pm$ 0.0326	0.9546 $\pm$ 0.0348	+0.0037

Table 3: Per-class F1 on ResNet-34. Samples are test-set counts, identical across seeds because the split is stratified.

\Delta

F1 denotes the difference between the two matrices.

	Automatic	Assisted	Full review
Coverage	94.2%	1.9%	3.8%
Top-1 acc.	99.75%	77.1%	74.1%
Top-2 incl.	–	95.2%	96.1%

Table 4: Three-way diagnostic routing under

\mathbf{A}^{\mathrm{morph}}

at the default operating point

(\tau_{\mathrm{conf}},\tau_{A})=(0.95,0.015)

using ResNet-34.

	Assisted set			Full review
Annotated class	$n$	Share	Top-2 incl.	$n$	Share	Top-2 incl.
Nonpattern	21	3.2%	0.0% †	782	58.7%	100.0%
Center	66	9.9%	97.3%	78	5.8%	93.9%
Donut	43	6.5%	96.1%	3	0.2%	47.5% †
Edge-Loc	229	34.2%	99.3%	222	16.7%	93.8%
Edge-Ring	62	9.3%	99.6%	27	2.0%	88.2% †

Table 5: Composition of the assisted and full-review groups by annotated class (

\mathbf{A}^{\mathrm{morph}}

, ResNet-34). Counts are seed means rounded to the nearest integer; shares are the count divided by the group total. Each entry is rounded independently, so a column need not sum exactly to its total.

Figure 4: Operating-point behavior as

\tau_{A}

varies. The morphology-derived matrix produces a gradual change in assisted-set volume, whereas the uniform matrix exhibits a discrete cliff at its single off-diagonal value,

(1-\delta)/(|\mathcal{Y}_{d}|-1)=0.0286

Variant	$\tau_{A}$	$\alpha=0.1$	$\alpha=0.2$	$\alpha=0.3$	$\alpha=0.5$
No assisted action	–	0.0810	0.0810	0.0810	0.0810
$\mathbf{A}^{\mathrm{morph}}$	0.015	0.0636	0.0656	0.0675	0.0714
$\mathbf{A}^{\mathrm{uniform}}$	0.015	0.0711	0.0737	0.0762	0.0812
$\mathbf{A}^{\mathrm{morph}}$	0.040	0.0709	0.0720	0.0732	0.0754
$\mathbf{A}^{\mathrm{uniform}}$	0.040	0.0938	0.0938	0.0938	0.0938

Table 6: Expected per-sample routing cost on ResNet-34 under a common relative cost model. “No assisted action” removes the intermediate branch: a wafer that fails the confidence test is escalated rather than given a two-class set.

	Automatic		Assisted set			Full review
Method	Coverage	Top-1	Coverage	Named-patterns	Top-2 incl.	Coverage
CE $+$ confidence	93.9%	99.76%	4.8%	24.8%	98.1%	1.2%
Our framework	94.2%	99.75%	1.9%	100.0%	95.2%	3.8%

Table 7: Comparison of confidence-based routing and our framework. “Named-patterns” denotes the share of two-class outputs in which both classes correspond to named defect patterns, rather than one class being Nonpattern . Results are averaged over four seeds.

Panel of Table 8 — Table 8: Representative wafers that both approaches route to assisted diagnosis.

$\delta$	Variant	Macro-F1	Defect macro-F1
0.5	$\mathbf{A}^{\mathrm{morph}}$	0.9161 $\pm$ 0.0096	0.9183 $\pm$ 0.0133
0.5	$\mathbf{A}^{\mathrm{uniform}}$	0.9189 $\pm$ 0.0043	0.9221 $\pm$ 0.0082
0.8	$\mathbf{A}^{\mathrm{morph}}$	0.9201 $\pm$ 0.0076	0.9245 $\pm$ 0.0082
0.8	$\mathbf{A}^{\mathrm{uniform}}$	0.9093 $\pm$ 0.0090	0.9120 $\pm$ 0.0097
0.9	$\mathbf{A}^{\mathrm{morph}}$	0.9113 $\pm$ 0.0029	0.9148 $\pm$ 0.0051
0.9	$\mathbf{A}^{\mathrm{uniform}}$	0.9120 $\pm$ 0.0057	0.9150 $\pm$ 0.0042

Table 9: Sensitivity to the diagonal mass

\delta

using ResNet-34 at the selected mixing coefficient

\lambda=0.6

Backbone	Auto cov.	Auto top-1	Asst. cov.	Asst. top-2
ResNet-18	93.4%	99.80%	2.3%	95.7%
ResNet-34	94.2%	99.75%	1.9%	95.2%
ResNet-50	93.2%	99.77%	2.4%	95.9%
MobileNetV2	93.1%	99.76%	2.3%	95.6%
ShuffleNetV2	92.1%	99.79%	2.6%	95.8%
EfficientNet-B0	93.2%	99.79%	2.1%	96.3%

Table 10: Cross-backbone behavior of the selective diagnostic system under

\mathbf{A}^{\mathrm{morph}}

at the default operating point

(\tau_{\mathrm{conf}},\tau_{A})=(0.95,0.015)

. Each entry is a mean over four seeds; the last row is the standard deviation across the seven backbones.

Hyperparameter	Value
Optimizer	AdamW
Learning rate	$10^{-4}$
Weight decay	$10^{-4}$
Batch size	64
Maximum epochs	50
Learning-rate schedule	Cosine annealing

Table S1: Default training hyperparameters.

Hyperparameter	Value
Radial bins $B_{\rho}$	10
Angular sectors $B_{\theta}$	12
Peripheral radius threshold $\rho_{\mathrm{edge}}$	0.7
Hough accumulator threshold $T_{H}$	3
Descriptor dimension	23
Diagonal mass $\delta$	0.8

Table S2: Default descriptor and ambiguity-aware training hyperparameters.

$\delta$	$\lambda=0.3$	$\lambda=0.6$	$\lambda=1.0$
$0.5$	0.9227	0.9226	0.9153
$0.65$	0.9229	0.9252	0.9229
$0.8$	0.9239	0.9314	0.9210
$0.9$	0.9266	0.9257	0.9234

Table S3: Validation defect macro-F1 over the

(\delta,\lambda)

grid, ResNet-34 with

\mathbf{A}^{\mathrm{morph}}

. Each entry is a mean over four seeds; the selected setting is shown in bold.

Action under CE $+$ confidence	Action under our framework	Wafers
( Nonpattern pairs excluded)
Assisted diagnosis	Assisted diagnosis	290
Full review	Assisted diagnosis	173
Automatic diagnosis	Assisted diagnosis	206
Assisted diagnosis	Automatic diagnosis or full review	124

Table S4: Diagnostic action returned for the same wafer by the two approaches, using ResNet-34 and averaged over four seeds. The CE-based variant excludes any pair containing Nonpattern . Each row is a disjoint group of wafers; counts are seed means rounded to the nearest integer.

Classification

Classification maps observations to discrete labels, including familiar, unknown, hierarchical, or multiple categories.

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