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Dr. Peter Pyun (변경석박사), Principal Solution Architect Joint work with Dr. Andrew Liu Transfer learning based GPU accelerated deep learning for end-to-end industrial inspection

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Page 1: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

Dr. Peter Pyun (변경석박사), Principal Solution Architect

Joint work with Dr. Andrew Liu

Transfer learning based GPU

accelerated deep learning for

end-to-end industrial inspection

Page 2: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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JOIN US FOR 50-MINUTE SPEECH AT NEXT GTC SILICON VALLEY USA

(MARCH 17-19, 2019)

Invitation

Page 3: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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AGENDA

Industrial Defect Inspection for DAGM Dataset

1. NGC Docker Images

2. DL Model Set up - Unet

3. Data Preparation

4. Training with an NGC Tensorflow Container

5. Defect Segmentation – precision/recall

6. GPU Accelerated Inferencing – TF-TRT & TRT

Automatic Defect Inspection from Real GPU Production Dataset

Looking into the Future: Automating Defects Inspection for Advanced Packaging

Page 4: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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INDUSTRIAL DEFECT INSPECTION FOR DAGM DATASET

(Nvidia white paper available)

Page 5: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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INDUSTRIAL DEFECT INSPECTIONHow to apply end-to-end deep learning?

Page 6: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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NVIDIA END-TO-END DEEP LEARNING PLATFORM

DNN

Data (Curated/Annotated)

DGX Tesla

Nvidia GPU Cloud (NGC) docker container

AI TRAINING @DATA CENTER

TensorRTDRIVE AGX

TensorRT

Optimizer Runtime

Jetson AGX

Tesla/Turing

AI INFERENCING @EDGE

Page 7: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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NGC DOCKER IMAGES

Page 8: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

Benefits for Deep Learning Workflow

High Level Benefits and Feature Set

Single software stack

Develop once, deploy anywhere

Scale across teams of practitioners

Developer, DevOp, QC

Page 9: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

Automatic Defect Inspection Workflow

Training Inference

Tensorflow: NGC optimized docker image TF-TRT / TensorRT

NGC tensorflow:18.08-py3 1. NGC tensorflow:18.08-py3

(for TensorFlow-TensorRT)

2. NGC tensorrt:18.08-py3

Pre-Training

Titan VDGX-station

DGX DGX T4/V100

Page 10: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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MODEL SET UP

Page 11: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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WAYS FOR DEFECT INSPECTION

Depends on domain adaptation

Image SegmentationObject Detection

Image Classification

Label: 0 / 1 (Defect / Non Defect)

Label: Bounding-Box Label: Polygons Mask

Page 12: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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FROM LITERATURE: CNN/LENET (2016)

Source: Design of Deep Convolutional Neural Network Architectures for Automated Feature Extraction in Industrial Inspection, D. Weimer et al, 2016

Page 13: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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FROM LITERATURE CNN/LENET (2016)Coarse segmentation results - can we do better?

Source: Design of Deep Convolutional Neural Network Architectures for Automated Feature Extraction in Industrial Inspection, D. Weimer et al, 2016

Page 14: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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3X3 Conv2d+ReLU

2X2 MaxPool

2X2 Conv2dTranspose

copy and concatenate

U-Net structure

Page 15: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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ENCODING IN KERAS-TF

Convolution

Page 16: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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deconvolution

DECODING IN KERAS-TF

Page 17: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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Image segmentation on medical images

Same DL process for different application (i.e., healthcare)

MRI image

Left ventricle

heart disease

Data Science BOWL2016

Data Science BOWL 2017

CT image

Nodule

Lung cancer

Image

Nuclei

Drug discovery

Data Science BOWL2018

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DATA PREPARATION

Page 19: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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INDUSTRIAL OPTICAL INSPECTION

DAGM dataset by German Association for Pattern Recognition

• http://resources.mpi-inf.mpg.de/conferences/dagm/2007/prizes.html

Page 20: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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INDUSTRIAL OPTICAL INSPECTIONDAGM dataset

Pass NG Pass

NGNGPass Pass

NG

Page 21: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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DATA DETAILS

• Original images are 512 x 512 grayscale format

• Output is a tensor of size 512 x 512 x 1

• Each pixel belongs to one of two classes

• 6 defect classes

• 150 defects & 1000 defect-free images per class

Setting Training set

size

Validation set size Testing set size

Defect/Defect-free

1 100 30 20/1000

Page 22: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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MORE EXAMPLES

Page 23: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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TRAINING WITH NGC TENSORFLOW CONTAINER

Page 24: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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Dice Metric (IOU) for unbalanced dataset

• Metric to compare the similarity of two samples:

2𝐴𝑛𝑙________________________________

𝐴𝑛 + 𝐴𝑙

• Where: • An is the area of the contour predicted by the network • Al is the area of the contour from the label• Anl is the intersection of the two

• More accurately compute how well we’re predicting the contour against the label

Page 25: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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TRAINING FOR SMALL DATASET25

Check both train & validation loss to prevent overfitting

1. Start with small U-net (with 8 kernels in the 1st layer), then increases

complexity (i.e., doubling kernels)

2. Once model has enough capacity to fit small dataset, then try dropout, L1/L2

regularization.

*trained with binary cross entropy loss & Adam optimizer with learning rate = 0.001

Page 26: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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APPLICATION: INDUSTRIAL INSPECTION

• Challenges: Not all deviations from

the texture are necessarily defects.

Page 27: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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DEFECT SEGMENTATION – PRECISION/RECALL

Page 28: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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FINAL DECISION - SEGMENTATION

Page 29: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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INFERENCE PIPELINE

decision making(defect vs. non-defect)

Inference

Camera

Machine

P40

DGX Server

TF-TRT &

TensorRT

Fetch image

TF-TRT &

TensorRT

Detectors/Classifiers/Segment Composite Result Metadata

Data Center

/Cloud

Edge

Defect Pattern Ratio Defect Level Defect region size Defect counts

Domain Criteria Determine threshold

Precision/ Recall

Page 30: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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DEFECT VS. NON-DEFECT BY THRESHOLDING

Segmentation model outputs Numpy array of

class probability of each class (i.e. 2 classes –

defect/defect-free)

Thresholding

Declare as defect (white)

if probability is higher

than threshold (i.e., 0.5)

query image 512x512

Page 31: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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(Example) Precision/Recall diagram

Page 32: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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(Example) Simple binary anomaly detector

TP: True Positive, FP: False Positive, FN: False Negative, TN: True Negative.

*Red arrow means increasing threshold of probability on defect detection.

Threshold of probability of defect: higher number means harder for classifier to detect as defect class.

Higher threshold: FP lower, precision (TP/(TP+FP)) higher

FN higher, recall (TP/(TP+FN)) lower

Page 33: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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Precision/Recall Results

threshold 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

TP 137 135 135 135 135 135 135 133 131

TN 885 893 899 899 899 899 899 900 901

FP 16 8 2 2 2 2 2 1 0

FN 1 3 3 3 3 3 3 5 7

FP rate 0.0178 0.0089 0.0023 0.0023 0.0023 0.0023 0.0023 0.0011 0.0000

precision0.8954 0.9441 0.9854 0.9854 0.9854 0.9854 0.9854 0.9925 1.0000

recall 0.9928 0.9783 0.9783 0.9783 0.9783 0.9783 0.9783 0.9638 0.9493

Sweep experiments of thresholds verifies precision/recall trade-off.

Choose threshold per your application needs - precision (FP) or recall (FN) more important ?

Total image: 1039 (defects 138, non-defects: 901)

Page 34: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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Precision/Recall - reducing false positives

Precision =TP/(TP+FP) : 99.25%

Recall = TP/(TP+FN) : 96.38%

False alarm rate = FP/(FP+TN): 0.11%

*sensitivity=recall=true positive rate,

specificity=true negative rate=TN/(TN+FP),

false alarm rate=false positive rate

Defect Defect-free

Defect 99.25% (TP) 0.75% (FP)

Defect-free 0.55% (FN) 99.45% (TN)

Actual

Predict

Page 35: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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Final decisionFinal Defect Segmentation

(U-net/thresholding)

Page 36: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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GPU-ACCELERATED INFERENCING

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Automatic Defect Inspection Workflow

Training Inference

Tensorflow: NGC optimized docker image TF-TRT / TensorRT

NGC tensorflow:18.08-py3 1. NGC tensorflow:18.08-py3

(for TensorFlow-TensorRT)

2. NGC tensorrt:18.08-py3

Pre-Training

Titan VDGX-station

DGX DGX T4/V100

Page 38: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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TensorRT workflow

Called UFF, Universal Framework FormatONNX

Page 39: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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TensorRT IntegratedWith TensorFlow

Speed up TensorFlow model inference with TensorRT with new TensorFlow APIs

Simple API to use TensorRT within TensorFlow easily

Sub-graph optimization with fallback offers flexibility of TensorFlow and optimizations of TensorRT

Optimizations for FP32, FP16 and INT8 with use of Tensor Cores automatically

Speed Up TensorFlow Inference With TensorRT Optimizations

developer.nvidia.com/tensorrt

# Apply TensorRT optimizations

trt_graph = trt.create_inference_graph(frozen_graph_def,

output_node_name,

max_batch_size=batch_size,

max_workspace_size_bytes=workspace_size,

precision_mode=precision)

# INT8 specific graph conversion

trt_graph = trt.calib_graph_to_infer_graph(calibGraph)

Available from TensorFlow 1.7+https://github.com/tensorflow/tensorflow

Page 40: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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Inference Results

TF-TRT for fast prototyping, TRT for maximum performance

Inference method TF TF-TRT TRT

FP 32 bit images/sec 141.8 236.1 1079.8

perf. Increase 1 1.7 7.6

FP 16 bit* images/sec N/A 297.4 1219.7

perf. Increase 1 2.1 8.6

FP 16 bit*: by mixed precision TensorCore in V100 GPU

Page 41: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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SUMMARY

Challenges Delivers

Is Deep Learning for industrial

inspection completely a black-box

approach?

Insert tunable parameter(s) for final decision

1. Governs tradeoff between precision and recall.

2. Cost, throughput requirement sets criteria for parameters.

Training, inference environment is hard

to build, maintain, share.

Using NGC Docker images.

Model optimizations and speed up

throughput.

TF-TRT or TensorRT

Too many deep learning model out

there, how to choose the right model?

For small labelled dataset, U-Net model is great choice for

segmentation task, then apply transfer learning.

Page 42: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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AUTOMATIC DEFECT INSPECTIONFROM REAL GPU PRODUCTION DATASET

Peter Pyun, Andrew Liu, Ryan Shen, Julius Chan, NV operations team at Shenzhen, China

Page 43: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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AOI & DECISION FLOW

AOI testVerify

by OPNG

OK OK

NG

Pass to next station, no image

stored

Pass to next station, store all images in AOI

machine

Repair

OK NG

EscapeFalse Positives

True Positives

Defect

Page 44: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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False Positive Stats

Boards: 200Components: 332

Boards: 400Components: 604

Boards: 200Components: 272

Golden Sample

False Positive

MEC21 Y5

Golden Sample

False Positive

Limitation: hand-tuned AOI parameter can not reduce false positives of all components in PCBA

Page 45: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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WHY FALSE POSITIVES?

Golden Sample False Positives

GLARE

MEC21

Page 46: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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True Positives (MEC)

MEC17 MEC16

Golden Sample

True Positive

True Positive

Golden Sample

BROKEN

SHIFT

Page 47: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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WHERE IS MEC21?

Page 48: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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False Positive Statistics

Capacitors: False Positives (defect-free) = 1608,

True Positives (defects): 60

Page 49: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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False Positives (Capacitors)

Page 50: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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True Positives (Capacitors)

Page 51: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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Data Augmentation (Capacitors)

D0_C42

D0_C131

D0_C201

D0_C511

D0_C1090_3 D1_C1088 D1_C109

D1_C48

D1_C105D0_C1085

Page 52: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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LOOKING INTO THE FUTURE:

AUTOMATING DEFECTS DETECTION IN ADVANCED PACKAGING

Page 53: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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Rising Semiconductor Design & Verification Cost

Source: A. Olofsson, Program Manager, DARPA Microsystems Technology Office

* Courtesy of Jerry Chen

Page 54: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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Page 56: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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Defects in solder balls

Page 57: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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Defects in micro-Bumps in packaging

Page 58: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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X-ray Solder Balls (BGA): 3D movie

Page 59: Transfer learning based GPU accelerated deep learning for end-to-end …on-demand.gputechconf.com/gtc-kr/2018/pdf/AI_INDUSTRY... · 2018-11-26 · Dr. Peter Pyun (변경석박사),

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ACKNOWLEDGEMENT

SPECIAL THANKS TO VIRTUAL TEAM MEMBERS @NVIDIA:

JERRY CHEN,OWEN LI,

BOBBY WANG, BILL LIAO,

HOWARD MARKS,RICK COMPTON,TY MCKERCHER,MARC HAMILTON

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