ํ‹ฐ์Šคํ† ๋ฆฌ ๋ทฐ

AI/๋…ผ๋ฌธ ๋ฆฌ๋ทฐ Paper Review

DCGAN : ICLR 2016

ํ•ด๋“œ์œ„๊ทธ 2024. 1. 28. 17:02

Alec Radford & Luke Metz

DCGAN : UNSUPERVISED REPRESENTATION LEARNINGWITH DEEP CONVOLUTIONALGENERATIVE ADVERSARIAL NETWORKS

INTRODUCTION

GANs have been known to be unstable to train, often resulting in generators that produce nonsensical outputs.

CNN์„ ํ™œ์šฉํ•œ ๋น„์ง€๋„ํ•™์Šต์œผ๋กœ ์ง€๋„ํ•™์Šต๊ณผ ๋น„์ง€๋„ํ•™์Šต์˜ ์ฐจ์ด๋ฅผ ์ค„์ธ๋‹ค.

 

  1. CNN์„ ํ™œ์šฉํ•˜์—ฌ ์•ˆ์ •์ ์ธ train์„ ๊ฐ€๋Šฅํ•˜๊ฒŒ ํ–ˆ์œผ๋ฉฐ ์ด๋ฅผ DCGAN์ด๋ผ๊ณ  ํ•œ๋‹ค.
  2. ํŒ๋ณ„๊ธฐ๋ฅผ ์ด๋ฏธ์ง€ ๋ถ„๋ฅ˜๊ธฐ ์ž‘์—…์œผ๋กœ ์‚ฌ์šฉํ•˜์˜€๊ณ , ๋‹ค๋ฅธ ๋น„์ง€๋„ํ•™์Šต ์•Œ๊ณ ๋ฆฌ์ฆ˜๋“ค์— ๊ฒฝ์Ÿ์ ์ธ ์„ฑ๋Šฅ์„ ๋ณด์—ฌ์ค€๋‹ค.
  3. DCGAN์— ์˜ํ•ด ํ•™์Šต๋œ ํ•„ํ„ฐ๋ฅผ ๋ณด์—ฌ์ฃผ๊ณ , ํŠน์ • ํ•„ํ„ฐ๊ฐ€ ํŠน์ •ํ•œ objects๋ฅผ ์ƒ์„ฑํ•˜๊ฒŒ ํ•™์Šตํ•  ์ˆ˜ ์žˆ๋‹ค๋Š” ๊ฒƒ์„ ๋ณด์—ฌ์ค€๋‹ค.
  4. DCGAN์€ ์ƒ์„ฑ์ž๊ฐ€ ์ƒ์„ฑ๋œ ์ƒ˜ํ”Œ๋“ค์„ ์ž˜ ์กฐ์ ˆํ•˜๋„๋ก ํ•˜๋Š” ๋ฐฑํ„ฐ์˜ ์‚ฐ์ˆ  ํŠน์„ฑ์„ ๊ฐ€์ง€๋Š” ๊ฒƒ์„ ๋ณด์—ฌ์ค€๋‹ค.

RELATED WORK

Generative Adversarial Networks (Goodfellow et al., 2014) generated images suffering from being noisy and incomprehensible.

 

GAN์˜ ๋ฌธ์ œ์ 

- ํ›ˆ๋ จํ•  ๋•Œ ์•ˆ์ •์„ฑ์ด ๋–จ์–ด์ง.

- ๊ณ ํ•ด์ƒ๋„ ์ด๋ฏธ์ง€๋ฅผ ์ƒ์„ฑํ•˜๊ธฐ ์–ด๋ ค์›€.

 

APPROACH AND MODEL ARCHITECTURE

- CNN์„ ์‚ฌ์šฉํ•˜์—ฌ GAN์„ scale up ํ•˜์—ฌ ์ด๋ฏธ์ง€๋ฅผ ๋ชจ๋ธ๋งํ•˜๋ ค๋Š” ์‹œ๋„๋“ค์€ ์ด๋ฏธ ์žˆ์—ˆ์ง€๋งŒ, ์„ฑ๊ณต์ ์ด์ง€ ๋ชปํ–ˆ๋‹ค. ex) LAPGAN

- ๊ด‘๋ฒ”์œ„ํ•œ ๋ชจ๋ธ ํƒ์ƒ‰ ํ›„, ๋‹ค์–‘ํ•œ ๋ฐ์ดํ„ฐ์…‹์—์„œ ์•ˆ์ •์ ์ธ ํ•™์Šต๊ณผ ๋” ๋†’์€ ํ•ด์ƒ๋„, ๊นŠ์€ ์ƒ์„ฑ ๋ชจ๋ธ์„ ํ•™์Šตํ•  ์ˆ˜ ์žˆ๋Š” ๊ตฌ์กฐ๋ฅผ ํ™•์ธํ–ˆ๋‹ค.

- ์šฐ๋ฆฌ์˜ ์ ‘๊ทผ์˜ ํ•ต์‹ฌ์€ ์ตœ๊ทผ CNN ๊ตฌ์กฐ์˜ 3๊ฐ€์ง€ ๋ณ€ํ™”๋ฅผ ์ˆ˜์ •ํ•˜๊ณ  ์ฑ„ํƒํ•œ ๊ฒƒ์ด๋‹ค.

 

1. Max pooling to Strided Convolution

Spatial Pooling์€ down sample์˜ ๋Œ€ํ‘œ์ ์ธ ๊ธฐ๋ฒ•, ๋”ฐ๋กœ Max pooling layer๋ฅผ ๋„ฃ์–ด spatial resolution์„ ๋‚ฎ์ถฐ์ฃผ๋Š” ์ž‘์—…์„ ์ง„ํ–‰.

Spatial downsampling์„ ํ•™์Šตํ•˜๊ฒŒ ํ–ˆ๋‹ค. ์ด ์ ‘๊ทผ์„ ๋„ฃ์–ด Generator๋Š” Spatial downsampling ๊ณผ์ •์„ ํ•จ๊ป˜ ํ•™์Šต์‹œํ‚ฌ ์ˆ˜ ์žˆ๊ฒŒ ํ•˜๊ณ , Discriminator์—์„œ๋Š” spatial upsampling์ด ๊ฐ€๋Šฅํ•˜๊ฒŒ ํ–ˆ๋‹ค.

 

2. FC layer ์ œ๊ฑฐ

convolution feature์˜ top์— fully connected layer๋ฅผ ์ œ๊ฑฐํ•˜๋Š” ๊ฒƒ์ด๋‹ค. ์˜ˆ์‹œ๋กœ ์ด๋ฏธ์ง€ ๋ถ„๋ฅ˜ ๋ชจ๋ธ์— ํ™œ์šฉ๋œ global average pooling์ด ์žˆ๋‹ค. ์ด๊ฒƒ์€ ๋ชจ๋ธ ์•ˆ์ •์„ฑ์„ ํ–ฅ์ƒ์‹œ์ผฐ์ง€๋งŒ, ์ˆ˜๋ ด ์†๋„๋ฅผ ์†์ƒ์‹œ์ผฐ๋‹ค. ์ค‘๊ฐ„ ์˜์—ญ์€ ์ž˜ ์ž‘๋™ํ•จ.

๋งˆ์ง€๋ง‰์— D์˜ output๊ฒฐ๊ณผ๋ฅผ ํŒ๋‹จํ•˜๋Š” softmax layer์™€ G์—์„œ z๋ฅผ input์œผ๋กœ ๋„ฃ๋Š” ์ฒซ ๋ฒˆ์งธ layer๋ฅผ ์ œ์™ธํ•˜๊ณ  ๋ชจ๋“  FC layers๋ฅผ ์ œ๊ฑฐ

 

3. ๋ฐฐ์น˜์ •๊ทœํ™” ์‚ฌ์šฉ

๊ฐ ์œ ๋‹›์— ๋Œ€ํ•œ ์ž…๋ ฅ์„ ํ‰๊ท ๊ณผ ๋‹จ์œ„ ๋ถ„์‚ฐ์ด 0์ด ๋˜๋„๋ก ์ •๊ทœํ™”ํ•˜์—ฌ ํ•™์Šต์„ ์•ˆ์ •ํ™”ํ•œ๋‹ค. ์ดˆ๊ธฐํ™” ๋ถˆ๋Ÿ‰์œผ๋กœ ์ธํ•ด ๋ฐœ์ƒํ•˜๋Š” ํ›ˆ๋ จ ๋ฌธ์ œ๋ฅผ ํ•ด๊ฒฐํ•˜๊ณ  ์‹ฌ์ธต ๋ชจ๋ธ์—์„œ gradient flow์„ ๋•๋Š”๋‹ค. ์ด๋Š” deep generator๊ฐ€ ํ•™์Šต์„ ์‹œ์ž‘ํ•˜๋„๋ก ํ•˜๋Š” ๋ฐ ์ค‘์š”ํ•œ ๊ฒƒ์œผ๋กœ ์ž…์ฆ๋˜์—ˆ์œผ๋ฉฐ, generator๊ฐ€ GAN์—์„œ ํ”ํžˆ ๊ด€์ฐฐ๋˜๋Š” ์‹คํŒจ ๋ชจ๋“œ์ธ single point๋กœ ๋ถ•๊ดดํ•˜๋Š” ๊ฒƒ์„ ๋ฐฉ์ง€ํ•œ๋‹ค.

๋ชจ๋“  layer์— batchnorm์„ ์ง์ ‘ ์ ์šฉํ•˜๋ฉด ์ƒ˜ํ”Œ์˜ ์ง„๋™๊ณผ ๋ชจ๋ธ์˜ ๋ถˆ์•ˆ์ •์„ฑ์ด ๋ฐœ์ƒํ•จ.

-> generator output layer์™€ discriminator input layer์— ์ ์šฉํ•˜์ง€ ์•Š์Œ์œผ๋กœ ๋ฐฉ์ง€ํ•  ์ˆ˜ ์žˆ์Œ.

GAN๋…ผ๋ฌธ์—์„œ maxout ํ™œ์„ฑํ™” ์‚ฌ์šฉ VS discriminator์—์„œ, ํŠนํžˆ ๊ณ ํ•ด์ƒ๋„๋ชจ๋ธ์—์„œ leaky rectified ํ™œ์„ฑํ™” ์‚ฌ์šฉ

 

์•ˆ์ •์ ์ธ Deep Convolution GANs๋ฅผ ์œ„ํ•œ ๊ตฌ์กฐ ๊ฐ€์ด๋“œ

1. strided convolutions(ํŒ๋ณ„์ž), fractional-strided convolutions(์ƒ์„ฑ์ž)๋กœ ๋Œ€์ฒด

2. ์ƒ์„ฑ๊ธฐ์™€ ํŒ๋ณ„๊ธฐ ๋ชจ๋‘ batchnorm ์‚ฌ์šฉ (Generator์˜ output layer์™€ Discriminator์˜ input layer ์ œ์™ธ)

3. ๋” ๊นŠ์€ ๊ตฌ์กฐ๋ฅผ ์œ„ํ•ด fully connected hidden layers ์ œ๊ฑฐ

4. Generator์˜ output์—๋Š” Tanh๋ฅผ ์‚ฌ์šฉํ•˜๊ณ , ๋‚˜๋จธ์ง€๋Š” ReLU๋ฅผ ์‚ฌ์šฉ

5. ๋ชจ๋“  layers์— ๋Œ€ํ•ด Discriminator(ํŒ๋ณ„์ž)์—์„œ LeakyReLU ํ™œ์„ฑํ™” ์‚ฌ์šฉ

 

DETAILS OF ADVERSARIAL TRAINING

์ƒ์„ฑ์ž์˜ ๊ตฌ์กฐ

input์œผ๋กœ 100 x 1์˜ noise vector๋ฅผ ์‚ฌ์šฉํ•˜์—ฌ Project and reshape๋ผ๋Š” layer๋ฅผ ํ†ตํ•ด 1024 x 4 x 4๋กœ ํ™•์žฅ์ด ๋œ๋‹ค.

๊ทธ๋ฆฌ๊ณ  convolution layer๋กœ ๋„˜์–ด๊ฐ€ fractional-strided convolution layer๋ฅผ ๊ฑฐ์น˜๋ฉฐ 64 x 64 pixel์˜ ์ด๋ฏธ์ง€๋ฅผ ์ƒ์„ฑํ•œ๋‹ค.

 

ํŒ๋ณ„์ž์˜ ๊ตฌ์กฐ

 

ํŒ๋ณ„์ž๋Š” input์œผ๋กœ 64 x 64 ํฌ๊ธฐ์˜ ์ด๋ฏธ์ง€๋ฅผ ๋ฐ›์•„ ๋งˆ์ง€๋ง‰ sigmoid๋กœ 1 or 0์˜ 1์ฐจ์› ๊ฒฐ๊ณผ๋ฅผ ์ถœ๋ ฅํ•œ๋‹ค.

ํ™œ์„ฑํ™” ํ•จ์ˆ˜๋Š”  LeakyReLU๋ฅผ ์‚ฌ์šฉํ•˜๋Š”๋ฐ, ReLU์™€ ๋‹ค๋ฅธ ์ ์€ LeakyReLU๋Š” ์Œ์ˆ˜์˜์—ญ์—์„œ ์•ฝ๊ฐ„์˜ ๊ธฐ์šธ๊ธฐ๋ฅผ ๊ฐ–๋Š” ๊ฐ’์„ ์ถœ๋ ฅํ•œ๋‹ค๋Š” ์ ์ด ๋‹ค๋ฅด๋‹ค.

 

DCGAN์„ 3๊ฐœ์˜ ๋ฐ์ดํ„ฐ์…‹: LSUN, ์ด๋ฏธ์ง€๋„ท, ์ƒˆ๋กญ๊ฒŒ ์กฐํ•ฉ๋œ ์–ผ๊ตด ๋ฐ์ดํ„ฐ์…‹์— ๋Œ€ํ•ด ํ•™์Šตํ–ˆ๋‹ค.

- ํ•™์Šต ์ด๋ฏธ์ง€์—๋Š” ์ „์ฒ˜๋ฆฌ๊ฐ€ ์ ์šฉ๋˜์ง€ ์•Š์•˜๊ณ , tanh activation ํ•จ์ˆ˜์˜ [-1, 1]์˜ ๋ฒ”์œ„๋กœ ์Šค์ผ€์ผ๋ง

- ๋ชจ๋“  ๋ชจ๋ธ๋“ค์€ SGD๋กœ ๋ฏธ๋‹ˆ ๋ฐฐ์น˜ ์‚ฌ์ด์ฆˆ 128๋กœ ํ•™์Šต.

- ๋ชจ๋“  ๊ฐ€์ค‘์น˜๋“ค์€ zero-centered ์ •๊ทœ ๋ถ„ํฌ๋กœ ํ‘œ์ค€ ํŽธ์ฐจ 0.02๋กœ ์ดˆ๊ธฐํ™”.

- LeakyReLU์—์„œ ๋ชจ๋“  ๋ชจ๋ธ์— leak์˜ slope๋Š” 0.2๋กœ ์„ค์ •.

- ์ด์ „์˜ GAN ์—ฐ๊ตฌ๋“ค์€ ํ•™์Šต์„ ๊ฐ€์†ํ•˜๊ธฐ ์œ„ํ•ด์„œ ๋ชจ๋ฉ˜ํ…€์„ ์‚ฌ์šฉ VS ์šฐ๋ฆฌ๋Š” ์กฐ์ •๋œ ํ•˜์ดํผํŒŒ๋ผ๋ฏธํ„ฐ๋ฅผ ์‚ฌ์šฉํ•ด์„œ Adam ์˜ตํ‹ฐ๋งˆ์ด์ €๋ฅผ ์‚ฌ์šฉ

- learning rate 0.0002๋ฅผ ์ œ์•ˆ

- ์ถ”๊ฐ€์ ์œผ๋กœ ๋ชจ๋ฉ˜ํ…€ beta1์„ 0.9๋กœ ๋‘์—ˆ์„ ๋•Œ training oscillation๊ณผ ๋ถˆ์•ˆ์ •์„ฑ์ด ๋ฐœ๊ฒฌ, 0.5๋กœ ๋‘์—ˆ์„ ๋•Œ ํ•™์Šต ์•ˆ์ •์— ๋„์›€.

 

4.1 LSUN

- ์นจ์‹ค์‚ฌ์ง„

- 3๋ฐฑ๋งŒ์žฅ ์ด์ƒ์˜ ํ•™์Šต ์ƒ˜ํ”Œ

- ์ด๋ฏธ์ง€ ์ค‘๋ณต ์ œ๊ฑฐ ์ž‘์—…

- 100๊ฐœ ์ค‘ 1๊ฐœ ๋ฏธ๋งŒ์˜ false positive -> ๋†’์€ ์ •ํ™•๋„

one training

 

5 epochs

- ๋ถ€๋ถ„๋ถ€๋ถ„ noise๊ฐ€ ๋ฐœ์ƒํ•ด์„œ underfitting๋จ.

 

4.2 Faces

OpenCV ์–ผ๊ตด ๊ฒ€์ถœ์„ ์‚ฌ์šฉํ•ด์„œ ๊ณ ํ•ด์ƒ๋„ ์ด๋ฏธ์ง€ ๊ฒ€์ถœ

 

4.3 IMAGENET

 

EMPIRICAL VALIDATION OF DCGANS CAPABILITIES

5.1 Classifying CIFAR-10 using GANs as feature extractor

- ์„ฑ๋Šฅ

 

INVESTIGATING AND VISUALIZING THE INTERNALS OF THE NETWORKS

6.1 Walking in the Latent Space

 

- G์˜ input z์˜ ๊ณต๊ฐ„์ธ latent Space์—์„œ ์—์„œ ๋กœ ์‚ด์ง ์ด๋™ํ•œ๋‹ค ํ•˜๋”๋ผ๋„ ๊ธ‰์ž‘์Šค๋Ÿฌ์šด ๋ณ€ํ™”๊ฐ€ ์ผ์–ด๋‚˜์ง€ ์•Š๊ณ , ๋ถ€๋“œ๋Ÿฌ์šด ๋ณ€ํ™”๋ฅผ ๋ณด์—ฌ์ค˜์•ผ ํ•œ๋‹ค.

- ๊ฐ ์ค„ ๋งˆ๋‹ค z(latent vector)์˜ ๊ฐ’์„ ์กฐ๊ธˆ์”ฉ ๋ฐ”๊ฟ”๊ฐ€๋ฉด์„œ ๋ถ€๋“œ๋Ÿฝ๊ฒŒ ๊ฒฐ๊ณผ๊ฐ€ ๋ณ€๊ฒฝ๋˜๋Š” ๊ฒƒ์„ ํ™•์ธํ•  ์ˆ˜ ์žˆ๋‹ค.

- ํŠนํžˆ ๋งˆ์ง€๋ง‰ ์ค„์€ z์˜ ๊ฐ’์„ ๋ณ€ํ™”์‹œ์ผœ ์–ป์€ ๊ฒฐ๊ณผ๋กœ, ์™ผ์ชฝ์— ์žˆ๋˜ ํ‹ฐ๋น„๊ฐ€ ์ฐฝ๋ฌธ์œผ๋กœ ๋ณ€ํ™”ํ•œ ๊ฒƒ์„ ํ™•์ธํ•  ์ˆ˜ ์žˆ๋‹ค.

6.2 Visualizing the Discriminator Features

ํŒ๋ณ„์ž์˜ feature๋ฅผ ์‹œ๊ฐํ™”ํ•ด์„œ ๋‚˜์˜จ ๊ฒƒ

- CNN์˜ Black Box๋Š” ์ค‘๊ฐ„์— ์–ด๋–ค feature map์ด ์–ด๋– ํ•œ ์ž‘์šฉ์„ ํ•ด์„œ ์ด๋Ÿฐ ๊ฒฐ๊ณผ๊ฐ€ ๋‚˜์˜ค๋Š”์ง€, ์ธ๊ณผ๊ด€๊ณ„๋ฅผ ๋ช…ํ™•ํ•˜๊ฒŒ ์„ค๋ช…ํ•  ์ˆ˜ ์—†๋Š” ๋ฌธ์ œ์ ์ด ์žˆ์—ˆ๋‹ค. DCGAN์—์„œ๋Š” Discriminator์— ํ•™์Šต์„ ์‹œํ‚จ ๊ฒฐ๊ณผ, ํ•„ํ„ฐ์—์„œ ์นจ๋Œ€๋‚˜ ์ฐฝ๋ฌธ ๊ฐ™์ด ์นจ์‹ค์˜ ํŠน์ • ๋ถ€๋ถ„์—์„œ ํ™œ์„ฑํ™” ๋˜๋Š” ํ•„ํ„ฐ๋“ค์„ ๋ฐœ๊ฒฌํ–ˆ๋‹ค. ์ฆ‰, ๋‹ค์‹œ๋งํ•˜๋ฉด ํ•„ํ„ฐ๋“ค์ด ์นจ๋Œ€์˜ ์ผ๋ถ€๋ถ„์„ ํ•™์Šตํ•œ ๊ฒƒ์„ ๋ณผ ์ˆ˜ ์žˆ์Œ.

 

6.3 Manipulating the Generator Representation

 

6.3.1 FORGETTING TO DRAW CERTAIN OBJECTS
- ํ•™์Šต์ด ์ž˜ ๋˜์–ด์žˆ๋Š” filter๋ฅผ dropout ์‹œ์ผœ์„œ ์ด๋ฏธ์ง€์—์„œ ํ•ด๋‹น filter๊ฐ€ ๋งก๊ณ  ์žˆ๋˜ ๋ถ€๋ถ„์„ ์ œ๊ฑฐํ•˜๋Š” ๊ฒƒ์„ ๋ณด์—ฌ์ค€๋‹ค.

- ๋…ผ๋ฌธ์—์„œ ์ง„ํ–‰ํ•œ ์‹คํ—˜์€

1. 150๊ฐœ์˜ sample image์—์„œ 52๊ฐœ์˜ window๋ฅผ ์ฐพ์•„๋‚ด bounding box ์ฒ˜๋ฆฌ๋ฅผ ํ•œ๋‹ค.
2. ๊ณ ์ฐจ์› feature(high-level feature)์ค‘ window๋ฅผ activateํ•˜๋Š” feature๋ฅผ ๊ณ ๋ฅธ๋‹ค.
3. ๊ณ ๋ฅด๋Š” ๋ฐฉ๋ฒ•์€ window bounding boxes์•ˆ์—์„œ๋Š” positiveํ•œ ๊ฒฐ๊ณผ๋ฅผ ๋ณด์ด๊ณ , ๋‹ค๋ฅธ ๋žœ๋ค ์ด๋ฏธ์ง€์—์„œ๋Š” negativeํ•œ ๋ฐ˜์‘์„ ๋ณด์ด๋Š” ํ•„ํ„ฐ๋ฅผ ์ฐพ๋Š”๋‹ค.
์›๋ณธ์ด ์œ—์ค„, window ํ•„ํ„ฐ๋ฅผ dropout ํ•œ๊ฒŒ ์•„๋ž˜์ค„์ด๋‹ค. window๊ฐ€ ์‚ฌ๋ผ์ง„ ๊ฒƒ์„ ํ™•์ธํ•  ์ˆ˜ ์žˆ๋‹ค.

6.3.2 VECTOR ARITHMETIC ON FACE SAMPLES

- ๋ฒกํ„ฐ์—ฐ์‚ฐ์„ DCGAN์—์„œ๋„ ์‚ฌ์šฉํ•  ์ˆ˜ ์žˆ์Œ.

- ex) vector(“King”) - vector(“Man”) + vector(“Woman”) ์˜ ๊ฒฐ๊ณผ๋Š” ๊ฐ€์žฅ ๊ทผ์ ‘ํ•œ ์ด์›ƒ์˜ ๋ฒกํ„ฐ์ธ Queen์˜ ๊ฒฐ๊ณผ๋ฅผ ์ฆ๋ช….

 

- ๊ฐ ์นดํ…Œ๊ณ ๋ฆฌ ๋งˆ๋‹ค ์„ธ๊ฐœ์˜ z๋ฅผ ํ‰๊ท ๋‚ด์„œ Z vector๋ฅผ ์ƒ์„ฑํ•˜๊ณ , ํ‰๊ท ๊ฐ’์œผ๋กœ ๊ตฌํ•œ ๊ฐ Z vector๋“ค์„ ์—ฐ์‚ฐํ•ด์ฃผ๋ฉด ๊ฒฐ๊ณผ๊ฐ€ ๋‚˜์˜จ๋‹ค.

- ex) ์•ˆ๊ฒฝ์„ ์“ด ๋‚จ์ž - ์•ˆ๊ฒฝ์„ ์•ˆ ์“ด ๋‚จ์ž + ์•ˆ๊ฒฝ์„ ์•ˆ ์“ด ์—ฌ์ž = ์•ˆ๊ฒฝ์„ ์“ด ์—ฌ์ž

 

 

- ํšŒ์ „ : ์™ผ์ชฝ์„ ๋ณด๊ณ  ์žˆ๋Š” ์–ผ๊ตด๊ณผ ์˜ค๋ฅธ์ชฝ์„ ๋ณด๊ณ  ์žˆ๋Š” ์–ผ๊ตด ๋ฒกํ„ฐ๋“ค์˜ ํ‰๊ท ์„ ๊ณ„์‚ฐ ํ›„, ๋‘ ๋ฒกํ„ฐ๋ฅผ ์ž‡๋Š” ์ถ•์„ interpolateํ•ด์„œ G์— ๋Œ€์ž…ํ•œ ๊ฒฐ๊ณผ, ํšŒ์ „ํ•˜๋Š” ์–ผ๊ตด๋“ค์ด ๋‚˜์˜ด.

CONCLUSION AND FUTURE WORK

- ๋ชจ๋ธ ๋ถˆ์•ˆ์ •์„ฑ collapse ๋ฌธ์ œ

- ์ด ํ”„๋ ˆ์ž„์›Œํฌ๋ฅผ ๋น„๋””์˜ค, ์˜ค๋””์˜ค์™€ ๊ฐ™์€ ๋‹ค๋ฅธ ๋„๋ฉ”์ธ์— ํ™•์žฅํ•˜๋Š” ๊ฒƒ๋„ ํฅ๋ฏธ๋กœ์šธ ๊ฒƒ์ด๋ผ ์ƒ๊ฐ

 

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