강의 3기 AI개론 4차시 — Perceptron BP ActivationF

4장 인공지능 개론

• “부록3 매트플롯립 입문”에서 한글 폰트를 올바르게 출력하기 위한 설치 방법을 설명했다. 설치 방법은 다음과 같다.

!sudo apt-get install -y fonts-nanum* | tail -n 1
!sudo fc-cache -fv
!rm -rf ~/.cache/matplotlib

debconf: unable to initialize frontend: Dialog
debconf: (No usable dialog-like program is installed, so the dialog based frontend cannot be used. at /usr/share/perl5/Debconf/FrontEnd/Dialog.pm line 78, <> line 4.)
debconf: falling back to frontend: Readline
debconf: unable to initialize frontend: Readline
debconf: (This frontend requires a controlling tty.)
debconf: falling back to frontend: Teletype
dpkg-preconfigure: unable to re-open stdin: 
Processing triggers for fontconfig (2.13.1-4.2ubuntu5) ...
/usr/share/fonts: caching, new cache contents: 0 fonts, 1 dirs
/usr/share/fonts/truetype: caching, new cache contents: 0 fonts, 3 dirs
/usr/share/fonts/truetype/humor-sans: caching, new cache contents: 1 fonts, 0 dirs
/usr/share/fonts/truetype/liberation: caching, new cache contents: 16 fonts, 0 dirs
/usr/share/fonts/truetype/nanum: caching, new cache contents: 39 fonts, 0 dirs
/usr/local/share/fonts: caching, new cache contents: 0 fonts, 0 dirs
/root/.local/share/fonts: skipping, no such directory
/root/.fonts: skipping, no such directory
/usr/share/fonts/truetype: skipping, looped directory detected
/usr/share/fonts/truetype/humor-sans: skipping, looped directory detected
/usr/share/fonts/truetype/liberation: skipping, looped directory detected
/usr/share/fonts/truetype/nanum: skipping, looped directory detected
/var/cache/fontconfig: cleaning cache directory
/root/.cache/fontconfig: not cleaning non-existent cache directory
/root/.fontconfig: not cleaning non-existent cache directory
fc-cache: succeeded

# 필요 라이브러리 설치
 
!pip install torchviz | tail -n 1

Successfully installed nvidia-cublas-cu12-12.4.5.8 nvidia-cuda-cupti-cu12-12.4.127 nvidia-cuda-nvrtc-cu12-12.4.127 nvidia-cuda-runtime-cu12-12.4.127 nvidia-cudnn-cu12-9.1.0.70 nvidia-cufft-cu12-11.2.1.3 nvidia-curand-cu12-10.3.5.147 nvidia-cusolver-cu12-11.6.1.9 nvidia-cusparse-cu12-12.3.1.170 nvidia-nvjitlink-cu12-12.4.127 torchviz-0.0.3

• 모든 설치가 끝나면 한글 폰트를 바르게 출력하기 위해 [런타임] -> **[런타임 다시시작]**을 클릭한 다음, 아래 셀부터 코드를 실행해 주십시오.

# 라이브러리 임포트
 
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
from IPython.display import display
 
# 폰트 관련 용도
import matplotlib.font_manager as fm
 
# Colab, Linux
# 나눔 고딕 폰트의 경로 명시
path = '/usr/share/fonts/truetype/nanum/NanumGothic.ttf'
font_name = fm.FontProperties(fname=path, size=10).get_name()
 
# Window
# font_name = "NanumBarunGothic"
 
# Mac
# font_name = "AppleGothic"

# 기본 폰트 설정
plt.rcParams['font.family'] = font_name
 
# 기본 폰트 사이즈 변경
plt.rcParams['font.size'] = 14
 
# 기본 그래프 사이즈 변경
plt.rcParams['figure.figsize'] = (6,6)
 
# 기본 그리드 표시
# 필요에 따라 설정할 때는, plt.grid()
plt.rcParams['axes.grid'] = True
plt.rcParams["grid.linestyle"] = ":"
 
# 마이너스 기호 정상 출력
plt.rcParams['axes.unicode_minus'] = False
 
# 넘파이 부동소수점 자릿수 표시
np.set_printoptions(suppress=True, precision=4)

퍼셉트론 (Perceptron)

import torch
from torch import nn
import torch.nn.functional as F

선형 퍼셉트론 구현

## 선형 퍼셉트론 구현
 
def perceptron(x, w, b = 0):
    if not isinstance(x, np.ndarray) or not isinstance(x, np.ndarray):
        x = np.array(x)
        w = np.array(w)
    y = np.sum(x*w) + b
    return y
 
x = [1, 2, 3]
w = [1, 2, 3]
# x = np.array([1, 2, 3])
# w = np.array([1, 2, 3])
 
y = perceptron(x, w)
print("result =", y)

result = 14

## 선형 퍼셉트론 구현: 랜텀 initial weights
 
def perceptron(x):
    w = np.random.rand(len(x))
    b = np.random.rand()
    y = np.sum(x*w) + b
    return y, w, b
 
x = np.array([1, 2, 3])
w = np.array([1, 2, 3])
 
y, w, b = perceptron(x)
print("result =", y.round(3))
print("weight = ", w)
print("b = ", round(b, 3))
 

result = 3.872
weight =  [0.6354 0.9663 0.1028]
b =  0.996

Pytorch 를 이용한 perceptron

## Pytorch 를 이용한 perceptron
# torch.manual_seed(0)
 
input_size = 10
output_size = 1
y = nn.Linear(input_size, output_size)
 
print("weights = \n", y.weight)
print("bias = \n", y.bias)
print("="*50)
 
# 난수 생성
x = torch.rand(input_size)
print("x input = \n", x)
print("output = ", y(x))

weights = 
 Parameter containing:
tensor([[-0.2100, -0.1679, -0.2891,  0.2916,  0.1475,  0.0402, -0.2919, -0.1315,
         -0.0679,  0.0026]], requires_grad=True)
bias = 
 Parameter containing:
tensor([-0.0885], requires_grad=True)
==================================================
x input = 
 tensor([0.6266, 0.7196, 0.6680, 0.5833, 0.0691, 0.9878, 0.5864, 0.4230, 0.2783,
        0.4751])
output =  tensor([-0.5584], grad_fn=<ViewBackward0>)

오류 순전파 (Forward propagation)

def sigmoid(x):
    return 1 / (1 + np.exp(-x))
 
def sse(y, x):
    return (y-x)**2
 
def perceptron(x, w, b = 0):
    if not isinstance(x, np.ndarray) or not isinstance(x, np.ndarray):
        x = np.array(x)
        w = np.array(w)
    y = np.sum(x*w) + b
    return y

활성화 함수 (Activation function)

## 시그모이드 (sigmoid)
def activation_plot(x, y, title:str):
    plt.plot(x, y)
    plt.title(title)
    # plt.grid(linestyle = ":")
    plt.show()

# numpy
x = np.linspace(-5, 5, 100)
def sigmoid(x):
    y = 1/(1 + np.exp(-x))
    return y
y = sigmoid(x)
 
# torch class
# torch_simoid = nn.Sigmoid()
# y = torch_simoid(torch.tensor(x))
# y = F.sigmoid(torch.tensor(x))
 
activation_plot(x, y, "Sigmoid")

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## Tanh (Hyperbolic Tangent)
def tanh(x):
    y = np.tanh(x)
        # y = (np.exp(x) - np.exp(-x))/ (np.exp(x) + np.exp(-x))
    return y
y = tanh(x)
 
# torch
torch_tanh = nn.Tanh()
y = torch_tanh(torch.tensor(x))
y = F.tanh(torch.tensor(x))
 
activation_plot(x, y, "Tanh")

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## ReLU (Rectified Linear Unit)
def relu(x):
    y = np.maximum(0, x)
    return y
 
# torch
# torch_relu = nn.ReLU()
# y = torch_relu(torch.tensor(x))
# y = F.relu(torch.tensor(x))
 
# y = relu(x)
activation_plot(x, y, "ReLU")

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## Leaky ReLU
def leakyRelu(x, alpha:float):
    y = np.maximum(alpha*x, x)
    return y
y = leakyRelu(x, 0.1)
 
# torch
# torch_lrelu = nn.LeakyReLU(0.1)
# y = torch_lrelu(torch.tensor(x))
# y = F.leaky_relu(torch.tensor(x), 0.1)
 
 
activation_plot(x, y, "Leaky ReLU")

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## Exponential ReLU
def eRelu(x, alpha):
    y = (x>0)*x + (x <= 0)*(alpha*(np.exp(x) - 1))
    return y
 
y = eRelu(x, 1.)
 
# torch
# torch_lrelu = nn.GELU(0.1)
# y = torch_lrelu(torch.tensor(x))
# y = F.leaky_relu(torch.tensor(x), 0.1)
 
activation_plot(x, y, "Exponential ReLU")

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WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.
WARNING:matplotlib.font_manager:findfont: Font family 'NanumGothic' not found.