실수치 회로, 역전파
해커가 알려주는 뉴럴 네트워크를 공부한 내용 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 import sys import random from math import exp class rgate: def mul(x,y): return x*y def add(x,y): return x+y class unit: value = 0.0 grad = 0.0 def __init__(self, value=0.0,grad=0.0): self.value = value self.grad = grad class u: value = 0.0 grad = 0.0 def __init__(self, value=0.0,grad=0.0): self.value = value self.grad = grad class mg: u0 = None u1 = None ru = None def __init__(self, u0=None,u1=None): self.u0 = None self.u1 = None self.ru = None def f(self, u0, u1): self.u0 = u0 self.u1 = u1 self.ru = unit(u0.value*u1.value,0) return self.ru def b(self): self.u0.grad += self.ru.grad * self.u1.value self.u1.grad += self.ru.grad * self.u0.value class ag: u0 = None u1 = None ru = None def f(self,u0, u1): self.u0 = u0 self.u1 = u1 self.ru = unit(u0.value+u1.value,0) return self.ru def b(self): self.u0.grad += self.ru.grad*1 self.u1.grad += self.ru.grad*1 class sg: u0 = None ru = None def sig(self, x): return 1/(1+exp(-x)) def f(self,u0): self.u0 = u0 self.ru = unit(self.sig(self.u0.value), 0) return self.ru def b(self): s = self.sig(self.u0.value) self.u0.grad += (s*(1-s))*self.ru.grad def fc(a,b,c,x,y): return 1/(1+exp(-(a*x+b*y+c))) class sqg: u0 = None ru = None def f(self,u0): self.u0 = u0 self.ru = unit(self.u0.value*self.u0.value,0.0) return self.ru def b(self): self.u0.grad += 2*self.u0.value*self.ru.grad class dg: u0 = None u1 = None ru = None def f(self,u0=unit(1.0,0.0),u1=unit(1.0,0.0)): self.u0 = u0 self.u1 = u1 self.ru = unit(self.u0.value/self.u1.value,0.0) return self.ru def b(self): self.u0.grad += (-1/(self.u0.value*self.u0.value)) class mag:#max gate u0 = None u1 = None ru = None def f(self,u0,u1): self.u0 = u0 self.u1 = u1 self.ru = unit(self.u0.value > self.u1.value and self.u0.value or self.u1.value , 0.0) return self.ru def b(self): self.u0.grad += self.ru.value == self.u0.value and 1.0*self.ru.grad or 0 self.u1.grad += self.ru.value == self.u1.value and 1.0*self.ru.grad or 0 class rg:#ReLU gate u0 = None ru = None def f(self,u0): self.u0 = u0 self.ru = unit(self.u0.value > 0 and self.u0.value or 0 , 0.0) return self.ru def b(self): self.u0.grad += self.ru.value > 0 and 1.0*self.ru.grad or 0 def sig(a): return 1/(1+exp(-a)) if __name__=='__main__': """ #Random Local Search,출력을 임의로 변화시켜 더 나은 출력을 찾는다 print(rgate.mul(1,2)) x = -2 y = 3 best_x = x best_y = y x_try=0 y_try=0 tweak_amout = 0.01 out = 0; best_out = -sys.maxsize-1 for each in range(100): print(each) x_try = x + tweak_amout*(random.random()*2-1) y_try = y + tweak_amout*(random.random()*2-1) out = rgate.mul(x_try,y_try) if(out>best_out): best_out = out best_x = x_try best_y = y_try print(best_x,best_y,best_out) """ """ #Numerical Gradient, 간단한 계산을 통해 기울기를 찾고 더 나은 출력을 도출해낸다 #기울기는 더 나은 출력을 위한 최선의 방향을 의미한다 #단일 뉴런으로 볼때는 큰 스텝이 좋은 출력을 내지만, 복잡하게 꼬여있는 경우 스텝이 크면 예상을 벗어나는 값이 나올 수 있다. #스텝의 크기는 눈을 가리고 언덕을 오를때의 보폭의 크기로 비유할 수 있다. 작으면 느리지만 확실하게 언덕을 오를 수 있지만, 크면 빠를수 있지만 다칠수 있다. x =-2 y = 3 out = rgate.mul(x,y) h = 0.0001 x_derivative = (rgate.mul(x+h,y)-out)/h y_derivative = (rgate.mul(x,y+h)-out)/h print(x_derivative) print(y_derivative) step_size = 0.01 out = rgate.mul(x,y) print(out) x = x + step_size*x_derivative y = y + step_size*y_derivative new_out = rgate.mul(x,y) print(new_out) """ """ #Analytic Gradient #기울기를 입,출력의 변화로 부터 계산할 경우 입력을 개수에 따라 계산하는 비용이 선형적으로 증가한다. #수백만 수억개가 있을때는 큰 비용이 들게 된다. #이 방법을 입출력에 변화를 주어 계산할 필요 없이, 미분공식으로 기울기는 구한다 x =-2 y = 3 out = rgate.mul(x,y) x_derivative = y #미분 결과에 의해 y_derivative = x #미분 결과에 의해 step_size = 0.01 out = rgate.mul(x,y) print(out) x = x + step_size*x_derivative y = y + step_size*y_derivative new_out = rgate.mul(x,y) print(new_out) """ """ 뉴럴네트워크 라이브러리를 기울기를 구할때 #3 공식기울기를 사용하지만, 검증은 계산기울기를 통해서 한다. 공식기울기는 효율적이지만 때로는 틀릴수도 있는 반면, 계산기울기는 비용은 크지만 확실한 값이다. """ """ #Backpropagation #연결된 게이트에서 #3공식기울기를 구할때는 체인룰을 적용한다. 체인룰은 곱셈으로 연결시키는 것이다. x = -2; y = 5; z =-4 q = rgate.add(x,y) f = rgate.mul(q,z) #print(q) print(f) d_f_wrt_q = z d_f_wrt_z = q d_q_wrt_x = 1.0 d_q_wrt_y = 1.0 d_f_wrt_x = d_q_wrt_x*d_f_wrt_q d_f_wrt_y = d_q_wrt_y*d_f_wrt_q g = [d_f_wrt_x,d_f_wrt_y,d_f_wrt_z] step = 0.01 x=x+step*g[0] y=y+step*g[1] z=z+step*g[2] q = rgate.add(x,y) f = rgate.mul(q,z) #print(q) print(f) """ a = unit(1.0, 0.0) b = unit(2.0, 0.0) c = unit(-3.0, 0.0) x = unit(-1.0, 0.0) y = unit(3.0 ,0.0) mg0 = mg() mg1 = mg() ag0 = ag() ag1 = ag() sg0 = sg() m1 = mg0.f(a, x) m2 = mg1.f(b, y) a1 = ag0.f(m1, m2) a2 = ag1.f(a1, c) s = sg0.f(a2) print(s.value) sg0.ru.grad = 1.0 sg0.b() ag0.b() ag1.b() mg0.b() mg1.b() step = 0.01 a.value += step*a.grad b.value += step*b.grad c.value += step*c.grad x.value += step*x.grad y.value += step*y.grad ax = mg0.f(a, x) by = mg1.f(b, y) ag0 = ag0.f(ax, by) ag1 = ag1.f(ag0, c) s = sg0.f(ag1) print(s.value) h = 0.001 a = 1 b = 2 c = -3 x = -1 y = 3 ga = (fc(a+h,b,c,x,y)-fc(a,b,c,x,y))/h gb = (fc(a,b+h,c,x,y)-fc(a,b,c,x,y))/h gc = (fc(a+h,b,c+h,x,y)-fc(a,b,c,x,y))/h gx = (fc(a+h,b,c,x+h,y)-fc(a,b,c,x,y))/h gy = (fc(a+h,b,c,x,y+h)-fc(a,b,c,x,y))/h print(ga) print(gb) print(gc) print(gx) print(gy) # * gate print() print("* gate") a = u(11.0,0.0) b = u(22.0,0.0) mg1 = mg() r1 = mg1.f(a,b) r1.grad = 1.0 mg1.b() da = mg1.u0.grad; print(da) db = mg1.u1.grad; print(db) print('------') # + gate print("+ gate") a = u(11.0,0.0) b = u(22.0,0.0) ag1 = ag() r1 = ag1.f(a,b) r1.grad = 1.0 ag1.b() da = ag1.u0.grad; print(da) db = ag1.u1.grad; print(db) print('------') # + gate, 3var print("+ gate, 3th var") #input def a = u(11.0,0.0) b = u(22.0,0.0) c = u(33.0,0.0) #gate def ag1 = ag() ag2 = ag() #cal f r1 = ag1.f(a,b) r2 = ag2.f(r1,c) #cal b r2.grad = 1.0 ag2.b() #r1.grad = ag2.u0.grad ag1.b() #print derivative dc = ag2.u0.grad; print(dc) db = ag1.u1.grad; print(db) da = ag1.u0.grad; print(da) print('------') # mixed gate print("mixed gate") #input def a = u(1.0,0.0) b = u(2.0,0.0) c = u(3.0,0.0) #gate def mg1 = mg() ag1 = ag() #cal f r1 = mg1.f(a,b) r2 = ag1.f(r1,c) #cal b r2.grad = 1.0 ag1.b() #r1.grad = ag1.u0.grad mg1.b() #print derivative dc = ag1.u0.grad; print(dc) db = mg1.u1.grad; print(db) da = mg1.u0.grad; print(da) print('------') # square gate print("square gate") #input def a = u(11.0,0.0) #gate def s1 = sqg() #cal f r1 = s1.f(a) #cal b r1.grad = 1.0 s1.b() #print derivative da = s1.u0.grad; print(da) print('------') # single neuron,ax+by+c print("single neuron,ax+by+c") #input def a = u(1.0,0.0) b = u(2.0,0.0) c = u(3.0,0.0) x = u(4.0,0.0) y = u(5.0,0.0) #gate def mg1 = mg() mg2 = mg() ag1 = ag() ag2 = ag() sg1 = sg() #cal f r1 = mg1.f(a,x) r2 = mg2.f(b,y) r3 = ag1.f(r1,r2) r4 = ag2.f(r3,c) r5 = sg1.f(r4) #cal b r5.grad = 1.0 sg1.b() #r4.grad = sg1.u0.grad ag2.b() #r3.grad = ag2.u0.grad ag1.b() #r2.grad = ag1.u1.grad mg2.b() #r1.grad = ag1.u0.grad mg1.b() #print derivative da = mg1.u0.grad; print(da) db = mg2.u0.grad; print(db) dc = ag2.u1.grad; print(dc) dx = mg1.u1.grad; print(dx) dy = mg2.u1.grad; print(dy) print('------') # Math.pow(((a*b+c),2); print("Math.pow(((a*b+c),2) gate") #input def a = u(3.0,0.0) b = u(2.0,0.0) c = u(1.0,0.0) #gate def mg1 = mg() ag1 = ag() sq1 = sqg() #cal f r1 = mg1.f(a,b) r2 = ag1.f(r1,c) r3 = sq1.f(r2) #cal b r3.grad = 1.0 sq1.b() ag1.b() mg1.b() #print derivative da = mg1.u0.grad; print(da) db = mg1.u1.grad; print(db) dc = ag1.u1.grad; print(dc) print('------') # division gate print("division gate") #input def a = u(3.0,0.0) #gate def dg1 = dg() #cal f r1 = dg1.f(a) #cal b r1.grad = 1.0 dg1.b() #print derivative da = dg1.u0.grad; print(da) print('------') # max gate print("max gate") #input def a = u(1.0,0.0) b = u(2.0,0.0) #gate def mag1 = mag() #cal f r1 = mag1.f(a,b) #cal b r1.grad = 1.0 mag1.b() #print derivative da = mag1.u0.grad; print(da) db = mag1.u1.grad; print(db) print('------') # ReLU gate print("ReLU gate") #input def a = u(1.0,0.0) #gate def rg1 = rg() #cal f r1 = rg1.f(a) #cal b r1.grad = 1.0 rg1.b() #print derivative da = rg1.u0.grad; print(da) print('------') # mixed gate, (a+b)/(c+d) print("mixed gate, (a+b)/(c+d)") #input def a = u(1.0,0.0) b = u(2.0,0.0) c = u(3.0,0.0) d = u(4.0,0.0) #gate def ag1 = ag() ag2 = ag() dg1 = dg() mg1 = mg() #cal f r1 = ag1.f(a,b) r2 = ag2.f(c,d) r3 = dg1.f(r2) r4 = mg1.f(r1,r3) #cal b r4.grad = 1.0 mg1.b() dg1.b() ag1.b() ag2.b() #print derivative da = ag1.u0.grad; print(da) db = ag1.u1.grad; print(db) dc = ag2.u0.grad; print(dc) dd = ag2.u1.grad; print(dd) print('------')