two_layer_neural_network

Source: https://github.com/jcjohnson/pytorch-examples#pytorch-nn

In this example we use the torch nn package to implement our two-layer network:

In R

Select device

library(rTorch)

device = torch$device('cpu')

# device = torch.device('cuda') # Uncomment this to run on GPU

 N is batch size; 
 D_in is input dimension;
 H is hidden dimension; 
 D_out is output dimension.

Create datasets

torch$manual_seed(0)
#> <torch._C.Generator>

N <- 64L; D_in <- 1000L; H <- 100L; D_out <- 10L

# Create random Tensors to hold inputs and outputs
x = torch$randn(N, D_in, device=device)
y = torch$randn(N, D_out, device=device)

Define the model

Use the nn package to define our model as a sequence of layers. nn.Sequential is a Module which contains other Modules, and applies them in sequence to produce its output. Each Linear Module computes output from input using a linear function, and holds internal Tensors for its weight and bias. After constructing the model we use the .to() method to move it to the desired device.

model = torch$nn$Sequential(
          torch$nn$Linear(D_in, H),
          torch$nn$ReLU(),
          torch$nn$Linear(H, D_out))$to(device)

Loss function

The nn package also contains definitions of popular loss functions; in this case we will use Mean Squared Error (MSE) as our loss function. Setting reduction='sum' means that we are computing the sum of squared errors rather than the mean; this is for consistency with the examples above where we manually compute the loss, but in practice it is more common to use mean squared error as a loss by setting reduction='elementwise_mean'.

loss_fn = torch$nn$MSELoss(reduction = 'sum')

Iterate through batches

learning_rate = 1e-4

for (t in 1:500) {
  # Forward pass: compute predicted y by passing x to the model. Module objects
  # override the __call__ operator so you can call them like functions. When
  # doing so you pass a Tensor of input data to the Module and it produces
  # a Tensor of output data.
  y_pred = model(x)

  # Compute and print loss. We pass Tensors containing the predicted and true
  # values of y, and the loss function returns a Tensor containing the loss.
  loss = loss_fn(y_pred, y)
  
  cat(t, "\t")
  cat(loss$item(), "\n")
  
  # Zero the gradients before running the backward pass.
  model$zero_grad()

  # Backward pass: compute gradient of the loss with respect to all the learnable
  # parameters of the model. Internally, the parameters of each Module are stored
  # in Tensors with requires_grad=True, so this call will compute gradients for
  # all learnable parameters in the model.
  loss$backward()

  # Update the weights using gradient descent. Each parameter is a Tensor, so
  # we can access its data and gradients like we did before.
  with(torch$no_grad(), {
      for (param in iterate(model$parameters())) {
        # in Python this code is much simpler. In R we have to do some conversions
        
        # param$data <- torch$sub(param$data,
        #                         torch$mul(param$grad$float(),
        #                           torch$scalar_tensor(learning_rate)))
        
        param$data <- param$data - param$grad * learning_rate
      }
   })
}  
#> 1    628.2839 
#> 2    584.9592 
#> 3    546.728 
#> 4    512.6885 
#> 5    482.1306 
#> 6    454.6265 
#> 7    429.5551 
#> 8    406.399 
#> 9    384.6441 
#> 10   364.3125 
#> 11   345.3866 
#> 12   327.6258 
#> 13   310.8002 
#> 14   294.8379 
#> 15   279.7325 
#> 16   265.308 
#> 17   251.6231 
#> 18   238.5361 
#> 19   226.0232 
#> 20   214.1025 
#> 21   202.7003 
#> 22   191.8059 
#> 23   181.4473 
#> 24   171.5948 
#> 25   162.2114 
#> 26   153.2922 
#> 27   144.8526 
#> 28   136.86 
#> 29   129.2786 
#> 30   122.0849 
#> 31   115.2736 
#> 32   108.8145 
#> 33   102.702 
#> 34   96.9281 
#> 35   91.47466 
#> 36   86.3278 
#> 37   81.47502 
#> 38   76.89146 
#> 39   72.56895 
#> 40   68.47774 
#> 41   64.62608 
#> 42   60.99714 
#> 43   57.56915 
#> 44   54.3427 
#> 45   51.30913 
#> 46   48.4516 
#> 47   45.7645 
#> 48   43.2405 
#> 49   40.86606 
#> 50   38.63006 
#> 51   36.52527 
#> 52   34.54914 
#> 53   32.69345 
#> 54   30.9498 
#> 55   29.30734 
#> 56   27.76275 
#> 57   26.31089 
#> 58   24.9431 
#> 59   23.6538 
#> 60   22.43881 
#> 61   21.29258 
#> 62   20.21278 
#> 63   19.19288 
#> 64   18.23302 
#> 65   17.32939 
#> 66   16.47696 
#> 67   15.67115 
#> 68   14.90951 
#> 69   14.19054 
#> 70   13.51087 
#> 71   12.86819 
#> 72   12.26046 
#> 73   11.68514 
#> 74   11.14105 
#> 75   10.62579 
#> 76   10.13727 
#> 77   9.67443 
#> 78   9.235745 
#> 79   8.81936 
#> 80   8.423415 
#> 81   8.047976 
#> 82   7.691305 
#> 83   7.352424 
#> 84   7.030395 
#> 85   6.724676 
#> 86   6.434433 
#> 87   6.158278 
#> 88   5.895441 
#> 89   5.645772 
#> 90   5.408593 
#> 91   5.182788 
#> 92   4.967783 
#> 93   4.762821 
#> 94   4.567942 
#> 95   4.381676 
#> 96   4.203955 
#> 97   4.034254 
#> 98   3.872373 
#> 99   3.717669 
#> 100  3.569852 
#> 101  3.42879 
#> 102  3.293934 
#> 103  3.165006 
#> 104  3.041733 
#> 105  2.923832 
#> 106  2.810992 
#> 107  2.702966 
#> 108  2.599546 
#> 109  2.500533 
#> 110  2.405609 
#> 111  2.314677 
#> 112  2.227567 
#> 113  2.143984 
#> 114  2.063824 
#> 115  1.986898 
#> 116  1.913161 
#> 117  1.842398 
#> 118  1.77456 
#> 119  1.709334 
#> 120  1.64675 
#> 121  1.586662 
#> 122  1.528932 
#> 123  1.473498 
#> 124  1.420194 
#> 125  1.369045 
#> 126  1.319939 
#> 127  1.272713 
#> 128  1.227352 
#> 129  1.183716 
#> 130  1.141713 
#> 131  1.101289 
#> 132  1.062379 
#> 133  1.024975 
#> 134  0.9889802 
#> 135  0.9543175 
#> 136  0.9209599 
#> 137  0.8888108 
#> 138  0.8578573 
#> 139  0.828075 
#> 140  0.7993811 
#> 141  0.7717422 
#> 142  0.7451235 
#> 143  0.7194628 
#> 144  0.6947174 
#> 145  0.6708718 
#> 146  0.6479479 
#> 147  0.6259133 
#> 148  0.6046655 
#> 149  0.5841969 
#> 150  0.5644467 
#> 151  0.5453879 
#> 152  0.5270226 
#> 153  0.509312 
#> 154  0.4922202 
#> 155  0.4757309 
#> 156  0.4598286 
#> 157  0.444492 
#> 158  0.4296912 
#> 159  0.4153878 
#> 160  0.4015924 
#> 161  0.3882794 
#> 162  0.3754345 
#> 163  0.3630294 
#> 164  0.3510535 
#> 165  0.3394946 
#> 166  0.3283299 
#> 167  0.3175527 
#> 168  0.3071378 
#> 169  0.2970789 
#> 170  0.2873671 
#> 171  0.2779845 
#> 172  0.2689149 
#> 173  0.2601575 
#> 174  0.2516952 
#> 175  0.2435159 
#> 176  0.2356067 
#> 177  0.2279707 
#> 178  0.2206163 
#> 179  0.2135031 
#> 180  0.2066278 
#> 181  0.199988 
#> 182  0.1935741 
#> 183  0.1873666 
#> 184  0.1813661 
#> 185  0.1755629 
#> 186  0.1699517 
#> 187  0.1645233 
#> 188  0.1592781 
#> 189  0.1542067 
#> 190  0.149301 
#> 191  0.1445545 
#> 192  0.1399648 
#> 193  0.1355246 
#> 194  0.1312279 
#> 195  0.1270718 
#> 196  0.1230509 
#> 197  0.1191625 
#> 198  0.115399 
#> 199  0.1117588 
#> 200  0.1082348 
#> 201  0.1048254 
#> 202  0.1015256 
#> 203  0.09833349 
#> 204  0.09524446 
#> 205  0.0922533 
#> 206  0.08935806 
#> 207  0.08655693 
#> 208  0.08384982 
#> 209  0.081232 
#> 210  0.07869583 
#> 211  0.07624327 
#> 212  0.0738695 
#> 213  0.07157086 
#> 214  0.06934651 
#> 215  0.0671912 
#> 216  0.06510548 
#> 217  0.0630878 
#> 218  0.0611335 
#> 219  0.05924014 
#> 220  0.05740607 
#> 221  0.05563042 
#> 222  0.05391053 
#> 223  0.05224558 
#> 224  0.05063397 
#> 225  0.04907332 
#> 226  0.04756238 
#> 227  0.04609917 
#> 228  0.0446822 
#> 229  0.04330759 
#> 230  0.04197593 
#> 231  0.04068634 
#> 232  0.03943768 
#> 233  0.03822812 
#> 234  0.0370564 
#> 235  0.03592146 
#> 236  0.03482136 
#> 237  0.03375633 
#> 238  0.0327246 
#> 239  0.03172487 
#> 240  0.03075593 
#> 241  0.02981687 
#> 242  0.02890735 
#> 243  0.02802622 
#> 244  0.02717285 
#> 245  0.02634558 
#> 246  0.02554371 
#> 247  0.02476675 
#> 248  0.0240143 
#> 249  0.02328515 
#> 250  0.02257836 
#> 251  0.02189306 
#> 252  0.02122923 
#> 253  0.02058575 
#> 254  0.01996238 
#> 255  0.01935788 
#> 256  0.01877213 
#> 257  0.01820429 
#> 258  0.01765402 
#> 259  0.01712051 
#> 260  0.01660351 
#> 261  0.01610242 
#> 262  0.0156171 
#> 263  0.01514632 
#> 264  0.01469009 
#> 265  0.01424752 
#> 266  0.01381863 
#> 267  0.01340292 
#> 268  0.01299987 
#> 269  0.01260905 
#> 270  0.01223013 
#> 271  0.01186274 
#> 272  0.01150682 
#> 273  0.0111617 
#> 274  0.01082683 
#> 275  0.01050223 
#> 276  0.01018802 
#> 277  0.009882836 
#> 278  0.009586995 
#> 279  0.009300183 
#> 280  0.009021979 
#> 281  0.008752229 
#> 282  0.008490788 
#> 283  0.008237117 
#> 284  0.007991165 
#> 285  0.007752791 
#> 286  0.007521485 
#> 287  0.00729729 
#> 288  0.0070798 
#> 289  0.006868829 
#> 290  0.006664461 
#> 291  0.006466233 
#> 292  0.006273943 
#> 293  0.006087383 
#> 294  0.005906438 
#> 295  0.005730878 
#> 296  0.005560733 
#> 297  0.005395614 
#> 298  0.005235502 
#> 299  0.005080266 
#> 300  0.004929713 
#> 301  0.004783633 
#> 302  0.004641939 
#> 303  0.004504489 
#> 304  0.004371175 
#> 305  0.004241788 
#> 306  0.004116328 
#> 307  0.003994633 
#> 308  0.003876575 
#> 309  0.003762146 
#> 310  0.003650998 
#> 311  0.003543299 
#> 312  0.003438761 
#> 313  0.003337309 
#> 314  0.003238867 
#> 315  0.0031434 
#> 316  0.003050815 
#> 317  0.002960989 
#> 318  0.002873863 
#> 319  0.002789256 
#> 320  0.002707202 
#> 321  0.002627575 
#> 322  0.002550329 
#> 323  0.002475383 
#> 324  0.002402639 
#> 325  0.002332083 
#> 326  0.002263665 
#> 327  0.002197253 
#> 328  0.0021328 
#> 329  0.002070281 
#> 330  0.002009582 
#> 331  0.001950708 
#> 332  0.001893577 
#> 333  0.001838136 
#> 334  0.001784306 
#> 335  0.001732112 
#> 336  0.001681432 
#> 337  0.0016323 
#> 338  0.001584614 
#> 339  0.001538318 
#> 340  0.00149336 
#> 341  0.001449755 
#> 342  0.001407453 
#> 343  0.001366422 
#> 344  0.001326558 
#> 345  0.001287868 
#> 346  0.001250318 
#> 347  0.001213876 
#> 348  0.00117851 
#> 349  0.0011442 
#> 350  0.001110891 
#> 351  0.001078564 
#> 352  0.001047205 
#> 353  0.001016748 
#> 354  0.000987183 
#> 355  0.0009584787 
#> 356  0.0009306203 
#> 357  0.0009035908 
#> 358  0.0008773552 
#> 359  0.0008518948 
#> 360  0.0008271908 
#> 361  0.0008032027 
#> 362  0.0007798997 
#> 363  0.0007572919 
#> 364  0.0007353517 
#> 365  0.0007140448 
#> 366  0.0006933782 
#> 367  0.0006733016 
#> 368  0.0006538091 
#> 369  0.0006348886 
#> 370  0.0006165295 
#> 371  0.0005986958 
#> 372  0.0005813859 
#> 373  0.0005645752 
#> 374  0.0005482732 
#> 375  0.0005324451 
#> 376  0.0005170752 
#> 377  0.00050215 
#> 378  0.0004876566 
#> 379  0.0004735905 
#> 380  0.0004599217 
#> 381  0.000446661 
#> 382  0.0004337932 
#> 383  0.000421295 
#> 384  0.000409168 
#> 385  0.000397383 
#> 386  0.0003859476 
#> 387  0.0003748359 
#> 388  0.000364068 
#> 389  0.0003535805 
#> 390  0.0003434142 
#> 391  0.0003335507 
#> 392  0.0003239612 
#> 393  0.0003146584 
#> 394  0.0003056151 
#> 395  0.0002968509 
#> 396  0.0002883257 
#> 397  0.0002800551 
#> 398  0.0002720189 
#> 399  0.000264218 
#> 400  0.0002566472 
#> 401  0.0002492882 
#> 402  0.0002421443 
#> 403  0.0002352033 
#> 404  0.000228468 
#> 405  0.000221927 
#> 406  0.0002155735 
#> 407  0.000209406 
#> 408  0.0002034151 
#> 409  0.0001976036 
#> 410  0.0001919538 
#> 411  0.000186465 
#> 412  0.000181138 
#> 413  0.0001759652 
#> 414  0.0001709464 
#> 415  0.0001660616 
#> 416  0.0001613203 
#> 417  0.0001567196 
#> 418  0.0001522457 
#> 419  0.0001479028 
#> 420  0.0001436849 
#> 421  0.0001395875 
#> 422  0.0001356086 
#> 423  0.0001317492 
#> 424  0.0001279981 
#> 425  0.0001243516 
#> 426  0.0001208117 
#> 427  0.0001173674 
#> 428  0.0001140324 
#> 429  0.0001107887 
#> 430  0.0001076371 
#> 431  0.000104577 
#> 432  0.0001016119 
#> 433  9.872603e-05 
#> 434  9.591727e-05 
#> 435  9.320263e-05 
#> 436  9.055879e-05 
#> 437  8.798708e-05 
#> 438  8.549038e-05 
#> 439  8.306588e-05 
#> 440  8.071403e-05 
#> 441  7.842657e-05 
#> 442  7.62079e-05 
#> 443  7.40515e-05 
#> 444  7.195051e-05 
#> 445  6.991543e-05 
#> 446  6.79373e-05 
#> 447  6.601425e-05 
#> 448  6.414913e-05 
#> 449  6.233487e-05 
#> 450  6.057473e-05 
#> 451  5.886107e-05 
#> 452  5.719856e-05 
#> 453  5.558319e-05 
#> 454  5.401246e-05 
#> 455  5.24875e-05 
#> 456  5.100614e-05 
#> 457  4.957083e-05 
#> 458  4.817137e-05 
#> 459  4.681194e-05 
#> 460  4.549512e-05 
#> 461  4.420892e-05 
#> 462  4.296327e-05 
#> 463  4.175395e-05 
#> 464  4.057565e-05 
#> 465  3.943508e-05 
#> 466  3.832371e-05 
#> 467  3.724535e-05 
#> 468  3.619579e-05 
#> 469  3.517841e-05 
#> 470  3.419127e-05 
#> 471  3.322741e-05 
#> 472  3.229243e-05 
#> 473  3.138653e-05 
#> 474  3.050298e-05 
#> 475  2.964781e-05 
#> 476  2.881304e-05 
#> 477  2.800681e-05 
#> 478  2.721956e-05 
#> 479  2.645602e-05 
#> 480  2.57129e-05 
#> 481  2.499174e-05 
#> 482  2.429051e-05 
#> 483  2.361012e-05 
#> 484  2.294818e-05 
#> 485  2.230642e-05 
#> 486  2.167962e-05 
#> 487  2.107264e-05 
#> 488  2.048336e-05 
#> 489  1.991114e-05 
#> 490  1.935353e-05 
#> 491  1.88103e-05 
#> 492  1.82841e-05 
#> 493  1.777284e-05 
#> 494  1.727619e-05 
#> 495  1.67922e-05 
#> 496  1.632309e-05 
#> 497  1.586889e-05 
#> 498  1.54238e-05 
#> 499  1.499398e-05 
#> 500  1.457493e-05

These two expression are equivalent, with the first being the long version natural way of doing it in PyTorch. The second is using the generics in R for subtraction, multiplication and scalar conversion.

param$data <- torch$sub(param$data,
                        torch$mul(param$grad$float(),
                          torch$scalar_tensor(learning_rate)))
}

param$data <- param$data - param$grad * learning_rate