Mac Sync
This commit is contained in:
unlockable
@@ -1,56 +1,56 @@
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Epoch 01: loss = inf
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Epoch 02: loss = inf
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Epoch 03: loss = 6.678
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Epoch 04: loss = 4.361
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Epoch 05: loss = 3.110
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Epoch 06: loss = 2.099
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Epoch 07: loss = 1.698
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Epoch 08: loss = 1.320
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Epoch 09: loss = 0.970
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Epoch 10: loss = 0.891
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Epoch 10: validation accuracy = 66.0%
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Epoch 11: loss = 0.817
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Epoch 12: loss = 0.723
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Epoch 13: loss = 0.512
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Epoch 14: loss = 0.353
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Epoch 15: loss = 0.202
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Epoch 16: loss = 0.182
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Epoch 17: loss = 0.184
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Epoch 18: loss = 0.191
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Epoch 19: loss = 0.175
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Epoch 20: loss = 0.166
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Epoch 20: validation accuracy = 68.0%
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Epoch 21: loss = 0.146
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Epoch 22: loss = 0.105
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Epoch 23: loss = 0.109
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Epoch 24: loss = 0.074
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Epoch 25: loss = 0.097
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Epoch 26: loss = 0.047
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Epoch 27: loss = 0.038
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Epoch 28: loss = 0.037
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Epoch 29: loss = 0.024
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Epoch 30: loss = 0.021
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Epoch 30: validation accuracy = 68.8%
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Epoch 31: loss = 0.019
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Epoch 32: loss = 0.024
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Epoch 33: loss = 0.023
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Epoch 34: loss = 0.014
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Epoch 35: loss = 0.013
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Epoch 36: loss = 0.012
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Epoch 37: loss = 0.011
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Epoch 38: loss = 0.013
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Epoch 39: loss = 0.013
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Epoch 40: loss = 0.016
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Epoch 40: validation accuracy = 70.5%
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Epoch 41: loss = 0.015
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Epoch 42: loss = 0.009
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Epoch 43: loss = 0.011
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Epoch 44: loss = 0.008
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Epoch 45: loss = 0.008
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Epoch 46: loss = 0.010
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Epoch 47: loss = 0.009
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Epoch 48: loss = 0.007
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Epoch 49: loss = 0.007
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Epoch 50: loss = 0.010
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Epoch 50: validation accuracy = 70.5%
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Epoch 01: loss = inf
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Epoch 02: loss = inf
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Epoch 03: loss = 6.678
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Epoch 04: loss = 4.361
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Epoch 05: loss = 3.110
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Epoch 06: loss = 2.099
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Epoch 07: loss = 1.698
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Epoch 08: loss = 1.320
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Epoch 09: loss = 0.970
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Epoch 10: loss = 0.891
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Epoch 10: validation accuracy = 66.0%
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Epoch 11: loss = 0.817
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Epoch 12: loss = 0.723
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Epoch 13: loss = 0.512
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Epoch 14: loss = 0.353
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Epoch 15: loss = 0.202
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Epoch 16: loss = 0.182
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Epoch 17: loss = 0.184
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Epoch 18: loss = 0.191
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Epoch 19: loss = 0.175
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Epoch 20: loss = 0.166
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Epoch 20: validation accuracy = 68.0%
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Epoch 21: loss = 0.146
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Epoch 22: loss = 0.105
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Epoch 23: loss = 0.109
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Epoch 24: loss = 0.074
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Epoch 25: loss = 0.097
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Epoch 26: loss = 0.047
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Epoch 27: loss = 0.038
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Epoch 28: loss = 0.037
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Epoch 29: loss = 0.024
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Epoch 30: loss = 0.021
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Epoch 30: validation accuracy = 68.8%
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Epoch 31: loss = 0.019
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Epoch 32: loss = 0.024
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Epoch 33: loss = 0.023
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Epoch 34: loss = 0.014
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Epoch 35: loss = 0.013
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Epoch 36: loss = 0.012
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Epoch 37: loss = 0.011
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Epoch 38: loss = 0.013
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Epoch 39: loss = 0.013
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Epoch 40: loss = 0.016
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Epoch 40: validation accuracy = 70.5%
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Epoch 41: loss = 0.015
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Epoch 42: loss = 0.009
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Epoch 43: loss = 0.011
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Epoch 44: loss = 0.008
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Epoch 45: loss = 0.008
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Epoch 46: loss = 0.010
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Epoch 47: loss = 0.009
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Epoch 48: loss = 0.007
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Epoch 49: loss = 0.007
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Epoch 50: loss = 0.010
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Epoch 50: validation accuracy = 70.5%
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Model saved in ./saved_models/default.pth
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@@ -1,2 +1,2 @@
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[Info] Load model from .\saved_models\default.pth
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[Info] Load model from .\saved_models\default.pth
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[Info] Test accuracy = 72.0%
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@@ -1,2 +1,2 @@
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[Info] Load model from .\saved_models\adam_optim.pth
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[Info] Load model from .\saved_models\adam_optim.pth
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[Info] Test accuracy = 85.0%
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@@ -1,56 +1,56 @@
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Epoch 01: loss = inf
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Epoch 02: loss = inf
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Epoch 03: loss = inf
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Epoch 04: loss = inf
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Epoch 05: loss = inf
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Epoch 06: loss = inf
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Epoch 07: loss = inf
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Epoch 08: loss = inf
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Epoch 09: loss = 3.250
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Epoch 10: loss = 2.567
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Epoch 10: validation accuracy = 59.0%
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Epoch 11: loss = 1.963
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Epoch 12: loss = 1.558
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Epoch 13: loss = 1.320
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Epoch 14: loss = 0.911
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Epoch 15: loss = 0.808
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Epoch 16: loss = 0.932
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Epoch 17: loss = 0.861
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Epoch 18: loss = 0.748
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Epoch 19: loss = 0.783
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Epoch 20: loss = 0.809
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Epoch 20: validation accuracy = 65.5%
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Epoch 21: loss = 0.678
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Epoch 22: loss = 0.757
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Epoch 23: loss = 0.747
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Epoch 24: loss = 0.660
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Epoch 25: loss = 0.536
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Epoch 26: loss = 0.506
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Epoch 27: loss = 0.577
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Epoch 28: loss = 0.600
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Epoch 29: loss = 0.681
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Epoch 30: loss = 0.604
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Epoch 30: validation accuracy = 68.0%
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Epoch 31: loss = 0.552
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Epoch 32: loss = 0.671
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Epoch 33: loss = 0.604
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Epoch 34: loss = 0.600
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Epoch 35: loss = 0.818
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Epoch 36: loss = 0.659
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Epoch 37: loss = 0.375
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Epoch 38: loss = 0.380
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Epoch 39: loss = 0.418
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Epoch 40: loss = 0.431
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Epoch 40: validation accuracy = 73.5%
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Epoch 41: loss = 0.551
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Epoch 42: loss = 0.488
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Epoch 43: loss = 0.350
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Epoch 44: loss = 0.287
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Epoch 45: loss = 0.294
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Epoch 46: loss = 0.463
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Epoch 47: loss = 0.438
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Epoch 48: loss = 0.392
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Epoch 49: loss = 0.325
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Epoch 50: loss = 0.332
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Epoch 50: validation accuracy = 80.8%
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Epoch 01: loss = inf
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Epoch 02: loss = inf
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Epoch 03: loss = inf
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Epoch 04: loss = inf
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Epoch 05: loss = inf
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Epoch 06: loss = inf
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Epoch 07: loss = inf
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Epoch 08: loss = inf
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Epoch 09: loss = 3.250
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Epoch 10: loss = 2.567
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Epoch 10: validation accuracy = 59.0%
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Epoch 11: loss = 1.963
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Epoch 12: loss = 1.558
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Epoch 13: loss = 1.320
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Epoch 14: loss = 0.911
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Epoch 15: loss = 0.808
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Epoch 16: loss = 0.932
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Epoch 17: loss = 0.861
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Epoch 18: loss = 0.748
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Epoch 19: loss = 0.783
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Epoch 20: loss = 0.809
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Epoch 20: validation accuracy = 65.5%
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Epoch 21: loss = 0.678
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Epoch 22: loss = 0.757
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Epoch 23: loss = 0.747
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Epoch 24: loss = 0.660
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Epoch 25: loss = 0.536
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Epoch 26: loss = 0.506
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Epoch 27: loss = 0.577
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Epoch 28: loss = 0.600
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Epoch 29: loss = 0.681
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Epoch 30: loss = 0.604
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Epoch 30: validation accuracy = 68.0%
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Epoch 31: loss = 0.552
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Epoch 32: loss = 0.671
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Epoch 33: loss = 0.604
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Epoch 34: loss = 0.600
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Epoch 35: loss = 0.818
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Epoch 36: loss = 0.659
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Epoch 37: loss = 0.375
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Epoch 38: loss = 0.380
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Epoch 39: loss = 0.418
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Epoch 40: loss = 0.431
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Epoch 40: validation accuracy = 73.5%
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Epoch 41: loss = 0.551
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Epoch 42: loss = 0.488
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Epoch 43: loss = 0.350
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Epoch 44: loss = 0.287
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Epoch 45: loss = 0.294
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Epoch 46: loss = 0.463
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Epoch 47: loss = 0.438
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Epoch 48: loss = 0.392
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Epoch 49: loss = 0.325
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Epoch 50: loss = 0.332
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Epoch 50: validation accuracy = 80.8%
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Model saved in .\saved_models\adam_optim_cuda.pth
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@@ -1,2 +1,2 @@
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[Info] Load model from .\saved_models\adam_optim_lr1e-3_epoch100_momentum10.pth
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[Info] Load model from .\saved_models\adam_optim_lr1e-3_epoch100_momentum10.pth
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[Info] Test accuracy = 88.8%
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@@ -1,111 +1,111 @@
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Epoch 01: loss = inf
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Epoch 02: loss = inf
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Epoch 03: loss = inf
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Epoch 04: loss = inf
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Epoch 05: loss = inf
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Epoch 06: loss = inf
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Epoch 07: loss = inf
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Epoch 08: loss = inf
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Epoch 09: loss = inf
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Epoch 10: loss = inf
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Epoch 10: validation accuracy = 40.2%
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Epoch 11: loss = inf
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Epoch 12: loss = inf
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Epoch 13: loss = inf
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Epoch 14: loss = inf
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Epoch 15: loss = inf
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Epoch 16: loss = inf
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Epoch 17: loss = 2.360
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Epoch 18: loss = 2.086
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Epoch 19: loss = 1.684
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Epoch 20: loss = 1.453
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Epoch 20: validation accuracy = 53.0%
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Epoch 21: loss = 1.174
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Epoch 22: loss = 1.046
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Epoch 23: loss = 0.859
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Epoch 24: loss = 0.740
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Epoch 25: loss = 0.663
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Epoch 26: loss = 0.495
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Epoch 27: loss = 0.566
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Epoch 28: loss = 0.521
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Epoch 29: loss = 0.470
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Epoch 30: loss = 0.363
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Epoch 30: validation accuracy = 59.0%
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Epoch 31: loss = 0.365
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Epoch 32: loss = 0.305
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Epoch 33: loss = 0.333
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Epoch 34: loss = 0.293
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Epoch 35: loss = 0.191
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Epoch 36: loss = 0.295
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Epoch 37: loss = 0.275
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Epoch 38: loss = 0.461
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Epoch 39: loss = 0.509
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Epoch 40: loss = 0.298
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Epoch 40: validation accuracy = 65.2%
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Epoch 41: loss = 0.186
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Epoch 42: loss = 0.395
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Epoch 43: loss = 0.323
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Epoch 44: loss = 0.309
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Epoch 45: loss = 0.199
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Epoch 46: loss = 0.285
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Epoch 47: loss = 0.290
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Epoch 48: loss = 0.302
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Epoch 49: loss = 0.235
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Epoch 50: loss = 0.190
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Epoch 50: validation accuracy = 71.2%
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Epoch 51: loss = 0.294
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Epoch 52: loss = 0.311
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Epoch 53: loss = 0.254
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Epoch 54: loss = 0.289
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Epoch 55: loss = 0.264
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Epoch 56: loss = 0.213
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Epoch 57: loss = 0.166
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Epoch 58: loss = 0.218
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Epoch 59: loss = 0.231
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Epoch 60: loss = 0.283
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Epoch 60: validation accuracy = 74.8%
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Epoch 61: loss = 0.324
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Epoch 62: loss = 0.245
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Epoch 63: loss = 0.277
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Epoch 64: loss = 0.286
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Epoch 65: loss = 0.255
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Epoch 66: loss = 0.263
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Epoch 67: loss = 0.272
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Epoch 68: loss = 0.272
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Epoch 69: loss = 0.260
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Epoch 70: loss = 0.271
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Epoch 70: validation accuracy = 79.0%
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Epoch 71: loss = 0.310
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Epoch 72: loss = 0.301
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Epoch 73: loss = 0.305
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Epoch 74: loss = 0.311
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Epoch 75: loss = 0.329
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Epoch 76: loss = 0.295
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Epoch 77: loss = 0.300
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Epoch 78: loss = 0.316
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Epoch 79: loss = 0.326
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Epoch 80: loss = 0.352
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Epoch 80: validation accuracy = 77.5%
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Epoch 81: loss = 0.344
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Epoch 82: loss = 0.326
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Epoch 83: loss = 0.326
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Epoch 84: loss = 0.335
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Epoch 85: loss = 0.342
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Epoch 86: loss = 0.361
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Epoch 87: loss = 0.337
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Epoch 88: loss = 0.339
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Epoch 89: loss = 0.339
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Epoch 90: loss = 0.341
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Epoch 90: validation accuracy = 82.8%
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Epoch 91: loss = 0.350
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Epoch 92: loss = 0.359
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Epoch 93: loss = 0.352
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Epoch 94: loss = 0.363
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Epoch 95: loss = 0.347
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Epoch 96: loss = 0.341
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Epoch 97: loss = 0.336
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Epoch 98: loss = 0.348
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Epoch 99: loss = 0.365
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Epoch 100: loss = 0.350
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Epoch 100: validation accuracy = 85.2%
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Epoch 01: loss = inf
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Epoch 02: loss = inf
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Epoch 03: loss = inf
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Epoch 04: loss = inf
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Epoch 05: loss = inf
|
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Epoch 06: loss = inf
|
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Epoch 07: loss = inf
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Epoch 08: loss = inf
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Epoch 09: loss = inf
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Epoch 10: loss = inf
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Epoch 10: validation accuracy = 40.2%
|
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Epoch 11: loss = inf
|
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Epoch 12: loss = inf
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Epoch 13: loss = inf
|
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Epoch 14: loss = inf
|
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Epoch 15: loss = inf
|
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Epoch 16: loss = inf
|
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Epoch 17: loss = 2.360
|
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Epoch 18: loss = 2.086
|
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Epoch 19: loss = 1.684
|
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Epoch 20: loss = 1.453
|
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Epoch 20: validation accuracy = 53.0%
|
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Epoch 21: loss = 1.174
|
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Epoch 22: loss = 1.046
|
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Epoch 23: loss = 0.859
|
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Epoch 24: loss = 0.740
|
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Epoch 25: loss = 0.663
|
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Epoch 26: loss = 0.495
|
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Epoch 27: loss = 0.566
|
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Epoch 28: loss = 0.521
|
||||
Epoch 29: loss = 0.470
|
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Epoch 30: loss = 0.363
|
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Epoch 30: validation accuracy = 59.0%
|
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Epoch 31: loss = 0.365
|
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Epoch 32: loss = 0.305
|
||||
Epoch 33: loss = 0.333
|
||||
Epoch 34: loss = 0.293
|
||||
Epoch 35: loss = 0.191
|
||||
Epoch 36: loss = 0.295
|
||||
Epoch 37: loss = 0.275
|
||||
Epoch 38: loss = 0.461
|
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Epoch 39: loss = 0.509
|
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Epoch 40: loss = 0.298
|
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Epoch 40: validation accuracy = 65.2%
|
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Epoch 41: loss = 0.186
|
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Epoch 42: loss = 0.395
|
||||
Epoch 43: loss = 0.323
|
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Epoch 44: loss = 0.309
|
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Epoch 45: loss = 0.199
|
||||
Epoch 46: loss = 0.285
|
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Epoch 47: loss = 0.290
|
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Epoch 48: loss = 0.302
|
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Epoch 49: loss = 0.235
|
||||
Epoch 50: loss = 0.190
|
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Epoch 50: validation accuracy = 71.2%
|
||||
Epoch 51: loss = 0.294
|
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Epoch 52: loss = 0.311
|
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Epoch 53: loss = 0.254
|
||||
Epoch 54: loss = 0.289
|
||||
Epoch 55: loss = 0.264
|
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Epoch 56: loss = 0.213
|
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Epoch 57: loss = 0.166
|
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Epoch 58: loss = 0.218
|
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Epoch 59: loss = 0.231
|
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Epoch 60: loss = 0.283
|
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Epoch 60: validation accuracy = 74.8%
|
||||
Epoch 61: loss = 0.324
|
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Epoch 62: loss = 0.245
|
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Epoch 63: loss = 0.277
|
||||
Epoch 64: loss = 0.286
|
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Epoch 65: loss = 0.255
|
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Epoch 66: loss = 0.263
|
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Epoch 67: loss = 0.272
|
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Epoch 68: loss = 0.272
|
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Epoch 69: loss = 0.260
|
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Epoch 70: loss = 0.271
|
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Epoch 70: validation accuracy = 79.0%
|
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Epoch 71: loss = 0.310
|
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Epoch 72: loss = 0.301
|
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Epoch 73: loss = 0.305
|
||||
Epoch 74: loss = 0.311
|
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Epoch 75: loss = 0.329
|
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Epoch 76: loss = 0.295
|
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Epoch 77: loss = 0.300
|
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Epoch 78: loss = 0.316
|
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Epoch 79: loss = 0.326
|
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Epoch 80: loss = 0.352
|
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Epoch 80: validation accuracy = 77.5%
|
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Epoch 81: loss = 0.344
|
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Epoch 82: loss = 0.326
|
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Epoch 83: loss = 0.326
|
||||
Epoch 84: loss = 0.335
|
||||
Epoch 85: loss = 0.342
|
||||
Epoch 86: loss = 0.361
|
||||
Epoch 87: loss = 0.337
|
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Epoch 88: loss = 0.339
|
||||
Epoch 89: loss = 0.339
|
||||
Epoch 90: loss = 0.341
|
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Epoch 90: validation accuracy = 82.8%
|
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Epoch 91: loss = 0.350
|
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Epoch 92: loss = 0.359
|
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Epoch 93: loss = 0.352
|
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Epoch 94: loss = 0.363
|
||||
Epoch 95: loss = 0.347
|
||||
Epoch 96: loss = 0.341
|
||||
Epoch 97: loss = 0.336
|
||||
Epoch 98: loss = 0.348
|
||||
Epoch 99: loss = 0.365
|
||||
Epoch 100: loss = 0.350
|
||||
Epoch 100: validation accuracy = 85.2%
|
||||
Model saved in .\saved_models\adam_optim_lr1e-3_epoch100_momentum10.pth
|
||||
@@ -1,244 +1,244 @@
|
||||
% Homework Template
|
||||
\documentclass[a4paper]{article}
|
||||
\usepackage{ctex}
|
||||
\usepackage{amsmath, amssymb, amsthm}
|
||||
\usepackage{moreenum}
|
||||
\usepackage{mathtools}
|
||||
\usepackage{url}
|
||||
\usepackage{bm}
|
||||
\usepackage{enumitem}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{subcaption}
|
||||
\usepackage{booktabs} % toprule
|
||||
\usepackage[mathcal]{eucal}
|
||||
\usepackage[thehwcnt = 1]{iidef}
|
||||
\usepackage{listings}
|
||||
\usepackage[x11names]{xcolor}
|
||||
\usepackage{float}
|
||||
\usepackage[colorlinks, linkcolor=black, anchorcolor=green, citecolor=blue]{hyperref}
|
||||
|
||||
\DeclareMathOperator{\arctanh}{arctanh}
|
||||
% \DeclareMathOperator{\diag}{diag}
|
||||
|
||||
\setenumerate[1]{label=(\arabic{*})}
|
||||
\setenumerate[2]{label=\arabic{*})}
|
||||
|
||||
\definecolor{codekeyword}{RGB}{171, 0, 216}
|
||||
\definecolor{codetypename}{RGB}{29, 37, 251}
|
||||
\definecolor{codevariable}{RGB}{10, 23, 126}
|
||||
\definecolor{codestring}{RGB}{157, 0, 25}
|
||||
\definecolor{codecomment}{RGB}{31, 129, 19}
|
||||
|
||||
\newfontfamily\cascadia[Ligatures=ResetAll]{Cascadia Code}
|
||||
% \newfontfamily\codefont[Ligatures=ResetAll]{Cascadia Code}
|
||||
\newfontfamily\codefont[Ligatures=ResetAll]{Fira Code}[Contextuals={Alternate}]
|
||||
% To enable ligature in listing, go check lstfiracode's github page and copy firacodestyle's settings.
|
||||
|
||||
\lstset{
|
||||
basicstyle = \small\codefont,
|
||||
% ---
|
||||
tabsize = 4,
|
||||
showstringspaces = false,
|
||||
numbers = left,
|
||||
numberstyle = \cascadia,
|
||||
% ---
|
||||
breaklines = true,
|
||||
captionpos = t,
|
||||
% ---
|
||||
frame = l,
|
||||
flexiblecolumns,
|
||||
columns = fixed,
|
||||
}
|
||||
|
||||
\thecourseinstitute{清华大学电子工程系}
|
||||
\thecoursename{\textbf{媒体与认知} \space 课堂2}
|
||||
\theterm{2023-2024学年春季学期}
|
||||
\hwname{作业}
|
||||
\begin{document}
|
||||
\courseheader
|
||||
% 请在YOUR NAME处填写自己的姓名
|
||||
\name{高艺轩}
|
||||
\vspace{3mm}
|
||||
\centerline{\textbf{\Large{理论部分}}}
|
||||
|
||||
\section{单选题（15分）}
|
||||
% 请在？处填写答案
|
||||
\subsection{\underline{B}}
|
||||
|
||||
\subsection{\underline{A}}
|
||||
|
||||
\subsection{\underline{B}}
|
||||
|
||||
\subsection{\underline{A}}
|
||||
|
||||
\subsection{\underline{B}}
|
||||
|
||||
\section{计算题（15 分）}
|
||||
\subsection{设隐含层为$\mathbf{z}=\mathbf{W}^T\mathbf{x}+\mathbf{b}$，其中$\mathbf{x}\in R^{(m \times 1)}$，$\mathbf{z}\in R^{(n\times 1)}$，$\mathbf{W}\in R^{(m\times n)}$，$\mathbf{b} \in R^{(n\times 1)}$均为已知，其激活函数如下：
|
||||
$$\mathbf{y}=\delta(\mathbf{z})=tanh(\mathbf{z})$$
|
||||
tanh表示双曲正切函数。若训练过程中的目标函数为L，且已知L对$\mathbf{y}$的导数 $\frac{\partial L}{\partial \mathbf{y}}=[\frac{\partial L}{\partial y_1},\frac{\partial L}{\partial y_2},...,\frac{\partial L}{\partial y_n}]^T$和$\mathbf{y}=[y_1,y_2,...,y_n]^T$的值。
|
||||
}
|
||||
\subsubsection{请使用$\mathbf{y}$表示出$\frac{\partial \mathbf{y}^T}{\partial \mathbf{z}}$, 这里的$\mathbf{y}^T$ 为行向量。
|
||||
}
|
||||
|
||||
\begin{proof}[解]
|
||||
首先，对$i \neq j$，$\dfrac{\partial y_i}{\partial z_j} = 0$。
|
||||
|
||||
同时$y_i = \tanh(z_i) = \tanh(\arctanh(y_i))$，因此
|
||||
\[\frac{\partial y_i}{\partial z_i} = 1 - \tanh^2(z_i) = 1 - y_i^2\]
|
||||
因此
|
||||
\[\dfrac{\partial \boldsymbol{y}^\mathrm{T}}{\partial \boldsymbol{z}} = \diag\{1 - y_1^2, 1 - y_2^2, \dots, 1 - y_n^2\} \qedhere\]
|
||||
\end{proof}
|
||||
|
||||
\subsubsection{请使用$\mathbf{y}$和$\frac{\partial L}{\partial \mathbf{y}}$表示$\frac{\partial L}{\partial \mathbf{x}}$，$\frac{\partial L}{\partial \mathbf{W}}$，$\frac{\partial L}{\partial \mathbf{b}}$。
|
||||
}
|
||||
提示:$\frac{\partial L}{\partial \mathbf{x}}$，$\frac{\partial L}{\partial \mathbf{W}}$，$\frac{\partial L}{\partial \mathbf{b}}$与x,W,b具有相同维度。
|
||||
|
||||
\begin{proof}[解]
|
||||
由链式法则
|
||||
\[\frac{\partial L}{\partial \boldsymbol{x}} = \frac{\partial \boldsymbol{z}^\mathrm{T}}{\partial \boldsymbol{x}} \frac{\partial \boldsymbol{y}^\mathrm{T}}{\partial \boldsymbol{z}} \frac{\partial L}{\partial \boldsymbol{y}} = W \diag\{1 - y_1^2, 1 - y_2^2, \dots, 1 - y_n^2\} \frac{\partial L}{\partial \boldsymbol{y}}\]
|
||||
|
||||
对于$\dfrac{\partial L}{\partial W}$，
|
||||
\[\frac{\partial \boldsymbol{z}^T}{\partial W} = \begin{bmatrix}
|
||||
\boldsymbol{x} & \boldsymbol{x} & \cdots & \boldsymbol{x}
|
||||
\end{bmatrix}_{m \times n}\]
|
||||
|
||||
\begin{align*}
|
||||
\frac{\partial L}{\partial W} & = \frac{\partial \boldsymbol{z}^\mathrm{T}}{\partial W} \frac{\partial \boldsymbol{y}^\mathrm{T}}{\partial \boldsymbol{z}} \frac{\partial L}{\partial \boldsymbol{y}}\\
|
||||
& = \begin{bmatrix}
|
||||
\boldsymbol{x} & \boldsymbol{x} & \cdots & \boldsymbol{x}
|
||||
\end{bmatrix}_{m \times n} \diag\{1 - y_1^2, 1 - y_2^2, \dots, 1 - y_n^2\} \frac{\partial L}{\partial \boldsymbol{y}}
|
||||
\end{align*}
|
||||
|
||||
对于$\dfrac{\partial L}{\partial \boldsymbol{b}}$，由链式法则
|
||||
\[\frac{\partial L}{\partial \boldsymbol{b}} = \frac{\partial \boldsymbol{z}^\mathrm{T}}{\partial \boldsymbol{b}} \frac{\partial \boldsymbol{y}^\mathrm{T}}{\partial \boldsymbol{z}} \frac{\partial L}{\partial \boldsymbol{y}} = I_n \frac{\partial \boldsymbol{y}^\mathrm{T}}{\partial \boldsymbol{z}} \frac{\partial L}{\partial \boldsymbol{y}} = \diag\{1 - y_1^2, 1 - y_2^2, \dots, 1 - y_n^2\} \frac{\partial L}{\partial \boldsymbol{y}} \qedhere\]
|
||||
\end{proof}
|
||||
\vspace{6mm}
|
||||
\centerline{\textbf{\Large{编程部分}}}
|
||||
|
||||
|
||||
\vspace{3mm}
|
||||
% 请根据是否选择自选课题的情况选择“编程作业报告”或“自选课题开题报告”中的一项完成
|
||||
\section{编程作业报告}
|
||||
% 请在此处完成编程作业报告
|
||||
完成后的代码也可以在 \href{https://git.unlockableworld.com/unlockable/MediaNCognition}{\url{https://git.unlockableworld.com/unlockable/MediaNCognition}}中找到。
|
||||
\begin{enumerate}
|
||||
\item 使用默认配置进行训练和测试。
|
||||
\begin{enumerate}
|
||||
\item 训练模型。
|
||||
|
||||
输入：
|
||||
\lstinputlisting{codes/1.1.in.txt}
|
||||
|
||||
输出：
|
||||
\lstinputlisting{codes/1.1.out.txt}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=0.9\linewidth]{img/1default_train.png}
|
||||
\end{figure}
|
||||
|
||||
\item 测试模型。
|
||||
|
||||
输入：
|
||||
\lstinputlisting{codes/1.2.in.txt}
|
||||
|
||||
输出：
|
||||
\lstinputlisting{codes/1.2.out.txt}
|
||||
\end{enumerate}
|
||||
\item 调整参数、使用Adam优化器训练并测试。
|
||||
\begin{enumerate}
|
||||
\item 训练模型。
|
||||
|
||||
输入：
|
||||
\lstinputlisting{codes/2.1.in.txt}
|
||||
|
||||
输出：
|
||||
\lstinputlisting{codes/2.1.out.txt}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=0.9\linewidth]{img/2adam_optim.png}
|
||||
\end{figure}
|
||||
\item 测试性能。
|
||||
|
||||
输入：
|
||||
\lstinputlisting{codes/2.2.in.txt}
|
||||
|
||||
输出：
|
||||
\lstinputlisting{codes/2.2.out.txt}
|
||||
\end{enumerate}
|
||||
|
||||
\item 使用效果最佳的模型测试。
|
||||
经过简单的尝试，发现使用
|
||||
\lstinputlisting{codes/self_train.in.txt}
|
||||
可以使测试集准确率达到88.8\%，有略微的提升。训练的loss曲线：
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=.9\linewidth]{img/3found_best.png}
|
||||
\end{figure}
|
||||
使用它进行预测：
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\begin{subfigure}[b]{.3\linewidth}
|
||||
\includegraphics[width=\linewidth]{img/predict/predict01.png}
|
||||
\subcaption{预测：A}
|
||||
\end{subfigure}
|
||||
\hfill
|
||||
\begin{subfigure}[b]{.3\linewidth}
|
||||
\includegraphics[width=\linewidth]{img/predict/predict02.png}
|
||||
\subcaption{预测：B}
|
||||
\end{subfigure}
|
||||
\hfill
|
||||
\begin{subfigure}[b]{.3\linewidth}
|
||||
\includegraphics[width=\linewidth]{img/predict/predict03.png}
|
||||
\subcaption{预测：M}
|
||||
\end{subfigure}
|
||||
|
||||
\begin{subfigure}[b]{.3\linewidth}
|
||||
\includegraphics[width=\linewidth]{img/predict/predict04.png}
|
||||
\subcaption{预测：R}
|
||||
\end{subfigure}
|
||||
\hfill
|
||||
\begin{subfigure}[b]{.3\linewidth}
|
||||
\includegraphics[width=\linewidth]{img/predict/predict05.png}
|
||||
\subcaption{预测：M}
|
||||
\end{subfigure}
|
||||
\hfill
|
||||
\begin{subfigure}[b]{.3\linewidth}
|
||||
\includegraphics[width=\linewidth]{img/predict/predict06.png}
|
||||
\subcaption{预测：O}
|
||||
\end{subfigure}
|
||||
|
||||
\hfill
|
||||
\begin{subfigure}[b]{.3\linewidth}
|
||||
\includegraphics[width=\linewidth]{img/predict/predict07.png}
|
||||
\subcaption{预测：B}
|
||||
\end{subfigure}
|
||||
\hfill
|
||||
\begin{subfigure}[b]{.3\linewidth}
|
||||
\includegraphics[width=\linewidth]{img/predict/predict08.png}
|
||||
\subcaption{预测：W}
|
||||
\end{subfigure}
|
||||
\hfill
|
||||
\end{figure}
|
||||
\item 遇到的问题及解决方法
|
||||
\begin{enumerate}
|
||||
\item 代码中对灰度图像的矩阵进行标准化时，\lstinline{numpy}显示不能对\lstinline{NumpyGenericArray}进行对\lstinline{float}的\lstinline{/}操作。改用\lstinline{np.div()}解决了这个问题。
|
||||
\item 在利用训练好的模型进行预测时，发现自己找到的大部分模型都预测错误；最后与训练集的图片进行了对比，发现主要问题是裁切字母时留下了过大的边距，导致模型不能正确理解输入。重新裁剪边框后，得到正确的结果。
|
||||
\end{enumerate}
|
||||
\item 建议：希望下次发布作业代码可以利用清华的git。
|
||||
\end{enumerate}
|
||||
|
||||
|
||||
|
||||
|
||||
% \section{自选课题开题报告}
|
||||
% 请在此处介绍自选课题
|
||||
|
||||
\end{document}
|
||||
|
||||
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: late\rvx
|
||||
%%% TeX-master: t
|
||||
%%% End:
|
||||
% Homework Template
|
||||
\documentclass[a4paper]{article}
|
||||
\usepackage{ctex}
|
||||
\usepackage{amsmath, amssymb, amsthm}
|
||||
\usepackage{moreenum}
|
||||
\usepackage{mathtools}
|
||||
\usepackage{url}
|
||||
\usepackage{bm}
|
||||
\usepackage{enumitem}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{subcaption}
|
||||
\usepackage{booktabs} % toprule
|
||||
\usepackage[mathcal]{eucal}
|
||||
\usepackage[thehwcnt = 1]{iidef}
|
||||
\usepackage{listings}
|
||||
\usepackage[x11names]{xcolor}
|
||||
\usepackage{float}
|
||||
\usepackage[colorlinks, linkcolor=black, anchorcolor=green, citecolor=blue]{hyperref}
|
||||
|
||||
\DeclareMathOperator{\arctanh}{arctanh}
|
||||
% \DeclareMathOperator{\diag}{diag}
|
||||
|
||||
\setenumerate[1]{label=(\arabic{*})}
|
||||
\setenumerate[2]{label=\arabic{*})}
|
||||
|
||||
\definecolor{codekeyword}{RGB}{171, 0, 216}
|
||||
\definecolor{codetypename}{RGB}{29, 37, 251}
|
||||
\definecolor{codevariable}{RGB}{10, 23, 126}
|
||||
\definecolor{codestring}{RGB}{157, 0, 25}
|
||||
\definecolor{codecomment}{RGB}{31, 129, 19}
|
||||
|
||||
\newfontfamily\cascadia[Ligatures=ResetAll]{Cascadia Code}
|
||||
% \newfontfamily\codefont[Ligatures=ResetAll]{Cascadia Code}
|
||||
\newfontfamily\codefont[Ligatures=ResetAll]{Fira Code}[Contextuals={Alternate}]
|
||||
% To enable ligature in listing, go check lstfiracode's github page and copy firacodestyle's settings.
|
||||
|
||||
\lstset{
|
||||
basicstyle = \small\codefont,
|
||||
% ---
|
||||
tabsize = 4,
|
||||
showstringspaces = false,
|
||||
numbers = left,
|
||||
numberstyle = \cascadia,
|
||||
% ---
|
||||
breaklines = true,
|
||||
captionpos = t,
|
||||
% ---
|
||||
frame = l,
|
||||
flexiblecolumns,
|
||||
columns = fixed,
|
||||
}
|
||||
|
||||
\thecourseinstitute{清华大学电子工程系}
|
||||
\thecoursename{\textbf{媒体与认知} \space 课堂2}
|
||||
\theterm{2023-2024学年春季学期}
|
||||
\hwname{作业}
|
||||
\begin{document}
|
||||
\courseheader
|
||||
% 请在YOUR NAME处填写自己的姓名
|
||||
\name{高艺轩}
|
||||
\vspace{3mm}
|
||||
\centerline{\textbf{\Large{理论部分}}}
|
||||
|
||||
\section{单选题（15分）}
|
||||
% 请在？处填写答案
|
||||
\subsection{\underline{B}}
|
||||
|
||||
\subsection{\underline{A}}
|
||||
|
||||
\subsection{\underline{B}}
|
||||
|
||||
\subsection{\underline{A}}
|
||||
|
||||
\subsection{\underline{B}}
|
||||
|
||||
\section{计算题（15 分）}
|
||||
\subsection{设隐含层为$\mathbf{z}=\mathbf{W}^T\mathbf{x}+\mathbf{b}$，其中$\mathbf{x}\in R^{(m \times 1)}$，$\mathbf{z}\in R^{(n\times 1)}$，$\mathbf{W}\in R^{(m\times n)}$，$\mathbf{b} \in R^{(n\times 1)}$均为已知，其激活函数如下：
|
||||
$$\mathbf{y}=\delta(\mathbf{z})=tanh(\mathbf{z})$$
|
||||
tanh表示双曲正切函数。若训练过程中的目标函数为L，且已知L对$\mathbf{y}$的导数 $\frac{\partial L}{\partial \mathbf{y}}=[\frac{\partial L}{\partial y_1},\frac{\partial L}{\partial y_2},...,\frac{\partial L}{\partial y_n}]^T$和$\mathbf{y}=[y_1,y_2,...,y_n]^T$的值。
|
||||
}
|
||||
\subsubsection{请使用$\mathbf{y}$表示出$\frac{\partial \mathbf{y}^T}{\partial \mathbf{z}}$, 这里的$\mathbf{y}^T$ 为行向量。
|
||||
}
|
||||
|
||||
\begin{proof}[解]
|
||||
首先，对$i \neq j$，$\dfrac{\partial y_i}{\partial z_j} = 0$。
|
||||
|
||||
同时$y_i = \tanh(z_i) = \tanh(\arctanh(y_i))$，因此
|
||||
\[\frac{\partial y_i}{\partial z_i} = 1 - \tanh^2(z_i) = 1 - y_i^2\]
|
||||
因此
|
||||
\[\dfrac{\partial \boldsymbol{y}^\mathrm{T}}{\partial \boldsymbol{z}} = \diag\{1 - y_1^2, 1 - y_2^2, \dots, 1 - y_n^2\} \qedhere\]
|
||||
\end{proof}
|
||||
|
||||
\subsubsection{请使用$\mathbf{y}$和$\frac{\partial L}{\partial \mathbf{y}}$表示$\frac{\partial L}{\partial \mathbf{x}}$，$\frac{\partial L}{\partial \mathbf{W}}$，$\frac{\partial L}{\partial \mathbf{b}}$。
|
||||
}
|
||||
提示:$\frac{\partial L}{\partial \mathbf{x}}$，$\frac{\partial L}{\partial \mathbf{W}}$，$\frac{\partial L}{\partial \mathbf{b}}$与x,W,b具有相同维度。
|
||||
|
||||
\begin{proof}[解]
|
||||
由链式法则
|
||||
\[\frac{\partial L}{\partial \boldsymbol{x}} = \frac{\partial \boldsymbol{z}^\mathrm{T}}{\partial \boldsymbol{x}} \frac{\partial \boldsymbol{y}^\mathrm{T}}{\partial \boldsymbol{z}} \frac{\partial L}{\partial \boldsymbol{y}} = W \diag\{1 - y_1^2, 1 - y_2^2, \dots, 1 - y_n^2\} \frac{\partial L}{\partial \boldsymbol{y}}\]
|
||||
|
||||
对于$\dfrac{\partial L}{\partial W}$，
|
||||
\[\frac{\partial \boldsymbol{z}^T}{\partial W} = \begin{bmatrix}
|
||||
\boldsymbol{x} & \boldsymbol{x} & \cdots & \boldsymbol{x}
|
||||
\end{bmatrix}_{m \times n}\]
|
||||
|
||||
\begin{align*}
|
||||
\frac{\partial L}{\partial W} & = \frac{\partial \boldsymbol{z}^\mathrm{T}}{\partial W} \frac{\partial \boldsymbol{y}^\mathrm{T}}{\partial \boldsymbol{z}} \frac{\partial L}{\partial \boldsymbol{y}}\\
|
||||
& = \begin{bmatrix}
|
||||
\boldsymbol{x} & \boldsymbol{x} & \cdots & \boldsymbol{x}
|
||||
\end{bmatrix}_{m \times n} \diag\{1 - y_1^2, 1 - y_2^2, \dots, 1 - y_n^2\} \frac{\partial L}{\partial \boldsymbol{y}}
|
||||
\end{align*}
|
||||
|
||||
对于$\dfrac{\partial L}{\partial \boldsymbol{b}}$，由链式法则
|
||||
\[\frac{\partial L}{\partial \boldsymbol{b}} = \frac{\partial \boldsymbol{z}^\mathrm{T}}{\partial \boldsymbol{b}} \frac{\partial \boldsymbol{y}^\mathrm{T}}{\partial \boldsymbol{z}} \frac{\partial L}{\partial \boldsymbol{y}} = I_n \frac{\partial \boldsymbol{y}^\mathrm{T}}{\partial \boldsymbol{z}} \frac{\partial L}{\partial \boldsymbol{y}} = \diag\{1 - y_1^2, 1 - y_2^2, \dots, 1 - y_n^2\} \frac{\partial L}{\partial \boldsymbol{y}} \qedhere\]
|
||||
\end{proof}
|
||||
\vspace{6mm}
|
||||
\centerline{\textbf{\Large{编程部分}}}
|
||||
|
||||
|
||||
\vspace{3mm}
|
||||
% 请根据是否选择自选课题的情况选择“编程作业报告”或“自选课题开题报告”中的一项完成
|
||||
\section{编程作业报告}
|
||||
% 请在此处完成编程作业报告
|
||||
完成后的代码也可以在 \href{https://git.unlockableworld.com/unlockable/MediaNCognition}{\url{https://git.unlockableworld.com/unlockable/MediaNCognition}}中找到。
|
||||
\begin{enumerate}
|
||||
\item 使用默认配置进行训练和测试。
|
||||
\begin{enumerate}
|
||||
\item 训练模型。
|
||||
|
||||
输入：
|
||||
\lstinputlisting{codes/1.1.in.txt}
|
||||
|
||||
输出：
|
||||
\lstinputlisting{codes/1.1.out.txt}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=0.9\linewidth]{img/1default_train.png}
|
||||
\end{figure}
|
||||
|
||||
\item 测试模型。
|
||||
|
||||
输入：
|
||||
\lstinputlisting{codes/1.2.in.txt}
|
||||
|
||||
输出：
|
||||
\lstinputlisting{codes/1.2.out.txt}
|
||||
\end{enumerate}
|
||||
\item 调整参数、使用Adam优化器训练并测试。
|
||||
\begin{enumerate}
|
||||
\item 训练模型。
|
||||
|
||||
输入：
|
||||
\lstinputlisting{codes/2.1.in.txt}
|
||||
|
||||
输出：
|
||||
\lstinputlisting{codes/2.1.out.txt}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=0.9\linewidth]{img/2adam_optim.png}
|
||||
\end{figure}
|
||||
\item 测试性能。
|
||||
|
||||
输入：
|
||||
\lstinputlisting{codes/2.2.in.txt}
|
||||
|
||||
输出：
|
||||
\lstinputlisting{codes/2.2.out.txt}
|
||||
\end{enumerate}
|
||||
|
||||
\item 使用效果最佳的模型测试。
|
||||
经过简单的尝试，发现使用
|
||||
\lstinputlisting{codes/self_train.in.txt}
|
||||
可以使测试集准确率达到88.8\%，有略微的提升。训练的loss曲线：
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=.9\linewidth]{img/3found_best.png}
|
||||
\end{figure}
|
||||
使用它进行预测：
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\begin{subfigure}[b]{.3\linewidth}
|
||||
\includegraphics[width=\linewidth]{img/predict/predict01.png}
|
||||
\subcaption{预测：A}
|
||||
\end{subfigure}
|
||||
\hfill
|
||||
\begin{subfigure}[b]{.3\linewidth}
|
||||
\includegraphics[width=\linewidth]{img/predict/predict02.png}
|
||||
\subcaption{预测：B}
|
||||
\end{subfigure}
|
||||
\hfill
|
||||
\begin{subfigure}[b]{.3\linewidth}
|
||||
\includegraphics[width=\linewidth]{img/predict/predict03.png}
|
||||
\subcaption{预测：M}
|
||||
\end{subfigure}
|
||||
|
||||
\begin{subfigure}[b]{.3\linewidth}
|
||||
\includegraphics[width=\linewidth]{img/predict/predict04.png}
|
||||
\subcaption{预测：R}
|
||||
\end{subfigure}
|
||||
\hfill
|
||||
\begin{subfigure}[b]{.3\linewidth}
|
||||
\includegraphics[width=\linewidth]{img/predict/predict05.png}
|
||||
\subcaption{预测：M}
|
||||
\end{subfigure}
|
||||
\hfill
|
||||
\begin{subfigure}[b]{.3\linewidth}
|
||||
\includegraphics[width=\linewidth]{img/predict/predict06.png}
|
||||
\subcaption{预测：O}
|
||||
\end{subfigure}
|
||||
|
||||
\hfill
|
||||
\begin{subfigure}[b]{.3\linewidth}
|
||||
\includegraphics[width=\linewidth]{img/predict/predict07.png}
|
||||
\subcaption{预测：B}
|
||||
\end{subfigure}
|
||||
\hfill
|
||||
\begin{subfigure}[b]{.3\linewidth}
|
||||
\includegraphics[width=\linewidth]{img/predict/predict08.png}
|
||||
\subcaption{预测：W}
|
||||
\end{subfigure}
|
||||
\hfill
|
||||
\end{figure}
|
||||
\item 遇到的问题及解决方法
|
||||
\begin{enumerate}
|
||||
\item 代码中对灰度图像的矩阵进行标准化时，\lstinline{numpy}显示不能对\lstinline{NumpyGenericArray}进行对\lstinline{float}的\lstinline{/}操作。改用\lstinline{np.div()}解决了这个问题。
|
||||
\item 在利用训练好的模型进行预测时，发现自己找到的大部分模型都预测错误；最后与训练集的图片进行了对比，发现主要问题是裁切字母时留下了过大的边距，导致模型不能正确理解输入。重新裁剪边框后，得到正确的结果。
|
||||
\end{enumerate}
|
||||
\item 建议：希望下次发布作业代码可以利用清华的git。
|
||||
\end{enumerate}
|
||||
|
||||
|
||||
|
||||
|
||||
% \section{自选课题开题报告}
|
||||
% 请在此处介绍自选课题
|
||||
|
||||
\end{document}
|
||||
|
||||
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: late\rvx
|
||||
%%% TeX-master: t
|
||||
%%% End:
|
||||
|
||||
Reference in New Issue
Block a user