Learning rate differential in PyTorch - Model Pipeline Trace

Model Pipeline - Learning rate differential

This pipeline shows how using different learning rates for different parts of a neural network helps the model learn better. It trains a simple model with two layers, each having its own learning rate.

Data Flow - 6 Stages

1Data in

1000 rows x 10 columns→Synthetic dataset creation with 10 features and binary labels→1000 rows x 10 columns

[[0.5, -1.2, 0.3, ..., 0.1], label=1]

↓

2Preprocessing

1000 rows x 10 columns→Normalize features to zero mean and unit variance→1000 rows x 10 columns

[[0.0, -0.8, 0.2, ..., 0.05], label=1]

↓

3Feature Engineering

1000 rows x 10 columns→No additional features added→1000 rows x 10 columns

[[0.0, -0.8, 0.2, ..., 0.05], label=1]

↓

4Model Trains

1000 rows x 10 columns→Train 2-layer neural network with differential learning rates: 0.01 for first layer, 0.001 for second layer→Model weights updated

Layer1 weights shape: (5, 10), Layer2 weights shape: (1, 5)

↓

5Metrics Improve

Training epochs→Loss decreases and accuracy increases over 10 epochs→Final loss ~0.25, accuracy ~88%

Epoch 10: loss=0.25, accuracy=0.88

↓

6Prediction

1 row x 10 columns→Model predicts probability for binary class→1 row x 1 column (probability)

[0.85]

Training Trace - Epoch by Epoch

Loss
1.0 | *
0.9 |  *
0.8 |   *
0.7 |    *
0.6 |     *
0.5 |      *
0.4 |       *
0.3 |        *
0.2 |         *
    +----------------
     1 2 3 4 5 6 7 8 9 10 Epochs

Epoch	Loss ↓	Accuracy ↑	Observation
1	0.85	0.55	High loss and low accuracy at start
2	0.65	0.68	Loss decreases, accuracy improves
3	0.50	0.75	Model learns important patterns
4	0.40	0.80	Steady improvement
5	0.35	0.83	Learning rate differential helps stabilize training
6	0.30	0.85	Loss continues to decrease
7	0.28	0.86	Accuracy improves slowly
8	0.27	0.87	Model converging
9	0.26	0.87	Small improvements
10	0.25	0.88	Training stabilizes with good accuracy

Prediction Trace - 5 Layers

Layer 1: Input Layer

Layer 2: First Layer (learning rate 0.01)

Layer 3: Activation (ReLU)

Layer 4: Second Layer (learning rate 0.001)

Layer 5: Sigmoid Activation

Model Quiz - 3 Questions

Why use different learning rates for different layers?

A To make training slower overall

B To allow faster learning in some layers and stable updates in others

C To reduce the number of layers

D To increase the model size

Key Insight

Using different learning rates for different layers helps the model learn faster in some parts while keeping other parts stable. This balance improves training speed and final accuracy.

Practice

1. What does learning rate differential mean in PyTorch training?

easy

A. Changing the learning rate randomly during training

B. Setting different learning rates for different parts of a model

C. Using the same learning rate for the entire model

D. Freezing all model layers during training

Solution

1. Step 1: Understand learning rate concept

   The learning rate controls how fast a model updates its knowledge during training.

2. Step 2: Define learning rate differential

   Learning rate differential means assigning different learning rates to different parts of the model to control their update speed.

3. Final Answer:

   Setting different learning rates for different parts of a model -> Option B

4. Quick Check:

   Learning rate differential = Different rates per model part [OK]

Hint: Different parts can learn at different speeds [OK]

Common Mistakes:

• Thinking learning rate is always the same for all layers
• Confusing learning rate differential with random rate changes
• Believing freezing layers means changing learning rate

2. Which PyTorch code snippet correctly sets different learning rates for two parameter groups?

easy

A. optimizer = torch.optim.SGD(model.parameters(), lr=0.01, lr2=0.001)

B. optimizer = torch.optim.SGD(model.parameters(), lr=[0.01, 0.001])

C. optimizer = torch.optim.SGD([{'params': model.layer1.parameters(), 'lr': 0.01}, {'params': model.layer2.parameters(), 'lr': 0.001}], momentum=0.9)

D. optimizer = torch.optim.SGD([model.layer1, model.layer2], lr=0.01)

Solution

1. Step 1: Check PyTorch optimizer syntax for param groups

   PyTorch allows passing a list of dicts with 'params' and 'lr' keys to set different learning rates.

2. Step 2: Identify correct syntax

   optimizer = torch.optim.SGD([{'params': model.layer1.parameters(), 'lr': 0.01}, {'params': model.layer2.parameters(), 'lr': 0.001}], momentum=0.9) correctly uses a list of dicts with separate learning rates for layer1 and layer2 parameters.

3. Final Answer:

   optimizer = torch.optim.SGD([{'params': model.layer1.parameters(), 'lr': 0.01}, {'params': model.layer2.parameters(), 'lr': 0.001}], momentum=0.9) -> Option C

4. Quick Check:

   Param groups with separate 'lr' keys = Correct syntax [OK]

Hint: Use list of dicts with 'params' and 'lr' keys [OK]

Common Mistakes:

• Passing lr as a list directly to optimizer
• Using unknown keyword like lr2
• Passing layers instead of parameters

3. Given this code, what is the learning rate for model.layer2 during training?

optimizer = torch.optim.Adam([
  {'params': model.layer1.parameters(), 'lr': 0.005},
  {'params': model.layer2.parameters(), 'lr': 0.0005}
])

medium

A. 0.0005

B. 0.05

C. 0.0055

D. 0.005

Solution

1. Step 1: Identify learning rates assigned to each layer

   Layer1 has lr=0.005, Layer2 has lr=0.0005 as per the optimizer param groups.

2. Step 2: Find learning rate for model.layer2

   From the second dict, model.layer2.parameters() uses lr=0.0005.

3. Final Answer:

   0.0005 -> Option A

4. Quick Check:

   Layer2 lr = 0.0005 from param groups [OK]

Hint: Check param group with layer2 parameters [OK]

Common Mistakes:

• Adding learning rates instead of selecting correct one
• Confusing layer1 lr with layer2 lr
• Assuming default lr overrides param groups

4. Identify the error in this PyTorch optimizer setup for learning rate differential:

optimizer = torch.optim.SGD([
  {'params': model.layer1.parameters(), 'lr': 0.01},
  {'params': model.layer2.parameters()}
], lr=0.001)

medium

A. Missing learning rate for second param group causes error

B. Using lr=0.001 outside param groups is invalid

C. Parameters should be passed as model.layer1, not model.layer1.parameters()

D. SGD optimizer does not support param groups

Solution

1. Step 1: Review param groups and learning rates

   First param group has lr=0.01, second param group has no lr specified.

2. Step 2: Understand default lr behavior

   When param groups are used, each group should have lr or optimizer's lr applies. Here, lr=0.001 is passed but second group lacks explicit lr, causing confusion.

3. Final Answer:

   Missing learning rate for second param group causes error -> Option A

4. Quick Check:

   All param groups need lr or default applies [OK]

Hint: Each param group must have lr or rely on optimizer lr [OK]

Common Mistakes:

• Assuming optimizer lr applies to all param groups automatically
• Passing parameters instead of parameter iterators
• Believing SGD can't use param groups

5. You want to fine-tune a pretrained model by training only the last layer fast and freezing the rest. Which learning rate setup is best?

hard

A. Set same lr=0.01 for all layers

B. Freeze last layer and train others with lr=0.01

C. Set lr=0.01 for all layers except last layer with lr=0

D. Set lr=0 for all layers except last layer with lr=0.01

Solution

1. Step 1: Understand freezing and learning rate

   Freezing means no updates, which can be done by setting lr=0 or disabling gradients.

2. Step 2: Apply learning rate differential for fine-tuning

   Set lr=0 for frozen layers to prevent updates, and higher lr for last layer to train it fast.

3. Final Answer:

   Set lr=0 for all layers except last layer with lr=0.01 -> Option D

4. Quick Check:

   Freeze layers = lr 0, train last layer fast [OK]

Hint: Freeze layers by lr=0, train last layer with higher lr [OK]

Common Mistakes:

• Using same learning rate for all layers when freezing
• Freezing last layer instead of others
• Not setting lr=0 for frozen layers