Beginner Explanation
Imagine you have a very smart robot that can recognize different animals in pictures, but you want to teach it to tell the difference between cats and dogs specifically. Instead of training the robot from scratch, you use what it already knows about animals and just add a simple new layer on top that helps it make that specific distinction. This new layer is like a pair of glasses that helps the robot see the world in a way that’s best for telling cats from dogs. This new layer is what we call a ‘linear probe.’ It takes the robot’s existing knowledge and fine-tunes it for a specific task without starting over.Technical Explanation
Linear probes are a technique used in transfer learning, where a pre-trained model (like a neural network trained on a large dataset) is used to extract features from input data. A linear classifier (usually a logistic regression or a simple feedforward neural network) is then trained on these features to perform a specific task. The linear probe is typically trained on a smaller dataset that corresponds to the task at hand. Here’s a simple code example using PyTorch: “`python import torch import torch.nn as nn import torch.optim as optim # Assume `features` are the output from a pre-trained model # and `labels` are the corresponding labels for a specific task. features = torch.randn(100, 512) # 100 samples, 512 features labels = torch.randint(0, 2, (100,)) # Binary classification # Define a simple linear probe class LinearProbe(nn.Module): def __init__(self, input_dim): super(LinearProbe, self).__init__() self.linear = nn.Linear(input_dim, 2) # 2 classes def forward(self, x): return self.linear(x) # Training the linear probe model = LinearProbe(512) criterion = nn.CrossEntropyLoss() optimizer = optim.Adam(model.parameters(), lr=0.001) for epoch in range(100): optimizer.zero_grad() outputs = model(features) loss = criterion(outputs, labels) loss.backward() optimizer.step() “` This example shows how to set up and train a linear probe on top of features extracted from a pre-trained model.Academic Context
Linear probes have gained attention in the field of transfer learning and representation learning as a method to evaluate the quality of learned representations. They are particularly useful for understanding how well a pre-trained model generalizes to new tasks. The mathematical foundation lies in linear classification, where the decision boundary is defined by a linear combination of input features. Key papers in this area include ‘BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding’ (Devlin et al., 2018), which discusses the effectiveness of linear probes for probing contextualized representations in NLP tasks, and ‘Do ImageNet Classifiers Generalize to ImageNet?’ (Azulay and Weiss, 2019), which evaluates the transferability of learned features in computer vision.Code Examples
Example 1:
import torch
import torch.nn as nn
import torch.optim as optim
# Assume `features` are the output from a pre-trained model
# and `labels` are the corresponding labels for a specific task.
features = torch.randn(100, 512) # 100 samples, 512 features
labels = torch.randint(0, 2, (100,)) # Binary classification
# Define a simple linear probe
class LinearProbe(nn.Module):
def __init__(self, input_dim):
super(LinearProbe, self).__init__()
self.linear = nn.Linear(input_dim, 2) # 2 classes
def forward(self, x):
return self.linear(x)
# Training the linear probe
model = LinearProbe(512)
criterion = nn.CrossEntropyLoss()
optimizer = optim.Adam(model.parameters(), lr=0.001)
for epoch in range(100):
optimizer.zero_grad()
outputs = model(features)
loss = criterion(outputs, labels)
loss.backward()
optimizer.step()Example 2:
def __init__(self, input_dim):
super(LinearProbe, self).__init__()
self.linear = nn.Linear(input_dim, 2) # 2 classesExample 3:
def forward(self, x):
return self.linear(x)Example 4:
optimizer.zero_grad()
outputs = model(features)
loss = criterion(outputs, labels)
loss.backward()
optimizer.step()Example 5:
import torch
import torch.nn as nn
import torch.optim as optim
# Assume `features` are the output from a pre-trained modelExample 6:
import torch.nn as nn
import torch.optim as optim
# Assume `features` are the output from a pre-trained model
# and `labels` are the corresponding labels for a specific task.Example 7:
import torch.optim as optim
# Assume `features` are the output from a pre-trained model
# and `labels` are the corresponding labels for a specific task.
features = torch.randn(100, 512) # 100 samples, 512 featuresExample 8:
class LinearProbe(nn.Module):
def __init__(self, input_dim):
super(LinearProbe, self).__init__()
self.linear = nn.Linear(input_dim, 2) # 2 classes
Example 9:
def __init__(self, input_dim):
super(LinearProbe, self).__init__()
self.linear = nn.Linear(input_dim, 2) # 2 classes
def forward(self, x):Example 10:
def forward(self, x):
return self.linear(x)
# Training the linear probe
model = LinearProbe(512)View Source: https://arxiv.org/abs/2511.16674v1