Direct Answer Yes, a convolutional neural network (CNN) can have negative weights. In a CNN, weights are learned parameters that determine how input data is transformed through layers. These weights are initialized with values that can be positive or negative (e.g., using methods like He or Xavier initialization) and are adjusted during training via backpropagation. There is no inherent restriction in the architecture of a CNN that prevents weights from becoming negative. For example, a convolutional filter might learn to detect edges by combining both positive and negative weights to emphasize transitions between light and dark regions in an image.
Examples and Technical Details Negative weights play a functional role in CNNs. Consider a convolutional filter designed to detect horizontal edges. Such a filter might have positive weights in one row and negative weights in the next to compute the difference between pixel intensities, highlighting edges. During training, if a specific feature (e.g., a dark-to-light gradient) is better represented by subtracting activation values, the network will learn negative weights for that purpose. Even after activation functions like ReLU (which outputs zeros for negative inputs), the weights themselves remain unconstrained. For instance, a filter in the first layer could have negative weights to suppress irrelevant patterns, while deeper layers might use negative weights to combine or contrast features from previous layers.
Implications for Model Behavior The presence of negative weights increases the flexibility of CNNs. For example, in image classification, a filter with negative weights might learn to de-emphasize noise or irrelevant textures, improving the model’s ability to focus on meaningful patterns. In practice, this is why normalization techniques (e.g., batch normalization) often center data around zero—it allows both positive and negative weights to contribute meaningfully. Developers should note that while negative weights are normal, their magnitude can be controlled via regularization techniques (e.g., L1/L2 regularization) to prevent overfitting. Overall, negative weights are a natural outcome of training and are critical for enabling CNNs to model complex, real-world data effectively.