What is the difference between theoretical and effective receptive fields in CNNs?

The theoretical receptive field (TRF) is the full region of an input image that *could* influence a CNN neuron. The effective receptive field (ERF) is the smaller region whose pixels actually have a meaningful influence on that neuron's output.

How are they different?

• Theoretical receptive field: Determined by network architecture—kernel sizes, strides, dilation, and depth. It describes all input positions connected to an output through computational paths.
• Effective receptive field: Describes the *strength* of each input pixel's contribution. It depends on the model's weights and, for nonlinear networks, can depend on the input.

Simple example

Imagine a feature-map neuron with a theoretical receptive field of 15×15 pixels. All 225 positions can potentially affect it, but the strongest influence might be concentrated near the center. The effective receptive field therefore covers a smaller, more influential portion of that 15×15 area.

Research on deep CNNs has shown that this influence often forms an approximately Gaussian-shaped pattern: central pixels matter more, while influence weakens toward the edges. This is a common finding, not a universal shape for every network and input.

How can the effective receptive field be measured?

Select an output neuron, compute its gradient with respect to input pixels using backpropagation, and examine the magnitude of those gradients. Larger magnitudes indicate stronger local sensitivity. Averaging across images can reveal the typical influence pattern.

Why does the difference matter?

A large theoretical receptive field does not guarantee that a network effectively uses context across that whole region. This matters when detecting large objects or understanding broad spatial structure.

For the basic definition, see “What is the receptive field of a neuron in a CNN?”. Next: “What is a dilated convolution and when is it useful?”

Research: Understanding the Effective Receptive Field in Deep Convolutional Neural Networks.

Further reading: Computing Receptive Fields of Convolutional Neural Networks.