Calculating Receptive Field for Convolutional Neural Networks

ODSC - Open Data Science
5 min readSep 18, 2024

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Convolutional neural networks (CNNs) differ from conventional, fully connected neural networks (FCNNs) because they process information in distinct ways. CNNs use a three-dimensional convolution layer and a selective type of neuron to compute critical artificial intelligence processes.

This includes image and object identification and detection. It still simulates biological systems but is distanced from some aspects of the input to process data faster and create maps representing the input’s components. Receptive fields are the backbone of CNN efficacy.

What Are Receptive Fields in CNNs?

Receptive fields in CNNs are sections of the data’s input. Different neuron layers analyze distinct collections, which collaborate to understand the bigger picture. Because each layer analyzes a section without knowing the comprehensive input, it is almost like looking at an abstract painting. However, the AI crystallizes the pieces into a coherent decision by combining learnings from the other neuron layers.

This is critical because every layer’s assessment of a receptive field influences the quality of the output. Even if the conclusions are not wholly accurate, data scientists can learn from how much and what kind of information it pools from the field. Then, they can train the set or use different techniques to examine them. Numerous calculation methods have attempted to make this process as accurate as possible.

How Can You Actionably Calculate Receptive Field?

Each strategy for calculating receptive fields is a type of arithmetic. The size of the receptive field is influenced by the pixelated squares’ size — also known as kernels — as well as stride, padding, and pooling operations.

Calculation Types

There are three calculation types when calculating receptive fields: forward, backward, and recursive.

  • Forward calculation: In this method, you will calculate the size of the receptive field at each layer based on how filters and strides affect the input. Forward calculation moves from input to output, looking at how each layer contributes to the receptive field.
  • Backward calculation: This method starts from the output and works backward to determine how changes in the input affect that output. In backward calculation, you examine one neuron’s output and determine what receptive field size would generate that output.
  • Recursive calculation: Recursive calculation involves repeatedly applying the formula used by the CNN to compute the receptive field. It’s often used for detailed layer-by-layer analysis.

Beginning With the Input Layer

Start calculating receptive fields by locating a 1x1 pixel in the input image. Every pixel connects to neurons through various layers, so understanding this initial connection is a necessary first step for most.

Find Your Formula

After finding the input layer, discover the field’s size by doing the following:

  1. Start with a 1x1 pixel at the input layer
  2. For each layer (l), calculate the receptive field ( RF_l ) using the following formula: [ RF_l = RF_{l-1} + (K_l — 1) \times D_l \times S_{l-1} ]

a. ( RF_{l-1} ) is the previous layer’s receptive field size

b. ( K_l ) is the kernel size at layer ( l )

c. ( D_l) is the dilation factor at layer ( l )

d. ( S_{l-1} ) is the stride at layer ( l-1 )

3. If pooling layers are present, adjust the formula to: [ RF_{l} = RF_{l-1} + (P_{l} — 1) \times S_{l-1} ]

a. ( P_l ) is the pooling size at layer ( l )

4. Continue redoing the equation for each layer until you determine the receptive field size throughout the network

What Are the Applications of Receptive Fields for CNNs?

Data scientists know most of the power behind receptive fields is related to computer vision for AI. How do their calculations have a real-world impact?

Facial Recognition for Enhanced Cybersecurity

Phones, computers, and other digital devices need increased protective measures, such as facial recognition and biometrics. Companies want this to be as precise as possible to promise customers it will not misconstrue someone else’s face as the device owner’s likeness. Accurate receptive field calculations when analyzing the input of a person’s face directly correlate with how attuned electronics are at verifying access.

Autonomous Driving

Autonomous vehicles use computer vision and a medley of other sensors to analyze their surroundings. It could notice road lines or animals sprinting unexpectedly across the street to generate decisions to break or swerve.

A vehicle’s capability of knowing the objective meanings of road signs while considering more subjective images, like pedestrian body movement, is crucial for real-time decision-making. With drivers potentially becoming obsolete before 2030 because self-driving transportation is on the rise, intuitive receptive field calculation is a matter of health and safety for passengers.

Environmental Forecasting

CNNs can analyze receptive fields from current and historical images, providing countless comparative insights in fields like archaeology, climatology, conservation, and history. Calculations from receptive fields over time may demonstrate everything from the speed of habitat loss to urbanization.

One study analyzed CNNs’ abilities to view spatio-temporal climate data, and it predicted weather patterns. Combining this information with machine learning algorithms and data scientists could yield groundbreaking insights to advance sector research.

The Foundation of Convolutional Neural Networks

Neural networks and machine learning are the typical highlights in AI-focused conversations and publications. However, receptive field calculations are why CNNs are as robust as they are. As smart technologies expand in scope and type, parsing receptive fields will become more pivotal in humanity’s understanding of the world through technology’s eyes.

Eleanor Hecks specializes in AI and modeling topics as the editor-in-chief of Designerly Magazine. Through her writing and research, she aims to enhance understanding and appreciation of the ever-evolving technology landscape.

Originally posted on OpenDataScience.com

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