LeNet is a series of convolutional neural network structure proposed by LeCun et al..^[1] The earliest version, LeNet-1, was trained in 1989. In general, when "LeNet" is referred to without a number, it refers to LeNet-5 (1998), the most well-known version.

Convolutional neural networks are a kind of feed-forward neural network whose artificial neurons can respond to a part of the surrounding cells in the coverage range and perform well in large-scale image processing. LeNet-5 was one of the earliest convolutional neural networks and was historically important during the development of deep learning.^[2]

In 1988, LeCun joined the Adaptive Systems Research Department at AT&T Bell Laboratories in Holmdel, New Jersey, United States, headed by Lawrence D. Jackel.

In 1988, LeCun et al. published a neural network design that recognize handwritten zip code. However, its convolutional kernels were hand-designed.^[3]

In 1989, Yann LeCun et al. at Bell Labs first applied the backpropagation algorithm to practical applications, and believed that the ability to learn network generalization could be greatly enhanced by providing constraints from the task's domain. He combined a convolutional neural network trained by backpropagation algorithms to read handwritten numbers and successfully applied it in identifying handwritten zip code numbers provided by the US Postal Service. This was the prototype of what later came to be called LeNet-1.^[4] In the same year, LeCun described a small handwritten digit recognition problem in another paper, and showed that even though the problem is linearly separable, single-layer networks exhibited poor generalization capabilities. When using shift-invariant feature detectors on a multi-layered, constrained network, the model could perform very well. He believed that these results proved that minimizing the number of free parameters in the neural network could enhance the generalization ability of the neural network.^[5]

In 1990, their paper described the application of backpropagation networks in handwritten digit recognition again. They only performed minimal preprocessing on the data, and the model was carefully designed for this task and it was highly constrained. The input data consisted of images, each containing a number, and the test results on the postal code digital data provided by the US Postal Service showed that the model had an error rate of only 1% and a rejection rate of about 9%.^[6]

Their research continued for the next four years, and in 1994 MNIST database was developed, for which LeNet-1 was too small, hence a new LeNet-4 was trained on it.^[7]

A year later the AT&T Bell Labs collective introduced LeNet-5 and reviewed various methods on handwritten character recognition in paper, using standard handwritten digits to identify benchmark tasks. These models were compared and the results showed that the latest network outperformed other models.^[8]

By 1998 Yann LeCun, Leon Bottou, Yoshua Bengio, and Patrick Haffner were able to provided examples of practical applications of neural networks, such as two systems for recognizing handwritten characters online and models that could read millions of checks per day.^[1]

The research achieved great success and aroused the interest of scholars in the study of neural networks. While the architecture of the best performing neural networks today are not the same as that of LeNet, the network was the starting point for a large number of neural network architectures, and also brought inspiration to the field.

LeNet has several common motifs of modern convolutional neural networks, such as convolutional layer, pooling layer and full connection layer.^[4]

• Every convolutional layer includes three parts: convolution, pooling, and nonlinear activation functions
• Using convolution to extract spatial features (Convolution was called receptive fields originally)
• Subsampling average pooling layer
• tanh activation function
• fully connected layers in the final layers for classification
• Sparse connection between layers to reduce the complexity of computation

Before LeNet-1, the 1988 architecture^[3] was a hybrid approach. The first stage scaled, deskewed, and skeletonized the input image. The second stage was a convolutional layer with 18 hand-designed kernels. The third stage was a fully connected network with one hidden layer.

The LeNet-1 architecture has 3 hidden layers (H1-H3) and an output layer.^[4] It has 1256 units, 64660 connections, and 9760 independent parameters.

• H1 (Convolutional): with kernels.
• H2 (Convolutional): with kernels.
• H3: 30 units fully connected to H2.
• Output: 10 units fully connected to H3, representing the 10 digit classes (0-9).

The dataset was 9298 grayscale images, digitized from handwritten zip codes that appeared on U.S. mail passing through the Buffalo, New York post office.^[9] The training set had 7291 data points, and test set had 2007. Both training and test set contained ambiguous, unclassifiable, and misclassified data. Training took 3 days on a Sun workstation.

Compared to the previous 1988 architecture, there was no skeletonization, and the convolutional kernels were learned automatically by backpropagation.

A later version of LeNet-1 has four hidden layers (H1-H4) and an output layer. It takes a 28x28 pixel image as input, though the active region is 16x16 to avoid boundary effects.^[10]

• H1 (Convolutional): with kernels. This layer has trainable parameters (100 from kernels, 4 from biases).

• H2 (Pooling): by average pooling.

• H3 (Convolutional): with kernels. Some kernels take input from 1 feature map, while others take inputs from 2 feature maps.

• H4 (Pooling): by average pooling.

• Output: 10 units fully connected to H4, representing the 10 digit classes (0-9).

The network 4635 units, 98442 connections, and 2578 trainable parameters. It was started by a previous CNN^[11] with 4 times as many trainable parameters, then optimized by Optimal Brain Damage.^[12] One forward pass requires about 140,000 multiply-add operations.^[7]

LeNet-4 was a larger version of LeNet-1 designed to fit the larger MNIST database. It had more feature maps in its convolutional layers, and had an additional layer of hidden units, fully connected to both the last convolutional layer and to the output units. It has 2 convolutions, 2 average poolings, and 2 fully connected layers. It has about 17000 trainable parameters.^[7]

One forward pass requires about 260,000 multiply-add operations.^[7]

LeNet-5 is similar to LeNet-4, but with more fully connected layers. Its architecture is shown in the image on the right. It has 2 convolutions, 2 average poolings, and 3 fully connected layers.

LeNet-5 was trained for about 20 epoches over MNIST. It took 2 to 3 days of CPU time on a Silicon Graphics Origin 2000 server, using a single 200 MHz R10000 processor.^[1]

Recognizing simple digit images is the most classic application of LeNet as it was created because of that.

Yann LeCun et al. created LeNet-1 in 1989. The paper Backpropagation Applied to Handwritten Zip Code Recognition^[4] demonstrates how such constraints can be integrated into a backpropagation network through the architecture of the network. And it had been successfully applied to the recognition of handwritten zip code digits provided by the U.S. Postal Service.^[4]

After the development of LeNet-1, as a demonstration for real-time application, they loaded the neural network into a AT&T DSP-32C digital signal processor^[13] with a peak performance of 12.5 million multiply-add operations per second. It could normalize-and-classify 10 digits a second, or classify 30 normalized digits a second. Shortly afterwards, the research group started working with a development group and a product group at NCR (acquired by AT&T in 1991). It resulted in ATM machines that could read the numerical amounts on checks using a LeNet loaded on DSP-32C. Later, NCR deployed a similar system in large cheque reading machines in bank back offices.^[14]

The LeNet-5 means the emergence of CNN and defines the basic components of CNN.^[1] But it was not popular at that time because of the lack of hardware, especially since GPUs and other algorithms, such as SVM, could achieve similar effects or even exceed LeNet.

Since the success of AlexNet in 2012, CNN has become the best choice for computer vision applications and many different types of CNN have been created, such as the R-CNN series. Nowadays, CNN models are quite different from LeNet, but they are all developed on the basis of LeNet.

A three-layer tree architecture imitating LeNet-5 and consisting of only one convolutional layer, has achieved a similar success rate on the CIFAR-10 dataset.^[15]

Increasing the number of filters for the LeNet architecture results in a power law decay of the error rate. These results indicate that a shallow network can achieve the same performance as deep learning architectures.^[16]

• LeNet-5, convolutional neural networks. An online project page for LeNet maintained by Yann LeCun, containing animations and bibliography.
• projects:lush [leon.bottou.org]. Lush, an object-oriented programming language. It contains SN, a neural network simulator. The LeNet series was written in SN.