Convolutional Neural Networks (LeNet)

LeNet sets the CNN template

LeNet-5 (Yann LeCun et al., 1989; deployed in the 1990s) recognized handwritten digits on bank checks.

Its organization—a convolutional encoder in which spatial dimensions shrink and channels grow, followed by a dense head—influenced many later CNN architectures.

LeNet-5 architecture

LeNet-5 data flow on a 28×28 handwritten digit. Spatial dims shrink; channels grow.

Layer-by-layer

Conv1: 1→6 channels, 5×5 kernel, padding 2 (28→28)
AvgPool: stride 2 → 14×14
Conv2: 6→16 channels, 5×5, no padding → 10×10
AvgPool: stride 2 → 5×5
Flatten → 16·5·5 = 400 → 120 → 84 → 10

Two conv→sigmoid→avgpool blocks, three FC layers, 10 logits.

Compressed view

Same network, vertical schematic (the textbook version):

Compact LeNet-5 schematic.

Two takeaways

Pyramid shape: spatial dimensions halve at each pooling layer while the number of channels increases. Many later CNNs retain this pattern.
The bottleneck is the flatten: 400 × 120 = 48000 weights from conv block to first dense layer. Modern CNNs replace the dense stack with global average pooling, which is much cheaper.

Implementation setup

The figure translates directly to a Sequential model. Xavier initialization helps keep the sigmoid layers from saturating early in training:

from d2l import jax as d2l
from flax import nnx
from jax import numpy as jnp

LeNet in code

LeNet initialization

class LeNet(d2l.Classifier):
    """The LeNet-5 model."""
    def __init__(self, lr=0.1, num_classes=10, kernel_init=None, rngs=None):
        super().__init__()
        self.save_hyperparameters(ignore=['rngs', 'kernel_init'])
        rngs = nnx.Rngs(d2l.get_key()) if rngs is None else rngs
        kernel_init = (nnx.initializers.xavier_uniform() if kernel_init is None
                       else kernel_init)
        self.net = nnx.Sequential(
            nnx.Conv(1, 6, kernel_size=(5, 5), padding='SAME',
                     kernel_init=kernel_init, rngs=rngs),
            nnx.sigmoid,
            lambda x: nnx.avg_pool(x, window_shape=(2, 2), strides=(2, 2)),
            nnx.Conv(6, 16, kernel_size=(5, 5), padding='VALID',
                     kernel_init=kernel_init, rngs=rngs),
            nnx.sigmoid,
            lambda x: nnx.avg_pool(x, window_shape=(2, 2), strides=(2, 2)),
            lambda x: x.reshape((x.shape[0], -1)),  # flatten
            nnx.Linear(400, 120, kernel_init=kernel_init, rngs=rngs),
            nnx.sigmoid,
            nnx.Linear(120, 84, kernel_init=kernel_init, rngs=rngs),
            nnx.sigmoid,
            nnx.Linear(84, num_classes, kernel_init=kernel_init, rngs=rngs))

Tracing shapes through the network

To check tensor shapes, pass a dummy (1, 1, 28, 28) input through the layers and print the shape after each. Match this against the figure to verify the architecture is wired correctly:

@d2l.add_to_class(d2l.Classifier)
def layer_summary(self, X_shape):
    X = jnp.zeros(X_shape)
    for layer in self.net.layers:
        X = layer(X)
        print(layer.__class__.__name__, 'output shape:\t', X.shape)

model = LeNet()
model.layer_summary((1, 28, 28, 1))

Conv output shape:   (1, 28, 28, 6)
PjitFunction output shape:   (1, 28, 28, 6)
function output shape:   (1, 14, 14, 6)
Conv output shape:   (1, 10, 10, 16)
PjitFunction output shape:   (1, 10, 10, 16)
function output shape:   (1, 5, 5, 16)
function output shape:   (1, 400)
Linear output shape:     (1, 120)
PjitFunction output shape:   (1, 120)
Linear output shape:     (1, 84)
PjitFunction output shape:   (1, 84)
Linear output shape:     (1, 10)

The output confirms 28→28→14→10→5→flatten→120→84→10, matching the diagram.

Training on Fashion-MNIST

Cross-entropy loss + SGD + 10 epochs. Same Trainer API as every previous chapter; only the model changes:

trainer = d2l.Trainer(max_epochs=10, num_gpus=1)
data = d2l.FashionMNIST(batch_size=128)
model = LeNet(lr=0.1)
trainer.fit(model, data)

Compare the result with the dense MLP from the previous chapter to assess the effect of LeNet’s convolutional inductive bias.

What 30 years of progress changed

LeNet’s 1998 architecture vs. modern best practice:

LeNet (1998)	Modern (2020s)
sigmoid activation	ReLU / GELU
average pooling	max pool / strided conv
no normalization	BatchNorm / LayerNorm
dense head	global average pool + 1 linear
Xavier init	He init
5 layers, ~60k params	50+ layers, millions of params

Each substitution is a section of the next chapter, Modern CNNs (He initialization was introduced in the builder’s guide). The overall convolutional encoder + head organization is retained.

Recap

LeNet-5 demonstrated a CNN in a deployed recognition system.
Architectural template: conv encoder (spatial ↓, channels ↑) → flatten → dense head.
Later CNNs such as ResNet and EfficientNet retain the encoder–head organization while changing its components and scale.
The next chapter swaps every component for its modern equivalent and goes much deeper.