Implementation:Fastai Fastbook Loss Functions

Knowledge Sources	fastbook fastai docs PyTorch nn.functional docs
Domains	Deep Learning, Classification, Loss Functions
Last Updated	2026-02-09 17:00 GMT

Overview

Concrete tool for measuring distance between tensors provided by torch.nn.functional, wrapping L1 loss (mean absolute error) and MSE loss (mean squared error) as standard PyTorch loss functions.

Description

PyTorch provides F.l1_loss and F.mse_loss as built-in implementations of the two most common distance metrics. In the fastbook Chapter 4 "pixel similarity" baseline, these functions measure how far a single digit image is from the per-class mean template. The image is classified by determining which template yields a smaller distance.

Usage

Import these functions when you need to:

• Compute L1 or L2 distance between two tensors of the same shape.
• Establish a baseline classifier using template matching.
• Use a standard loss function in a training loop (MSE loss is differentiable and commonly used for regression).

Code Reference

Source Location

• Repository: fastbook
• File: 04_mnist_basics.ipynb (Chapter 4), "Pixel Similarity" section

Signature

torch.nn.functional.l1_loss(input, target, reduction='mean') -> Tensor
torch.nn.functional.mse_loss(input, target, reduction='mean') -> Tensor

# Manual equivalents from the book:
dist_l1 = (a_3 - mean3).abs().mean()
dist_mse = ((a_3 - mean3)**2).mean().sqrt()

Import

import torch.nn.functional as F

I/O Contract

Inputs

Name	Type	Required	Description
input	Tensor, shape (H, W) or any shape	Yes	The image tensor (or prediction tensor) to measure distance from
target	Tensor, same shape as input	Yes	The template tensor (or ground-truth tensor) to measure distance to
reduction	str	No	How to reduce the output: 'mean' (default), 'sum', or 'none'

Outputs

Name	Type	Description
loss	Tensor (scalar when reduction='mean')	The computed L1 or MSE distance between input and target

Usage Examples

Basic Usage

import torch
import torch.nn.functional as F
from fastai.vision.all import *

# Load data and compute mean templates
path = untar_data(URLs.MNIST_SAMPLE)
threes = (path/'train'/'3').ls().sorted()
sevens = (path/'train'/'7').ls().sorted()

stacked_threes = torch.stack([tensor(Image.open(o)) for o in threes]).float() / 255
stacked_sevens = torch.stack([tensor(Image.open(o)) for o in sevens]).float() / 255
mean3 = stacked_threes.mean(0)
mean7 = stacked_sevens.mean(0)

# Pick a sample digit 3
a_3 = stacked_threes[1]

# Measure L1 distance to each template
dist_3_l1 = F.l1_loss(a_3, mean3)
dist_7_l1 = F.l1_loss(a_3, mean7)
print(f"L1 to mean3: {dist_3_l1:.4f}, L1 to mean7: {dist_7_l1:.4f}")
# L1 to mean3: 0.1114, L1 to mean7: 0.1586

# Measure MSE distance to each template
dist_3_mse = F.mse_loss(a_3, mean3).sqrt()
dist_7_mse = F.mse_loss(a_3, mean7).sqrt()
print(f"RMSE to mean3: {dist_3_mse:.4f}, RMSE to mean7: {dist_7_mse:.4f}")
# RMSE to mean3: 0.2021, RMSE to mean7: 0.3021

# Classification: closer to mean3 -> predict 3
if dist_3_l1 < dist_7_l1:
    print("Predicted: 3")
else:
    print("Predicted: 7")

Manual Computation (Without F.l1_loss / F.mse_loss)

# These are equivalent to the PyTorch built-in functions:
dist_3_abs = (a_3 - mean3).abs().mean()          # same as F.l1_loss(a_3, mean3)
dist_3_sqr = ((a_3 - mean3)**2).mean().sqrt()    # same as F.mse_loss(a_3, mean3).sqrt()

Related Pages

Implements Principle

• Principle:Fastai_Fastbook_Distance_Classification

Requires Environment

• Environment:Fastai_Fastbook_Python_FastAI_Environment