Convolutional neural networks for matlab

MatConvNet User Manual

Convolutional Neural Networks for MATLAB

Version 1.0-beta

Andrea Vedaldi Karel Lenc

Contents

1 Introduction 1

2 Introduction to convolutional neural netowrks 2

2.1 MatConvNet on a glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.2 The structure and evaluation of CNNs . . . . . . . . . . . . . . . . . . . . . 3

3.4 Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.5 Softmax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.6 Log-loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.7 Softmax log-loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Network wrappers and examples 11

4.1 Pre-trained models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.2 Learning models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.3 Running large scale experiments . . . . . . . . . . . . . . . . . . . . . . . . . 13

5 About MatConvNet 13

5.1 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

combined to create CNNs. Section 4 discusses more abstract CNN wrappers and example

code and models.

2 Introduction to convolutional neural netowrks

A Convolutional Neural Network (CNN) is can be viewed as a function f mapping some data

x, for example an image, on some output vector y. The function f is the composition of

a sequence (or directed acyclic graph) of simpler functional blocks f

1

, . . . , f

all or some of these blocks are convolutional, in the sense that they take an image as input

and produce an image as output by applying a translation invariant and local operator,

such as a linear filter. MatConvNet contains implementation for the most commonly used

example is image classification; in this case the output of the CNN is a vector y = f(x) ∈ R

containing the confidence that x belong to any of C possible classes. Given training data

(x

(i)

, y

(i)

) (where y

(i)

is the indicator vector of the class of x

(i)

, the parameters are learned

by solving

argmin

`

f(x

(i)

; w

1

, . . . , w

where ` is a suitable loss function (e.g. the hinge or log loss).

The optimization problem (1) is usually non-convex and very large as complex CNN archi-

tectures need to be trained from hundred-thousands or even million of examples. Therefore

efficiency is a paramount. The objective is usually optimized using a variant of stochastic gra-

dient descent. The algorithm is, conceptually, very simple: at each iteration a training point

is selected at random, the derivative of the loss term for that training sample is computed

resulting in a gradient vector, and parameters are incrementally updated by stepping down

the gradient. The key operation here is to compute the derivative of the objective function,

Larger models, in particular, may require in practice to run calculations on a GPU. MatCon-

vNet has integrated GPU support based on nVidia CUDA.

MatConvNet has a simple design philosophy. Rather than wrapping CNNs around complex

layers of software, it exposes simple functions to compute CNN building blocks, such as

convolution and ReLU operators. These building blocks are easy to combine into a complete

CNNs or learning algorithms. While several real-world examples of small and large CNN

architectures and training routines are provided, it is always possible to go back to the basics

and build your own, using the efficiency of MATLAB in prototyping. Often no C coding is

required at all to try a new architectures. As such, MatConvNet is an ideal playground for

research.

MatConvNet contains the following elements:

and the last dimension image instances. A computational block f is therefore represented as

follows:

y

w

Formally, x is a 4D tensor stacking N 3D images

x ∈ R

H×W ×D×N