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CMPT310 Neural Networks
创建日期：2024-08-02 18:15:23
标签： CMPT310
Neural Networks

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Detecting Handwritten Prime Digits


with Neural Networks

100 points

1 Introduction

Prime numbers are fantastic. In this assignment we will use Multi Layer Perceptrons

to detect handwritten prime digits. But before doing such a difficult

task I suggest to try and solve an easier problem with MLP. If you succeed,

which I know you will, you can proceed with tackling the challenging problem

of detecting handwritten prime digits.

2 Regression - Toy Data

The first task is to learn the function that generated the following data, using

a simple neural network.

The function that produced this data is actually y = x

2+, where  ～ N(0, σ)

is a random noise from a normal distribution with a small variance. We are going

to use an MLP with one hidden layer, which each has 5 neurons, to learn

1

an approximation of this function using the data that we have. This assignment

comes with a starting code, which is incomplete and you are supposed to

complete it.

2.1 Technical Details

2.1.1 Code

The code that comes with this assignment has multiple files including:

assignment

toy example regressor.py

layers.py

neural network.py

utils.py

? toy_example_regressor.py contains most of the codes that are related

to the training procedure, including loading data and iteratively feeding

mini-batches of data to the neural network, plotting the approximated

function and the data, etc. Please read this file and understand it but you

don’t need to modify this.

? layers.py contains definition of the layers that we use in this assignment,

including DenseLayer, SigmoidLayer, and L2LossLayer. Your main responsibility

is to implement forward and backward functions for these

layers.

? neural_network.py contains the definition of a neural network (NeuralNet

class), which is an abstract class. This class basically takes care of running

forward pass and propagating the gradients, backwards, from loss to the

first layer.

? utils.py contains some useful functions.

2.1.2 Data

The training data for this problem, which consists of input data and labels, can

be generated by the function get_data(), which you can find in the main file,

toy_example_regressor.py.

2.1.3 Network Structure

For the regression problem (i.e. the first task) we defined a new class, SimpleNet

, which is inherited from NeuralNet. SimpleNet contains two DenseLayer

s, which one of them has hidden neurons with Sigmoid activation functions.

Network definition can be found in toy_example_regressor.py.

2

2.2 Your Task (total: 80 points)

2.2.1 Implementing compute_activations, compute_gradients, and update_weights

functions

There are three type of layers completely implemented in the layers.py file:

DenseLayer, Sigmoid, and L2LossLayer. However, implementation of DenseLayer

is incomplete. You are supposed to implement the following functions

? DenseLayer: This is a simple dense (or linear or fully connected) layer

that has two types of parameters: weights w and biases b.

– compute_activations (15 points): The value of every output neuron

is oi = x.wi + bi

. The number of input and output neurons are

specified in the __init__ function.

– compute_gradients (20 points): Assume that gradient of the loss

with respect to the output neurons, self._output_error_gradient

, are computed by the next layer already. You need to compute the

gradients of the loss with respect to all the parameters of this layer

(i.e. b and w) and store them in self.dw and self.db so that you

can use them the update the parameters later. Needless to say that

shape of dw and w should be equal, and same goes for db and b. In

addition, you should compute the gradient of the loss with respect

to the input, which is the output of the previous layer, and store it

in self._input_error_gradient. This value will be passed on to

the previous layer in the network, which will be used to compute the

gradients recursively (Back Propagation).

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