ML for physical and natural scientists 2023 10
dr.federica bianco  fbb.space  fedhere  fedhere
Generative AI: autoencoders
this slide deck:
Deep Learning
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recap
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multilayer perceptron
w: weight
sets the sensitivity of a neuron
b: bias:
updown weights a neuron
multilayer perceptron
output
layer of perceptrons
w: weight
sets the sensitivity of a neuron
b: bias:
updown weights a neuron
f: activation function:
turns neurons onoff
multilayer perceptron
w: weight
sets the sensitivity of a neuron
b: bias:
updown weights a neuron
f: activation function:
turns neurons onoff
layer connectivity
output
input layer
hidden layer
output layer
Fully connected: all nodes go to all nodes of the next layer.
output
input layer
hidden layer
output layer
Sparcely connected: all nodes go to all nodes of the next layer.
layer connectivity
output
input layer
hidden layer
output layer
Sparcely connected: all nodes go to all nodes of the next layer.
The last layer is always connected
layer connectivity
how does it relate to matrix multiplication
each layer is a matrix
Except this is a very misleading representation
there are no biases or activation functions
each layer should be a different shape
1x3
3x5
5x2
=
2x1
what we are doing is just a series of matrix multiplictions.
DeepNeuralNetwork
what we are doing is exactly a series of matrix multiplictions.
3x5
5x2
2x1
=
DeepNeuralNetwork
what we are doing is exactly a series of matrix multiplictions.
3x5
5x2
2x1
=
DeepNeuralNetwork
what we are doing is exactly a series of matrix multiplictions.
3x5
5x2
2x1
=
DeepNeuralNetwork
what we are doing is exactly a series of matrix multiplictions.
DeepNeuralNetwork
The purpose is to approximate a function φ
y = φ(x)
which (in general) is not linear with linear operations
DeepNeuralNetwork
The purpose is to approximate a function φ
y = φ(x)
which (in general) is not linear with linear operations
output
input layer
hidden layer
output layer
hidden layer
32 parameters and
?? hyperparameters
activation functions 
loss function  1
optimization method  1
architecture  M
how many hyperparameters?
Parameters and hyperparameters
Training models with this many parameters requires a lot of care:
. defining the metric
. optimization schemes
. training/validation/testing sets
But just like our simple linear regression case, the fact that small changes in the parameters leads to small changes in the output for the right activation functions.
define a cost function, e.g.
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proper care of your DNN
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NN are a vast topics and we only have 2 weeks!
Some FREE references!
michael nielsen
better pedagogical approach, more basic, more clear
ian goodfellow
mathematical approach, more advanced, unfinished
michael nielsen
better pedagogical approach, more basic, more clear
Lots of parameters and lots of hyperparameters! What to choose?
cheatsheet

architecture  wide networks tend to overfit, deep networks are hard to train
 number of epochs  the sweet spot is when learning slows down, but before you start overfitting... it may take DAYS! jumps may indicate bad initial choices (like in all gradient descent)
 loss function  needs to be appropriate to the task, e.g. classification vs regression

activation functions  needs to be consistent with the loss function
 optimization scheme  needs to be appropriate to the task and data
 learning rate in optimization  balance speed and accuracy
 batch size  smaller batch size is faster but leads to overtraining
An article that compars various DNNs
An article that compars various DNNs
accuracy comparison
An article that compars various DNNs
accuracy comparison
An article that compars various DNNs
batch size
Lots of parameters and lots of hyperparameters! What to choose?
cheatsheet
 architecture  wide networks tend to overfit, deep networks are hard to train

number of epochs  the sweet spot is when learning slows down, but before you start overfitting... it may take DAYS! jumps may indicate bad initial choices

loss function  needs to be appropriate to the task, e.g. classification vs regression

activation functions  needs to be consistent with the loss function
 optimization scheme  needs to be appropriate to the task and data
 learning rate in optimization  balance speed and accuracy
 batch size  smaller batch size is faster but leads to overtraining
What should I choose for the loss function and how does that relate to the activation functiom and optimization?
Lots of parameters and lots of hyperparameters! What to choose?
Lots of parameters and lots of hyperparameters! What to choose?
cheatsheet
always check your loss function! it should go down smoothly and flatten out at the end of the training.
not flat? you are still learning!
too flat? you are overfitting...
loss (gallery of horrors)
jumps are not unlikely (and not necessarily a problem) if your activations are discontinuous (e.g. relu)
when you use validation you are introducing regularizations (e.g. dropout) so the loss can be smaller than for the training set
loss and learning rate (not that the appropriate learning rate depends on the chosen optimization scheme!)
Building a DNN
with keras and tensorflow
autoencoder for image recontstruction
What should I choose for the loss function and how does that relate to the activation functiom and optimization?
loss  good for  activation last layer  size last layer 

mean_squared_error  regression  linear  one node 
mean_absolute_error  regression  linear  one node 
mean_squared_logarithmit_error  regression  linear  one node 
binary_crossentropy  binary classification  sigmoid  one node 
categorical_crossentropy  multiclass classification  sigmoid  N nodes 
Kullback_Divergence  multiclass classification, probabilistic inerpretation  sigmoid  N nodes 
On the interpretability of DNNs
generative AI
1
Applications

Image Generation (and 3D Shape Generation)

Semantic ImagetoPhoto Translation

Image Resolution Increase

TexttoSpeech Generator

SpeechtoSpeech Conversion

Text Generation (Chat GP3)

Music Generation

ImagetoImage Conversion
GANs
GANs
VAE
Diffusion models
VAE
Autoencoders
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Unsupervised learning with
Neural Networks
What do NN do? approximate complex functions with series of linear functions
.... so if my layers are smaller what I have is a compact representation of the data
Unsupervised learning with
Neural Networks
What do NN do? approximate complex functions with series of linear functions
To do that they extract information from the data
Each layer of the DNN produces a representation of the data a "latent representation" .
The dimensionality of that latent representation is determined by the size of the layer (and its connectivity, but we will ignore this bit for now)
.... so if my layers are smaller what I have is a compact representation of the data
Autoencoder Architecture
Feed Forward DNN:
the size of the input is 5,
the size of the last layer is 2
Autoencoder Architecture
 Encoder: outputs a lower dimensional representation z of the data x (similar to PCA, tSNE...)
 Decoder: Learns how to reconstruct x given z: learns p(xz)
Autoencoder Architecture
Building a DNN
with keras and tensorflow
Trivial to build, but the devil is in the details!
Building a DNN
with keras and tensorflow
Trivial to build, but the devil is in the details!
from keras.models import Sequential
#can upload pretrained models from keras.models
from keras.layers import Dense, Conv2D, MaxPooling2D
#create model
model = Sequential()
#create the model architecture by adding model layers
model.add(Dense(10, activation='relu', input_shape=(n_cols,)))
model.add(Dense(10, activation='relu'))
model.add(Dense(1))
#need to choose the loss function, metric, optimization scheme
model.compile(optimizer='adam', loss='mean_squared_error')
#need to learn what to look for  always plot the loss function!
model.fit(x_train, y_train, validation_data=(x_test, y_test),
epochs=20, batch_size=100, verbose=1)
#note that the model allows to give a validation test,
#this is for a 3fold cross valiation: trainvalidatetest
#predict
test_y_predictions = model.predict(validate_X)
Building a DNN
with keras and tensorflow
autoencoder for image recontstruction
encoder
This autoencoder model has a 64neuron bottle neck. This means it will generate a compressed representation of the data out of that layer which is 16dimensional (the original size is 784 pixels)
Building a DNN
with keras and tensorflow
autoencoder for image recontstruction
This autoencoder model has a 64neuron bottle neck. This means it will generate a compressed representation of the data out of that layer which is 16dimensional (the original size is 784 pixels)
Building a DNN
with keras and tensorflow
autoencoder for image recontstruction
decoder
This autoencoder model has a 64neuron bottle neck. This means it will generate a compressed representation of the data out of that layer which is 16dimensional (the original size is 784 pixels)
Building a DNN
with keras and tensorflow
autoencoder for image recontstruction
This autoencoder model has a 64neuron bottle neck. This means it will generate a compressed representation of the data out of that layer which is 16dimensional (the original size is 784 pixels)
bottle neck
Building a DNN
with keras and tensorflow
autoencoder for image recontstruction
This simple model has 200K parameters!
My original choice is to train it with "adadelta" with a mean squared loss function, all activation functions are relu, appropriate for a linear regression
Building a DNN
with keras and tensorflow
autoencoder for image recontstruction
What should I choose for the loss function and how does that relate to the activation functiom and optimization?
Building a DNN
with keras and tensorflow
autoencoder for image recontstruction
What should I choose for the loss function and how does that relate to the activation functiom and optimization?
loss  good for  activation last layer  size last layer 

mean_squared_error  regression  linear  one node 
mean_absolute_error  regression  linear  one node 
mean_squared_logarithmit_error  regression  linear  one node 
binary_crossentropy  binary classification  sigmoid  one node 
categorical_crossentropy  multiclass classification  sigmoid  N nodes 
Kullback_Divergence  multiclass classification, probabilistic inerpretation  sigmoid  N nodes 
autoencoder for image recontstruction
model_digits64.add(Dense(ndim,
activation='linear'))
model_digits64_sig.compile(optimizer="adadelta",
loss="mean_squared_error")
model_digits64_sig.add(Dense(ndim,
activation='sigmoid'))
model_digits64_sig.compile(optimizer="adadelta",
loss="mean_squared_error")
model_digits64_sig.add(Dense(ndim,
activation='sigmoid'))
model_digits64_bce.compile(optimizer="adadelta",
loss="binary_crossentropy")
loss function: did not finish learning, it is still decreasing rapidly
The predictions are far too detailed. While the input is not binary, it does not have a lot of details. Maybe approaching it as a binary problem (with a sigmoid and a binary cross entropy loss) will give better results
loss function: also did not finish learning, it is still decreasing rapidly
A sigmoid gives activation gives a much better result!
Binary cross entropy loss function: It is more appriopriate when the output layer is sigmoid
Even better results!
original
predicted
predicted
original
predicted
original
predicted
autoencoder for image recontstruction
A more ambitious model has a 16 neurons bottle neck: we are trying to extract 16 numbers to reconstruct the entire image! its pretty remarcable! those 16 number are extracted features from the data
predicted
original
latent
representation
models are neutral, the bias is in the data (or is it?)
Why does this AI model whitens Obama face?
Simple answer: the data is biased. The algorithm is fed more images of white people
models are neutral, the bias is in the data (or is it?)
Why does this AI model whitens Obama face?
Simple answer: the data is biased. The algorithm is fed more images of white people
But really, would the opposite have been acceptable? The bias is in society
Joy Boulamwini
models are neutral, the bias is in the data (or is it?)
comparing generative AI models
3
see also https://arxiv.org/pdf/2103.04922.pdf
The latent space is assumed to be Gaussian distributed  this causes inaccuracy (blurry) generation
similar to a VAE but with a NN in the middle that approximates the true distribution of the latent space
The latent space is assumed to be Gaussian distributed  this causes inaccuracy (blurry) generation
Normalizing Flows
have two networks trained at the same time that compete again each other in a minimax game.
The generator generates images, starting with pure noise.
The discriminator classifies the image from the generator as Real/Fake
trained not to be fooled by the generator.
generator is trained to make better images
Ian Goodfellow et al., 2014 Generative Adversarial Networks
GANs: Generative Adversarial NN
trained not to be fooled by the generator.
generator is trained to make better images
Minmax Loss Function:
minimize
maximize
GANs: Generative Adversarial NN
trained not to be fooled by the generator.
generator is trained to make better images
Minmax Loss Function:
minimize
maximize
log(D(G(z)))
change introduced to minimize geneerator saturation
GANs: Generative Adversarial NN
DDPM:Denoising Diffusion Probabilistic Model
Ho Jain Abbel 2006
Which generative AI is right for you??
resources
Neural Network and Deep Learning
an excellent and free book on NN and DL
http://neuralnetworksanddeeplearning.com/index.html
Deep Learning An MIT Press book in preparation
Ian Goodfellow, Yoshua Bengio and Aaron Courville
https://www.deeplearningbook.org/lecture_slides.html
History of NN
https://cs.stanford.edu/people/eroberts/courses/soco/projects/neuralnetworks/History/history2.html
DNN for time series
RNN
RNN architecture
input layer
output layer
hidden layers
Feedforward architecture
RNN architecture
output layer
hidden layers
Feedforward NN architecture
Recurrent NN architecture
input layer
output layer
RNN hidden layers
output layer
hidden layers
input layer
RNN architecture
input layer
output layer
RNN hidden layers
current state
previous state
Remember the statespace problem!
we want process a sequence of vectors x applying a recurrence formula at every time step:
RNN architecture
input layer
output layer
RNN hidden layers
Remember the statespace problem!
we want process a sequence of vectors x applying a recurrence formula at every time step:
current state
previous state
features
(can be time dependent)
function with parameters q
MLTSA:
state space model (from week 4)
A Statespace model is a model to derive the value of a timedependent variable x(t), the state, generated by a noisy Markovian process, from observations of a variable y(t), also subject to noise, linearly related to the target variable
Definition
RNN architecture
input layer
output layer
RNN hidden layers
Simplest possible RNN
Whh
Wxh
Why
RNN architecture
input layer
Alternative graphical representation of RNN
Whh
h(t1)
h(t)
h(t+1)
h(t+2)
h(t+3)
h(t+4)
y(t)
y(t+1)
y(t+2)
y(t+4)
y(t+3)
y(t+5)
Why
Why
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the weights are the same! always the same Whh and Why
RNN architecture
appllications
image captioning:
one image to a
sequence of worods
sentiment analysis
sequence of words to one sentiment
language translator
sequence of words to sequence of words
online: video classification frame by frame
RNN architecture
more complicated RNNs
Some layers will be recurrent, others will not. Does not need to be fully connected
RNN architecture
input layer
e(t)
h(t1)
h(t)
h(t+1)
h(t+2)
h(t+3)
h(t+4)
y(t)
y(t+1)
y(t+2)
y(t+4)
y(t+3)
y(t+5)
Why
Why
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Wxh
each output has its own loss
Why
e(t+1)
e(t+2)
e(t+3)
e(t+4)
e(t+5)
vanishing gradient problem!
input layer
h(t1)
h(t)
h(t+1)
h(t+2)
h(t+3)
h(t+4)
y(t)
y(t+1)
y(t+2)
y(t+4)
y(t+3)
y(t+5)
Why
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