Visualization of hidden node activity
in a feed forward neural network
Adam Arvay
Feed forward neural networks
• Function finding device
• Learns a function to transform a set of inputs
into the desired output
• Uses supervised learning
Network building software
• PyBrain v0.3
• Modular machine learning library for Python
• PyBrain is short for Python-Based
Reinforcement Learning, Artificial Intelligence
and Neural Network Library
Visualization tools
• NetworkX
– Used for keeping track of node names and edges
• matplotlib/pyplot/pylab
– Drawing everything
Data set
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Iris data set
150 total data points
4 inputs
3 outputs (classifications)
50 of each classification type
CSV file
Networks analyzed
• 3 networks were constructed with different
numbers of hidden layers
– 4 input nodes (linear)
– 4, 7, 10 hidden nodes (sigmoid)
– 3 output nodes (softmax)
• Trained with back-propigation
• Training/validation data selected randomly
• 250 epochs
Visualizations
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Mean squared errors during training
Network state
Average activation levels
Absolute hidden node sensitivity
Weighted hidden node sensitivity
Activation scatter
Mean squared error
• Quick way to evaluate training efficacy
• Plot the error vs. training time (epochs)
• Expect error to go down with increased
training
• Greatly depends on quality of training data
Mean squared error
Network state visualization
• Displays abstract logical connections between
nodes in a spatial layout
• Size to represent activation level
• Colored and line style used to depict
connection type. Black for positive, red
dashed for negative
Network state visualization
• A snapshot of what the network is currently
doing
• Interactivity:
– Shows the state of the network under a particular
activation
– Visible edge threshold magnitude can be set
– Edges can be labeled
Network state
Network state
Network state
Network state all connections
Network state all connections with all
labels
Network state 7 nodes no labels
Network state 7 nodes
Network state 7 nodes
Network state 10 nodes
Network state 10 nodes
Network state 10 all connections
Network state
• Gives information about current state of
network
• Interactive
• Can get cluttered with many nodes and
connections
• Difficult to see trends
Average activation levels
• Gives an idea of the network behavior over
time for a particular classification type
• Can detect pattern differences in hidden layer
between classification types
• Shows the average activation level of a hidden
node across a classification type
• No interactivity
4 nodes, setosa
4 nodes, versacolor
4 nodes, virginica
7 nodes setosa
7 nodes versacolor
7 nodes virginica
10 nodes setosa
10 nodes versacolor
10 nodes virginica
Average activation
• Can see some patterns between classificaitons
• Easy to spot changes and non-changes
• Doesn’t depict the variance in the activations
Absolute hidden node sensitivity
• A quick way to determine the sensitivity of a
hidden node to its inputs
• Can detect nodes which are insensitive to all
inputs
• Can detect which inputs are ignored by all
nodes
• Can detect patterns of connections across
nodes
Hidden node sensitivity
Hidden node sensitivity
Hidden node sensitivity
Weighted sensitivity
• Accounts for differences in magnitude of the
input parameters
• In the iris data set, the first input has a much
larger average value than the last input.
• Normalizes the weights to the inputs
Weighted sensitivity
Weighted sensitivity
Weighted sensitivity
Comparison
non-weighted vs weighted
Activation scatter
• Used along with average activation to get
more information about the activation activity
of hidden nodes across a classification type
• Can get a sense of the variance of a particular
node
• Color used to represent a node along with
data labels.
Activation scatter setosa
Activation scatter versacolor
Activation scatter virginica
Conclusion
• 4 main visualization tools
– Training data
– Network state
– Average activation
– Hidden node sensitivity
• Designed to be used with 3 layer networks
with arbitrary number of nodes per layer