3.18. Plotting¶

First, let’s train up a simple network to explore. This one is trained to compute XOR:

In [1]:

from conx import Network, Layer, SGD

#net = Network("XOR Network", 2, 4, 1, activation="sigmoid")

net = Network("XOR 2-4-1 Network")
net.add(Layer("input", shape=2))
net.add(Layer("hidden", shape=4, activation='sigmoid'))
net.add(Layer("output", shape=1, activation='sigmoid'))
net.connect()

dataset = [
    ([0, 0], [0], "1"),
    ([0, 1], [1], "2"),
    ([1, 0], [1], "3"),
    ([1, 1], [0], "4")
]
net.compile(loss='mean_squared_error', optimizer=SGD(lr=0.3, momentum=0.9))
net.dataset.load(dataset)

Using Theano backend.
conx, version 3.5.0

In [2]:

net.get_weights_as_image("hidden", None).size

Out[2]:

(4, 2)

In [3]:

net.get_weights_as_image("hidden", None).resize((400, 200))

Out[3]:

In [4]:

net.plot_layer_weights('hidden', cmap="RdBu")

In [5]:

if net.saved():
    net.load()
    net.plot_loss_acc()
else:
    net.reset(seed=3863479522)
    net.train(epochs=2000, accuracy=1, report_rate=25, plot=True, record=True)
    net.save()

In [6]:

net.plot('loss', ymin=0)

3.18.1. plot_activation_map¶

This plotting function allows us to see the activation of a specific unit in a specific layer, as a function of the activations of two other units from an earlier layer. In this example, we show the behavior of the single output unit as the two input units are varied across the range 0.0 to 1.0:

In [7]:

net.plot_activation_map('input', (0,1), 'output', 0)

We can verify the above output activation map by running different input vectors through the network manually:

In [8]:

input=[1,1];net.propagate(input)[0]

Out[8]:

0.09831498563289642

In [9]:

# map of hidden[2] activation as a function of inputs
net.plot_activation_map('input', (0,1), 'hidden', 2, show_values=True)

----------------------------------------------------------------------------------------------------
Activation of hidden[2] as a function of input[0] and input[1]
rows: input[1] decreasing from 1.00 to 0.00
cols: input[0] increasing from 0.00 to 1.00

0.09 0.09 0.08 0.08 0.08 0.07 0.07 0.07 0.06 0.06 0.06 0.06 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04
0.10 0.10 0.09 0.09 0.09 0.08 0.08 0.08 0.07 0.07 0.07 0.06 0.06 0.06 0.06 0.05 0.05 0.05 0.05 0.04
0.11 0.11 0.10 0.10 0.10 0.09 0.09 0.08 0.08 0.08 0.07 0.07 0.07 0.07 0.06 0.06 0.06 0.05 0.05 0.05
0.12 0.12 0.12 0.11 0.11 0.10 0.10 0.09 0.09 0.09 0.08 0.08 0.08 0.07 0.07 0.07 0.06 0.06 0.06 0.06
0.14 0.13 0.13 0.12 0.12 0.11 0.11 0.10 0.10 0.10 0.09 0.09 0.08 0.08 0.08 0.07 0.07 0.07 0.07 0.06
0.15 0.15 0.14 0.14 0.13 0.13 0.12 0.12 0.11 0.11 0.10 0.10 0.09 0.09 0.09 0.08 0.08 0.08 0.07 0.07
0.17 0.16 0.16 0.15 0.14 0.14 0.13 0.13 0.12 0.12 0.11 0.11 0.10 0.10 0.10 0.09 0.09 0.09 0.08 0.08
0.19 0.18 0.17 0.17 0.16 0.15 0.15 0.14 0.14 0.13 0.13 0.12 0.12 0.11 0.11 0.10 0.10 0.09 0.09 0.09
0.21 0.20 0.19 0.18 0.18 0.17 0.16 0.16 0.15 0.15 0.14 0.13 0.13 0.12 0.12 0.11 0.11 0.11 0.10 0.10
0.23 0.22 0.21 0.20 0.19 0.19 0.18 0.17 0.17 0.16 0.16 0.15 0.14 0.14 0.13 0.13 0.12 0.12 0.11 0.11
0.25 0.24 0.23 0.22 0.21 0.21 0.20 0.19 0.18 0.18 0.17 0.16 0.16 0.15 0.15 0.14 0.14 0.13 0.13 0.12
0.27 0.26 0.25 0.24 0.23 0.23 0.22 0.21 0.20 0.20 0.19 0.18 0.18 0.17 0.16 0.16 0.15 0.14 0.14 0.13
0.29 0.28 0.27 0.27 0.26 0.25 0.24 0.23 0.22 0.22 0.21 0.20 0.19 0.19 0.18 0.17 0.17 0.16 0.15 0.15
0.32 0.31 0.30 0.29 0.28 0.27 0.26 0.25 0.24 0.24 0.23 0.22 0.21 0.20 0.20 0.19 0.18 0.18 0.17 0.16
0.35 0.33 0.32 0.31 0.30 0.30 0.29 0.28 0.27 0.26 0.25 0.24 0.23 0.22 0.22 0.21 0.20 0.19 0.19 0.18
0.37 0.36 0.35 0.34 0.33 0.32 0.31 0.30 0.29 0.28 0.27 0.26 0.25 0.25 0.24 0.23 0.22 0.21 0.21 0.20
0.40 0.39 0.38 0.37 0.36 0.35 0.34 0.33 0.32 0.31 0.30 0.29 0.28 0.27 0.26 0.25 0.24 0.23 0.23 0.22
0.43 0.42 0.41 0.40 0.39 0.37 0.36 0.35 0.34 0.33 0.32 0.31 0.30 0.29 0.28 0.27 0.26 0.26 0.25 0.24
0.46 0.45 0.44 0.42 0.41 0.40 0.39 0.38 0.37 0.36 0.35 0.34 0.33 0.32 0.31 0.30 0.29 0.28 0.27 0.26
0.49 0.48 0.47 0.45 0.44 0.43 0.42 0.41 0.40 0.39 0.38 0.37 0.35 0.34 0.33 0.32 0.31 0.30 0.29 0.28
----------------------------------------------------------------------------------------------------

In [10]:

# map of output activation as a function of hidden units 2,3
net.plot_activation_map('hidden', (2,3), 'output', 0)

How does the network actually solve the problem? We can look at the intermediary values at the hidden layer by plotting each of the 4 hidden units in this manner:

In [11]:

for i in range(4):
    net.plot_activation_map('input', (0,1), 'hidden', i)

In [12]:

net.playback(lambda net, epoch:
             net.plot_activation_map(title="Epoch %s" % epoch, interactive=False))

3.18.2. Adding Additional Hidden Layers¶

In [13]:

from conx import Network, Layer, SGD

net = Network("XOR 2-4-2-1 Network")
net.add(Layer("input", shape=2))
net.add(Layer("hidden", shape=4, activation='sigmoid'))
net.add(Layer("hidden2", shape=2, activation='sigmoid'))
net.add(Layer("output", shape=1, activation='sigmoid'))
net.connect()

dataset = [
    ([0, 0], [0], "1"),
    ([0, 1], [1], "2"),
    ([1, 0], [1], "3"),
    ([1, 1], [0], "4")
]
net.compile(loss='mean_squared_error', optimizer=SGD(lr=0.3, momentum=0.9))
net.dataset.load(dataset)

In [14]:

if net.saved():
    net.load()
    net.plot_loss_acc()
else:
    net.reset(seed=3863479522)
    net.train(epochs=2000, accuracy=1, report_rate=25, plot=True)
    net.save()

In [15]:

for i in range(2):
    net.plot_activation_map('hidden', (0,1), 'hidden2', i)

3.18.3. Plotting training error (loss) and training accuracy (acc)¶

In [16]:

net.plot("loss")

In [17]:

net.plot("acc")

In [18]:

net.plot(["loss", "acc"])

In [19]:

net.plot("all")

3.18.4. Plotting Your Own Data¶

In [20]:

from conx import plot, scatter, get_symbol

In [21]:

data = ["Type 1", [(0, 1), (1, 2), (2, .5)]]
scatter(data)

In [22]:

data = ["My Data", [1, 2, 6, 3, 4, 1]]
symbols = {"My Data": "rx"}
plot(data, symbols=symbols)

In [24]:

data = [["My Data", [1, 2, 6, 3, 4, 1]],
        ["Your Data", [2, 4, 5, 1, 2, 6]]]
symbols = {"My Data": "rx-", "Your Data": "bo-"}
plot(data, symbols=symbols)