def test_predict():
net = nn.SimpleNetwork(np.array([[.1, -.2], [-.3, .4], [.5, -.6]]),
np.array([[-.7, .8, -.9], [.10, -.11, .12]]))
input_matrix = np.array([[13, -14, 15], [-16, 17, -18]])
predictions = net.predict(input_matrix)
[[h11, h12], [h21, h22]] = [[
s(13 * .1 + -14 * -.3 + 15 * .5),
s(13 * -.2 + -14 * .4 + 15 * -.6)
], [s(-16 * .1 + 17 * -.3 - 18 * .5),
s(-16 * -.2 + 17 * .4 + -18 * -.6)]]
npt.assert_allclose(
predictions,
np.array([[
s(h11 * -.7 + h12 * .10),
s(h11 * .8 + h12 * -.11),
s(h11 * -.9 + h12 * .12)
],
[
s(h21 * -.7 + h22 * .10),
s(h21 * .8 + h22 * -.11),
s(h21 * -.9 + h22 * .12)
]]))
binary_predictions = net.predict_zero_one(input_matrix)
npt.assert_array_equal(binary_predictions, np.array([[0, 1, 0], [1, 0,
1]]))
def test_gradients():
net = nn.SimpleNetwork(np.array([[.1, .3, .5], [-.5, -.3, -.1]]),
np.array([[.2, -.2], [.4, -.4], [.6, -.6]]))
input_matrix = np.array([[0, 0], [1, 0], [0, 1], [1, 1]])
output_matrix = np.array([[1, 1], [0, 1], [1, 0], [0, 0]])
[[hi11, hi12, hi13], [hi21, hi22, hi23], [hi31, hi32, hi33],
[hi41, hi42,
hi43]] = hi = [[.1 * 0 + -.5 * 0, .3 * 0 + -.3 * 0, .5 * 0 + -.1 * 0],
[.1 * 1 + -.5 * 0, .3 * 1 + -.3 * 0, .5 * 1 + -.1 * 0],
[.1 * 0 + -.5 * 1, .3 * 0 + -.3 * 1, .5 * 0 + -.1 * 1],
[.1 * 1 + -.5 * 1, .3 * 1 + -.3 * 1, .5 * 1 + -.1 * 1]]
[[h11, h12, h13], [h21, h22, h23], [h31, h32, h33],
[h41, h42, h43]] = [[s(x) for x in row] for row in hi]
[[oi11, oi12], [oi21, oi22], [oi31, oi32], [oi41, oi42]] = oi = [
[h11 * .2 + h12 * .4 + h13 * .6, h11 * -.2 + h12 * -.4 + h13 * -.6],
[h21 * .2 + h22 * .4 + h23 * .6, h21 * -.2 + h22 * -.4 + h23 * -.6],
[h31 * .2 + h32 * .4 + h33 * .6, h31 * -.2 + h32 * -.4 + h33 * -.6],
[h41 * .2 + h42 * .4 + h43 * .6, h41 * -.2 + h42 * -.4 + h43 * -.6]
]
[[o11, o12], [o21, o22], [o31, o32],
[o41, o42]] = [[s(x) for x in row] for row in oi]
[[do11, do12], [do21, do22], [do31, do32],
[do41, do42]] = [[(o11 - 1) * sg(oi11), (o12 - 1) * sg(oi12)],
[(o21 - 0) * sg(oi21), (o22 - 1) * sg(oi22)],
[(o31 - 1) * sg(oi31), (o32 - 0) * sg(oi32)],
[(o41 - 0) * sg(oi41), (o42 - 0) * sg(oi42)]]
[[dh11, dh12, dh13], [dh21, dh22, dh23], [dh31, dh32, dh33],
[dh41, dh42, dh43]] = [[(.2 * do11 + -.2 * do12) * sg(hi11),
(.4 * do11 + -.4 * do12) * sg(hi12),
(.6 * do11 + -.6 * do12) * sg(hi13)],
[(.2 * do21 + -.2 * do22) * sg(hi21),
(.4 * do21 + -.4 * do22) * sg(hi22),
(.6 * do21 + -.6 * do22) * sg(hi23)],
[(.2 * do31 + -.2 * do32) * sg(hi31),
(.4 * do31 + -.4 * do32) * sg(hi32),
(.6 * do31 + -.6 * do32) * sg(hi33)],
[(.2 * do41 + -.2 * do42) * sg(hi41),
(.4 * do41 + -.4 * do42) * sg(hi42),
(.6 * do41 + -.6 * do42) * sg(hi43)]]
[input_to_hidden_gradient,
hidden_to_output_gradient] = net.gradients(input_matrix, output_matrix)
np.testing.assert_allclose(
hidden_to_output_gradient,
np.array([[(do11 * h11 + do21 * h21 + do31 * h31 + do41 * h41) / 4,
(do12 * h11 + do22 * h21 + do32 * h31 + do42 * h41) / 4],
[(do11 * h12 + do21 * h22 + do31 * h32 + do41 * h42) / 4,
(do12 * h12 + do22 * h22 + do32 * h32 + do42 * h42) / 4],
[(do11 * h13 + do21 * h23 + do31 * h33 + do41 * h43) / 4,
(do12 * h13 + do22 * h23 + do32 * h33 + do42 * h43) / 4]]))
np.testing.assert_allclose(
input_to_hidden_gradient,
np.array([[(0 * dh11 + 1 * dh21 + 0 * dh31 + 1 * dh41) / 4,
(0 * dh12 + 1 * dh22 + 0 * dh32 + 1 * dh42) / 4,
(0 * dh13 + 1 * dh23 + 0 * dh33 + 1 * dh43) / 4],
[(0 * dh11 + 0 * dh21 + 1 * dh31 + 1 * dh41) / 4,
(0 * dh12 + 0 * dh22 + 1 * dh32 + 1 * dh42) / 4,
(0 * dh13 + 0 * dh23 + 1 * dh33 + 1 * dh43) / 4]]))