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symbolic_nn_tests/symbolic_nn_tests/experiment_1/semantic_loss.py

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3.5 KiB
Python

import torch
def create_semantic_cross_entropy(semantic_matrix):
def semantic_cross_entropy(input, target):
ce_loss = torch.nn.functional.cross_entropy(input, target)
penalty_tensor = semantic_matrix[target.argmax(dim=1)]
abs_diff = (target - input).abs()
semantic_penalty = (abs_diff * penalty_tensor).sum()
return ce_loss * semantic_penalty
return semantic_cross_entropy
# NOTE: This similarity matrix defines loss scaling factors for misclassification
# of numbers from our QMNIST dataset. Visually similar numbers (e.g: 3/8) are
# penalised less harshly than visually distinct numbers as this mistake is "less
# mistaken" given our understanding of the visual characteristics of numerals.
# By using this scaling matric we can inject human knowledge into the model via
# the loss function, making this an example of a "semantic loss function"
SIMILARITY_MATRIX = torch.tensor(
[
[2.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
[1.0, 2.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.5, 1.0, 1.0],
[1.0, 1.0, 2.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
[1.0, 1.0, 1.0, 2.0, 1.0, 1.0, 1.0, 1.0, 1.5, 1.0],
[1.0, 1.0, 1.0, 1.0, 2.0, 1.0, 1.0, 1.0, 1.0, 1.0],
[1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 1.5, 1.0, 1.0, 1.0],
[1.0, 1.0, 1.0, 1.0, 1.0, 1.5, 2.0, 1.0, 1.0, 1.0],
[1.0, 1.5, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 1.0, 1.0],
[1.0, 1.0, 1.0, 1.5, 1.0, 1.0, 1.0, 1.0, 2.0, 1.0],
[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0],
]
).to("cuda")
SIMILARITY_MATRIX /= SIMILARITY_MATRIX.sum() # Normalized to sum of 1
similarity_cross_entropy = create_semantic_cross_entropy(SIMILARITY_MATRIX)
# NOTE: The following matrix encodes a simpler semantic penalty for correctly/incorrectly
# identifying shapes with straight lines in their representation. This can be a bit fuzzy
# in cases like "9" though.
HASLINE_MATRIX = torch.tensor(
# 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
[False, True, False, False, True, True, False, True, False, True]
).to("cuda")
HASLINE_MATRIX = torch.stack([i ^ HASLINE_MATRIX for i in HASLINE_MATRIX]).type(
torch.float64
)
HASLINE_MATRIX += 1
HASLINE_MATRIX /= HASLINE_MATRIX.sum() # Normalize to sum of 1
hasline_cross_entropy = create_semantic_cross_entropy(HASLINE_MATRIX)
# NOTE: Similarly, we can do the same for closed circular loops in a numeric character
HASLOOP_MATRIX = torch.tensor(
# 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
[True, False, False, False, False, False, True, False, True, True]
).to("cuda")
HASLOOP_MATRIX = torch.stack([i ^ HASLOOP_MATRIX for i in HASLOOP_MATRIX]).type(
torch.float64
)
HASLOOP_MATRIX += 1
HASLOOP_MATRIX /= HASLOOP_MATRIX.sum() # Normalize to sum of 1
hasloop_cross_entropy = create_semantic_cross_entropy(HASLOOP_MATRIX)
# NOTE: We can also combine all of these semantic matrices
MULTISEMANTIC_MATRIX = SIMILARITY_MATRIX * HASLINE_MATRIX * HASLOOP_MATRIX
MULTISEMANTIC_MATRIX /= MULTISEMANTIC_MATRIX.sum()
multisemantic_cross_entropy = create_semantic_cross_entropy(MULTISEMANTIC_MATRIX)
# NOTE: As a final test, lets make something similar to tehse but where there's no knowledge,
# just random data. This will create a benchmark for the effects of this process wothout the
# "knowledge" component
GARBAGE_MATRIX = torch.rand(10, 10).to("cuda")
GARBAGE_MATRIX /= GARBAGE_MATRIX.sum()
garbage_cross_entropy = create_semantic_cross_entropy(GARBAGE_MATRIX)