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Kullback-Leibler divergence #131

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Apr 13, 2022
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31 changes: 31 additions & 0 deletions nn/loss.py
Original file line number Diff line number Diff line change
Expand Up @@ -55,3 +55,34 @@ def cross_entropy(*, target: nn.Tensor, estimated: nn.Tensor, estimated_type: st
else:
raise ValueError("estimated_kind must be 'probs', 'log-probs' or 'logits'")
return -nn.dot(target, log_prob, reduce=axis)


def kl_div(*, target: nn.Tensor, estimated: nn.Tensor, estimated_type: str, axis: Optional[nn.Dim] = None) -> nn.Tensor:
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"""
Kullback-Leibler divergence (https://en.wikipedia.org/wiki/Kullback-Leibler_divergence)

L(target, estimated) = target * log(target / estimated)
= target * (log(target) - log(estimated)
:param target: probs, normalized. can also be sparse
:param estimated: probs, log-probs or logits, specified via ``estimated_type``
:param estimated_type: "probs", "log-probs" or "logits"
:param axis: the axis to reduce over
:return: KL-div
"""
if not axis:
assert target.feature_dim
axis = target.feature_dim

if estimated_type == "probs":
log_est = nn.safe_log(estimated)
elif estimated_type == "log-probs":
log_est = estimated
elif estimated_type == "logits":
log_est = nn.log_softmax(estimated, axis=axis)
else:
raise ValueError("estimated_kind must be 'probs', 'log-probs' or 'logits'")

log_target = nn.safe_log(target)
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kl = target * (log_target - log_est)
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return kl
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