Verified80% confidenceFactExact time
The mathematical definition of entropy is H(p) = -∑ p(x_i) log p(x_i).
6
Sources
80%
Confidence
Long-term
Relevance
8/2/2026
First Seen
Sources
From Entropy to Cross-Entropy: An Information-Theoretic Derivation of the Logistic Regression Loss Function
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UnverifiedWith sigmoid activation combined with cross-entropy loss, differentiating the loss with respect to the weights simplifies to ∂L/∂w = (ŷ - y) · x.75% similarVerifiedCross-entropy = entropy of the true distribution + KL divergence.68% similarVerifiedClaude Shannon published 'A Mathematical Theory of Communication' in 1948, proposing the concept of information entropy, whereby low-probability events carry higher information content, with the formula I(x) = -log₂P(x).64% similarUnverifiedThe geometric energy dissipation theorem derives that entropy in a closed system evolves in an oscillatory rather than monotonically increasing manner.61% similarUnverifiedThe core scoring formula of U-Lens is: score = strength of the hidden state pointing toward different directions of doubt × average entropy of the reasoning tokens.59% similar
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