🏋️  Logit Space

Logit Space#

The pre-activation, log-odds scale on which linear models and nets operate.

Important

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What it is#

Logit space means working with the raw log-odds scores \(z\) (the logits) instead of the probabilities \(p = \sigma(z)\) — the “pre-sigmoid” world, where values span the whole real line rather than being squeezed into (0,1).

Why it’s used#

Computing the loss directly from logits is far more numerically stable. Converting a logit to a probability and then taking its log can underflow (a tiny \(p\) rounds to 0, and \(\log 0 = -\infty\)) or overflow (\(e^{z}\) for a large logit exceeds the float range); staying in logit space with the log-sum-exp trick avoids both. This is why frameworks fuse sigmoid + BCE (BCEWithLogitsLoss) and softmax + cross-entropy into a single from_logits op.

The payoff#

Better stability and cleaner gradients — the same reason log-space helps elsewhere. Logit space ties the log-odds, the sigmoid, and the cross-entropy loss into one numerically safe computation.


Theme: Model Training & Optimization  ·  All terminology


Hint

Mind map — connected ideas

Log-Odds · Binary Cross-Entropy (BCE) · Sigmoid Function · Loss Functions · Underflow · Log-Space


See also

Source article Adapted (context, re-expressed) in our own words from: Logit Space (insightful-data-lab.com).

Tags: purpose: reference topic: terminology level: intermediate