Where You'll Spot Logs in the Wild

The Log Sightings Cheat Sheet

Once you know what to look for, logs are everywhere in AI. A short field guide:

Cross-entropy loss — F.cross_entropy in PyTorch is NLLLoss(log_softmax(x)) under the hood.
Information / entropy — Shannon entropy is $H = - \sum p_{i} lo g p_{i}$ . Bits per token in a language model.
KL divergence — $D_{K L} (P ∥ Q) = \sum p_{i} lo g (p_{i} / q_{i})$ . Used in distillation, RLHF, variational autoencoders.
Logit transformation — $logit (p) = lo g \frac{p}{1 - p}$ . Maps probabilities (0,1) to all of ℝ. Inside every binary classifier.
Log scales in plotting — training curves on log y-axis, learning rate schedules on log scales, perplexity (exp of NLL) on log scales.
Quantization scaling — Q-format and dynamic-range encoding often use log spacing.
Boltzmann / softmax temperature — $P (x) \propto e^{- E (x) / T}$ . Energy = -log probability up to constants.

If a model is computing probabilities, it's almost certainly computing log-probabilities under the hood. Numerical stability demands it.

Track Reward

Logs are the universe's natural normalizer. Your ears do them. AI does them. Loss functions live in log-space. The next time you see F.log_softmax or cross_entropy or logsumexp, you'll see the underlying compression spell, not the syntax.

Code

Logs are quietly running everything·python

import torch
import torch.nn.functional as F

logits = torch.tensor([[2.0, 1.0, 0.5]])

# Three equivalent things, all built on logs:
# 1) Probabilities via softmax
probs = F.softmax(logits, dim=-1)
print(probs)

# 2) Log-probabilities via log_softmax (numerically stable)
log_probs = F.log_softmax(logits, dim=-1)
print(log_probs)

# 3) Negative log-likelihood loss for class 0
loss = F.nll_loss(log_probs, torch.tensor([0]))
print(loss.item())   # ~0.42 — same as cross_entropy on raw logits

Exercise

Look at any neural network training script you've seen. Search for log, entropy, softmax, nll. Count how many lines involve logs (often hidden behind a function name like cross_entropy). Realize that 'training a network' is mostly 'minimizing a sum of log-things.'

Hint

If you don't have a script handy, look at PyTorch tutorials. Almost every classification example uses cross-entropy — and cross-entropy IS log-likelihood-flipped.

Where You'll Spot Logs in the Wild

The Log Sightings Cheat Sheet

Track Reward

Code

External links

Exercise

Progress

Comments 2