Cross entropy loss

As explained in Experimentation for Engineers

A loss metric that measures the discrepancy between a probability distribution predicted by a model and the observed outcome distribution.

Cross-entropy measures prediction quality by comparing a model’s predicted probability distribution with observed outcomes. Out-of-sample cross-entropy can improve while the intended business metric stagnates, so it is not automatically a sufficient optimization target. section 7.1.1

Video recommendation

A model predicts P{swipe} from video features, then ranks videos by predicted swipe probability. Early improvements in out-of-sample cross-entropy coincide with higher DAU, but later improvements produce diminishing gains and eventually no DAU improvement. The engineering failure is optimizing the generic prediction metric without validating its connection to the business outcome. section 7.1.1

Figure 7.1 As the quality of the predictions, P{swipe}, produced by your ML model increases, the DAU increases, too, but at an ever-slower rate.

Shows prediction quality improving while DAU rises at an increasingly slower rate. section 7.1.1

How Experimentation for Engineers covers it

How deep it goes

Defines the metric through a production example but stops short of giving its formula or implementation.

Examples

Uses video swipe probabilities, feature-based ranking, successive model versions, and DAU outcomes.

What it assumes

Assumes familiarity with ML predictions, probability estimates, features, A/B tests, and business metrics.

What you can do after

Evaluate whether prediction improvements translate into the intended business metric rather than assuming correlation.

How it connects

Connects prediction quality with business metrics, A/B testing, recommendation ranking, and DAU.

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Also explained in

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  Math and Architectures of Deep LearningA classification loss that measures the mismatch between a predicted probability distribution over classes and the target distribution.
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  Grokking Machine LearningA multiclass classification loss that compares one-hot class labels with predicted class probabilities using cross-entropy.
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  Inside Deep Learning: Math, Algorithms, ModelsA differentiable classification loss that measures the mismatch between predicted and target probability distributions.
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  Learn Generative AI with PyTorchA loss measure that compares predicted token distributions with the target next tokens for multiclass sequence prediction.
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  Graph Neural Networks in ActionCrossEntropyLoss is a PyTorch loss module that measures classification error from logits and target class labels.
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  Build a Large Language Model (From Scratch)A measure of how far a language model's predicted token distribution is from the target token distribution, used to score predictions during training and evaluation.
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  Deep Learning with PyTorch, Second EditionA loss value based on cross-entropy, used here as the quantity minimized during training.
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  Knowledge Graphs and LLMs in ActionCross-entropy loss is a classification loss that penalizes incorrect probability assignments by comparing predicted probabilities with target labels.
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  Reinforcement Learning from Human FeedbackCross-entropy is the expected negative log probability assigned by one distribution to outcomes drawn from another distribution.
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  Machine Learning System DesignA classification loss that penalizes incorrect probabilistic predictions using the negative logarithm of the probability assigned to the true class.
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  Deep Learning with Python, Third EditionA classification loss that measures the mismatch between predicted probability distributions and true token labels.
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  How Large Language Models WorkA cross-entropy loss function measures the discrepancy between a target probability distribution and a model's predicted probability distribution.
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  Build a Text-to-Image Generator (from Scratch)Categorical cross-entropy loss measures the discrepancy between predicted class probabilities and the ground-truth class in multicategory classification.
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  Machine Learning for Tabular Data: XGBoost, Deep Learning, and AICrossEntropyLoss is a PyTorch loss-function module that combines class-logit normalization with negative log-likelihood for classification.
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  Natural Language Processing in Action, Second EditionLog loss is a probabilistic prediction metric based on the negative logarithm of the probability assigned to the observed target.
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  Deep Learning with R, Third EditionCategorical cross-entropy is a multiclass classification loss that measures the negative log-likelihood of the target class under predicted class probabilities and expects categorically encoded labels.
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  Build a Reasoning Model (From Scratch)A loss function that measures the average negative log probability assigned to the correct target tokens.
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  Grokking AI Algorithms, Second EditionCross-entropy loss is a prediction-error measure computed as the negative logarithm of the probability assigned to the correct outcome.

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Related concepts

• classifieraddresses · A classifier is a predictive computational model that assigns inputs to one or more discrete classes or categories.
• negative log-likelihoodequivalent to · Negative log-likelihood is the negative logarithm of the likelihood a probabilistic model assigns to observed data, commonly used as an objective or loss to minimize.
• focal lossincludes · Focal loss is a classification loss that downweights well-classified examples and emphasizes difficult or misclassified examples, especially under class imbalance.
• uncertaintymeasures · Uncertainty is incomplete knowledge or confidence about a value, state, interpretation, behavior, or outcome.
• likelihoodequivalent to · A likelihood is the probability of observed data under a specified probabilistic model, regarded as a function of candidate hypotheses or parameter values.

This explainer was generated by Manning's knowledge graph from the text of Experimentation for Engineers. The section links point to the parts of the book it draws on.