Cross entropy loss

As explained in How Large Language Models Work

A cross-entropy loss function measures the discrepancy between a target probability distribution and a model's predicted probability distribution.

Cross-entropy loss measures the discrepancy between a target probability distribution and a model’s predicted distribution. During training, it serves as a smoother proxy for accuracy, which changes in discrete jumps and is difficult to optimize directly. section 4.1.1

Why use a proxy?

If a model predicts cancer cases, the correct count might be 48, but actual cases cannot be 48.2. Accuracy therefore produces a nonsmooth target, while cross-entropy provides a better-behaved training objective. The trade-off is that training may optimize what is easy to learn rather than exactly what people want. section 4.1.1

Figure 4.2 Examples of a smooth function on the left and two nonsmooth functions on the right. The center example is mostly smooth, but one region is not smooth because the function has no value. On the right, the function is not smooth anywhere due to the hard change in value.

Compare smooth and nonsmooth functions to see why training objectives need to change gradually rather than jump between values. section 4.1.1

How How Large Language Models Work covers it

How deep it goes

Explains its proxy role but defers mathematical details and implementation.

Examples

Uses cancer-case counts and smooth-versus-nonsmooth function figures to illustrate the training problem.

What you can do after

Evaluate why training can optimize a proxy rather than the desired behavior.

How it connects

Connects accuracy, proxy problems, gradient descent, and incentive mismatch.

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

Compare how 19 books explain cross entropy loss →

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 How Large Language Models Work. The section links point to the parts of the book it draws on.