Softmax

As explained in Build a Reasoning Model (From Scratch)

A normalization function that converts logits into a probability distribution over possible next tokens.

Softmax converts rescaled next-token logits into probability scores so sampling can select the next token from a normalized distribution. section 4.4.3

The inference workflow uses softmax to:

• Normalize each logit to a value from 0 to 1, with all probability values summing to 1. section 4.4.3
• Reflect temperature effects: lower temperature concentrates probability, while higher temperature spreads it across more tokens. section 4.4.3
• Pass the resulting distribution to next-token sampling, such as torch.multinomial. section 4.4.3

A temperature-scaled distribution

Applying torch.softmax to logits scaled with temperature 5.0 gives the token " Berlin" the highest probability in the selected vocabulary range, but only 0.0003. At temperature 0.5, its probability rises to 0.3398, while competing probabilities move closer to zero. section 4.4.3

Figure 4.10 Overview of the sampling process for generating tokens. Here, we focus on steps 3.3 and 3.4, where the next-token scores are converted into a probability distribution. The next token will be sampled based on that distribution.

Follow the sampling workflow from rescaled logits through softmax probabilities to next-token selection. section 4.4.3

How Build a Reasoning Model (From Scratch) covers it

How deep it goes

Explains normalization, temperature effects, plotting, and PyTorch usage, then stops before deeper mathematical derivation.

Examples

Uses the " Berlin" token, probability-sum checks, plots, and repeated multinomial sampling.

What it assumes

Assumes logits and temperature scaling, while defining probability normalization through the inference workflow.

What you can do after

Apply it via PyTorch to normalize logits and feed probabilities into token sampling.

How it connects

Connects logits, temperature scaling, probability distributions, and next-token sampling.

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  Math and Architectures of Deep LearningA smooth function that converts an unnormalized score vector into a probability-like distribution over classes.
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  Grokking Machine LearningA function that converts multiple real-valued scores into positive values whose normalized values sum to one and represent class probabilities.
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  Inside Deep Learning: Math, Algorithms, ModelsA function that turns a vector of scores into normalized weights over items or classes by exponentiating and renormalizing them.
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  Deep Learning with R, Third EditionA softmax operation converts a vector of scores into nonnegative values that sum to one, typically representing class probabilities.
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Related concepts

• probability distributionproduces · A probability distribution is a mathematical specification assigning probabilities to the possible values or outcomes of a random variable, with total probability one.
• temperatureused by · A temperature parameter adjusts the concentration of a probability distribution, affecting sampling randomness or the likelihood of accepting less favorable transitions.
• reduction operationuses · A reduction operation combines multiple input values or partial results according to a combining rule to produce fewer results, often a single aggregate.
• probability theoryproduces · Probability theory is the branch of mathematics that formalizes uncertainty and analyzes random events and outcomes using probability measures.
• attentionused by · Attention is a neural-network mechanism that computes input-dependent weights to combine information according to its relevance to a computation.
• attention weightproduces · An attention weight is a computed coefficient, often normalized, that determines how strongly an input element or value contributes to an attention-based representation.

This explainer was generated by Manning's knowledge graph from the text of Build a Reasoning Model (From Scratch). The section links point to the parts of the book it draws on.