Nat

Definition

A nat is a unit of information based on the natural logarithm.

Bits use:

log base 2

Nats use:

natural log

often written as:

ln

Nat = information measured using natural logarithms.

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Why Another Unit?

Information can be measured using different logarithm bases.

The unit changes, but the underlying idea stays the same:

measure surprise or uncertainty

Bits are convenient for binary distinctions.

Nats are convenient in calculus and optimization because natural logarithms work cleanly with derivatives.

Nats are common when probability meets calculus.

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Bit vs Nat

Bit:

uses log base 2

Nat:

uses natural log

Both measure information.

They use different scales.

Bits and nats are like different units for the same kind of quantity.

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Simple Intuition

If an event is unlikely, it has high information.

That idea is true whether measured in bits or nats.

Example:

probability = low
information = high

The unit only changes the numeric scale.

Changing units does not change the underlying uncertainty.

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Why Nats Appear In Learning

Many learning losses use natural logs.

Example:

negative log likelihood

When natural log is used, the loss is measured in nats.

This is common because optimization often works with derivatives, and natural logs behave cleanly there.

Many probability-based learning losses are naturally measured in nats.

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Do You Need To Memorize The Conversion?

Not at this stage.

The useful distinction is:

bit -> base 2 information unit
nat -> natural log information unit

The concepts of surprise, entropy, and loss work with either unit.

Focus on the meaning first; the unit depends on the log base.

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Final Summary

• A nat is a unit of information.
• Nats use natural logarithms.
• Bits use log base 2.
• Both measure information, but on different scales.
• Nats are common in learning because natural logs work well with calculus.
• Negative log likelihood is often measured in nats.