Weight

Definition

A weight is a scalar attached to a feature.

Example:

score = w1*x1 + w2*x2

w1 is the weight for x1.

w2 is the weight for x2.

Weight = scalar influence assigned to a feature.

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Weight Controls Contribution

A feature contributes through multiplication by its weight.

Example:

score = 3*x1 + 1*x2

Here:

weight for x1 = 3
weight for x2 = 1

If both feature values are similar, x1 contributes more strongly.

Larger weight means stronger contribution, all else equal.

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Positive Weight

A positive weight increases the score when the feature increases.

Example:

score = 2*x

If:

x = 3

then:

score = 6

More x means higher score.

Positive weight pushes the score upward as the feature grows.

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Negative Weight

A negative weight decreases the score when the feature increases.

Example:

score = -2*x

If:

x = 3

then:

score = -6

More x means lower score.

Negative weight pushes the score downward as the feature grows.

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Zero Weight

A zero weight removes a feature's effect from the score.

Example:

score = 0*x1 + 4*x2

x1 has no effect because:

0*x1 = 0

Zero weight means the feature is ignored by the linear score.

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Weight Vector

Weights can be collected into a vector.

Example:

w = [2, -1, 4]
x = [3, 5, 2]

Weighted sum:

dot(w, x) = 2*3 + (-1)*5 + 4*2
          = 6 - 5 + 8
          = 9

The weight vector defines how the model looks at the input vector.

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Geometric Meaning

Weights define a direction in feature space.

The dot product:

dot(w, x)

measures how much the input aligns with that weight direction.

This connects perceptrons back to geometry.

A weight vector gives the model a direction of attention.

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Final Summary

• A weight is a scalar attached to a feature.
• It controls feature contribution.
• Positive weights increase the score.
• Negative weights decrease the score.
• Zero weights ignore a feature.
• Weights form a weight vector.
• The weight vector defines a direction for the classifier.