Weighted sum
A weighted sum is an expression formed by multiplying terms by corresponding scalar coefficients and adding the resulting products.
Math and Architectures of Deep Learning
A linear combination of values multiplied by coefficients.
- How it is used
- Combines input features into an interpretable model score before training estimates its weights.
- How deep it goes
- Defines scalar and vector forms, then connects them to dependence, bases, nonlinear models, and perceptrons.
- Examples
- Uses hardness and sharpness threat scores, binary logic gates, and probability-weighted expected values.
- What you can do after
- Evaluate/understand how weights and bias turn features or vectors into scores, decisions, and linear combinations.
Read how Math and Architectures of Deep Learning explains weighted sum →
Data Without Labels
A weighted sum is the sum obtained by multiplying each input by its corresponding coefficient and adding the results.
- How it is used
- Uses weighted sums to combine perceptron inputs and to form principal components from original variables.
- How deep it goes
- Explains multiplication by weights and subsequent activation, while illustrating PCA coefficients without detailing how to calculate them.
- Examples
- Uses a thresholded two-input perceptron and a home-variable equation combining area, bedrooms, distance, and schools.
- What you can do after
- Evaluate/understand how weighted inputs feed a perceptron’s output or become a PCA component.
Grokking AI Algorithms, Second Edition
A weighted sum is a sum of values after each value has been multiplied by a corresponding numerical weight, optionally incorporating a bias term.
- How it is used
- Calculates neuron inputs during forward propagation and blends Value vectors into context vectors during self-attention.
- How deep it goes
- Explains multiplication, addition, dot products, matrix multiplication, and activation, but stops short of theoretical proofs.
- Examples
- Uses scaled car-collision features, five hidden nodes, and attention-weighted token Value vectors as concrete calculation examples.
- What you can do after
- Build it from scratch by expressing one-neuron calculations as dot products and whole-layer calculations as matrix multiplications.
Read how Grokking AI Algorithms, Second Edition explains weighted sum →
Hacking Cryptography
A linear combination is an expression formed by multiplying values by coefficients and adding the resulting terms.
- How it is used
- Uses weighted sums to express LFSR output and recover unknown taps from observed bits.
- How deep it goes
- Explains recurrence equations, matrix inversion, Boolean arithmetic, and executable recovery code, stopping at LFSR exploitation.
- Examples
- Demonstrates three-bit LFSR recurrences, matrix equations, Go recovery functions, and timestamped known-plaintext decryption.
- What you can do after
- Diagnose weak LFSR constructions and recover their taps from sufficient observed or known-plaintext-derived bits.
Related concepts
- inner productequivalent to · An inner product is a scalar-valued operation on two vectors that combines their corresponding components, summing their products and, for complex vectors, using conjugation.
- vector spaceused by · A vector space is a set equipped with vector addition and scalar multiplication over a field that satisfy the vector-space axioms.
- modeincludes · The statistical mode is the value or category occurring most frequently in a set of observations or outcomes.
- matrix-matrix multiplicationproduced by · Matrix multiplication combines compatible matrices to form a result whose entries are sums of products between rows of the first matrix and columns of the second.
- neuronused by · A neuron is a computational unit in a neural network that transforms inputs, typically using learned parameters and an activation function, to produce an output.
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