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Reference

Glossary

Every term, symbol, and operation used in this book — defined in one place.

Attention (self-attention mechanism)

Lets each token build a weighted summary of other tokens so its representation becomes context-aware.

Attention(Q, K, V) = softmax((QKᵀ / √d_head) + M) V

Covered in: Part 6

Autoregressive

Generating one token at a time, feeding each chosen token back into the next step.

p(x₁, …, xₙ) = Π_t p(x_t | x₁, …, x_{t-1})

Covered in: Part 1

BPE (Byte Pair Encoding)

A tokenizer family that builds larger tokens by repeatedly merging frequent byte or character pairs.

merge* (bytes(text)) → token_ids

Covered in: Part 2

Causal Mask

The rule that stops a token from attending to future tokens during generation.

M_{ij} = 0 if j ≤ i, else -∞

Covered in: Part 6

Continuous Batching

A serving strategy that lets requests join and leave an active decode batch instead of waiting for full batch boundaries.

active_batch(t + 1) = active_batch(t) - finished + admitted

Covered in: Part 11, Part 12

d_model (model hidden dimension)

The width of the model’s main hidden vectors.

X ∈ ℝ^{T × d_model}

Covered in: Part 5

d_head (per-head dimension)

The width of one attention head’s query, key, and value vectors.

d_head = d_model / H

Covered in: Part 6

d_ff (feed-forward intermediate dimension)

The expanded width used inside the feed-forward network before projecting back down.

FFN: ℝ^{d_model} → ℝ^{d_ff} → ℝ^{d_model}

Covered in: Part 8

Decode

The autoregressive phase after prefill where the model generates new tokens one step at a time.

state_t → logits_t → token_{t+1} → state_{t+1}

Covered in: Part 11

Dot Product

A multiply-and-sum operation that measures alignment between two vectors.

a · b = Σ_i a_i b_i

Covered in: Part 6

Embedding

A learned vector looked up from the token ID that gives the model its starting representation for that token.

x_t = E[token_id_t]

Covered in: Part 3

Epsilon (ε)

A tiny constant added for numerical stability so divisions do not blow up near zero.

y = x / √(mean(x²) + ε)

Covered in: Part 7

Feed-Forward Network (FFN)

The per-token MLP inside each transformer block that expands, transforms, and projects features back down.

FFN(x) = W_down(σ(W_gate x) ⊙ W_up x)

Covered in: Part 8

FLOP / FLOPS

A floating-point operation, and the rate of floating-point operations per second.

FLOPS = total_FLOPs / seconds

Covered in: Part 11

GeLU

A smooth activation function often used in older transformer feed-forward networks.

GeLU(x) ≈ 0.5x(1 + tanh(√(2/π)(x + 0.044715x³)))

Covered in: Part 8

GGUF (file format)

A model file format popular in local inference tooling that stores weights, metadata, tokenizer data, and often quantized blocks.

GGUF = weights + metadata + tokenizer + quantisation descriptors

Covered in: Part 11

Greedy Decoding

Always choosing the single highest-scoring next token.

token_{t+1} = argmax_i logits_i

Covered in: Part 10

Hidden State

The model’s current internal vector representation for a token position at a given layer.

h_t^{(ℓ)} ∈ ℝ^{d_model}

Covered in: Part 5

KV Cache

Stored past keys and values that let decode reuse old attention state instead of recomputing it.

K_cache^{(ℓ)}, V_cache^{(ℓ)} = append over time positions

Covered in: Part 6, Part 11

Key (K)

The vector a token exposes so other tokens can measure how relevant it is.

K = XW_K

Covered in: Part 6

Layer / Transformer Block

One repeated unit of attention, feed-forward computation, normalization, and residual addition.

x' = x + Attention(Norm(x))
y  = x' + FFN(Norm(x'))

Covered in: Part 5

lm_head (vocabulary projection)

The final projection that turns the last hidden state into one score per vocabulary token.

logits = hW_vocabᵀ

Covered in: Part 9

Logits

Unnormalized scores produced before softmax or decoding policy chooses the next token.

z_i = h · w_i

Covered in: Part 9

MoE (Mixture of Experts)

A model design where a router activates only a subset of expert FFNs for each token.

y = Σ_{e ∈ TopM(g(x))} g_e(x) · Expert_e(x)

Covered in: Part 8

Multi-Head Attention

Running several attention heads in parallel so the model can attend through multiple learned subspaces at once.

head_h = Attention(Q_h, K_h, V_h)
MHA(x) = Concat(head₁, …, head_H)W_O

Covered in: Part 6

Normalisation (RMSNorm)

A scaling layer that normalizes by root-mean-square magnitude and then applies a learned gain.

RMSNorm(x) = γ ⊙ x / √(mean(x²) + ε)

Covered in: Part 7

Paged Attention

A cache-management approach that stores KV state in page-like chunks so long sequences and many sessions are easier to manage.

KV_cache = {page₀, page₁, …, page_n}

Covered in: Part 11, Part 12

Prefill

The initial forward pass over the prompt that builds the first hidden states and KV cache before autoregressive decode begins.

prompt_tokens → hidden states + initial KV cache

Covered in: Part 11

Query (Q)

The vector a token uses to ask which other tokens matter right now.

Q = XW_Q

Covered in: Part 6

Quantisation

Storing weights or activations in fewer bits to save memory and bandwidth, usually with some controlled error.

q = round(w / s),   w ≈ s · q

Covered in: Part 11

Residual Connection

A skip path that adds the input of a sublayer back to its output so information and gradients have a short route through depth.

y = x + F(x)

Covered in: Part 5

RoPE (Rotary Position Embedding)

A way of encoding position by rotating paired vector components as a function of token position.

RoPE(x, θ) = [x₁ cosθ - x₂ sinθ, x₁ sinθ + x₂ cosθ, …]

Covered in: Part 4

SafeTensors (file format)

A simple tensor-serialization format designed to load model weights safely without arbitrary code execution.

SafeTensors = named_tensors + metadata (no executable pickle payload)

Covered in: Part 11

Sampling

The policy that turns logits into an actual next-token choice.

x_{t+1} ~ P(. | x_{≤t})

Covered in: Part 10

SiLU / Swish

A smooth activation used in many modern LLM FFNs.

SiLU(x) = xσ(x)

Covered in: Part 8

Softmax

Turns a vector of raw scores into a normalized probability-like distribution.

softmax(z)_i = exp(z_i) / Σ_j exp(z_j)

Covered in: Part 6, Part 10

Speculative Decoding

A serving technique where a cheaper draft path proposes future tokens and the full model verifies them.

draft_tokens → verify_with_target_model → accept/reject prefix

Covered in: Part 12

SwiGLU

A gated FFN pattern that multiplies an SiLU-activated branch with an ungated branch before projecting down.

SwiGLU(x) = W_down(SiLU(W_gate x) ⊙ W_up x)

Covered in: Part 8

Temperature (τ)

A scaling factor that sharpens or flattens the sampling distribution before choosing the next token.

p_i ∝ exp(logit_i / τ)

Covered in: Part 10

Token / Tokenizer

A token is one vocabulary unit; the tokenizer is the front-end that turns raw text into token IDs and back.

tokenizer(text) → [id₁, id₂, …, id_T]

Covered in: Part 2

Top-K

A decoding filter that keeps only the K highest-scoring candidate tokens before sampling.

S = arg top-K_i logits_i

Covered in: Part 10

Top-P (Nucleus)

A decoding filter that keeps the smallest set of tokens whose cumulative probability reaches a threshold p.

find smallest S such that Σ_{i ∈ S} p_i ≥ p

Covered in: Part 10

Value (V)

The vector content attention mixes together after the query-key scores decide which positions matter.

V = XW_V

Covered in: Part 6

Vocabulary (V)

The full set of token IDs the model can read and emit.

|Vocabulary| = V

Covered in: Part 2, Part 9

Wo (attention output projection)

The matrix that mixes concatenated head outputs back into the model hidden width.

y = Concat(head₁, …, head_H)W_O

Covered in: Part 6