01

08 · useful win

Build causal self-attention, then a Transformer

Derive masked weighted aggregation, add multiple heads, residual pathways, normalization, and feed-forward computation.

Derive causal attention as content-dependent weighted aggregation.
02

The invariant chain

token states becomes a testable update

token states
queries + keys
masked affinities
softmax weights
weighted values
03

Why it works

Attention is a communication mechanism

Each token emits a query describing what it seeks, a key describing what it offers, and a value carrying the information to aggregate. Query-key similarity creates data-dependent weights over allowed source positions.

1Attention is a communication mechanism
2Causality is enforced before softmax
3masked affinities becomes observable
04

Implementation compass

A Transformer block has two kinds of work

q, k, v = x @ Wq, x @ Wk, x @ Wv       # [B,T,H]
wei = q @ k.transpose(-2, -1) * H**-0.5   # [B,T,T]
wei = wei.masked_fill(causal_mask == 0, float('-inf'))
wei = F.softmax(wei, dim=-1)
out = wei @ v                              # [B,T,H]
ShapeWrite every semantic axis beside the tensor.
ReferenceCompare one output against the smallest trusted version.
Scale gateOverfit one controlled batch before a real run.
05

Build gate

Derive causal attention as content-dependent weighted aggregation.

Implement the progression: uniform average → learned weights → masked self-attention.
Assert that changing a future token cannot change an earlier output.
Combine heads in parallel and verify the final channel dimension.
Stop and inspect

Masking after softmax

Scaling by the model width instead of head width

BUILD → TEST → EXPLAIN