Attention & Transformers

Causal Self-Attention Mask

How decoder-only Transformers prevent future-token leakage by masking attention logits before softmax.

status: reviewimportance: criticaldifficulty 3/5math: undergraduateread: 12mlive demo

Back to Attention & Transformers Next: Decoder-Only Transformer Forward Pass (review)

Concept Structure

Causal Self-Attention Mask

01Intuition

Start with the picture, metaphor, or geometric mechanism.

02Math

Make the objects explicit and connect them with notation.

03Code

Mirror the equations with runnable implementation details.

04Interactive Demo

Manipulate the mechanism and watch the idea respond.

2prerequisites

2next concepts

3related links

Learner Contract

What this page should let you do.

You are here becauseHow decoder-only Transformers prevent future-token leakage by masking attention logits before softmax.

This Attention & Transformers concept is the current idea: keep the same invariant visible across Intuition, Math, Code, Interactive Demo.

Before thisRaw Text to Packed Causal-LM Examples (review)

2 prerequisites listed; refresh them before leaning on the math or code.

Raw Text to Packed Causal-LM Examples (review)Scaled Dot-Product Attention & Transformer Layers

By the end4/4 sections ready | runnable code expected | live demo

Explain the mechanism, trace the main notation, and test one prediction in the live demo.

Do this firstIntuition

Read the intuition before the notation; the math should name a mechanism you already felt.

Then go nextDecoder-Only Transformer Forward Pass (review)

Follow this edge after making one prediction here; the next page should reuse the result, not restart the route.

Test the linkManipulate one control and predict the visible change.Then continue to Decoder-Only Transformer Forward Pass (review)

Claim/source review status

Substantive review recorded

1/1 claims have bounded review metadata; still check caveats and source scope.Metadata-derived; review may be AI-assisted. Not a human certification.

Claims1/1 reviewed

Sources2 cited

Codeattached

Demolive

Reviewed2026-07-02

Updatedpage 2026-07-02

Learning item flow

4/4 sections readyAsk about this Research room

ConceptCausal Self-Attention MaskAttention & Transformers EquationCausal Self-Attention Mask equation 1Exact equation CodeCausal Self-Attention Mask runnable code 1Exact runnable code DemoCausal Self-Attention Mask interactive demoInteractive demo ClaimIn autoregressive decoder self-attention, query position i may attend...Exact claim check SourceAttention Is All You NeedExact source

ConceptCausal Self-Attention MaskAttention & Transformers

3 sources attachedLocal snapshot ready

concept:attention-transformers/causal-self-attention-mask

Codenearby Predictbefore reveal Roomitem handoff

01IntuitionStart with the picture, metaphor, or geometric mechanism.02MathMake the objects explicit and connect them with notation.03CodeMirror the equations with runnable implementation details.04Interactive DemoManipulate the mechanism and watch the idea respond.

Intuition

Build the mental picture first so the rest of the page has something to attach to.

Section prompt

In a decoder-only language model, position $i$ is trying to predict what comes next using only the tokens it is allowed to know.

Without a causal mask, the token at position $i$ could attend to position $i+1$ , position $i+2$ , and so on. During training, those future tokens are sitting in the same matrix. If the model can read them, the task is no longer honest next-token prediction.

The causal mask is the read-permission rule:

query row $i$ can read key columns $j \le i$ , and cannot read future columns $j > i$ .

This is different from the loss mask in the previous page. A loss mask decides which labels contribute to the objective. A causal attention mask decides which token representations can be read while computing an attention output.

Math

Translate the story into symbols, assumptions, and a derivation you can inspect.

Section prompt

Equation 1 $Q = XW_Q,\qquad K = XW_K,\qquad V = XW_V,$ Equation 2 $s_{ij} = \frac{q_i^\top k_j}{\sqrt{d_k}}.$

Let $X \in \mathbb{R}^{T \times d_{\text{model}}}$ be the sequence of hidden states. For one attention head,

Q = XW_Q,\qquad K = XW_K,\qquad V = XW_V,

with $Q,K,V \in \mathbb{R}^{T \times d_k}$ .

The unmasked score from query position $i$ to key position $j$ is

s_{ij} = \frac{q_i^\top k_j}{\sqrt{d_k}}.

For causal self-attention, define a mask

M_{ij} = \begin{cases} 0, & j \le i, \\\\ -\infty, & j > i. \end{cases}

Then attention probabilities are computed row-wise:

a_{ij} = \operatorname{softmax}_j(s_{ij} + M_{ij}).

So every future column receives zero probability:

j > i \quad\Rightarrow\quad a_{ij} = 0.

The output for position $i$ is

o_i = \sum_{j=0}^{T-1} a_{ij}v_j.

The mask changes which values can enter that sum. It does not change which labels count toward the loss.

Code

Keep the implementation aligned with the notation so the algorithm is legible.

Section prompt

Runnable code 1import numpy as np def softmax(x): x = x - np.max(x) e = np.exp(x) return e / e.sum() scores...python

import numpy as np

def softmax(x):
    x = x - np.max(x)
    e = np.exp(x)
    return e / e.sum()

scores = np.array([
    [0.20, 0.50, -0.10, 0.30, 1.40, 0.90],
    [0.10, 0.30, 0.70, 0.20, 1.10, 0.40],
    [0.40, 0.20, 0.50, 0.80, 0.90, 0.10],
    [0.31, 0.47, 0.15, 0.25, 1.10, 0.90],
    [0.05, 0.15, 0.35, 0.20, 0.60, 0.70],
    [0.20, 0.10, 0.30, 0.05, 0.40, 0.55],
])

T = scores.shape[0]
mask = np.triu(np.ones((T, T)), k=1).astype(bool)
masked_scores = scores.copy()
masked_scores[mask] = -np.inf

i = 3
before = softmax(scores[i])
after = softmax(masked_scores[i])

print("query position:", i)
print("allowed keys:", [j for j in range(T) if j <= i])
print("future mass before mask:", round(before[i + 1:].sum(), 3))
print("future mass after mask:", round(after[i + 1:].sum(), 3))
assert np.allclose(after[i + 1:], 0.0)

Interactive Demo

Use direct manipulation to connect the explanation to a moving system.

Section prompt

Before reveal, pick which key positions a query row is allowed to read. The reveal shows the lower-triangular mask, the leak that would happen without it, and the masked softmax row where future-token probability is exactly zero.

Live Concept Demo

Explore Causal Self-Attention Mask

The stage is code-native and interactive. Use it to test the explanation against the mechanism.

difficulty 3/5undergraduatecode-aligned

Demo Prediction Checkpoint

Manipulate one control and predict the visible change.

Commit to what Causal Self-Attention Mask should make visible before reading the result.

After The First Pass

Turn the concept into an inspected object.

Once the invariant is visible in the intuition, math, code, and demo, use these panels to inspect the mechanism visually, check source support, practice the idea, and attach a grounded research question.

Mechanism Storyboard

See the idea move before the page explains it

How decoder-only Transformers prevent future-token leakage by masking attention logits before softmax.

Prediction open01 / Intuition

Prediction lens

Start with the picture, metaphor, or geometric mechanism.

Commit first

Before reading further, choose the kind of change Causal Self-Attention Mask should make visible.

Visual Inquiry

Make the image answer a mathematical question

How decoder-only Transformers prevent future-token leakage by masking attention logits before softmax.

4/4 stages readyLive demo connected

Visual cueWhich visible object should carry the first intuition?

Inspection depth2/4

Prediction

Which visible object should carry the first intuition?

Commit first

Pick the cue that should make Causal Self-Attention Mask easier to reason about before the page gives the answer.

Source Grounding

Canonical references for the mechanism on this page.

paper · 2017Attention Is All You NeedVaswani et al.

Primary Transformer source. The decoder self-attention layer masks subsequent positions so autoregressive predictions cannot depend on future outputs.

Open source

reference · 2026Dive into Deep Learning: Transformer DecoderZhang, Lipton, Li, and Smola

Pedagogical source for decoder self-attention attending only up to the query position and preserving autoregression.

Open source

course-notes · 2026Stanford CS336: Language Modeling from ScratchStanford CS336 course staff

Course-level route source for implementing language-model components from scratch; this page uses it for route placement, not exact code claims.

Open source

Claim Review

How decoder-only Transformers prevent future-token leakage by masking attention logits before softmax.

Status1 substantive review recorded

Claims without a substantive review badge still need exact source-support review.

Sources3 references

vaswani-2017-attention, d2l-transformer-decoder, cs336-language-modeling-from-scratch

Local checks4 local checks

Use equations, runnable code, and demos to check whether the source support is operational.

Substantively reviewedIn autoregressive decoder self-attention, query position i may attend only to key positions j <= i; future positions j > i are masked before softmax so their attention probability is zero.Claim metadata: source checked

Vaswani et al. state that decoder self-attention is modified to prevent positions from attending to subsequent positions and that illegal connections are masked by setting softmax inputs to negative infinity. D2L states that decoder self-attention may use positions only up to the query position to preserve autoregression.

Sources: Attention Is All You Need, Dive into Deep Learning: Transformer DecoderThis checks the causal read-permission mask only. Padding masks, document-boundary masks, packed-sequence block masks, efficient kernels, KV-cache layout, and exact framework APIs are separate implementation details.A bounded review summary is present; still check caveats and exact reference scope.

Checked Vaswani et al. sections 3.1 and 3.2.3 plus D2L Transformer decoder text for masked decoder self-attention. The page is review-status pending GPT Pro publication critique.

Reviewer: codex-local-source-audit; reviewed 2026-07-02

source-span-vaswani-2017-attention source-span-d2l-transformer-decoder Equation 1 Equation 2 Runnable code 1 Interactive demo

Source support candidates

paper 2017Attention Is All You Need

Primary Transformer source. The decoder self-attention layer masks subsequent positions so autoregressive predictions cannot depend on future outputs.

reference 2026Dive into Deep Learning: Transformer Decoder

Pedagogical source for decoder self-attention attending only up to the query position and preserving autoregression.

course-notes 2026Stanford CS336: Language Modeling from Scratch

Course-level route source for implementing language-model components from scratch; this page uses it for route placement, not exact code claims.

Mechanism checks

Equation 1

Q = XW_Q,\qquad K = XW_K,\qquad V = XW_V,

Equation 2

s_{ij} = \frac{q_i^\top k_j}{\sqrt{d_k}}.

Runnable code 1import numpy as np def softmax(x): x = x - np.max(x) e = np.exp(x) return e / e.sum() scores...Demo stateLive mechanism probe

Practice Loop

Try the idea before it explains itself

How decoder-only Transformers prevent future-token leakage by masking attention logits before softmax.

Readiness0/3 checks ready

Predict

Before touching the demo, predict one visible change that should happen in Causal Self-Attention Mask.

Hint 1

Reveal when your model needs a nudge.

Hint 2

Reveal when your model needs a nudge.

Hint 3

Reveal when your model needs a nudge.

Your answer canvas

Local checks

Claim

A concrete answer is on the canvas.

Mechanism

The answer names why the claim should hold.

Bridge

It touches the page context or a neighboring idea.

Misconception check

Grounded research drawerClose

ConceptCausal Self-Attention MaskAttention & Transformers

Runnable code comparisonCausal Self-Attention Mask runnable code 1scores = np.array([Prediction before revealCausal Self-Attention Mask interactive demoManipulate one control and predict the visible change.

Grounded room questionWhat is the smallest example that makes Causal Self-Attention Mask click without losing the math?Local snapshot ready

Research Room

Attach the question to a claim, equation, code, or demo

Pick the concept, equation, source, runnable code, claim, misconception, or demo state before asking for help. The handoff keeps that page item in context.

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conceptAttention & Transformers

Causal Self-Attention Mask

Attached question

What is the smallest example that makes Causal Self-Attention Mask click without losing the math?

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Evidence to inspect

References to inspect: attached references on this page.
Definition, prerequisite, and contrast concept links
The equation or runnable code that makes the concept operational
One demo state that shows the invariant instead of a slogan

What would resolve this

The learner can state the mechanism in their own words
The learner can name the prerequisite that would repair confusion
The learner can predict how the mechanism changes under one perturbation

Grounded AI handoff

I am working in Continuous Function's research reading room. Object: concept - Causal Self-Attention Mask Selected item key: recorded for copy. Context: Attention & Transformers Page anchor: recorded for copy. Open question: What is the smallest example that makes Causal Self-Attention Mask click without losing the math? Evidence to inspect: - References to inspect: attached references on this page. - Definition, prerequisite, and contrast concept links - The equation or runnable code that makes the concept operational - One demo state that shows the invariant instead of a slogan What would resolve this: - The learner can state the mechanism in their own words - The learner can name the prerequisite that would repair confusion - The learner can predict how the mechanism changes under one perturbation Answer as a careful research tutor: stay source-grounded, separate verified evidence from assumptions, name the relevant math objects, and end with one next action.

View it in context

concept/concept-notebook/attention-transformers/causal-self-attention-mask
concept:attention-transformers/causal-self-attention-mask

Learning Map

Before / Now / Try / Next

BeforeRaw Text to Packed Causal-LM Examples (review)

NowIntuition -> Math -> Code -> Demo

TryManipulate one control and predict the visible change.

NextDecoder-Only Transformer Forward Pass (review)

Intuitionready
Mathready
Codeready
Interactive Demoready

AI Companion

Ask beside the selected object

How decoder-only Transformers prevent future-token leakage by masking attention logits before softmax.

Your question

GoalComfortStyleStuck on

Context prompt

You are my AI learning companion for Continuous Function. Current context: Attention & Transformers concept. Learning surface: Causal Self-Attention Mask. What this page says: How decoder-only Transformers prevent future-token leakage by masking attention logits before softmax. Current section: Intuition, math, code, and interactive demo. Suggested next step: Manipulate one control and predict the visible change.. Learner goal: Understand the idea. Learner comfort level: New to this. Preferred explanation style: Visual first. Task: Explain the central idea in plain language, then restate it with the exact math objects from the page. Answer in a way that helps me learn: ask one clarifying question only if needed, use intuition before notation, and end with one thing I should try on the page.

Domain

Attention & Transformers

attention-transformersself-attentioncausal-language-modelingtransformer-implementation

Prerequisites

Raw Text to Packed Causal-LM Examples (review)Scaled Dot-Product Attention & Transformer Layers

Leads To

Decoder-Only Transformer Forward Pass (review)Transformer Implementation From Scratch (planned)

Positional Encoding Efficient Attention at Scale: KV Cache, GQA & FlashAttention Long Context Engineering: RoPE Scaling, KV Compression & Memory Optimization

Within this domain