From Immediate to Prediction: Understanding Prefill, Decode, and the KV Cache in LLMs

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Within the earlier article, we noticed how a language mannequin converts logits into possibilities and samples the following token. However the place do these logits come from?

On this tutorial, we take a hands-on method to grasp the technology pipeline:

How the prefill part processes your complete immediate in a single parallel go
How the decode part generates tokens one by one utilizing beforehand computed context
How the KV cache eliminates redundant computation to make decoding environment friendly

By the tip, you’ll perceive the two-phase mechanics behind LLM inference and why the KV cache is crucial for producing lengthy responses at scale.

Let’s get began.

From Immediate to Prediction: Understanding Prefill, Decode, and the KV Cache in LLMs
Picture by Neda Astani. Some rights reserved.

Overview

This text is split into three elements; they’re:

How Consideration Works Throughout Prefill
The Decode Section of LLM Inference
KV Cache: The right way to Make Decode Extra Environment friendly

How Consideration Works Throughout Prefill

Think about the immediate:

Immediately’s climate is so …

As people, we are able to infer the following token needs to be an adjective, as a result of the final phrase “so” is a setup. We additionally comprehend it most likely describes climate, so phrases like “good” or “heat” are extra possible than one thing unrelated like “scrumptious“.

Transformers arrive on the identical conclusion by consideration. Throughout prefill, the mannequin processes your complete immediate in a single ahead go. Each token attends to itself and all tokens earlier than it, increase a contextual illustration that captures relationships throughout the total sequence.

The mechanism behind that is the scaled dot-product consideration system:

$$
textual content{Consideration}(Q, Okay, V) = mathrm{softmax}left(frac{QK^prime}{sqrt{d_k}}proper)V
$$

We are going to stroll by this concretely beneath.

To make the eye computation traceable, we assign every token a scalar worth representing the data it carries:

Place	Tokens	Values
1	Immediately	10
2	climate	20
3	is	1
4	so	5

Phrases like “is” and “so” carry much less semantic weight than “Immediately” or “climate“, and as we’ll see, consideration naturally displays this.

Consideration Heads

In actual transformers, consideration weights are steady values discovered throughout coaching by the $Q$ and $Okay$ dot product. The conduct of consideration heads are discovered and normally unattainable to explain. No head is hardwired to “attend to even positions”. The 4 guidelines beneath are simplified illustration to make consideration mechanism extra intuitive, whereas the weighted aggregation over $V$ is identical.

Listed here are the principles in our toy instance:

Attend to tokens at even quantity positions
Attend to the final token
Attend to the primary token
Attend to each token

For simplicity on this instance, the outputs from these heads are then mixed (averaged).

Let’s stroll by the prefill course of:

Immediately

Even tokens → none
Final token → Immediately → 10
First token → Immediately → 10
All tokens → Immediately → 10

climate

Even tokens → climate → 20
Final token → climate → 20
First token → Immediately → 10
All tokens → common(Immediately, climate) → 15

Even tokens → climate → 20
Final token → is → 1
First token → Immediately → 10
All tokens → common(Immediately, climate, is) → 10.33

Even tokens → common(climate, so) → 12.5
Final token → so → 5
First token → Immediately → 10
All tokens → common(Immediately, climate, is, so) → 9

Parallelizing Consideration

If the immediate contained 100,000 tokens, computing consideration step-by-step can be extraordinarily gradual. Happily, consideration may be expressed as tensor operations, permitting all positions to be computed in parallel.

That is the important thing thought of prefill part in LLM inference: Once you present a immediate, there are a number of tokens in it and they are often processed in parallel. Such parallel processing helps velocity up the response time for the primary token generated.

To stop tokens from seeing future tokens, we apply a causal masks, to allow them to solely attend to itself and earlier tokens.

import torch tokens = [“Today”, “weather”, “is”, “so”] n = len(tokens) d_k = 64 V = torch.tensor([[10.], [20.], [1.], [5.]], dtype=torch.float32) positions = torch.arange(1, n + 1).float() # 1-based: [1, 2, 3, 4] idx = torch.arange(n) causal_mask = idx.unsqueeze(1) >= idx.unsqueeze(0) print(causal_mask)

import torch

tokens = [“Today”, “weather”, “is”, “so”]

n = len(tokens)

d_k = 64

V = torch.tensor([[10.], [20.], [1.], [5.]], dtype=torch.float32)

positions = torch.arange(1, n + 1).float() # 1-based: [1, 2, 3, 4]

idx = torch.arange(n)

causal_mask = idx.unsqueeze(1) >= idx.unsqueeze(0)

print(causal_mask)

Output:

tensor([[ True, False, False, False], [ True, True, False, False], [ True, True, True, False], [ True, True, True, True]])

tensor([[ True, False, False, False],

[ True, True, False, False],

[ True, True, True, False],

[ True, True, True, True]])

Now, we are able to begin writing the “guidelines” for the 4 consideration heads.

Somewhat than computing scores from discovered $Q$ and $Okay$ vectors, we handcraft them on to match our 4 consideration guidelines. Every head produces a rating matrix of form (n, n), with one rating per query-key pair, which will get masked and handed by softmax to provide consideration weights:

def selector(situation, dimension): “””Return a (dimension, d_k) tensor of +1/-1 relying on situation.””” val = torch.the place(situation, torch.ones( dimension), -torch.ones(dimension)) # (dimension,) # (dimension, d_k) return val.unsqueeze(1).broaden(dimension, d_k).contiguous() # Shared question: each row asks for a property, and Okay encodes which tokens match it. Q = torch.ones(n, d_k) # Head 1: choose even positions # Okay says whether or not every token is at a fair place. K1 = selector(positions % 2 == 0, n) scores1 = (Q @ K1.T) / (d_k ** 0.5) # Head 2: choose the final token # Okay says whether or not every token is the final one. K2 = selector(positions == n, n) scores2 = (Q @ K2.T) / (d_k ** 0.5) # Head 3: choose the primary token # Okay says whether or not every token is the primary one. K3 = selector(positions == 1, n) scores3 = (Q @ K3.T) / (d_k ** 0.5) # Head 4: choose all seen tokens uniformly # Okay says all of the tokens K4 = selector(positions == positions, n) scores4 = (Q @ K4.T) / (d_k ** 0.5) # Stack all head rating matrices: form (4, n, n) scores = torch.stack([scores1, scores2, scores3, scores4], dim=0) # Apply causal masks so place i can solely attend to positions <= i scores = scores.masked_fill(~causal_mask.unsqueeze(0), -1e9) # Convert logits to consideration weights weights = torch.softmax(scores, dim=-1) # Non-compulsory safeguard for absolutely masked rows all_masked = (scores <= -1e4).all(dim=-1, keepdim=True) weights = torch.the place(all_masked, torch.zeros_like(weights), weights) # Compute contexts: (heads, n, n) @ (n, 1) -> (heads, n, 1) contexts = (weights @ V).squeeze(-1) print(“Contexts by consideration head (rows) x token place (columns):n”, contexts) context4 = contexts[:, -1] print(“nContext for last immediate place:n”, context4)

def selector(situation, dimension):

“”“Return a (dimension, d_k) tensor of +1/-1 relying on situation.”“”

val = torch.the place(situation, torch.ones(

dimension), –torch.ones(dimension)) # (dimension,)

# (dimension, d_k)

return val.unsqueeze(1).broaden(dimension, d_k).contiguous()

# Shared question: each row asks for a property, and Okay encodes which tokens match it.

Q = torch.ones(n, d_k)

# Head 1: choose even positions

# Okay says whether or not every token is at a fair place.

K1 = selector(positions % 2 == 0, n)

scores1 = (Q @ K1.T) / (d_k ** 0.5)

# Head 2: choose the final token

# Okay says whether or not every token is the final one.

K2 = selector(positions == n, n)

scores2 = (Q @ K2.T) / (d_k ** 0.5)

# Head 3: choose the primary token

# Okay says whether or not every token is the primary one.

K3 = selector(positions == 1, n)

scores3 = (Q @ K3.T) / (d_k ** 0.5)

# Head 4: choose all seen tokens uniformly

# Okay says all of the tokens

K4 = selector(positions == positions, n)

scores4 = (Q @ K4.T) / (d_k ** 0.5)

# Stack all head rating matrices: form (4, n, n)

scores = torch.stack([scores1, scores2, scores3, scores4], dim=0)

# Apply causal masks so place i can solely attend to positions <= i

scores = scores.masked_fill(~causal_mask.unsqueeze(0), –1e9)

# Convert logits to consideration weights

weights = torch.softmax(scores, dim=–1)

# Non-compulsory safeguard for absolutely masked rows

all_masked = (scores <= –1e4).all(dim=–1, keepdim=True)

weights = torch.the place(all_masked, torch.zeros_like(weights), weights)

# Compute contexts: (heads, n, n) @ (n, 1) -> (heads, n, 1)

contexts = (weights @ V).squeeze(–1)

print(“Contexts by consideration head (rows) x token place (columns):n”, contexts)

context4 = contexts[:, –1]

print(“nContext for last immediate place:n”, context4)

Output:

Contexts by consideration heads (rows) x token place (columns): tensor([[10.0000, 20.0000, 20.0000, 12.5000], [10.0000, 15.0000, 10.3333, 5.0000], [10.0000, 10.0000, 10.0000, 10.0000], [10.0000, 15.0000, 10.3333, 9.0000]]) Context for last immediate place: tensor([12.5000, 5.0000, 10.0000, 9.0000])

Contexts by consideration heads (rows) x token place (columns):

tensor([[10.0000, 20.0000, 20.0000, 12.5000],

[10.0000, 15.0000, 10.3333, 5.0000],

[10.0000, 10.0000, 10.0000, 10.0000],

[10.0000, 15.0000, 10.3333, 9.0000]])

Context for last immediate place:

tensor([12.5000, 5.0000, 10.0000, 9.0000])

The results of this step is named a context vector, which represents a weighted abstract of all earlier tokens.

From contexts to logits

Every consideration head has discovered to select up on totally different patterns within the enter. Collectively, the 4 context values [12.5, 5.0, 10.0, 9.0] kind a abstract of what “Immediately’s climate is so…” represents. It would then challenge to a matrix, which every column encodes how sturdy a given vocabulary is related to every consideration head’s sign, to provide logit rating per phrase.

… logits = context @ W_vocab

...

logits = context @ W_vocab

For our instance, let’s say we now have “good”, “heat”, and “scrumptious” within the vocab:

… vocab = [“nice”, “warm”, “delicious”] # Every column corresponds to a vocab phrase # Every row corresponds to at least one consideration head characteristic W_vocab = torch.tensor([ [0.8, 0.6, 0.1], # head 1 weights → good, heat, scrumptious [0.5, 0.4, 0.2], # head 2 weights [0.1, 0.2, 0.5], # head 3 weights [0.2, 0.3, 0.1], # head 4 weights ]) # form: (4, 3) logits = context4 @ W_vocab # (4,) @ (4, 3) → (3,) for phrase, logit in zip(vocab, logits): print(f”{phrase:10s} {logit.merchandise():.3f}”) “`

...

vocab = [“nice”, “warm”, “delicious”]

# Every column corresponds to a vocab phrase

# Every row corresponds to at least one consideration head characteristic

W_vocab = torch.tensor([

[0.8, 0.6, 0.1], # head 1 weights → good, heat, scrumptious

[0.5, 0.4, 0.2], # head 2 weights

[0.1, 0.2, 0.5], # head 3 weights

[0.2, 0.3, 0.1], # head 4 weights

]) # form: (4, 3)

logits = context4 @ W_vocab # (4,) @ (4, 3) → (3,)

for phrase, logit in zip(vocab, logits):

print(f“{phrase:10s} {logit.merchandise():.3f}”)

```

So the logits for “good” and “heat” are a lot larger than “scrumptious”.

good 15.300 heat 14.200 scrumptious 8.150

good 15.300

heat 14.200

scrumptious 8.150

The Decode Section of LLM Inference

Now suppose the mannequin generates the following token: “good“. The duty is now to generate the following token with the prolonged immediate:

Immediately’s climate is so good …

The primary 4 phrases within the prolonged immediate are the identical as the unique immediate. And now we now have the fifth phrase within the immediate.

Throughout decode, we don’t recompute consideration for all earlier tokens because the consequence can be the identical. As a substitute, we compute consideration just for the brand new token to avoid wasting time and compute sources. This produces a single new consideration row.

new_token = “good” tokens = tokens + [new_token] new_value = torch.tensor([[7.0]]) # worth of “good” is 7 V = torch.cat([V, new_value], dim=0) n = len(tokens) idx = torch.arange(n) pos = torch.arange(1, n + 1).float() # [1, 2, 3, 4, 5] print(“New tokens: “, tokens) print(“New Values: “, V)

new_token = “good”

tokens = tokens + [new_token]

new_value = torch.tensor([[7.0]]) # worth of “good” is 7

V = torch.cat([V, new_value], dim=0)

n = len(tokens)

idx = torch.arange(n)

pos = torch.arange(1, n + 1).float() # [1, 2, 3, 4, 5]

print(“New tokens: “, tokens)

print(“New Values: “, V)

Output:

New tokens: [‘Today’, ‘weather’, ‘is’, ‘so’, ‘nice’] New Values: tensor([[10.], [20.], [ 1.], [ 5.], [ 7.]])

New tokens: [‘Today’, ‘weather’, ‘is’, ‘so’, ‘nice’]

New Values: tensor([[10.],

[20.],

[ 1.],

[ 5.],

[ 7.]])

Now, we apply the 4 consideration heads and compute the brand new context vector:

# Rebuild all Okay matrices for the following token (n=5) # We are going to introduce KV-cache later K1_new = selector(pos % 2 == 0, n) # even positions → +1 K2_new = selector(pos == n, n) # final token → +1 K3_new = selector(pos == 1, n) # first token → +1 K4_new = selector(pos == pos, n) # all tokens → +1 # Throughout decode, solely compute Q for the NEW token (one row) Q_new = torch.ones(1, d_k) scores1_new = (Q_new @ K1_new.T) / (d_k ** 0.5) # (1, 5) scores2_new = (Q_new @ K2_new.T) / (d_k ** 0.5) # (1, 5) scores3_new = (Q_new @ K3_new.T) / (d_k ** 0.5) # (1, 5) scores4_new = (Q_new @ K4_new.T) / (d_k ** 0.5) # (1, 5) # Stack: form (4, 1, 5) new_scores = torch.stack( [scores1_new, scores2_new, scores3_new, scores4_new], dim=0) # No causal masks wanted — new token can see all earlier tokens by definition new_weights = torch.softmax(new_scores, dim=-1) # (4, 1, 5) context5 = (new_weights @ V).squeeze() # (4,) print(“Seen tokens:”, tokens) print(“Context for brand spanking new token place:n”, context5)

# Rebuild all Okay matrices for the following token (n=5)

# We are going to introduce KV-cache later

K1_new = selector(pos % 2 == 0, n) # even positions → +1

K2_new = selector(pos == n, n) # final token → +1

K3_new = selector(pos == 1, n) # first token → +1

K4_new = selector(pos == pos, n) # all tokens → +1

# Throughout decode, solely compute Q for the NEW token (one row)

Q_new = torch.ones(1, d_k)

scores1_new = (Q_new @ K1_new.T) / (d_k ** 0.5) # (1, 5)

scores2_new = (Q_new @ K2_new.T) / (d_k ** 0.5) # (1, 5)

scores3_new = (Q_new @ K3_new.T) / (d_k ** 0.5) # (1, 5)

scores4_new = (Q_new @ K4_new.T) / (d_k ** 0.5) # (1, 5)

# Stack: form (4, 1, 5)

new_scores = torch.stack(

[scores1_new, scores2_new, scores3_new, scores4_new], dim=0)

# No causal masks wanted — new token can see all earlier tokens by definition

new_weights = torch.softmax(new_scores, dim=–1) # (4, 1, 5)

context5 = (new_weights @ V).squeeze() # (4,)

print(“Seen tokens:”, tokens)

print(“Context for brand spanking new token place:n”, context5)

Output:

Seen tokens: [‘Today’, ‘weather’, ‘is’, ‘so’, ‘nice’] Context for brand spanking new token place: tensor([12.5000, 7.0000, 10.0000, 8.6000])

Seen tokens: [‘Today’, ‘weather’, ‘is’, ‘so’, ‘nice’]

Context for brand spanking new token place:

tensor([12.5000, 7.0000, 10.0000, 8.6000])

Nonetheless, not like prefill the place your complete immediate is processed in parallel, decoding should generate tokens one by one (autoregressively) as a result of the long run tokens haven’t but been generated. With out caching, each decode step would recompute keys and values for all earlier tokens from scratch, making the overall work throughout all decode steps $O(n^2)$ in sequence size. KV cache reduces this to $O(n)$ by computing every token’s $Okay$ and $V$ precisely as soon as.

KV Cache: The right way to Make Decode Extra Environment friendly

To make the autoregressive docoding environment friendly, we are able to retailer the keys ($Okay$) and values ($V$) for each token individually for every consideration head. On this simplified instance we might use just one cache. Then, throughout decoding, when a brand new token is generated, the mannequin doesn’t recompute keys and values for all earlier tokens. It computes the question for the brand new token, and attends to the cached keys and values from earlier tokens.

If we take a look at the earlier code once more, we are able to see that there isn’t a must recompute $Okay$ for your complete tensor:

K1_new = selector(pos % 2 == 0, n) # even positions → +1

K1_new = selector(pos % 2 == 0, n) # even positions → +1

As a substitute, we are able to merely compute Okay for the brand new place, and fasten it to the Okay matrix we now have already computed and saved in cache:

K1_new = selector(new_pos % 2 == 0, 1) # is pos 5 even? → -1 K1_cache = torch.cat([K1, K1_new], dim=0) # (4→5, d_k)

K1_new = selector(new_pos % 2 == 0, 1) # is pos 5 even? → -1

K1_cache = torch.cat([K1, K1_new], dim=0) # (4→5, d_k)

Right here’s the total code for decode part utilizing KV cache:

# In decode we solely compute the question for the NEW token (place 5). new_pos = pos[-1:] # tensor([5.]) # Compute ONLY the brand new token’s key for every head K1_new = selector(new_pos % 2 == 0, 1) # is pos 5 even? → -1 K2_new = selector(new_pos == n, 1) # is pos 5 final? → +1 K3_new = selector(new_pos == 1, 1) # is pos 5 first? → -1 K4_new = selector(new_pos == new_pos, 1) # at all times → +1 # Append new key to the cached prefill keys K1_cache = torch.cat([K1, K1_new], dim=0) # (4→5, d_k) K2[-1] = -torch.ones(d_k) # place 4 is now not final K2_cache = torch.cat([K2, K2_new], dim=0) K3_cache = torch.cat([K3, K3_new], dim=0) K4_cache = torch.cat([K4, K4_new], dim=0) # Q is just for the brand new token Q_dec = torch.ones(1, d_k) scores1_dec = (Q_dec @ K1_cache.T) / (d_k ** 0.5) scores2_dec = (Q_dec @ K2_cache.T) / (d_k ** 0.5) scores3_dec = (Q_dec @ K3_cache.T) / (d_k ** 0.5) scores4_dec = (Q_dec @ K4_cache.T) / (d_k ** 0.5) # Stack → (4 heads × 1 question × n keys) scores_dec = torch.stack([scores1_dec, scores2_dec, scores3_dec, scores4_dec], dim=0) # Softmax over key dimension weights_dec = torch.softmax(scores_dec, dim=-1) # Edge case: all-masked rows → zero context (identical guard as prefill) all_masked_dec = (scores_dec <= -1e4).all(dim=-1, keepdim=True) weights_dec = torch.the place(all_masked_dec, torch.zeros_like(weights_dec), weights_dec) # Context vectors: (4 × 1 × n) @ (n × 1) → (4 × 1 × 1) → squeeze → (4,) contexts_dec = (weights_dec @ V).squeeze(-1).squeeze(-1) print(“nDecode context for ‘good’ (one worth per head):n”, contexts_dec)

# In decode we solely compute the question for the NEW token (place 5).

new_pos = pos[–1:] # tensor([5.])

# Compute ONLY the brand new token’s key for every head

K1_new = selector(new_pos % 2 == 0, 1) # is pos 5 even? → -1

K2_new = selector(new_pos == n, 1) # is pos 5 final? → +1

K3_new = selector(new_pos == 1, 1) # is pos 5 first? → -1

K4_new = selector(new_pos == new_pos, 1) # at all times → +1

# Append new key to the cached prefill keys

K1_cache = torch.cat([K1, K1_new], dim=0) # (4→5, d_k)

K2[–1] = –torch.ones(d_k) # place 4 is now not final

K2_cache = torch.cat([K2, K2_new], dim=0)

K3_cache = torch.cat([K3, K3_new], dim=0)

K4_cache = torch.cat([K4, K4_new], dim=0)

# Q is just for the brand new token

Q_dec = torch.ones(1, d_k)

scores1_dec = (Q_dec @ K1_cache.T) / (d_k ** 0.5)

scores2_dec = (Q_dec @ K2_cache.T) / (d_k ** 0.5)

scores3_dec = (Q_dec @ K3_cache.T) / (d_k ** 0.5)

scores4_dec = (Q_dec @ K4_cache.T) / (d_k ** 0.5)

# Stack → (4 heads × 1 question × n keys)

scores_dec = torch.stack([scores1_dec, scores2_dec, scores3_dec, scores4_dec], dim=0)

# Softmax over key dimension

weights_dec = torch.softmax(scores_dec, dim=–1)

# Edge case: all-masked rows → zero context (identical guard as prefill)

all_masked_dec = (scores_dec <= –1e4).all(dim=–1, keepdim=True)

weights_dec = torch.the place(all_masked_dec, torch.zeros_like(weights_dec), weights_dec)

# Context vectors: (4 × 1 × n) @ (n × 1) → (4 × 1 × 1) → squeeze → (4,)

contexts_dec = (weights_dec @ V).squeeze(–1).squeeze(–1)

print(“nDecode context for ‘good’ (one worth per head):n”, contexts_dec)

Output:

Decode context for ‘good’ (one worth per head): tensor([12.5000, 6.0000, 10.0000, 8.6000])

Decode context for ‘good’ (one worth per head):

tensor([12.5000, 6.0000, 10.0000, 8.6000])

Discover that is an identical to the consequence we computed with out the cache. KV cache doesn’t change what the mannequin computes, however it eliminates redundant computations.

KV cache is totally different from the cache in different software that the item saved will not be changed however up to date. Each new token added to the immediate appends a brand new row to the tensor saved. Implementing a KV cache that may effectively replace the tensor is the important thing to make LLM inference sooner.

Additional Readings

Under are some sources that you could be discover helpful:

Abstract

On this article, we walked by the 2 phases of LLM inference. Throughout prefill, the total immediate is processed in a single parallel ahead go and the keys and values for each token are computed and saved. Throughout decode, the mannequin generates one token at a time, utilizing solely the brand new token’s question towards the cached keys and values to keep away from redundant recomputation. Prefill warms up the KV cache and decode updates it. Sooner prefill means sooner you see the primary token within the response and sooner decode means sooner you see the remainder of the response. Collectively, these two phases clarify why LLMs can course of lengthy prompts shortly however generate output token by token, and why KV cache is crucial for making that technology sensible at scale.

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From Immediate to Prediction: Understanding Prefill, Decode, and the KV Cache in LLMs

Overview

How Consideration Works Throughout Prefill

Consideration Heads

Parallelizing Consideration

From contexts to logits

The Decode Section of LLM Inference

KV Cache: The right way to Make Decode Extra Environment friendly

Additional Readings

Abstract

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Sovereign collaboration in a worldwide world: how Webex delivers knowledge residency, safety, and administrative management

Constructing a ‘Human-in-the-Loop’ Approval Gate for Autonomous Brokers

Automations for sports activities followers 2026

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From Immediate to Prediction: Understanding Prefill, Decode, and the KV Cache in LLMs

Overview

How Consideration Works Throughout Prefill

Consideration Heads

Parallelizing Consideration

From contexts to logits

The Decode Section of LLM Inference

KV Cache: The right way to Make Decode Extra Environment friendly

Additional Readings

Abstract

LEAVE A REPLY

Subscribe

More like thisRelated

About us

The latest posts

Newsletter Subscribe

More like this
Related