Thread (29 posts)

Origin: Information Retrieval Systems

The Q, K, V terminology comes from database/information retrieval systems, where:

• Query: What you're searching for
• Key: Index/identifier for stored items
• Value: The actual content associated with each key

Database Analogy

# Traditional key-value store
database = {
    "cat": "a small domesticated carnivorous mammal",     # key: value
    "dog": "a domesticated carnivorous mammal",           # key: value
    "bird": "a warm-blooded vertebrate with feathers"     # key: value
}

query = "cat"  # What we're looking for
result = database[query]  # Retrieve value using exact key match

Attention as Soft Lookup

Attention transforms this into a soft, differentiable lookup:

# Hard lookup (database)
if query == key:
    return value
    
# Soft lookup (attention)
similarity = dot_product(query, key)
weight = softmax(similarity)  
return weight * value  # Weighted combination

The Intuition

1. Query (Q): "What am I looking for?"

The query represents the current position asking: "What information do I need from other positions?"

Example: In "The cat sat on the ___", the blank position creates a query looking for relevant context.

2. Key (K): "What do I have to offer?"

Each position advertises what kind of information it contains via its key representation.

Example: The word "cat" might have a key that signals "I'm an animal/subject noun"

3. Value (V): "Here's my actual content"

The value is the actual information content that gets passed along if there's a match.

Example: The "cat" position's value might encode rich semantic information about cats, plurality, etc.

Visual Intuition

Think of a library:

QUERY: "I need books about cooking"

KEYS (spine labels):
- "French Cuisine" 
- "Quantum Physics"
- "Italian Recipes"
- "Garden Design"

VALUES (book contents):
- [Full French cookbook]
- [Physics textbook]
- [Italian cookbook]
- [Gardening guide]

ATTENTION PROCESS:
1. Compare query with all keys
2. "French Cuisine" (high similarity: 0.4)
3. "Quantum Physics" (low similarity: 0.0)
4. "Italian Recipes" (high similarity: 0.5)
5. "Garden Design" (low similarity: 0.1)

RESULT: Weighted mix of cookbooks' contents

In Transformer Context

# For each token position i:
Q[i] = "What information do I (token i) need?"
K[j] = "What information does token j contain?"
V[j] = "Here's the actual information from token j"

# Attention computes:
attention[i,j] = softmax(Q[i] · K[j] / sqrt(d))
output[i] = Σ(attention[i,j] * V[j])

Real Example: "The cat sat"

For the word "sat":

• Q("sat"): "I'm a verb, I need a subject"
• K("the"): "I'm a determiner"
• K("cat"): "I'm a noun, likely a subject"
• V("cat"): [Semantic features of 'cat']

The high Q-K similarity between "sat" and "cat" means "sat" will strongly attend to "cat"'s value.

Why Separate K and V?

This separation is crucial because:

1. Matching (via K) and Content (via V) are different tasks
2. What makes a good search key isn't always what you want to retrieve

Example in language:

• Key: "I'm a pronoun referring to something"
• Value: "The actual entity being referred to"

Mathematical Foundation

The attention formula: $\text{Attention}(Q,K,V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V$

Can be read as:

1. $QK^T$: Compare all queries with all keys
2. $\text{softmax}$: Convert similarities to probabilities
3. Multiply by $V$: Retrieve weighted combination of values

In Gemma's Implementation

# Each position creates its own Q,K,V
qkv = self.qkv_proj(hidden_states)  # Linear projection
xq, xk, xv = qkv.split([...])        # Split into three parts

# Q asks, K advertises, V delivers
scores = torch.matmul(q, k.transpose(2, 3))  # Q-K matching
attention = F.softmax(scores)                 # Convert to weights  
output = torch.matmul(attention, v)          # Weighted V retrieval

The beauty is that these projections are learned - the model discovers what kinds of queries, keys, and values are useful for the task at hand.

Origins and Deep Intuition of Q, K, V

The names come from the "Attention is All You Need" paper (2017) and represent a soft, differentiable memory retrieval mechanism.

The Core Operation

The attention mechanism computes:

Attention(Q, K, V) = softmax(QK^T / √d)V

This is fundamentally a weighted average of values, where weights are determined by similarity between queries and keys.

The Retrieval Metaphor

The authors conceptualized attention as a continuous addressing scheme for memory:

1. Query (Q): "What information am I looking for?"

   • Each position in the sequence asks: "Given my current representation, what should I pay attention to?"
   • In Gemma: Q = X·W_q where X is the current token's representation

2. Key (K): "What information do I contain/advertise?"

   • Each position broadcasts: "This is what I represent"
   • Keys are content descriptors - they encode what information is stored at each position
   • In Gemma: K = X·W_k

3. Value (V): "What information do I actually provide?"

   • The actual content to be retrieved and aggregated
   • Often different from the key - you search by one representation but retrieve another
   • In Gemma: V = X·W_v

Why This Separation Matters

Consider processing "The cat sat on the mat":

When processing "sat", it needs to understand its subject:

• Q (from "sat"): "I'm a verb, looking for my subject"
• K (from "cat"): "I'm a noun, could be a subject"
• K (from "the"): "I'm a determiner"
• V (from "cat"): [actual semantic content about 'cat']

The dot product Q·K measures compatibility. High scores mean "this key matches what I'm querying for."

Mathematical Intuition

# For each query position i and key position j:
score[i,j] = dot(Q[i], K[j]) / sqrt(d)
# This measures: "How relevant is position j to position i's query?"

# Softmax converts scores to probabilities
weights[i,:] = softmax(scores[i,:])
# This means: "What fraction of attention should position i pay to each position?"

# Final output aggregates values
output[i] = sum(weights[i,j] * V[j] for j in positions)
# This means: "Weighted combination of all values, weighted by relevance"

Key Insights

1. Learned Projections: W_q, W_k, W_v are learned to create useful query/key/value spaces

   • The model learns what aspects to query for
   • What aspects to advertise as keys
   • What information to actually pass as values

2. Asymmetry is Crucial:

   • K ≠ V allows searching by one criterion but retrieving different information
   • Like having an index on one column but retrieving entire rows

3. Soft Selection: Unlike hard database lookups, attention computes a weighted average

   • Every position contributes, weighted by relevance
   • Differentiable, allowing gradient-based learning

In Gemma's Implementation

# Project to different spaces
qkv = self.qkv_proj(hidden_states)  # Single matrix multiply
xq, xk, xv = qkv.split([q_size, kv_size, kv_size], dim=-1)

# Q asks "what should I attend to?"
# K says "this is what I offer for matching"  
# V says "this is what you get if you attend to me"

The beauty is that these projections are learned. The model discovers:

• What questions to ask (Q projection)
• How to advertise content for matching (K projection)
• What information to actually provide (V projection)

This creates a flexible, learnable attention pattern that can capture linguistic relationships, dependencies, and contextual information - far more powerful than fixed attention patterns or hard lookups.

Excellent question! You've hit on a key insight about how transformers process sequences. Let me explain why the attention mask is necessary.

The Key Insight: Parallel Processing

During both training and inference (especially prefill), all tokens in a sequence are processed simultaneously, not one by one. This is what makes transformers efficient.

Example: Processing "The cat sat"

When the model processes this sequence, all three tokens are in memory at once:

# All tokens are embedded simultaneously
input_token_ids = [234, 1876, 3457]  # "The", "cat", "sat"
hidden_states = self.embedder(input_token_ids)
# Shape: [1, 3, 2304] - all 3 tokens have embeddings

Why We Need the Mask

Without a mask, when computing attention for position 0 ("The"), the attention mechanism would see:

• Position 0: "The" ✓
• Position 1: "cat" ✗ (shouldn't see this yet!)
• Position 2: "sat" ✗ (shouldn't see this yet!)

Here's what happens in the attention computation:

# Query from position 0 ("The")
q_0 = query[0]  # Shape: [heads, head_dim]

# WITHOUT mask, attention scores would be:
scores = torch.matmul(q_0, all_keys.transpose())
# This computes attention to ALL positions including future ones!

# WITH mask:
mask_tensor = torch.triu(torch.full(size, -inf), diagonal=1)
# Creates:
# [[  0, -inf, -inf],
#  [  0,    0, -inf],
#  [  0,    0,    0]]

scores = scores + mask[0]  # Adds -inf to positions 1 and 2
# After softmax, -inf becomes 0 probability

The Mask Creation

# From the code:
mask_tensor = torch.full((1, 1, max_seq_len, max_seq_len), -2.3819763e38)
mask_tensor = torch.triu(mask_tensor, diagonal=1)

This creates an upper triangular matrix of -infinity values:

Position:  0    1    2    3   ...
    0    [ 0  -inf -inf -inf ...]  # Token 0 sees only position 0
    1    [ 0    0  -inf -inf ...]  # Token 1 sees positions 0,1
    2    [ 0    0    0  -inf ...]  # Token 2 sees positions 0,1,2
    3    [ 0    0    0    0  ...]  # Token 3 sees positions 0,1,2,3

Two Scenarios Where This Matters

1. Training/Prompt Processing (Parallel)

# Processing entire prompt at once
prompt = "The cat sat on the"
tokens = [234, 1876, 3457, 892, 234]  # All 5 tokens

# Without mask, token 0 would attend to all 5 tokens!
# With mask, token 0 only attends to itself

2. Generation with KV Cache

# Even during generation, the KV cache contains ALL positions
k_cache = torch.zeros(batch, max_seq_len, heads, dim)
v_cache = torch.zeros(batch, max_seq_len, heads, dim)

# When generating token at position 5:
# - Positions 0-4: Have actual key/values
# - Positions 5-max: Are zeros
# The mask ensures we don't attend to the zero-filled future positions

The Sliding Window Complication

For Gemma 2's local attention, there's an additional mask:

if self.attn_type == AttentionType.LOCAL_SLIDING:
    # Only attend to last 4096 tokens
    sliding_mask = torch.triu(all_ones, -sliding_window_size + 1) * 
                   torch.tril(all_ones, sliding_window_size - 1)
    mask = torch.where(sliding_mask == 1, mask, -inf)

Summary

The attention mask is necessary because:

1. Parallel Processing: Multiple tokens are processed simultaneously during training and prefill
2. Causal Consistency: Ensures each token only sees its past, maintaining autoregressive property
3. KV Cache Safety: Prevents attending to uninitialized future cache positions
4. Training-Inference Parity: Same masking pattern works for both training and inference

Without the mask, the model would "cheat" by looking at future tokens during training, breaking the fundamental assumption that language models predict the next token based only on previous context.

Great observation! Yes, you're right about the fixed contribution. Let me break this down:

First Non-BOS Token Attention

When processing the first "real" token (position 1), it attends to:

1. Position 0 (BOS): Fixed contribution
2. Position 1 (itself): Variable based on the token

# For token at position 1
# Q: query from current token (varies)
# K, V at position 0: always from BOS token (fixed)
# K, V at position 1: from current token (varies)

scores = torch.matmul(q, k.transpose(2, 3))
# scores[:, :, 0, 0] - attention to BOS (fixed pattern)
# scores[:, :, 0, 1] - self-attention (varies)

The attention weights might vary, but the BOS token's key-value contribution is always the same, creating a consistent "initialization signal" for all sequences.

Fixed Prefix Scenario

With a fixed prefix, this effect is amplified:

# Example: "You are a helpful assistant" as prefix
prefix_tokens = tokenizer.encode("You are a helpful assistant")
# Tokens: [BOS, 'You', 'are', 'a', 'helpful', 'assistant']

# After processing the prefix:
# KV cache positions 0-5 contain fixed representations

Impact on Generation

1. Consistent Context: Every subsequent token attends to the same prefix representations
2. Prefix as "Soft Prompt": Acts like learned prompt embeddings but in key-value space
3. Attention Patterns:

# For any new token at position N:
for i in range(prefix_length):
    # Attention to positions 0..prefix_length-1 gives fixed contributions
    fixed_contribution += attention_weights[i] * v_cache[i]

for i in range(prefix_length, N):
    # Attention to positions prefix_length..N-1 varies with context
    variable_contribution += attention_weights[i] * v_cache[i]

Interesting Implications

1. BOS as Universal Context: The BOS token acts as a universal initialization that all sequences share

2. Prefix Caching: With fixed prefixes, you can:

   # Precompute prefix KV cache once
   prefix_kv_cache = process_prefix(prefix_tokens)
   
   # Reuse for multiple completions
   for prompt in prompts:
       kv_cache = copy(prefix_kv_cache)
       generate_from_cache(prompt, kv_cache)
   

3. System Prompts: This is why system prompts work well - they provide consistent context:

   system = "You are a helpful, harmless AI assistant."
   # This creates fixed KV contributions that shape all responses
   

Attention Distribution

For early tokens, the attention distribution is quite concentrated:

# Token at position 1: can only attend to 2 positions (BOS + self)
# Token at position 10: can attend to 11 positions
# Token at position 100: can attend to 101 positions

# Early tokens have more concentrated attention, 
# making fixed contributions more influential

So yes, the BOS token (and any fixed prefix) provides a consistent "anchoring" signal that influences all subsequent generation. This is part of why models can maintain consistent behavior/style across a generation - they're partially conditioned on these fixed attention contributions.