### Install mixture-of-attention

Source: https://github.com/lucidrains/mixture-of-attention/blob/main/README.md

Install the package using pip. This is the primary method for obtaining the library.

```bash
pip install mixture-of-attention
```

--------------------------------

### Initialize Transformer and AutoregressiveWrapper for Training

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Set up a Transformer model and wrap it with AutoregressiveWrapper for training on datasets like enwik8. Configure model dimensions, vocabulary size, and training parameters.

```python
import gzip
import torch
import numpy as np
from torch.optim import Adam
from torch.utils.data import DataLoader, Dataset

from mixture_of_attention.transformer import Transformer
from mixture_of_attention.autoregressive_wrapper import AutoregressiveWrapper

# Configuration
SEQ_LEN = 512
BATCH_SIZE = 4
LEARNING_RATE = 1e-4
GRADIENT_ACCUMULATE_EVERY = 4

# Initialize model
model = Transformer(
    num_tokens=256,
    dim=512,
    depth=8,
    num_experts=2,
    seq_len=SEQ_LEN,
    local_attn_window_size=64,
    num_routed_queries=32,
    num_routed_key_values=64,
    cosine_sim_routing=True,
    use_triton=True
)
model = AutoregressiveWrapper(model).cuda()
```

--------------------------------

### Initialize and Use Attend Module

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Initialize the Attend module for efficient attention computation. It supports Flash Attention, causal masking, and key padding masks. Automatic GPU optimization selects the best attention implementation.

```python
import torch
from mixture_of_attention.attend import Attend

# Initialize attend module
attend = Attend(
    dropout=0.1,                  # Attention dropout
    causal=False,                 # Causal masking
    flash=True                    # Use Flash Attention (requires PyTorch 2.0+)
)

# Query, Key, Value tensors: (batch, heads, seq_len, dim_head)
q = torch.randn(2, 8, 128, 64)
k = torch.randn(2, 8, 128, 64)
v = torch.randn(2, 8, 128, 64)

# Attention computation
output = attend(q, k, v)  # Returns: (2, 8, 128, 64)

# With key padding mask: (batch, key_seq_len)
mask = torch.ones((2, 128)).bool()
mask[:, 100:] = False  # Mask out positions 100+

output = attend(q, k, v, mask=mask)

# Causal attention for autoregressive models
causal_attend = Attend(
    dropout=0.0,
    causal=True,                  # Apply causal mask
    flash=True
)

# Automatic GPU detection for optimal Flash Attention config
# - A100 GPUs: Uses flash attention
# - Other GPUs: Uses math or memory-efficient attention
output = causal_attend(q, k, v)
```

--------------------------------

### Initialize MixtureOfAttention

Source: https://github.com/lucidrains/mixture-of-attention/blob/main/README.md

Instantiate the MixtureOfAttention module. Ensure dimensions and expert configurations match your model requirements. This is for non-autoregressive use cases.

```python
import torch
from mixture_of_attention import MixtureOfAttention

mixture_of_attn = MixtureOfAttention(
    dim = 512,
    dim_context = 256,
    num_routed_queries = 16,
    num_routed_key_values = 16,
    num_experts = 2,
    dim_head = 64,
    heads = 8
)

x = torch.randn(1, 1024, 512)
mask = torch.ones((1, 1024)).bool()

context = torch.randn(1, 512, 256)
context_mask = torch.ones((1, 512)).bool()

mixture_of_attn(x, context = context, mask = mask) # (1, 1024, 512)
```

--------------------------------

### Execute training loop

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Performs model training with gradient accumulation and clipping.

```python
optimizer = Adam(model.parameters(), lr=LEARNING_RATE)

for batch in train_loader:
    model.train()

    # Gradient accumulation
    for _ in range(GRADIENT_ACCUMULATE_EVERY):
        loss = model(batch)
        loss.backward(loss / GRADIENT_ACCUMULATE_EVERY)

    # Gradient clipping and update
    torch.nn.utils.clip_grad_norm_(model.parameters(), 0.5)
    optimizer.step()
    optimizer.zero_grad()

    print(f"Training loss: {loss.item():.4f}")
```

--------------------------------

### Coordinate Descent Algorithms

Source: https://github.com/lucidrains/mixture-of-attention/blob/main/README.md

BibTeX entry for the paper on coordinate descent algorithms, relevant for optimization techniques.

```bibtex
@article{Wright2015CoordinateDA,
    title   = {Coordinate descent algorithms},
    author  = {Stephen J. Wright},
    journal = {Mathematical Programming},
    year    = {2015},
    volume  = {151},
    pages   = {3-34}
}
```

--------------------------------

### Initialize MixtureOfAutoregressiveAttention

Source: https://github.com/lucidrains/mixture-of-attention/blob/main/README.md

Instantiate the MixtureOfAutoregressiveAttention module. Configure local and routed attention window sizes according to your needs. This variant is designed for autoregressive tasks.

```python
import torch
from mixture_of_attention import MixtureOfAutoregressiveAttention

mixture_of_attn = MixtureOfAutoregressiveAttention(
    dim = 512,
    local_attn_window_size = 64,       # local attention window size
    routed_window_size = None,         # will be set to the same as local_attn_window_size if None. ideally less than or equal to local attention window size for full receptive field
    num_routed_queries = 12,
    num_routed_key_values = 12,
    num_experts = 2,
    dim_head = 64,
    heads = 8
)

x = torch.randn(1, 1023, 512)

out = mixture_of_attn(x) # (1, 1023, 512)
```

--------------------------------

### Initialize Mixture of Autoregressive Attention

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Initialize the MixtureOfAutoregressiveAttention module with specified dimensions, attention window sizes, number of experts, and other configuration parameters. Use Flash Attention for performance if available.

```python
import torch
from mixture_of_attention import MixtureOfAutoregressiveAttention

mixture_of_attn = MixtureOfAutoregressiveAttention(
    dim=512,                      # Input dimension
    local_attn_window_size=64,    # Local attention window size (required)
    routed_window_size=None,      # Routed window size (defaults to local_attn_window_size)
    num_routed_queries=12,        # Number of queries to route per expert
    num_routed_key_values=12,     # Number of key-values to route per expert
    num_experts=2,                # Number of attention experts
    dim_head=64,                  # Dimension per attention head
    heads=8,                      # Number of attention heads
    dropout=0.0,                  # Attention dropout
    flash_attn=True,              # Use Flash Attention
    prenorm=True,                 # Apply RMS normalization
    use_triton=False,             # Use Triton kernels (disable if not available)
    average_routed=False          # Whether to average expert outputs
)
```

--------------------------------

### Initialize MixtureOfAutoregressiveAttention

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Import the MixtureOfAutoregressiveAttention class for causal attention implementations.

```python
import torch
from mixture_of_attention import MixtureOfAutoregressiveAttention
```

--------------------------------

### FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness

Source: https://github.com/lucidrains/mixture-of-attention/blob/main/README.md

BibTeX entry for the FlashAttention paper, detailing a fast and memory-efficient exact attention mechanism with IO-awareness.

```bibtex
@inproceedings{dao2022flashattention,
    title   = {Flash{A}ttention: Fast and Memory-Efficient Exact Attention with {IO}-Awareness},
    author  = {Dao, Tri and Fu, Daniel Y. and Ermon, Stefano and Rudra, Atri and R{\'e}, Christopher},
    booktitle = {Advances in Neural Information Processing Systems},
    year    = {2022}
}
```

--------------------------------

### Einops: Clear and Reliable Tensor Manipulations with Einstein-like Notation

Source: https://github.com/lucidrains/mixture-of-attention/blob/main/README.md

BibTeX entry for the einops library, which simplifies tensor manipulations using Einstein-like notation.

```bibtex
@inproceedings{rogozhnikov2022einops,
    title   = {Einops: Clear and Reliable Tensor Manipulations with Einstein-like Notation},
    author  = {Alex Rogozhnikov},
    booktitle = {International Conference on Learning Representations},
    year    = {2022},
    url     = {https://openreview.net/forum?id=oapKSVM2bcj}
}
```

--------------------------------

### Initialize and Use Transformer Model

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Initialize a Transformer model with specified parameters and perform a forward pass. The model can be wrapped with AutoregressiveWrapper for training and generation.

```python
import torch

# Initialize transformer model
model = Transformer(
    num_tokens=256,               # Vocabulary size (e.g., 256 for byte-level)
    dim=512,                      # Model dimension
    depth=8,                      # Number of transformer layers
    seq_len=512,                  # Maximum sequence length
    local_attn_window_size=64,    # Local attention window
    num_routed_queries=32,        # Queries to route per expert
    num_routed_key_values=64,     # Key-values to route per expert
    num_experts=2,                # Number of attention experts
    dim_head=64,                  # Dimension per attention head
    heads=8,                      # Number of attention heads
    ff_mult=4,                    # Feed-forward expansion multiplier
    cosine_sim_routing=True,      # Use cosine similarity for routing
    routed_window_size=None,      # Override routed window size
    use_triton=True,              # Use Triton kernels
    routed_rotary_emb=True        # Use rotary embeddings for routed attention
)

# Input: token indices (batch, sequence_length)
x = torch.randint(0, 256, (2, 512))

# Forward pass returns logits
logits = model(x)  # Returns: (2, 512, 256)

# Wrap for autoregressive training and generation
model = AutoregressiveWrapper(
    model,
    pad_value=0                   # Padding token value
)

# Training: input includes target (shifted by 1)
x = torch.randint(0, 256, (2, 513))  # seq_len + 1
loss = model(x)  # Returns cross-entropy loss

# Generation
prompt = torch.randint(0, 256, (1, 128))  # Prompt tokens
generated = model.generate(
    prompt,
    seq_len=256,                  # Number of tokens to generate
    temperature=1.0,              # Sampling temperature
    filter_thres=0.9              # Top-k filtering threshold
)  # Returns: (1, 256) generated tokens
```

--------------------------------

### Initialize and Use MixtureOfAttention

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Configure and execute cross-attention and self-attention using the MixtureOfAttention class.

```python
import torch
from mixture_of_attention import MixtureOfAttention

# Initialize mixture of attention with 2 experts
mixture_of_attn = MixtureOfAttention(
    dim=512,                      # Input dimension
    dim_context=256,              # Context dimension (for cross-attention)
    num_routed_queries=16,        # Number of queries to route per expert
    num_routed_key_values=16,     # Number of key-values to route per expert
    num_experts=2,                # Number of attention experts
    dim_head=64,                  # Dimension per attention head
    heads=8,                      # Number of attention heads
    local_attn=False,             # Whether to use local attention in parallel
    local_attn_window_size=None,  # Window size for local attention
    flash_attn=True,              # Use Flash Attention (requires PyTorch 2.0+)
    prenorm=True,                 # Apply RMS normalization before attention
    use_triton=True,              # Use Triton kernels for routing
    average_routed=False          # Whether to average routed outputs
)

# Input tensor: (batch, sequence_length, dim)
x = torch.randn(1, 1024, 512)
mask = torch.ones((1, 1024)).bool()

# Cross-attention context: (batch, context_length, dim_context)
context = torch.randn(1, 512, 256)
context_mask = torch.ones((1, 512)).bool()

# Forward pass - cross-attention
output = mixture_of_attn(
    x,
    context=context,
    mask=mask,
    context_mask=context_mask
)  # Returns: (1, 1024, 512)

# Self-attention (no context provided)
self_attn = MixtureOfAttention(
    dim=512,
    num_routed_queries=16,
    num_routed_key_values=16,
    num_experts=2,
    dim_head=64,
    heads=8,
    local_attn=True,               # Enable local attention for self-attention
    local_attn_window_size=64      # Local attention window
)

x = torch.randn(1, 1024, 512)
output = self_attn(x, mask=mask)  # Returns: (1, 1024, 512)
```

--------------------------------

### Load enwik8 data

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Reads and prepares the enwik8 dataset for training and validation.

```python
with gzip.open("./data/enwik8.gz") as file:
    data = np.frombuffer(file.read(int(95e6)), dtype=np.uint8).copy()
    np_train, np_valid = np.split(data, [int(90e6)])
    data_train = torch.from_numpy(np_train)
    data_val = torch.from_numpy(np_valid)

train_dataset = TextSamplerDataset(data_train, SEQ_LEN)
train_loader = DataLoader(train_dataset, batch_size=BATCH_SIZE, shuffle=True)
```

--------------------------------

### Initialize and Apply Rotary Positional Embeddings

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Initialize RotaryEmbedding and apply it to query and key tensors. Ensure the dimension matches `dim_head`.

```python
import torch
from mixture_of_attention.rotary_emb import RotaryEmbedding, apply_rotary_pos_emb

# Initialize rotary embedding
rotary_emb = RotaryEmbedding(
    dim=64,                       # Dimension (should match dim_head)
    theta=10000                   # Base frequency
)

# Generate position embeddings for sequence
seq_len = 1024
freqs = rotary_emb(seq_len)  # Returns: (seq_len, dim)

# Apply to query/key tensors
# q, k shape: (batch, heads, seq_len, dim_head)
q = torch.randn(2, 8, 1024, 64)
k = torch.randn(2, 8, 1024, 64)

# Apply rotary embeddings
q_rotated = apply_rotary_pos_emb(freqs, q)
k_rotated = apply_rotary_pos_emb(freqs, k)
```

--------------------------------

### Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems

Source: https://github.com/lucidrains/mixture-of-attention/blob/main/README.md

BibTeX entry for a paper on stabilized sparse scaling algorithms for entropy-regularized transport problems.

```bibtex
@article{Schmitzer2016StabilizedSS,
    title   = {Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems},
    author  = {Bernhard Schmitzer},
    journal = {ArXiv},
    year    = {2016},
    volume  = {abs/1610.06519}
}
```

--------------------------------

### Multi-Expert Attention with Scaling Factors

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Apply scaling factors to queries, keys, values, and output in multi-expert attention. Ensure scaling tensor dimensions are compatible.

```python
# With scaling factors for routed attention
output = multi_expert_attn(
    x,
    mask=mask,
    queries_scale=torch.ones(2, 4, 128, 1),   # Scale queries
    keys_scale=torch.ones(2, 4, 1, 128, 1),   # Scale keys
    values_scale=torch.ones(2, 4, 1, 128, 1), # Scale values
    output_scale=torch.ones(2, 4, 128, 1)     # Scale output
)
```

--------------------------------

### CoLT5: Faster Long-Range Transformers with Conditional Computation

Source: https://github.com/lucidrains/mixture-of-attention/blob/main/README.md

BibTeX entry for the CoLT5 paper, which explores conditional computation for efficient long-range transformers.

```bibtex
@inproceedings{Ainslie2023CoLT5FL,
    title   = {CoLT5: Faster Long-Range Transformers with Conditional Computation},
    author  = {Joshua Ainslie and Tao Lei and Michiel de Jong and Santiago Ontan'on and Siddhartha Brahma and Yury Zemlyanskiy and David Uthus and Mandy Guo and James Lee-Thorp and Yi Tay and Yun-Hsuan Sung and Sumit Sanghai},
    year    = {2023}
}
```

--------------------------------

### Multi-Expert Grouped Attention Initialization

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Initialize Attention with multiple expert groups for parallel processing. Set causal=True for autoregressive tasks and prenorm=True for pre-layer normalization.

```python
# Multi-expert grouped attention
multi_expert_attn = Attention(
    dim=512,
    dim_head=64,
    heads=8,
    groups=4,                     # 4 expert groups processed in parallel
    causal=True,                  # Causal for autoregressive
    flash=True,
    prenorm=True
)
```

--------------------------------

### Generate text sequences

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Uses the trained model to generate text from a random prompt.

```python
model.eval()
prompt = torch.randint(0, 256, (1, 128)).cuda()
generated = model.generate(prompt, seq_len=512, temperature=0.8)
print("Generated:", "".join(chr(max(32, t)) for t in generated[0]))
```

--------------------------------

### Transformer Model Initialization

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Initialize the Transformer class, which utilizes mixture of autoregressive attention layers. Suitable for language modeling and sequence generation.

```python
import torch
from mixture_of_attention.transformer import Transformer
from mixture_of_attention.autoregressive_wrapper import AutoregressiveWrapper
```

--------------------------------

### Initialize Base Attention Module

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Initialize the base Attention module for multi-head attention. Supports grouped experts, rotary embeddings, and Flash Attention. Set causal=True for autoregressive tasks.

```python
import torch
from mixture_of_attention import Attention

# Basic single-expert attention
attn = Attention(
    dim=512,                      # Input dimension
    dim_head=64,                  # Dimension per head
    dim_context=None,             # Context dimension (defaults to dim)
    heads=8,                      # Number of attention heads
    causal=False,                 # Causal masking for autoregressive
    groups=1,                     # Number of expert groups
    dropout=0.0,                  # Attention dropout
    flash=True,                   # Use Flash Attention
    prenorm=False                 # Apply RMS normalization
)
```

--------------------------------

### Define TextSamplerDataset class

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

A PyTorch Dataset implementation for sampling sequences from a large tensor.

```python
class TextSamplerDataset(Dataset):
    def __init__(self, data, seq_len):
        self.data = data
        self.seq_len = seq_len

    def __getitem__(self, index):
        rand_start = torch.randint(0, self.data.size(0) - self.seq_len, (1,))
        full_seq = self.data[rand_start:rand_start + self.seq_len + 1].long()
        return full_seq.cuda()

    def __len__(self):
        return self.data.size(0) // self.seq_len
```

--------------------------------

### Self-Attention Forward Pass

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Perform a self-attention forward pass using the Attention module. Input shape is (batch, sequence, dim). A boolean mask can be provided.

```python
# Input: (batch, sequence, dim)
x = torch.randn(2, 128, 512)
mask = torch.ones((2, 128)).bool()

# Self-attention
output = attn(x, mask=mask)  # Returns: (2, 128, 512)
```

--------------------------------

### Forward Pass with Mixture of Autoregressive Attention

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Perform a forward pass with the MixtureOfAutoregressiveAttention module. Input tensor shape is (batch, sequence_length, dim). Optionally override routing parameters.

```python
# Input tensor: (batch, sequence_length, dim)
x = torch.randn(1, 1023, 512)

# Forward pass - autoregressive attention
output = mixture_of_attn(x)  # Returns: (1, 1023, 512)
```

```python
# With dynamic routing parameters
output = mixture_of_attn(
    x,
    num_routed_queries=8,         # Override default routed queries
    num_routed_key_values=8       # Override default routed key-values
)
```

--------------------------------

### Cross-Attention Forward Pass

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Perform a cross-attention forward pass by providing a separate context tensor. The context tensor shape is (batch, context_sequence, dim).

```python
# Cross-attention with context
context = torch.randn(2, 64, 512)
output = attn(x, context=context, mask=mask)
```

--------------------------------

### Multi-Expert Grouped Attention Forward Pass

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Perform a forward pass with multi-expert grouped attention. Input tensor shape is (batch, groups, sequence, dim).

```python
# Input with expert dimension: (batch, groups, sequence, dim)
x = torch.randn(2, 4, 128, 512)
mask = torch.ones((2, 4, 128)).bool()

output = multi_expert_attn(x, mask=mask)  # Returns: (2, 4, 128, 512)
```

--------------------------------

### Mixture of Autoregressive Attention with Rotary Embeddings

Source: https://context7.com/lucidrains/mixture-of-attention/llms.txt

Apply rotary embeddings for positional encoding with MixtureOfAutoregressiveAttention. Ensure rotary embedding dimension matches dim_head.

```python
from mixture_of_attention.rotary_emb import RotaryEmbedding

rotary_emb = RotaryEmbedding(dim=64)  # Same as dim_head
pos_emb = rotary_emb(seq_len=1023)    # Generate position embeddings

output = mixture_of_attn(x, rotary_emb=pos_emb)
```

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