### Install Strassen Attention

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

Install the package via pip.

```shell
$ pip install strassen-attention
```

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

### Causal StrassenTransformer for Language Modeling

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

Configure a causal StrassenTransformer with rotary embeddings and grouped-query attention for language modeling. Ensure PyTorch is installed.

```python
import torch
from strassen_attention import StrassenTransformer

causal_transformer = StrassenTransformer(
    dim=768,
    depth=12,
    heads=12,
    dim_head=64,
    causal=True,
    rotary_embed=True,
    ff_expansion=4.0,
    final_norm=True,   # Apply final RMSNorm
    attn_kwargs=dict(
        qk_rmsnorm=True,
        attn_logits_clamp_value=40.,
        kv_heads=4,    # Grouped-query attention
        dim_head_values=64
    )
)

lm_input = torch.randn(1, 2048, 768)
lm_output = causal_transformer(lm_input)
```

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

### Initialize Strassen Transformer

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

Import the StrassenTransformer module for building full encoder/decoder stacks.

```python
import torch
from strassen_attention import StrassenTransformer
```

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

### Simple Language Model Head with StrassenTransformer

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

Implement a basic language model using StrassenTransformer and a linear layer for logits. Requires PyTorch.

```python
import torch
from strassen_attention import StrassenTransformer

class StrassenLM(torch.nn.Module):
    def __init__(self, vocab_size, dim, depth, heads):
        super().__init__()
        self.embed = torch.nn.Embedding(vocab_size, dim)
        self.transformer = StrassenTransformer(
            dim=dim, depth=depth, heads=heads, causal=True, rotary_embed=True
        )
        self.to_logits = torch.nn.Linear(dim, vocab_size, bias=False)

    def forward(self, token_ids):
        x = self.embed(token_ids)
        x = self.transformer(x)
        return self.to_logits(x)

model = StrassenLM(vocab_size=32000, dim=512, depth=6, heads=8)
tokens = torch.randint(0, 32000, (2, 128))
logits = model(tokens)
print(f"Logits shape: {logits.shape}")  # torch.Size([2, 128, 32000])
```

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

### Basic StrassenTransformer for Sequence Modeling

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

Instantiate a bidirectional StrassenTransformer for general sequence modeling tasks. Requires PyTorch.

```python
import torch
from strassen_attention import StrassenTransformer

transformer = StrassenTransformer(
    dim=512,
    depth=6,           # Number of transformer layers
    heads=8,
    dim_head=64,
    causal=False,      # Bidirectional (encoder-style)
    ff_expansion=4.0   # Feedforward expansion factor
)

x = torch.randn(2, 256, 512)  # (batch, seq_len, dim)
output = transformer(x)
print(f"Transformer output: {output.shape}")  # torch.Size([2, 256, 512])
```

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

### Integration in a U-Net Style Architecture

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

Demonstrates integrating FeatureMapWrapper within a U-Net block for residual attention. Requires PyTorch.

```python
import torch
from strassen_attention import StrassenTransformer, FeatureMapWrapper

# Integration in a U-Net style architecture
class UNetBlock(torch.nn.Module):
    def __init__(self, channels, transformer_depth=2):
        super().__init__()
        self.conv = torch.nn.Conv2d(channels, channels, 3, padding=1)
        self.attn = FeatureMapWrapper(
            StrassenTransformer(dim=channels, depth=transformer_depth, heads=8)
        )

    def forward(self, x):
        x = self.conv(x)
        x = self.attn(x) + x  # Residual attention
        return x

unet_block = UNetBlock(channels=128, transformer_depth=2)
fmap = torch.randn(4, 128, 64, 64)
output = unet_block(fmap)
print(f"U-Net block output: {output.shape}")  # torch.Size([4, 128, 64, 64])
```

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

### Initialize Strassen Transformer

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

Create a transformer model using the StrassenTransformer class.

```python
import torch
from strassen_attention.strassen_transformer import StrassenTransformer

transformer = StrassenTransformer(dim = 512, depth = 4)

x = torch.randn(1, 16 * 16, 512)
assert transformer(x).shape == x.shape
```

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

### Initialize Strassen Multi-Head Attention

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

Use the StrassenMHA module for multi-head attention with optional causal masking.

```python
import torch
from strassen_attention.strassen_mha import StrassenMHA

mha = StrassenMHA(dim = 512, causal = True)

tokens = torch.randn(1, 256, 512)

assert mha(tokens).shape == tokens.shape
```

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

### FeatureMapWrapper for Vision and U-Net Architectures

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

Adapt StrassenTransformer for multi-dimensional feature maps using FeatureMapWrapper. Handles reshaping for image and video data. Requires PyTorch.

```python
import torch
from strassen_attention import StrassenTransformer, FeatureMapWrapper

# Create transformer and wrap it for feature map processing
transformer = StrassenTransformer(
    dim=256,
    depth=4,
    heads=8,
    dim_head=32,
    causal=False
)

wrapped = FeatureMapWrapper(transformer)

# 2D feature maps (images): (batch, channels, height, width)
image_features = torch.randn(2, 256, 32, 32)
output_2d = wrapped(image_features)
print(f"2D output: {output_2d.shape}")  # torch.Size([2, 256, 32, 32])

# 3D feature maps (video): (batch, channels, depth, height, width)
video_features = torch.randn(1, 256, 8, 16, 16)
output_3d = wrapped(video_features)
print(f"3D output: {output_3d.shape}")  # torch.Size([1, 256, 8, 16, 16])
```

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

### Citation BibTeX

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

BibTeX entries for citing the relevant research papers.

```bibtex
@misc{kozachinskiy2025strassenattentionunlockingcompositional,
    title   = {Strassen Attention: Unlocking Compositional Abilities in Transformers Based on a New Lower Bound Method}, 
    author  = {Alexander Kozachinskiy and Felipe Urrutia and Hector Jimenez and Tomasz Steifer and Germán Pizarro and Matías Fuentes and Francisco Meza and Cristian B. Calderon and Cristóbal Rojas},
    year    = {2025},
    eprint  = {2501.19215},
    archivePrefix = {arXiv},
    primaryClass = {cs.LG},
    url     = {https://arxiv.org/abs/2501.19215}, 
}
```

```bibtex
@article{Peng2024OnLO,
    title     = {On Limitations of the Transformer Architecture},
    author    = {Binghui Peng and Srini Narayanan and Christos Papadimitriou},
    journal   = {ArXiv},
    year      = {2024},
    volume    = {abs/2402.08164},
    url       = {https://api.semanticscholar.org/CorpusID:267636545}
}
```

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

### Use Strassen Attention Function

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

Apply the strassen_attend function to query, key, and value tensors.

```python
import torch
from strassen_attention import strassen_attend

q = torch.randn(1, 8, 32, 16)
k = torch.randn(1, 8, 32, 16)
v = torch.randn(1, 8, 32, 16)

attended = strassen_attend(
    q,
    k,
    k.clone(),
    v,
    v.clone()
)

assert attended.shape == q.shape
```

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

### Compute Strassen Attention

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

The core attention function supports bidirectional or causal modes, cross-attention, and custom activation functions.

```python
import torch
from strassen_attention import strassen_attend

# Basic self-attention usage
# Input shapes: (batch, heads, sequence_length, head_dim)
q = torch.randn(2, 8, 128, 64)   # queries
k1 = torch.randn(2, 8, 128, 64)  # first set of keys
k2 = torch.randn(2, 8, 128, 64)  # second set of keys
v1 = torch.randn(2, 8, 128, 64)  # first set of values
v2 = torch.randn(2, 8, 128, 64)  # second set of values

# Non-causal attention (bidirectional)
output = strassen_attend(q, k1, k2, v1, v2)
print(f"Output shape: {output.shape}")  # torch.Size([2, 8, 128, 64])

# Causal attention for autoregressive models
causal_output = strassen_attend(
    q, k1, k2, v1, v2,
    causal=True,
    sim_clamp_value=30.0  # Soft-clamp similarities for numerical stability
)

# Cross-attention with different key/value sequence lengths
q_cross = torch.randn(2, 8, 64, 64)   # 64 query positions
k1_cross = torch.randn(2, 8, 256, 64) # 256 key positions
k2_cross = torch.randn(2, 8, 256, 64)
v1_cross = torch.randn(2, 8, 256, 64)
v2_cross = torch.randn(2, 8, 256, 64)

cross_output = strassen_attend(q_cross, k1_cross, k2_cross, v1_cross, v2_cross)
print(f"Cross-attention output: {cross_output.shape}")  # torch.Size([2, 8, 64, 64])

# Custom activation function (default is torch.exp)
custom_output = strassen_attend(
    q, k1, k2, v1, v2,
    activate_fn=torch.nn.functional.softplus
)
```

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