[Linear Attention] Update fused_recurrent.py for inference with nomalization=true

[yiyousong]

the current linear attention can save a $KV$ state cache. This works when normalization is not enabled. When normalization is enabled. the output should be $\frac{QKV}{QK1}$. we can see that $QK1$ or Q@sum(K) is missing earlier Keys

last pull request only modified one file, not sure why this happen, re-opened this, hope this version does contain two changes

Summary by CodeRabbit

• New Features
  • Enhanced attention processing by adding an optional cumulative tensor input. This update refines the output normalization logic, offering increased flexibility and precision in the computation without altering the overall control flow.

[coderabbitai[bot]]

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Walkthrough

The changes introduce an additional optional parameter in three functions to support cumulative tensor handling. The function fused_recurrent_linear_attn now accepts a tensor parameter cum_k (defaulting to None), and its call to normalize_output is updated accordingly. The normalize_output function also accepts an optional parameter cum_k and conditionally adds its value to k if provided. Similarly, the fused_chunk_linear_attn function is updated to include cum_k, affecting its normalization process. The changes adjust the function signatures and update internal computations without altering the overall control flow.

Changes

File(s)	Change Summary
fla/ops/linear_attn/fused_recurrent.py	Modified fused_recurrent_linear_attn to add an optional cum_k parameter (torch.Tensor, default None) and updated its call to normalize_output.
fla/ops/linear_attn/utils.py	Updated normalize_output to include an optional cum_k parameter (default None) and conditionally add this value to k during normalization.
fla/ops/linear_attn/fused_chunk.py	Modified fused_chunk_linear_attn to add an optional cum_k parameter (torch.Tensor, default None) and updated its call to normalize_output.

Sequence Diagram(s)

sequenceDiagram
    participant FR as fused_recurrent_linear_attn
    participant NO as normalize_output

    FR->>NO: Call normalize_output(q * scale, k, o, cum_k)
    alt cum_k provided
        NO->>NO: Compute k = k + cum_k
    else No cum_k
        NO->>NO: Proceed without modifying k
    end
    NO->>FR: Return normalized output

    participant FC as fused_chunk_linear_attn
    FC->>NO: Call normalize_output(q * scale, k, o, cum_k)
    alt cum_k provided
        NO->>NO: Compute k = k + cum_k
    else No cum_k
        NO->>NO: Proceed without modifying k
    end
    NO->>FC: Return normalized output

Poem

I'm a rabbit with a hop and a bound,
Celebrating changes that are newly found.
A tiny tensor tip adds a little spark,
In our code garden, lighting up the dark.
With cum_k on board, our functions sing—
A joyful leap forward, oh what a spring!
🐰✨

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[zhiyuan1i]

Thanks for contributing, can you @yiyousong add tests to your contribution? This will improve the robustness of the code

@yzhangcs could you please give some comments? tests: https://github.com/fla-org/flash-linear-attention/blob/main/tests/ops/test_linear_attn.py layers: https://github.com/fla-org/flash-linear-attention/blob/main/fla/layers/linear_attn.py

[yiyousong]

Thanks for contributing, can you @yiyousong add tests to your contribution? This will improve the robustness of the code

@yzhangcs could you please give some comments? tests: https://github.com/fla-org/flash-linear-attention/blob/main/tests/ops/test_linear_attn.py layers: https://github.com/fla-org/flash-linear-attention/blob/main/fla/layers/linear_attn.py

Sorry, I don't think I understand how the tests works.

[zhiyuan1i]

Thanks for contributing, can you @yiyousong add tests to your contribution? This will improve the robustness of the code @yzhangcs could you please give some comments? tests: https://github.com/fla-org/flash-linear-attention/blob/main/tests/ops/test_linear_attn.py layers: https://github.com/fla-org/flash-linear-attention/blob/main/fla/layers/linear_attn.py

Sorry, I don't think I understand how the tests works.

You could have a try:)

pip install pytest
export COMPILER_MODE=1 # to speed up
pytest tests/ops/test_linear_attn.py
pytest tests/layers/test_linearatten_layer.py

You can see it will test function automatically. The thing you need to do is to test your cum_k and see if there is a need to change fla/layers/linear_attn.py because I see you only change the kernel.

[yzhangcs]

@yiyousong Hello, could you please explain more on what does this arg mean and what's the purpose of imposing this arg

[yiyousong]

@yiyousong Hello, could you please explain more on what does this arg mean and what's the purpose of imposing this arg

Linear attention without normalization equals to $\phi(Q)\phi(K)V$ or $\Sigma (q_i \Sigma (k_j v_j))$. $\Sigma_{j=1}^N (k_j v_j)=\Sigma_{j=c}^N (k_j v_j)+\Sigma_{j=1}^c (k_j v_j)=\Sigma_{j=c}^N (k_j v_j)+cache$ this is your code when initial_state!=None The inputs $K$ should now contain tokens from position c to N (only tokens after cached positions)

Linear attention with normalization equals to $\frac{\phi(Q)\phi(K)V}{\phi(Q)\phi(K)1}$ or $\Sigma_{i=1}^N (\frac{q_i \Sigma (k_j v_j)}{q_i \Sigma k_j})$.
Focus on the $\Sigma k_j$. During generation, the inputs to the function is probably only just the last token (shorter than total when initial_state is not None). In this case the function will calculate the sum of K as $k_N$ which is significantly smaller than the sum of all Keys. To solve this, we need to cache the sum of the previous keys ($\Sigma_{i=1}^c k_i$). In this case the $\Sigma k_j$ can be recovered by add the cached sum ($\Sigma_{i=1}^c k_i$ ,shape [B,H,1,D]) to the cumulative sum of the current inputs ($\Sigma_{i=c}^N k_i$ ,shape [B,H,S,D]). From the math, you can see that this issue only happens when both cache and normalization are used at the same time.

However, implementation was harder than I thought, as the compiled function does not take if statement. So I cannot just simply add a few parameters.

Maybe you need to change all the code involving normalization and cache

[yzhangcs]

@yiyousong Thank you, good point! We do need to suuport this. But I dont think cum_k is a good name, some better APIs designs could be considered. How about making normalization as a part of initial/final-state?

[yzhangcs]

@yiyousong Hello r u still working on this PR?

[yiyousong]

@yiyousong Hello r u still working on this PR?

I was evaluating using my own code. (only used fla.ops, not fla.layers). Based on my experience, I believe although the "Z-state"(following naming from original linear attention) can be merged with the "memory-state", I would not recommend it, as "Z-state" is only needed when normalization is True. Changes on the lower-api is unavoidable.

[yiyousong]

These changes are based on the code I changed to work for my model. I probably won't work on this further. Maybe after May 15th I may continue to update this, but currently I am too busy to debug code I won't use.