Zhihang Lin

Zhihang Lin, Mingbao Lin, Yuan Xie et al.

This paper introduces Completion Pruning Policy Optimization (CPPO) to accelerate the training of reasoning models based on Group Relative Policy Optimization (GRPO). GRPO, while effective, incurs high training costs due to the need to sample multiple completions for each question. Our experiment and theoretical analysis reveal that the number of completions impacts model accuracy yet increases training time multiplicatively, and not all completions contribute equally to policy training -- their contribution depends on their relative advantage. To address these issues, we propose CPPO, which prunes completions with low absolute advantages, significantly reducing the number needed for gradient calculation and updates. Additionally, we introduce a dynamic completion allocation strategy to maximize GPU utilization by incorporating additional questions, further enhancing training efficiency. Experiments show that CPPO achieves up to $7.98\times$ speedup on GSM8K and $3.48\times$ on Math while preserving or even enhancing the accuracy compared to the original GRPO. We release our code at \href{https://github.com/lzhxmu/CPPO}{https://github.com/lzhxmu/CPPO}.

Dmitry Rybin, Yushun Zhang, Ding Tian et al.

We present Exact Causal Attention (ECA), a Strassen-style algorithm that computes exact Causal Attention using 10\% fewer operations. ECA improves a special class of matrix multiplications where either one operand or the output matrix is upper- or lower-triangular. This includes all matrix multiplication operations in the forward and backward pass of Causal Attention, such as masked product $\mathrm{Mask}(QK^{T})$. ECA is built upon algebraic identities discovered via machine learning and combinatorial search. We note that ECA cannot accelerate fused kernels such as FlashAttention on GPU. This is because ECA requires materialization of large intermediate expressions in the memory, while FlashAttention does not. However, it provides an alternative approach for compute-bound applications and can potentially be useful in scenarios with FLOPs considerations.