QKV Projections Require a Fraction of Their Memory

Abstract: The Multi-Head Attention mechanism is central to LLM operation, and multiple works target its compute and memory efficiency during training. While most works focus on approximating the scaled dot product, the memory consumption of the linear projections that compute the $Q$, $K$, and $V$ tensors from the input $x$ is often overlooked. To address this, we propose Point-Approximate Matrix Multiplication (PAMM), a novel tensor compression technique that reduces memory consumption of the $Q,K,V$ projections in attention layers by a factor of up to $\times 512$, effectively erasing their memory footprint, while achieving similar or better final perplexity. PAMM is fully composable with efficient attention techniques such as FlashAttention, making it a practical and complementary method for memory-efficient LLM training.