Time and Memory Trade-off of KV-Cache Compression in Tensor Transformer Decoding

The key-value (KV) cache in the tensor version of transformers presents a significant bottleneck during inference. While previous work analyzes the fundamental space complexity barriers in standard attention mechanisms [Haris and Onak, 2025], our work generalizes the space complexity barriers result to tensor attention version. Our theoretical contributions rely on a reduction from communication complexity and deduce the memory lower bound for tensor-structured attention mechanisms when $d = \Omega(\log n)$. Furthermore, we introduce two types of tensor attention cache and present a trade-off between time and memory for two scenarios. Overall, our work provides a theoretical foundation for us to understand the time-memory tradeoff of KV-Cache compression in tensor attention decoding and offers more perspectives in developing more memory-efficient tensor attention Transformer architectures.