Tensor Decomposition of Transformer Key-Value Caches: Spectral Structure and Format Comparison

The key-value (KV) cache is the dominant memory bottleneck in long-context language model inference. Existing compression methods apply low-rank factorization or quantization independently, without jointly allocating rank and precision under a shared storage budget. We introduce JoLT, a training-free compressor that treats grouped prefill caches as fourth-order tensors and applies partial Tucker decomposition along the token and feature modes, the two axes that carry low-rank structure, while leaving the head and layer modes intact. A rotated low-bit quantizer captures the truncation residual, and a single Lagrangian dual allocates per-group Tucker ranks and residual bit-widths under a global byte constraint. FlashJoLT replaces the exact token-mode SVD with a randomized approximation that matches JoLT within the free zone at a fraction of the compression cost, and a fused Triton decode kernel evaluates attention directly over the stored factors without materializing dense KV tensors. Across five models from four architecture families, covering multi-head attention, grouped-query attention, and mixture-of-experts architecture, JoLT achieves 2 - 3x compression with less than 0.2% perplexity degradation, without retraining. On RULER at 64K context with LLaMA-3.1-8B, retrieval accuracy remains near-lossless through 3x and declines by only 0.90 and 2.40pp at 4x and 5x, respectively. JoLT demonstrates that tensor-aware low-rank decomposition and quantized residuals, unified under a single storage budget, achieve near-lossless KV-cache compression across diverse model architectures without retraining.

Transformer inference on long sequences is expensive because softmax attention repeatedly reads from a large KV cache. The prevalent approach to this bottleneck is KV cache compression, which replaces the full cache with a compact summary. Despite its practical importance, the design of such summaries is largely driven by empirical experimentation. On the theoretical side, existing results show that KV cache compression can be impossible in the worst case, but offer little systematic guidance for designing algorithms in regimes where accurate compression is possible. We bridge this gap by characterizing the minimax risk of KV cache compression in terms of the intrinsic compressibility of a cache, revealing when and how accurate compression is possible. These results yield novel design principles for KV cache compression under causal masking that map efficiently to prefill and autoregressive decoding while achieving minimax-optimal risk. We instantiate these principles in a practical algorithm and report promising performance on LongBench in targeted experiments. Overall, our results provide a principled avenue for practical KV cache compression with theoretical guarantees.

Under modern test-time compute and agentic paradigms, language models process ever-longer sequences. Efficient text generation with transformer architectures is increasingly constrained by the Key-Value cache memory footprint and bandwidth. To address this limitation, we introduce Self-Pruned Key-Value Attention (SP-KV), a mechanism designed to predict future KV utility in order to reduce the size of the long-term KV cache. This strategy operates at a fine granularity: a lightweight utility predictor scores each key-value pair, and while recent KVs are always available via a local window, older pairs are written in the cache and used in global attention only if their predicted utility surpasses a given threshold. The LLM and the utility predictor are trained jointly end-to-end exclusively through next-token prediction loss, and are adapted from pretrained LLM checkpoints. Rather than enforcing a fixed compression ratio, SP-KV performs dynamic sparsification: the mechanism adapts to the input and typically reduces the KV cache size by a factor of $3$ to $10\times$, longer sequences often being more compressible. This leads to vast improvements in memory usage and decoding speed, with little to no degradation of validation loss nor performance on a broad set of downstream tasks. Beyond serving as an effective KV-cache reduction mechanism, our method reveals structured layer- and head-specific sparsity patterns that we can use to guide the design of hybrid local-global attention architectures.