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This research introduces JoLT, a novel compression technique for Large Language Model KV caches that leverages partial Tucker decomposition to achieve near-lossless 2-3x memory reduction. By jointly optimizing tensor ranks and residual bit-widths under strict budget constraints, the method maintains baseline accuracy on complex tasks like GSM8K retrieval even at high compression ratios. The approach directly addresses the growing throughput bottleneck caused by cache size in long-context inference scenarios without sacrificing model performance.
A JoLT for the KV Cache: Near-Lossless KV Cache Compression via Joint Tucker and JL-Residual Allocation for LLMs
arXiv:2607.12550v2 Announce Type: replace Abstract: The key-value (KV) cache has become the dominant memory cost of transformer inference: it grows with batch size, context length, and depth, and at long context it, rather than the model weights, sets the throughput ceiling. Existing reductions fall into two families. Low-rank methods factor two-dimensional slices of the cache, either per-head matrices or cross-layer feature blocks, and quantization methods lower the bit-width of every entry. Neither exploits the fact that the cache at a layer is naturally a third-order tensor whose three axes, the heads, the tokens, and the features, carry very different amounts of redundancy. We take this tensor view directly. Our method, JoLT (Joint Lagrangian Tucker), applies a partial Tucker decomposition that compresses only the token and feature axes while leaving the head and layer axes intact, then restores the energy that truncation discards with a rotated low-bit residual: a random orthogonal rotation followed by low-bit quantization. A single Lagrangian dual allocates the Tucker ranks and the residual bit-widths together, per layer group and separately for keys and values, under one byte budget. The result is a near-lossless 2-3x compression. Perplexity stays near-lossless on both a grouped-query-attention model (Mistral-7B-v0.3) and a multi-head-attention model (LLaMA-2-13B), and GSM8K accuracy and needle-in-a-haystack retrieval hold at the uncompressed baseline at 2x on both architectures and through 3x on the GQA model. At 2x, JoLT reconstructs the cache to relative Frobenius error 0.009 (K) and 0.006 (V) on both architectures. A randomized-SVD variant, FlashJoLT, delivers a 5-13x compression-time speedup at 1024-token context and matched quality.
Abstract:The key-value (KV) cache has become the dominant memory cost of transformer inference: it grows with batch size, context length, and depth, and at long context it, rather than the model weights, sets the throughput ceiling. Existing reductions fall into two families. Low-rank methods factor two-dimensional slices of the cache, either per-head matrices or cross-layer feature blocks, and quantization methods lower the bit-width of every entry. Neither exploits the fact that the cache at a layer is naturally a third-order tensor whose three axes, the heads, the tokens, and the features, carry very different amounts of redundancy. We take this tensor view directly. Our method, JoLT (Joint Lagrangian Tucker), applies a partial Tucker decomposition that compresses only the token and feature axes while leaving the head and layer axes intact, then restores the energy that truncation discards with a rotated low-bit residual: a random orthogonal rotation followed by low-bit quantization. A single Lagrangian dual allocates the Tucker ranks and the residual bit-widths together, per layer group and separately for keys and values, under one byte budget. The result is a near-lossless 2-3x compression. Perplexity stays near-lossless on both a grouped-query-attention model (Mistral-7B-v0.3) and a multi-head-attention model (LLaMA-2-13B), and GSM8K accuracy and needle-in-a-haystack retrieval hold at the uncompressed baseline at 2x on both architectures and through 3x on the GQA model. At 2x, JoLT reconstructs the cache to relative Frobenius error 0.009 (K) and 0.006 (V) on both architectures. A randomized-SVD variant, FlashJoLT, delivers a 5-13x compression-time speedup at 1024-token context and matched quality.
Machine Learning (cs.LG); Computation and Language (cs.CL); Optimization and Control (math.OC)
arXiv:2607.12550 [cs.LG]
(or arXiv:2607.12550v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.12550 Focus to learn more arXiv-issued DOI via DataCite
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