STAR-KV: Low-Rank KV Cache Compression via Soft Thresholding for Adaptive Rank Control

What limits KV-cache compression at extreme bit-rates? We argue that it is not the choice of compression scheme, but how its budget is allocated across attention heads. Existing methods apply rank and bit-width uniformly, ignoring that each head has a different optimal mix of rank truncation and quantization. We show that co-optimizing rank and bit-width per head, using only standard low-rank projection and scalar quantization, dominates uniform allocation, with the largest gains at low bit-rates. Our method, KV-COBRA (Co-Optimized Bit-Rank Allocation), formalizes this as a resource-allocation problem: it balances rank-truncation loss against quantization loss within each head, then redistributes budget across heads to minimize total distortion. A fused Hadamard rotation equalizes per-channel variance, and reordering the SVD basis by attention-KL importance makes the solver query-aware. The same allocator extends to joint $K{+}V$ compression. On perplexity, zero-shot, and long-context benchmarks from $0.5$ to $4$ bits per dimension (bpd), KV-COBRA shows the smallest accuracy degradation among evaluated methods at low bpd, with no per-token overhead.

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 ceiling on throughput. Two families of methods reduce it. 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 family 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, applies a partial Tucker decomposition that compresses only the token and feature axes while leaving the head and layer axes intact, and then restores the energy that truncation discards with a Johnson-Lindenstrauss (JL) rotated low-bit residual. 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, GSM8K accuracy, and RULER needle-in-a-haystack retrieval all stay at or within statistical noise of the uncompressed baseline on both a grouped-query-attention model (Mistral-7B-v0.3) and a multi-head-attention model (LLaMA-2-13B). At 2x, JoLT reconstructs the cache to relative Frobenius error 0.009 (K) and 0.006 (V) on both architectures, roughly an order of magnitude below cross-layer SVD and 4-bit quantization. A randomized-SVD variant, FlashJoLT, delivers a 5-13x compression-time speedup at matched quality.

As the inference phase of Large Language Models (LLMs) requires handling long context windows, the Key-Value (KV) cache initially appears to address this challenge but eventually becomes a significant bottleneck as the context window continues to grow. Low-rank compression has recently been studied as an effective approach to reduce KV cache memory while maintaining model performance. However, only a few existing methods treat the Key and Value caches differently, despite their distinct roles. Moreover, these methods typically employ fixed attention-head grouping, which may not fully exploit the structural similarity among attention heads. In this paper, we propose an improved low-rank KV cache compression framework. For the Key cache, we dynamically group attention heads based on Centered Kernel Alignment (CKA) similarity and allocate the rank budget adaptively under a parameter budget. For the Value cache, we adopt the same approach as ReCalKV, refining the low-rank decomposition through offline calibration to improve reconstruction quality. Experimental results on three instruction-tuned LLMs show that our method reduces the number of Key cache parameters while maintaining competitive accuracy. We further observe that the proposed strategy is particularly effective for Multi-Head Attention (MHA) models, whereas it should be applied more conservatively to Grouped-Query Attention (GQA) models, especially in long-context settings.