Bridging KV-Cache Quantization and Linear Attention: From Theory to Pretrained Weight Migration

Looped Transformers improve parameter efficiency by repeatedly applying shared Transformer blocks over multiple recurrent loops, increasing computational depth without increasing the parameter count. However, KV cache memory still scales with the number of loops, becoming a key memory bottleneck that limits batch size and inference throughput. KV cache quantization can alleviate this bottleneck, but existing methods often suffer substantial accuracy degradation at aggressive low-precision regimes. We observe that looped Transformers offer a unique opportunity: KV states across loops are highly similar. Based on this observation, we propose ResidualQuant, which uses the final-loop KV states as a reference and represents the remaining loops with low-precision residuals. Our method further combines least-square scaling and rotations applied to the residuals, as well as loop-wise mixed precision, to enable accurate quantization down to INT2 while retaining efficient reconstruction. Across multiple looped Transformer models and mathematical reasoning and code generation benchmarks, ResidualQuant consistently improves the accuracy-memory tradeoff over state-of-the-art rotation-based KV quantization. In particular, our method retains accuracy close to BF16 under mixed-precision settings while reducing theoretical KV storage by 80.7%, achieving up to 13.0% higher accuracy than the rotation-based baseline at the same memory budget. On an RTX 5090, the reduced KV memory traffic improves fixed-batch decode throughput by up to 2.73x, while the smaller memory footprint enables up to 2x larger batches, improving peak throughput by up to 4.15x.

The large KV-cache size of modern LLMs creates a barrier to efficient deployment. Recent work has explored replacing attention layers' RoPE positional embeddings with alternative decay-based mechanisms, which can then be used to prune KV-cache during inference. However, these decay functions have limited expressivity, and in practice devolve into sliding-window-like eviction patterns. In this work, we propose a unifying framework for complementary and novel decay mechanisms, capturing complex key statistics and interactions while preserving expressive RoPE embeddings and Softmax attention. The resulting Universal Attention is a highly expressive and end-to-end trainable architecture, whose composite decay mechanism acts as a natural, $\textit{adaptive}$ pruning criterion, removing tokens that contribute least to attention computation. Experimentally, Universal Attention achieves state-of-the-art $10\times$ compression on natural language and synthetic task data, while $\textit{improving}$ downstream performance compared to both state-of-the-art baselines and unpruned oracles. It further demonstrates superior long-context generalization with unprecedented $25\times$ compression at length 16k.

KV cache compression is essential for efficient long-context inference. Existing eviction methods permanently discard unselected tokens and consequently remove their aggregate contribution to attention. Merging-based alternatives preserve more information but can perturb retained keys and values that should remain exact. We observe that the information omitted by cache eviction can be formulated as residual statistics in both the numerator and denominator of softmax attention. Based on this observation, we propose ResKV, which divides a fixed KV budget into an exact main cache and a compact residual cache that reconstructs the contribution of omitted tokens. ResKV lets main-cache tokens and residual entries participate in the same softmax normalization, so residual entries restore both attention numerator and denominator mass rather than acting as a post-hoc correction. A construction-time validation proxy determines residual allocation for each layer and KV head, while a decode-time dynamic gate adjusts residual contributions for individual queries. Comprehensive evaluations on LongBench and RULER, covering query-aware and query-agnostic settings, multiple backbones, cache budgets, and representative compression baselines, demonstrate broad improvements under the same retained KV budget while preserving the practical efficiency of compressed decoding, including peak memory usage and long-context decode throughput.