Linear Predictability of Attention Heads in Large Language Models

Long-context LLM inference is bottlenecked by quadratic attention computation and growing KV-cache costs. Existing sparse attention and KV-compression methods typically decide which tokens or heads to preserve from runtime attention scores, observation windows, calibration prompts, or learned gates, making head diagnosis input-dependent and costly to deploy. We propose Autonomy-of-Heads (AoH), a data-free method that identifies retrieval and streaming heads from the spectral geometry of query-key projections. AoH defines the kernel attention operator $M_h = W_K^{h\top}W_Q^h$ and uses its effective-rank as a weight-space measure of head function: concentrated spectra indicate a small number of dominant query-key matching directions and are associated with retrieval heads, whereas diffuse spectra indicate the absence of a dominant global matching direction and are associated with streaming heads. We further derive an efficient $d_\text{head}$-dimensional computation that avoids constructing the full $d_\text{model}\times d_\text{model}$ matrix. We conducted extensive experiments across models demonstrating that at 50% sparsity, AoH retains 96.5% of Full Attention performance on average while reducing prefill and decode latency by up to 41.4% and 66.0%, respectively, and KV-cache memory by 50.0% at 256K tokens.

Due to the nature of quadratic attention, Large Language Models (LLMs) consume a lot of memory and energy: every new token costs more than the previous one, and its keys and values must be stored in memory indefinitely, which is unsustainable. Two main lines of work address this: compressing the KV cache, e.g., by evicting or quantizing keys and values, and retrofitting LLMs to use Linear Attention, which replaces the KV cache with a fixed-size state. Retrofitting has attracted a lot of attention, given its promise to solve the quadratic scaling problem with state-of-the-art performance at low cost. However, it has not been properly compared to the simplest form of KV-cache eviction: Sliding Window Attention (SWA) with attention sinks. In this work, we show that SWA with sinks performs as well or better than most retrofitted Linear Attention models across multiple LLMs and downstream tasks, with the largest gains on long-context and generative tasks. On long-context reasoning tasks (Needle-in-a-Haystack and BABILong), SWA achieves massively higher performance (2 to 10 times higher than linear attention). SWA requires no additional training, is extremely fast, and requires little memory, making it an extremely cheap and reliable solution. When the training budget is limited, switching to SWA is a much more effective way to reduce inference memory cost than retrofitting linear attention. Linear attention models have shown promise, but they require training from scratch or extensive retrofitting to reap their architectural benefits and come close to SWA.

Long-context inference in large language models is bottlenecked by Key--Value (KV) cache loading during the decoding stage, where the sequential nature of generation requires repeatedly transferring the KV cache from off-chip High-Bandwidth Memory (HBM) to on-chip Static Random-Access Memory (SRAM) at each step. While Multi-Head Latent Attention (MLA) significantly reduces the total KV cache size, it suffers from a sharding bottleneck during distributed decoding via Tensor Parallelism (TP). Since its single latent head cannot be partitioned, each device is forced to redundantly load the complete KV cache for every token, consuming excessive memory traffic and diminishing TP benefits like weight sharding. In this work, we propose Multi-Head Low-Rank Attention (MLRA), which enables partitionable latent states for efficient 4-way TP decoding. Extensive experiments show that MLRA achieves state-of-the-art perplexity and downstream task performance, while also delivering a 2.8$\times$ decoding speedup over MLA. Code is available at https://github.com/SongtaoLiu0823/MLRA. Pretrained weights, along with the training and evaluation data, are available at https://huggingface.co/Soughing/MLRA.