Linear Predictability of Attention Heads in Large Language Models

• URL: http://arxiv.org/abs/2603.13314v1
• Date: Wed, 04 Mar 2026 09:04:03 GMT
• Title: Linear Predictability of Attention Heads in Large Language Models
• Abstract summary: We show that pretrained Transformers exhibit a pervasive inter-head linear structure.<n>We exploit this by caching only reference-head KV states and reconstructing the remaining heads on the fly.
• Score: 0.5833117322405447
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Large language model (LLM) inference is increasingly bottlenecked by the Key-Value (KV) cache, yet the fine-grained structure of attention-head activations remains poorly understood. We show that pretrained Transformers exhibit a pervasive inter-head linear structure: for a given token, the Query, Key, and Value (QKV) vectors of an attention head can often be reconstructed as a linear combination of a small number of peer heads, typically within the same layer. Across Llama-3.1-8B, Falcon3-10B, OLMo-2-7B, and Qwen3-32B, just 2-5 reference heads recover many target heads with high fidelity (e.g., mean R^2 approx 0.76 for Keys on C4 with five references, and frequently R^2 > 0.85 on GSM8K). This predictability is learned rather than architectural: it is largely absent at random initialization, rises rapidly during pretraining as we track through OLMo-2 checkpoints, and is supported by a theoretical lower bound showing high mean-squared error for linear prediction at initialization. We further connect this emergence to increasing intra-layer alignment of Key projection subspaces. Finally, we exploit this redundancy for efficiency by caching only reference-head KV states and reconstructing the remaining heads on the fly via lightweight linear maps, achieving 2x KV-cache reduction with model-dependent accuracy trade-offs (4.5-5.5 percentage point average drop on Falcon3-10B and Qwen3-32B across five benchmarks, and larger drops on Llama-3.1-8B), and we find that reconstructing Keys is substantially less harmful than reconstructing Values.

Related papers

• On the Design of Qwen3.8-Next Architecture: Evaluation, Efficiency, and Training Stability [57.03393882933515]
  We describe the architecture and ablations of Qwen3.8-Flash-Next, a sparse mixture-of-experts model with 125B parameters, 6B activated per token, and 51B parameters of n-gram embedding tables held off the accelerator.<n>On fourteen pre-training benchmarks the model leads the 397B-A17B predecessor on eight and trails it on the rest by at most 2.6 points, at 1/3 the activated parameters, 1/3 the training tokens, and roughly 1/9 the training FLOPs.
  arXiv  Detail & Related papers  (2026-08-31T06:35:07Z)
• Architecture-Dependent Causal Transfer of Activation States Across Large Language Models [51.56484100374058]
  Internal language activation states can be transferred causally between different large language models.<n>Injecting projected activations into a target model during generation produces a statistically significant, preregistered causal effect.<n>We conclude that end-to-end activation-state transfer between LLMs, as currently implemented, is architecture-dependent rather than universal.
  arXiv  Detail & Related papers  (2026-08-17T09:53:27Z)
• KV Cache Compression Through the Lens of Transform Coding [9.884224071643606]
  We introduce Attention-Aware Transform Coding (AATC), which allocates bits over a calibration set to minimize attention-aware distortion.<n>Our method achieves near-lossless accuracy at approximately $5.8times$ compression, whereas each baseline degrades in at least some settings.
  arXiv  Detail & Related papers  (2026-08-14T11:08:01Z)
• Cross-Model KV Cache Transfer in LLM Families: A Closed-Form Linear Mapping for Prefill Reuse [3.9548951874725433]
  We propose cross-model KV cache transfer, where the receiver reuses the source's KV cache, skipping prefill.<n>We find that cross-model KV has substantial linear structure across matched-KV pairs, where source and target share KV head count and per-head dimension.<n>This linear mapper retains 73-98% of the receiver's standalone-prefill accuracy on four pairs, while two degrade sharply.
  arXiv  Detail & Related papers  (2026-08-04T16:26:47Z)
• DynaCalKV: Key-Value Cache Compression via Head Grouping and Adaptive Rank Allocation [0.0]
  We propose an improved low-rank KV cache compression framework.<n>We show that our method reduces the number of Key cache parameters while maintaining competitive accuracy.
  arXiv  Detail & Related papers  (2026-07-27T12:08:56Z)
• Where Reliability Lives in Vision-Language Models: A Mechanistic Study of Attention, Hidden States, and Causal Circuits [1.840562129212051]
  A pervasive takeaway holds that legible-language models (VLMs) are most trustworthy when their attention maps sharp.<n>We compare attention structure, generation dynamics, and hidden-state geometry against a single correctness label.<n>In 3-7B VLMs, reliability is read more reliably off hidden-state geometry, layer-wise margin formation, and sparse late-layer circuits than off attention-map sharpness.
  arXiv  Detail & Related papers  (2026-05-05T22:27:05Z)
• Near-Oracle KV Selection via Pre-hoc Sparsity for Long-Context Inference [54.467557491325046]
  We propose Pre-hoc Sparsity (PrHS), which selects KV entries before attention scoring and provides explicit accuracy control.<n>PrHS reduces retrieval overhead by over 90%, achieving 3x higher retrieval sparsity than HShare at matched or better accuracy.<n>It incurs under 1% average degradation on LongBench, lowers attention FLOPs by about 15% versus prior baselines, and yields a 9.9x speedup in attention-operator latency and 2.8x higher throughput.
  arXiv  Detail & Related papers  (2026-02-09T07:05:23Z)
• Explicit Multi-head Attention for Inter-head Interaction in Large Language Models [70.96854312026319]
  Multi-head Explicit Attention (MEA) is a simple yet effective attention variant that explicitly models cross-head interaction.<n>MEA shows strong robustness in pretraining, which allows the use of larger learning rates that lead to faster convergence.<n>This enables a practical key-value cache compression strategy that reduces KV-cache memory usage by 50% with negligible performance loss.
  arXiv  Detail & Related papers  (2026-01-27T13:45:03Z)
• KVLinC : KV Cache Quantization with Hadamard Rotation and Linear Correction [8.486713415198968]
  We propose KVLinC, a framework to mitigate attention errors introduced by KV cache quantization.<n> KVLinC combines a Hadamard rotation, which reduces quantization error in values, with lightweight linear correction adapters.<n>We show that KVLinC consistently matches or surpasses strong baselines while achieving higher KV-cache compression.
  arXiv  Detail & Related papers  (2025-10-06T21:08:11Z)
• PatternKV: Flattening KV Representation Expands Quantization Headroom [37.83913102876393]
  KV cache in autoregressive LLMs eliminates redundant recomputation but has emerged as the dominant memory and bandwidth bottleneck during inference.<n> KV quantization is a key lever for reducing cache cost, but accuracy drops sharply as the native KV distribution lacks flatness.<n>We show that the K cache maintains a stable structure that evolves gradually with context, while the V cache carries latent semantic regularities.
  arXiv  Detail & Related papers  (2025-10-05T12:09:14Z)
• KV-Latent: Dimensional-level KV Cache Reduction with Frequency-aware Rotary Positional Embedding [72.12756830560217]
  Large language models (LLMs) based on Transformer Decoders have become the preferred choice for conversational generative AI.<n>Despite the overall superiority of the Decoder architecture, the gradually increasing Key-Value cache during inference has emerged as a primary efficiency bottleneck.<n>By down-sampling the Key-Value vector dimensions into a latent space, we can significantly reduce the KV Cache footprint and improve inference speed.
  arXiv  Detail & Related papers  (2025-07-15T12:52:12Z)
• ReCalKV: Low-Rank KV Cache Compression via Head Reordering and Offline Calibration [69.57122277845293]
  We propose ReCalKV, a post-training low-rank KV cache compression approach with tailored strategies for Keys and Values.<n>For Keys, we propose Similarity aware Recontext (HSR), which clusters structurally similar heads into groups, enabling more accurate low-rank approximation.<n>For Values, we propose Offline Head-wise Value (OVC), which efficiently calibrates the value projection matrix using calibration data without training.
  arXiv  Detail & Related papers  (2025-05-30T08:49:27Z)
• Quantize What Counts: More for Keys, Less for Values [63.51476878610841]
  Large Language Models (LLMs) suffer inference-time memory bottlenecks dominated by the attention Key-Value ( KV) cache.<n>This paper proposes two theorems that anchor mixed-precision KV quantization in the intrinsic geometry of Transformer models.
  arXiv  Detail & Related papers  (2025-02-20T22:24:27Z)
• A Simple and Effective $L_2$ Norm-Based Strategy for KV Cache Compression [13.981807478365452]
  Existing approaches to reduce the Key-Value cache size involve either fine-tuning the model to learn a compression strategy or leveraging attention scores to reduce the sequence length. We find a clear correlation between the $L$ and the attention scores over cached KV pairs, where a low $L$ of a key embedding leads to a high attention score during decoding. Our experimental results show that this simple strategy can reduce the KV cache size by 50% on language modelling and needle-in-a-haystack tasks and 90% on passkey retrieval tasks without losing accuracy.
  arXiv  Detail & Related papers  (2024-06-17T11:35:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.