# Compression Barriers for Autoregressive Transformers

arXiv: https://arxiv.org/abs/2502.15955 · HTML: https://mlsanity.com/paper/2502.15955/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in KV cache optimization, one of 12 directions in Efficient LLM inference and serving.
- Builds on 41 of its 48 references that are in the map.
- First posted on arXiv 21 Feb 2025.

## Placed in

- Efficient LLM inference and serving / [KV cache optimization](https://mlsanity.com/inference/kv-cache-optimization/)

## Builds on (most cited first, 30 of 41)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision](https://mlsanity.com/paper/2407.08608/) (2024)
- [Model Tells You What to Discard: Adaptive KV Cache Compression for LLMs](https://mlsanity.com/paper/2310.01801/) (2023)
- [Scissorhands: Exploiting the Persistence of Importance Hypothesis for LLM KV Cache Compression at Test Time](https://mlsanity.com/paper/2305.17118/) (2023)
- [PyramidKV: Dynamic KV Cache Compression based on Pyramidal Information Funneling](https://mlsanity.com/paper/2406.02069/) (2024)
- [Transformers as Algorithms: Generalization and Stability in In-context Learning](https://mlsanity.com/paper/2301.07067/) (2023)
- [CacheGen: KV Cache Compression and Streaming for Fast Large Language Model Serving](https://mlsanity.com/paper/2310.07240/) (2023)
- [Adaptively Sparse Transformers](https://mlsanity.com/paper/1909.00015/) (2019)
- [On The Computational Complexity of Self-Attention](https://mlsanity.com/paper/2209.04881/) (2022)
- [Representational Strengths and Limitations of Transformers](https://mlsanity.com/paper/2306.02896/) (2023)
- [A Survey on Large Language Model Acceleration based on KV Cache Management](https://mlsanity.com/paper/2412.19442/) (2024)
- [Scatterbrain: Unifying Sparse and Low-rank Attention Approximation](https://mlsanity.com/paper/2110.15343/) (2021)
- [MiniCache: KV Cache Compression in Depth Dimension for Large Language Models](https://mlsanity.com/paper/2405.14366/) (2024)
- [Fast Attention Requires Bounded Entries](https://mlsanity.com/paper/2302.13214/) (2023)
- [RazorAttention: Efficient KV Cache Compression Through Retrieval Heads](https://mlsanity.com/paper/2407.15891/) (2024)
- [Keep the Cost Down: A Review on Methods to Optimize LLM' s KV-Cache Consumption](https://mlsanity.com/paper/2407.18003/) (2024)
- [HyperAttention: Long-context Attention in Near-Linear Time](https://mlsanity.com/paper/2310.05869/) (2023)
- [O(n) Connections are Expressive Enough: Universal Approximability of Sparse Transformers](https://mlsanity.com/paper/2006.04862/) (2020)
- [Transformers, parallel computation, and logarithmic depth](https://mlsanity.com/paper/2402.09268/) (2024)
- [A Practical Survey on Faster and Lighter Transformers](https://mlsanity.com/paper/2103.14636/) (2021)
- [QJL: 1-Bit Quantized JL Transform for KV Cache Quantization with Zero Overhead](https://mlsanity.com/paper/2406.03482/) (2024)
- [SKVQ: Sliding-window Key and Value Cache Quantization for Large Language Models](https://mlsanity.com/paper/2405.06219/) (2024)

## Built on by (most cited first, 5 of 5)

- [The risk of KV cache compression](https://mlsanity.com/paper/2607.01520/) (2026)
- [Time and Memory Trade-off of KV-Cache Compression in Tensor Transformer Decoding](https://mlsanity.com/paper/2503.11108/) (2025)
- [Thin Keys, Full Values: Reducing KV Cache via Low-Dimensional Attention Selection](https://mlsanity.com/paper/2603.04427/) (2026)
- [Query-Oblivious Coresets for Softmax Attention: Improved Bounds and Efficient Constructions](https://mlsanity.com/paper/2609.06327/) (2026)
- [Divergence Timing and Cumulative Disagreement under KV-Cache Eviction](https://mlsanity.com/paper/2609.16617/) (2026)

## Abstract (arXiv)

A key limitation of autoregressive Transformers is the large memory needed at inference-time to cache all previous key-value (KV) embeddings. Prior works address this by compressing the KV cache, but often assume specific structural properties of the embeddings. This raises the following natural question: Can truly sublinear space utilization be achieved without such assumptions? In this work, we answer this question in the negative. Any algorithm for attention-based token generation must use Theta(nd) space, where n is the number of tokens generated so far and d = Omega(log n) is the dimension of the KV embeddings. Our proof involves a reduction from a classic communication complexity problem and uses a randomized construction that leverages properties of projections in the spirit of the Johnson-Linderstrauss lemma. For the low-dimensional regime d = o(log n), we show that any algorithm requires Omega(d· ed) space and prove, using tight bounds on covering numbers, that SubGen, proposed by Zandieh, Han, Mirrokni and Karbasi, matches this bound. Further, we investigate how sparsity assumptions enable token generation in truly sublinear space, presenting impossibility results and proposing a new KV cache compression algorithm for sliding window attention when the value cache outside the window is unmasked. Finally, we analyze token generation's time complexity, using an indistinguishability argument to prove that no non-adaptive algorithm can compute attention online in sublinear time for all tokens.