High-Fidelity KV Cache Summarization Using Entropy and Low-Rank Reconstruction

High-Fidelity KV Cache Summarization Using Entropy and Low-Rank Reconstruction(jchandra.com)

64 points by jchandra 29 days ago | 17 comments

jchandra 29 days ago |

I’ve been exploring KV cache optimization for LLM inference.

Most methods (Top-K, sliding window) prune tokens. This works on average, but fails selectively — a few tokens cause large errors when removed.

I tried reframing the problem as approximating the attention function: Attn(Q, K, V)

Prototype: - entropy → identify weak tokens - OLS → reconstruct their contribution - SVD → compress them

Early results show lower error than Top-K at low memory, sometimes even lower memory overall.

This is still a small research prototype, would appreciate feedback or pointers to related work.

bee_rider 27 days ago |

Were there any downsides or difficulties?

It would be sort of surprising if an SVD-based opportunity was missed (since it is such a familiar tool). But, your entropy and least-squares ideas are necessary to set that up, so I guess it makes sense that you’d find some new territory here.

jchandra 27 days ago | |

That’s a great point and yeah, I’d agree SVD itself isn’t new at all.

On downsides: definitely a few. The biggest one is latency - SVD is fairly heavy, so even though it’s amortized (runs periodically, not per token), it still adds noticeable overhead. It’s also more complex than simple pruning, and I haven’t validated how well this holds on real downstream tasks yet.

This is very much a research prototype right now more about exploring a different tradeoff space than something ready for production.

cowartc 27 days ago |

Interesting direction. One question: How does this hold up outside the synthetic transformer on a real downstream task? Reconstruction error is the right measure but its one step removed from the end task. I'm curious whether HAE would show a similar gap on a downstream benchmark.

vivahir215 29 days ago |

Interesting Approach. Curious about the latency tradeoff: OLS + SVD are much heavier than Top-K.Have you benchmarked end-to-end inference latency?

scythmic_waves 27 days ago | |

From the conclusion:

> The primary trade-off observed is the increased calculation time for OLS and SVD steps. Consequently, the next phase of this work involves implementing these operations within custom Triton kernels to amortize latency. By viewing the cache through the lens of reconstruction fidelity rather than just memory capacity, we can develop more sustainable architectures for long-context inference.

Reading between the lines, the increase in latency was so significant that they didn't want to include it before they had a chance to try and optimize the problem away first.

Still interesting research. Hope they get good results!

jchandra 27 days ago | | |

Haha, that’s a very fair reading :)

Yeah, the latency hit is definitely real. That said, most of what I’ve run so far is CPU-bound, which likely exaggerates it quite a bit so I didn’t want to draw strong conclusions from that.

Would need proper GPU implementations to really understand where it lands.

jchandra 29 days ago | |

In this prototype, OLS + SVD isn’t per-token, it runs only when the recycle bin fills (amortized over multiple tokens).

That said, it’s still heavier than Top-K. I haven’t benchmarked end-to-end latency yet; this is mainly exploring the accuracy vs memory tradeoff.

jbellis 27 days ago |

Isn't the "KV Compression Strategies (FAIR)" chart showing that the fancy complex algorithm only barely beats simple topk?

The commentary says that topk "degrades rapidly at low ratios" but the same can be seen for HAE (Entropy + OLS).

jchandra 27 days ago | |

Fair point, the gap isn’t huge in that plot, and both degrade at low ratios. The difference is more in how they degrade: TopK can have sharper, localized failures, while HAE tends to be a bit more smooth. That doesn’t always show up strongly in average MSE.

That said, the gains are modest right now, this is still a research prototype exploring the tradeoff, and there’s clearly more work to be done.

bee_rider 27 days ago | |

Is it really that fancy and complex, though? The “entropy recycling bin” seems fancy to me, but the other stuff is least squares and an SVD, these are solid workhorse numerical routines.

rishabhaiover 27 days ago |

After a certain amount of context usage, I think I empirically see the stated issues with Top-K compression strategy. It doesn't catastrophically forget but nuances fade as I reach towards the tail end of my context limits.

jchandra 27 days ago | |

Yeah, that’s consistent. topK keeps the obvious tokens, but subtle context gets eroded over time rather than dropped all at once.

thw20 27 days ago |

Good work! This is very interesting. Here's a related work that construct low-rank approximation for attention: https://arxiv.org/abs/2505.12942.

Maybe the idea of Query calibration matrix Rxx is of interest to the author!

jchandra 27 days ago | |

Thanks, really appreciate the pointer. Will dig into it.

aesthesia 27 days ago |

I notice the experiments are all run with Gaussian token embeddings and weight matrices, which is a very different scenario than you would get in a real model. It shouldn't be much more difficult to try this with an actual model and data and get a much better sense of how well it compresses.

jchandra 27 days ago | |

I completely agree.Right now this is all on a synthetic setup to isolate the behavior and understand the reconstruction vs memory tradeoff. Real models will definitely behave differently.

I’ve started trying this out with actual models, but currently running things CPU-bound, so it’s pretty slow. Would ideally want to try this properly on GPU, but that gets expensive quickly

So yeah, still very much a research prototype — but validating this on real models/data is definitely the next step.