# Precomputing the Future-Offset Average in TriAttention

arXiv: https://arxiv.org/abs/2607.13051 · HTML: https://mlsanity.com/paper/2607.13051/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 3 of its 5 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- Efficient LLM inference and serving / [Efficient reasoning and agent inference](https://mlsanity.com/inference/efficient-reasoning-and-agent-inference/)

## Builds on (most cited first, 3 of 3)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [TriAttention: Efficient Long Reasoning with Trigonometric KV Compression](https://mlsanity.com/paper/2604.04921/) (2026)

## Abstract (arXiv)

TriAttention is a recent method for shrinking the KV cache of long-reasoning LLMs: it scores each cached key by how much attention it is likely to receive and evicts the lowest-scoring ones. Because a key does not know how far away its future queries will sit, the score is averaged over a ladder of 17 possible future distances. We point out that this average is free: the future distance enters the score only through the position-dependent rotation, so the whole 17-fold average collapses--exactly, by a one-line algebraic identity--into a single per-band weight that is computed once, offline. Scoring a key then costs one evaluation instead of seventeen, with no change to which keys get pruned. The saving is modest and lives entirely in TriAttention's pruning-score computation, not in the attention kernel; we present it as a small, exact complement to their method, and we confirm the identity numerically.