# Chiaroscuro Attention: Spending Compute in the Dark

arXiv: https://arxiv.org/abs/2606.08327 · HTML: https://mlsanity.com/paper/2606.08327/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 28 references that are in the map.
- First posted on arXiv 6 Jun 2026.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (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)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Global Filter Networks for Image Classification](https://mlsanity.com/paper/2107.00645/) (2021)
- [Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers](https://mlsanity.com/paper/2111.13587/) (2021)

## Abstract (arXiv)

We introduce CHIAR-Former (CHIAroscuro Attention-based tRansFormer), an efficient transformer that routes each token to either DCT spectral mixing (O(d log d), sub-quadratic) or full self-attention (O(n^2 d), quadratic in sequence length n) based on per-token spectral entropy H(x) in [0,1], which measures the frequency-domain complexity of each token embedding x. We make three contributions: (1) we discover routing collapse -- a three-operator system collapses to DCT+Attention, revealing the optimal operator subset; (2) we propose a learned task-level MetaRouter g = sigma(Linear(x-bar)) in [0,1], where x-bar is the batch-mean embedding and g soft-blends spectral and identity paths end-to-end; and (3) we demonstrate 35-40% FLOP reduction at 400M parameters with a 3.93 PPL cost on WikiText-103 (Test PPL 27.51 vs. 23.58). Under mixed-dataset training, CHIAR-Former dramatically outperforms full attention on small corpora, confirming the regularisation value of spectral mixing. The MetaRouter stabilises at g ~ 0.22, indicating that at scale the model reaches a robust compute-quality equilibrium: attention layers absorb representational complexity while spectral preprocessing efficiently anchors low-frequency structure.