# WHTMix: Efficient Stereo Depth Estimation via Walsh-Hadamard Token Mixing

arXiv: https://arxiv.org/abs/2607.25234 · HTML: https://mlsanity.com/paper/2607.25234/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 21 references that are in the map.
- First posted on arXiv 28 Jul 2026.

## Builds on (most cited first, 18 of 18)

- [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)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [CARLA: An Open Urban Driving Simulator](https://mlsanity.com/paper/1711.03938/) (2017)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [Pyramid Stereo Matching Network](https://mlsanity.com/paper/1803.08669/) (2018)
- [RAFT-Stereo: Multilevel Recurrent Field Transforms for Stereo Matching](https://mlsanity.com/paper/2109.07547/) (2021)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (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)
- [Revisiting Stereo Depth Estimation From a Sequence-to-Sequence Perspective with Transformers](https://mlsanity.com/paper/2011.02910/) (2020)
- [Iterative Geometry Encoding Volume for Stereo Matching](https://mlsanity.com/paper/2303.06615/) (2023)
- [FoundationStereo: Zero-Shot Stereo Matching](https://mlsanity.com/paper/2501.09898/) (2025)
- [Fast Walsh-Hadamard Transform and Smooth-Thresholding Based Binary Layers in Deep Neural Networks](https://mlsanity.com/paper/2104.07085/) (2021)
- [Energy Efficient Hadamard Neural Networks](https://mlsanity.com/paper/1805.05421/) (2018)
- [Hadamard Attention Recurrent Transformer: A Strong Baseline for Stereo Matching Transformer](https://mlsanity.com/paper/2501.01023/) (2025)

## Abstract (arXiv)

Stereo depth estimation for driving, robotics and augmented reality must run at high resolution under tight latency budgets, yet in transformer-based matchers the global self-attention that aggregates scene context grows quadratically with the number of pixels and comes to dominate runtime. We show that the joint self-attention stage of a stereo transformer, whose role is to spread context across both views, can be replaced by a data-independent Walsh-Hadamard token mixer that mixes tokens globally in the transform domain at log-linear cost, while the data-dependent cross-attention that performs left-right correspondence is retained. On synthetic driving data the mixer matches the attention baseline in end-point error while reducing model compute by a factor of 2.46 and single-image inference latency by a factor of 2.65. A complexity analysis shows the benefit is governed by the ratio of sequence length to channel width, which explains why high-resolution stereo matching is a particularly favorable setting and why classification transformers are not; we confirm this token-to-channel scaling on non-stereo long-sequence benchmarks. Furthermore, we introduce a hybrid log-disparity loss function designed to up-weight small-disparity pixels corresponding to long-range objects. This approach reduces the error on distant objects without incurring any additional computational overhead.