# HAMON: Passive Optical Sequence Mixing for Long-Horizon Forecasting

arXiv: https://arxiv.org/abs/2606.17028 · HTML: https://mlsanity.com/paper/2606.17028/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 20 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 13 of 13)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [All-Optical Machine Learning Using Diffractive Deep Neural Networks](https://mlsanity.com/paper/1804.08711/) (2018)
- [All-Optical Synthesis of an Arbitrary Linear Transformation Using Diffractive Surfaces](https://mlsanity.com/paper/2108.09833/) (2021)
- [Time-lapse image classification using a diffractive neural network](https://mlsanity.com/paper/2208.10802/) (2022)
- [Photonic reservoir computer based on frequency multiplexing](https://mlsanity.com/paper/2008.11247/) (2020)
- [Superposition Is Not Necessary: A Mechanistic Interpretability Analysis of Transformer Representations for Time Series Forecasting](https://mlsanity.com/paper/2605.05151/) (2026)

## Abstract (arXiv)

Simple linear and frequency-domain models remain surprisingly competitive in long-horizon time-series forecasting, and recent mechanistic evidence suggests that standard forecasting benchmarks may not require the dense superposed representations that make transformers powerful in other domains. This raises a substrate-level question: if the core forecasting operator is often low-complexity and approximately linear, does it need to be implemented as learned digital temporal mixing? We introduce HAMON, a passive diffractive optical forecasting core in which historical values are encoded onto an optical aperture, future positions are left dark, and cascaded trainable phase masks with free-space diffraction shape the forecast directly in the output field. At inference, prediction is performed by a single passive optical propagation pass with no trainable digital sequence-mixing layer. Across standard benchmarks, HAMON outperforms the strongest digital baselines considered on ETTm2 at all horizons and on ETTh2 at all but the longest horizon, improving MSE by up to 14% and doing so consistently across horizons rather than at isolated points. It is competitive on Weather and trails the strongest baselines on the remaining ETT settings and on the high-channel-count Traffic and Electricity datasets. Phase encoding, intensity-compatible readout, and phase-scrambling ablations, together with a TorchOptics cross-simulator check, indicate that the forecasts arise from the data-bearing optical field rather than from a digital forecasting head. Because the passive core uses standard Fourier optics, HAMON defines a concrete target for optical hardware and for passive physical sequence mixing.