🤖 machine learning

HAMON: Passive Optical Sequence Mixing for Long-Horizon Forecasting

The paper introduces HAMON, a passive diffractive optical forecasting core that leverages free-space diffraction and trainable phase masks to perform long-horizon time-series prediction without digital sequence mixing, achieving competitive or superior performance to strong digital baselines on several benchmarks while defining a concrete target for optical hardware implementation.

Original authors: Alper Yıldırım

Published 2026-06-16

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Alper Yıldırım

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to predict the weather for the next week based on the last week's data. Usually, computers do this by running complex digital math, crunching numbers in a silicon chip, layer by layer.

This paper introduces HAMON, a completely different way to do this. Instead of using a digital brain to calculate the future, HAMON uses light itself to "do the math."

Here is how it works, using simple analogies:

1. The Setup: A Window with a View

Think of HAMON as a special window.

The Past (The Input): You take the history of the data (like the last 336 hours of temperature) and paint it onto the left side of this window. If the temperature was high, the paint is bright; if low, it's dim.
The Future (The Output): The right side of the window is left completely dark. This represents the time period you want to predict.
The Goal: You want the light from the "Past" side to naturally flow across the window and magically form a picture of the "Future" on the dark side.

2. The Magic Trick: Passive Light

In a normal computer, you would need a processor to calculate how the past turns into the future. In HAMON, you don't need a processor for the heavy lifting.

Instead, you place a series of special, transparent sheets (called phase masks) between the past and the future. These sheets are like custom-made filters that bend and twist light in very specific ways.

When you shine the "Past" light through these sheets, the light waves interfere with each other (like ripples in a pond meeting).
Because of the laws of physics (specifically how light diffracts and spreads), the light naturally reshapes itself as it travels.
By the time the light reaches the "Future" side, the pattern of light is the prediction.

The Key Innovation: The computer only needs to figure out what shape these transparent sheets should be. Once they are designed, the actual prediction happens automatically as light passes through them. No digital math is needed during the prediction itself. It's like setting up a domino chain: once you push the first one, the rest fall on their own.

3. Why Do This?

The author noticed that for long-term predictions, the "math" required is actually quite simple and linear (straightforward). It doesn't need the super-complex, heavy-duty digital brain that modern AI usually uses.

Since light naturally performs these simple linear calculations for free as it travels, why use a slow, energy-hungry digital chip? HAMON asks: "Can we just let physics do the work?"

4. What Did They Find?

The researchers tested this idea using a computer simulation of light (since they haven't built a physical glass-and-lens machine yet).

The Results: On several standard weather and energy datasets, HAMON performed surprisingly well. In some cases, it was even better than the strongest digital AI models currently available.
The Proof: They did "sanity checks" to make sure the light was actually doing the work. When they scrambled the light patterns or changed how the light entered, the predictions got worse. This proved the system wasn't just "cheating" with a digital calculator hidden at the end; the light itself was carrying the information.

5. The Catch (What It Isn't)

It's not a finished product yet: This is currently a simulation. They haven't built a physical device with real glass and lasers yet.
It's not a full replacement: The system still needs a digital computer to "prepare" the data (normalize it) before shining it into the light, and to "read" the result after the light passes through. But the core "thinking" part is done by passive light.

The Bottom Line

HAMON is a proof-of-concept that says: We don't always need a digital brain to predict the future. Sometimes, if you set up the right physical environment (like a series of light-bending sheets), nature will do the prediction for you just by letting light travel through it. It's a step toward using the laws of physics to make faster, more efficient AI.

Technical Summary: HAMON – Passive Optical Sequence Mixing for Long-Horizon Forecasting

Problem Statement

Long-horizon time-series forecasting has traditionally relied on deep learning architectures, particularly Transformers, which utilize dense, superposed representations and digital matrix multiplication. However, recent evidence suggests that competitive performance on standard benchmarks does not necessarily require these complex nonlinear features. Lightweight linear models (e.g., DLinear) and frequency-domain models (e.g., FITS) have demonstrated that the core forecasting operator is often low-complexity and approximately linear.

This observation raises a fundamental question regarding the computational substrate: If the core forecasting operation is essentially a linear mixing of temporal or spectral components, must it be implemented via learned digital arithmetic? The paper posits that linear operators, which are computationally expensive in silicon (requiring multiply-accumulate operations), can be performed "for free" by passive physical media, specifically coherent light propagation governed by Fourier optics.

Methodology

The authors introduce HAMON (Passive Optical Sequence Mixing), a forecasting architecture that replaces the digital sequence-mixing layer with a passive diffractive optical core.

Core Architecture

HAMON reframes the forecasting task as a diffraction problem:

Input Encoding: A multivariate historical time series $x \in \mathbb{R}^{L \times C}$ $x \in R^{L \times C}$ is normalized (using reversible instance normalization, RevIN) and encoded onto a one-dimensional optical aperture of width $G$ $G$ .
- Amplitude Encoding: Normalized values directly set the field amplitude.
- Phase Encoding: The aperture has unit magnitude, and normalized values modulate the phase ( $e^{i\alpha \pi x}$ ).
- The "future" positions on the aperture are left dark (zero intensity).
Passive Optical Core: The input field propagates through a series of $N$ $N$ cascaded, trainable phase masks separated by free-space propagation distances $z$ $z$ .
- Phase Masks: Each layer $\ell$ applies a phase shift $\phi_\ell$ via element-wise multiplication: $U \leftarrow U \odot \exp(i\phi_\ell)$ .
- Propagation: Between masks, the field propagates using the angular-spectrum method (Fourier optics), simulating diffraction and interference.
- Readout: The field is propagated to a readout plane. The forecast is extracted from the initially dark region corresponding to the future time steps.
  - Coherent Readout: Uses the real part of the complex field.
  - Intensity Readout: Uses the squared magnitude $|U|^2$ .
  - Differential Intensity Readout: Subtracts intensities from two dark regions to produce a signed output compatible with standard detectors.
Output Processing: The readout is denormalized to produce the final forecast $y \in \mathbb{R}^{H \times C}$ .

Training

The system is trained via digital backpropagation through a differentiable wave-optics simulator. The trainable parameters are exclusively the phase profiles of the masks $\{\phi_\ell\}_{\ell=1}^N$ . The loss function combines Mean Squared Error (MSE) on the forecast with an auxiliary backcast term to reconstruct the input history. No digital linear forecasting head is applied after the optical core.

Key Contributions

Substrate Substitution: HAMON demonstrates that the sequence-mixing operator in competitive forecasters can be moved from digital silicon to passive light. It replaces the learned digital linear layer with a trainable diffractive propagation operator.
Passive Inference: Unlike previous optical neural networks that rely on nonlinear reservoirs or digital readout heads, HAMON performs the entire sequence-mixing computation via a single passive optical propagation pass.
Hardware-Aware Design: The architecture is designed with hardware constraints in mind, offering variants (Phase/Differential-Intensity) that are compatible with standard intensity detectors, avoiding the need for coherent amplitude readout.
Mechanistic Validation: Through ablation studies (phase scrambling, interface variations) and cross-simulator checks (TorchOptics), the authors verify that the forecasting capability arises from the data-bearing optical field and the physics of diffraction, not from the digital boundary conditions.

Experimental Results

HAMON was evaluated on standard long-horizon forecasting benchmarks (ETT, Weather, Electricity, Traffic) with prediction horizons $H \in \{96, 192, 336, 720\}$ and a lookback of $L=336$ .

Performance:
- ETTm2: HAMON outperformed the strongest digital baselines (including PatchTST and DLinear) at all horizons, improving MSE by up to 14%.
- ETTh2: Outperformed baselines at all horizons except the longest (720).
- Other Datasets: HAMON was competitive on Weather and trailed the strongest baselines on ETTh1, ETTm1, Electricity, and Traffic.
Readout Variants: The detector-compatible "HAMON-DiffInt" variant (phase encoding + differential intensity readout) remained competitive with the coherent readout variant, particularly improving performance on ETTm1 and Weather.
Ablations:
- Phase Scrambling: Zeroing, shuffling, or sign-flipping the input phase significantly degraded performance, confirming the model relies on the temporal phase structure of the data.
- Depth: Increasing layers from 16 to 24 yielded only marginal improvements, suggesting the 16-layer configuration captures the necessary physics.
- Context Length: Increasing the lookback from 96 to 336 improved performance, indicating the optical aperture benefits from additional historical context.

Significance and Claims

The paper explicitly frames HAMON not as a new digital state-of-the-art model, but as a substrate-level investigation. The primary claim is that the core computation of modern sequence models—specifically the linear mixing required for long-horizon forecasting—can be instantiated as a passive physical process.

Modest Scope: The authors acknowledge that HAMON is not a fully optical end-to-end learner; normalization, encoding, and readout remain digital or electro-optic boundary operations.
Simulation vs. Hardware: The results are based on wave-optics simulations. The paper does not claim experimental hardware validation but argues that the underlying physics (Fourier optics, diffraction, interference) is standard and well-understood.
Future Direction: HAMON defines a concrete target for optical hardware implementation. It suggests that "passive physical sequence mixing" is a plausible research program, potentially offering energy-efficient inference by offloading linear operations from digital processors to diffractive optics.

In summary, HAMON validates the hypothesis that if a forecasting task can be solved by a linear operator, that operator does not strictly require digital implementation and can be effectively realized through trainable passive diffraction.