HAMON: Passive Optical Sequence Mixing for Long-Horizon Forecasting

Alper Y{\i}ld{\i}r{\i}m

REVIEW 3 major objections 4 minor 12 references

HAMON: Passive Optical Sequence Mixing for Long-Horizon Forecasting

T0 review · 3 major / 4 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read The paper claims that the sequence-mixing computation behind competitive time-series forecasters can be handed to passive light—phase masks and free-space diffraction—instead of a trained digital layer.

desk verdict Genuinely new diffractive-optics forecasting core, honestly simulated, but the passive-light hardware claim is unproven and the baseline comparison is too thin. read the letter →

arxiv 2606.17028 v2 pith:TWLI6LOV submitted 2026-06-15 cs.LG cs.AIcs.AR

Alper Y{i}ld{i}r{i}m This is my paper

classification cs.LGcs.AIcs.AR

keywords timeseriesforecastingopticalcomputingdiffractiveneuralnetworkspassiveinferenceFourieropticssequencemixingphasemaskslong-horizon

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper asks whether the linear temporal-mixing operator that makes simple forecasters competitive must run in digital silicon, or whether it can be handed to passive physics. HAMON encodes history onto an optical aperture, leaves forecast positions dark, and lets cascaded trainable phase masks plus free-space diffraction shape the forecast in the output field. At inference, prediction is a single passive propagation pass with no trainable digital mixing layer. On standard benchmarks the optical core outperforms the strongest digital baselines considered on ETTm2 at all horizons and on ETTh2 up to H=336, improving MSE by up to 14%; it stays competitive on Weather and trails on high-channel datasets. The authors frame HAMON as a substrate test, not a digital leaderboard entry: the claim is that competitive forecasting behavior survives when the mixing computation is moved into passive optics.

What carries the argument

The central object is the passive diffractive core: N cascaded trainable phase-only masks (U ← U⊙exp(iφℓ)) interleaved with free-space propagation via the angular-spectrum method from Fourier optics. The input field carries the normalized history on the first L aperture positions; the forecast region is initially dark and its output field is read coherently or through differential intensity. All trainable parameters are the phase profiles φℓ, trained by backpropagation through a differentiable wave-optics simulator. The core is a linear transform of the input field, so inference is a single passive propagation pass with no digital multiply-accumulate for sequence mixing.

What would settle it

Build a tabletop Fourier-optical setup with the trained phase masks (or a spatial light modulator applying them) and measure forecast MSE on ETTm2; if the physical forecast error exceeds the simulated error by more than the paper's cross-simulator gap (about 9% MSE) or the dark forecast region carries no signal, the central claim fails. A cheaper check: re-run the 1D angular-spectrum simulation with finite aperture, phase quantization to 8 levels, and detector noise and see if the reported gains on ETTm2/ETTh2 persist.

Watch

Extended reading notes

Core claim

Central claim: the learned sequence-mixing operator behind competitive forecasters can be implemented as a passive optical propagation operator — cascaded trainable phase-only masks separated by free-space diffraction — with digital computation confined to the boundary. History is encoded onto an optical aperture, forecast positions are left dark, and the output field in that region is the forecast. Ablations show the forecast depends on the data-bearing optical field rather than a digital head; intensity-compatible readout remains competitive; and an independent two-dimensional wave-optics simulator preserves the behavior. The paper frames HAMON as a substrate-substitution study: the questi

Load-bearing premise

The results assume that the ideal simulated optics—perfect phase masks, no evanescent modes, no hardware noise—translate unchanged to a real device; the paper states explicitly that no experimental hardware validation was performed.

Editorial extensions

If this is right

A passive optical core of phase masks and diffraction can match or beat strong digital forecasters on several standard benchmarks, with up to 14% MSE improvement on ETTm2 across all horizons.
The forecast is produced by the data-bearing optical field, not a digital forecasting head: destroying the phase pattern degrades accuracy, and intensity-compatible readout remains competitive.
Detector-compatible differential-intensity readout keeps the approach relevant to practical opto-electronic hardware without adding a digital temporal-mixing layer.
Longer optical context (336 vs 96 lookback) improves accuracy, especially on high-channel datasets, indicating the aperture benefits from more illuminated history positions.
The core behavior is preserved under an independent two-dimensional wave-optics simulator, reducing (but not eliminating) the risk that results are an artifact of one custom simulator.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If hardware validation succeeds, a forecasting core built from passive phase masks could perform inference with near-zero dynamic power: the multiply-accumulate work is replaced by diffraction that happens at the speed of light.
The approach suggests a general template beyond forecasting: any approximately linear operator that dominates an application's compute could, in principle, be instantiated as a passive optical transform, with training done digitally and inference left to physics.
A natural testable extension is to fabricate or simulate a prototype with finite apertures, phase quantization (e.g., 8-bit spatial light modulator), and detector noise, and measure whether HAMON's benchmark gains survive at realistic hardware tolerances; the paper explicitly flags this as the open step.
The technique may extend to high-channel datasets through wavelength-division or spatial multiplexing, since the current shortfall on Electricity and Traffic appears tied to channel count rather than to the optical mixing mechanism itself.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

One thing to know: HAMON is not another digital forecasting model. It is a substrate study: train phase masks in simulation so that light diffracts an amplitude- or phase-encoded history into an initially dark forecast region, and read the forecast from the optical field. The specific construction — dark forecast slots plus cascaded phase masks to fill them with the future — is not in the D2NN, reservoir, or FITS papers it cites. That is a real novelty, and it makes the paper worth reading even if the hardware never ships.

What the paper does well: the simulation work is careful and honest. Three seeds are reported, the implementation is accelerated via the transfer matrix, and the independent TorchOptics cross-check is a good idea. The phase-scrambling ablation supports the claim that the phase-encoded variants use the data-bearing structure. And the paper explicitly says, in §5, that it does not claim experimental hardware validation. Credit where due: for a proof-of-concept, the internal logic holds together.

Soft spots, in proportion. The main one is the gap between the claims and the evidence. The abstract says the sequence-mixing operator can be moved 'out of digital silicon and into passive light.' What is actually shown is that a 1D angular-spectrum simulator, with ideal phase masks and no detector noise, produces competitive MSE numbers. The TorchOptics check narrows the risk of a single-simulator artifact, but it still shows a 9.31% MSE difference on ETTh1 at Gy=64, and the detector-compatible differential-intensity variant is not cross-checked at all because it is 'more sensitive to finite-aperture and simulator-convention differences' (App. C). Unmodeled hardware effects on the order of tens of percent would erase the claimed 14% advantage on ETTm2. So the interesting hypothesis is untested at the physical level. That doesn't kill the paper, but it should change the wording.

Second, the benchmark comparison is thinner than it looks. All digital baseline numbers are taken from FITS (Xu et al. 2024), without re-running or error bars, and iTransformer — which the paper cites — is missing from the tables even though it is a strong baseline on ETT and Weather. A referee should ask for a fairer table or for the claim to be narrowed to 'competitive with the strongest baselines we compared against.'

Third, minor: hyperparameters like α_ph and backcast weight α are hand-set, and the phase-scrambling ablation covers only the phase-encoded intensity variant, not the headline amplitude-coherent configuration.

Overall: this is a serious, honest proof-of-concept with a real new idea. The simulation evidence is consistent, and the limitations are stated. But the headline should be about a simulated optical core, not an achieved physical one.

For you: read the method and Table 2 if you care about substrate questions or optical ML; skip the benchmarking details. It deserves a serious referee — send it out, but the authors should be pushed to fix the baseline table and soften the hardware language.

Referee Report

3 major / 4 minor

Summary. HAMON is a proposed passive diffractive optical core for long-horizon time-series forecasting. Historical values modulate a 1D optical aperture, the forecast interval is left dark, and a stack of trainable phase masks separated by free-space propagation transforms the field so that the forecast is read from the initially dark region. The model is trained by digital backpropagation through an angular-spectrum simulator; at inference the sequence-mixing computation is a single passive optical pass. Experiments on ETT, Weather, Electricity, and Traffic with 336-step lookback and horizons 96–720 report MSE/MAE, with three-seed statistics for HAMON. On ETTm2 and on ETTh2 up to H=336, HAMON-Coh improves on the strongest baseline considered (FITS) by up to 14%; it is competitive on Weather and trails on the remaining datasets. Ablations cover readout interfaces, depth, context length, and input-phase scrambling; a TorchOptics 2D cross-check of one checkpoint is reported in Appendix C.

Significance. If the simulation results are reliable, the paper provides evidence that the linear temporal-mixing operator used by competitive lightweight forecasters can in principle be instantiated by passive diffractive optics, without a trainable digital sequence-mixing layer. The manuscript is careful in several respects: it reports three-seed means and standard deviations for HAMON, includes a phase-scrambling sanity check, tests a detector-compatible intensity readout, and validates one checkpoint in an independent 2D simulator. Code and checkpoints are promised at a public repository. The significance is limited by the absence of any experimental hardware validation and by the use of point-estimate baseline numbers from the literature, so the central 'substrate' claim rests entirely on idealized simulation.

major comments (3)

[Abstract; §1; §5; App. C] The abstract's central claim that the sequence-mixing operator can be 'moved out of digital silicon and into passive light' is supported only by simulation. §5 concedes that 'the present results are simulation-based and do not claim experimental hardware validation,' and App. C's independent 2D check shows a 9.31% MSE difference on ETTh1 at Gy=64, with the detector-compatible differential-intensity variant explicitly excluded because it is 'more sensitive to finite-aperture and simulator-convention differences.' The claimed margins over FITS are as small as 4% (ETTh2 H=336, Table 2), so the unmodeled hardware effects listed in §5 (finite apertures, phase quantization, alignment, detector nonuniformity, loss, noise, calibration drift) could erase the advantage. Please either re-scope the central claims to 'simulated passive optical core' throughout, or add a quantitative hardware-error se
[§4.2, Tables 2-3] The baseline MSE values are taken from Xu et al. [2024] as point estimates, with no error bars and no re-run under the same protocol, while HAMON results are three-seed means. The paper's comparative claim—'outperforms the strongest digital baselines considered... consistently across horizons'—rests on margins as small as 4% on ETTh2 H=336 (0.341 vs. 0.354) and on point estimates for Weather in Table 3. Without baseline variance or a matched evaluation pipeline, these differences are not shown to be outside noise. Please re-run the strongest baselines (at least FITS) with the same lookback, horizons, and seeds, or report confidence intervals, and soften any statements that imply statistical dominance.
[§3.1, Eq. (2), Eq. (11)] Two central hyperparameters are never reported: the propagation distance z between phase masks in the angular-spectrum kernel (Eq. (2)) and the backcast loss weight α in the objective (Eq. (11)). Both are part of the model definition and are needed to reproduce the results or to build the proposed hardware. Please add a table of optical and loss hyperparameters (λ, d, grid size, z, N, α_ph, α) and state how z was chosen.

minor comments (4)

[Abstract] The abstract should state explicitly that all results are from simulation, not hardware, to avoid implying a fabricated optical system.
[References [Yıldırım, 2026]] The motivational citation to the author's own mechanistic-interpretability preprint is not peer-reviewed and is load-bearing only for the paper's framing; please either cite peer-reviewed evidence or clearly flag the preprint as non-peer-reviewed motivation.
[§3.2, Eq. (10)] The differential-intensity readout is underspecified: it is not described how the two dark forecast regions are formed in the optical system (two separate propagation arms, two output regions in the same plane, or two runs). Please clarify the optical layout.
[Figure 2] The relative-improvement values in Figure 2 are hard to read; consider adding a table with the exact percentages for each dataset/horizon, especially the negative values.

Circularity Check

0 steps flagged · score 2.0 of 10

No constructional circularity: benchmark results are self-contained, with only a minor motivational self-citation.

full rationale

The paper's central empirical claim is not circular by construction. The forecast operator is trained with Eq. (11) under MSE supervision and evaluated on held-out test sets (Tables 2-3); the phase masks are learned parameters, not fitted to the reported test metrics. The phase-scrambling check (Sec. 4.5) and TorchOptics cross-simulator check (App. C) are sanity checks rather than derivations, and the cross-simulator 9.31% MSE difference is explicitly reported as an implementation-consistency limitation, not concealed. The only circularity-adjacent element is the motivational citation to the author's own mechanistic preprint (Yıldırım 2026) in Sec. 1 and the abstract, used to support the premise that standard benchmarks may not require strong superposition. That same-author preprint is not machine-checked or independently reproduced in the paper, so it is not independent evidence. However, it is not load-bearing for the actual forecast results: the empirical contribution does not reduce to that citation, and Sec. 5 explicitly disclaims hardware validation and lists remaining physical effects. Thus there is no self-definitional reduction, no fitted input renamed as prediction, and no self-citation chain forcing the central claim. Score 2 reflects the minor motivational self-citation rather than any constructional circularity.

Assumptions & free parameters 4 free parameters · 3 assumptions · 0 invented entities

HAMON introduces no new physical entity; it reuses phase masks, free-space diffraction, and intensity detectors. The dark forecast region is a readout convention, not a new object. The main free choices are hyperparameters (α_ph, backcast weight, depth, context length) and the simulation-fidelity assumption.

free parameters (4)

phase scale α_ph = 0.3
Used for phase-encoded variants (§3.2, Tables 4–5); chosen by hand rather than swept, and it affects the nonlinear input embedding and detector-compatible results.
backcast loss weight α
Eq. (11) adds α·MSE(x̂, x_norm); the value is not reported in the text, so the loss balance is an unstated choice that shapes the optimized phase masks.
number of phase-mask layers N = 16 (24 in ablation)
Depth is a design choice; the 24-layer ablation (§4.4) changes average MSE only marginally, so 16 is not strongly evidenced as the right capacity.
lookback/context L and grid size = L=336, grid 1120; L=96, grid 1024
Context length changes results substantially on Electricity and Traffic (App. B); L=336 is the main configuration and appears chosen rather than selected by an explicit criterion.

assumptions (3)

domain assumption Angular-spectrum propagation with d=10 µm, λ=1 µm, and λfmax=0.05 accurately represents physical free-space diffraction in the sampled region.
Eq. (2) in §3.1; only propagating modes are retained. Finite-aperture and edge effects are ignored in the main simulator and only partially checked in the TorchOptics cross-simulator (App. C).
standard math Standard Fourier optics is a sufficient model for coherent light through ideal phase masks and free space.
Goodman [2005] is the cited textbook basis; this is accepted physics, but its conversion into a trainable forecasting core is not experimentally validated.
domain assumption The benchmarks' forecasting operator can be approximated by a low-complexity, near-linear sequence-mixing map.
§1 motivates this from DLinear/FITS and the author's mechanistic preprint; if this premise fails, a passive linear core would not be competitive on other datasets.

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Cite this review

Pith. "Pith review of HAMON: Passive Optical Sequence Mixing for Long-Horizon Forecasting." pith.science (2026). https://pith.science/paper/TWLI6LOV

@misc{pith2026260617028,
  author       = {Pith},
  title        = {Pith review of: HAMON: Passive Optical Sequence Mixing for Long-Horizon Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TWLI6LOV}},
  note         = {Machine review of arXiv:2606.17028}
}

read the original abstract

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.

Figures

Figures reproduced from arXiv: 2606.17028 by the authors.

**Figure 3.** Phase-scrambling sanity check for four-layer phase/differential-intensity HAMON. Values [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

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Reference graph

Works this paper leans on

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Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.

[1] [2024]

URLhttps://doi.org/10.1063/5.0191977

doi: 10.1063/5.0191977. URLhttps://doi.org/10.1063/5.0191977. Joseph W. Goodman.Introduction to Fourier Optics. Roberts and Company, 3 edition,

work page doi:10.1063/5.0191977

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arXiv

[3] [12]

We report mean± standard deviation over three seeds

12 A Full Amplitude-Coherent HAMON Results Table 6: HAMON-336 long-term forecasting results. We report mean± standard deviation over three seeds. Dataset Metric 96 192 336 720 ETTh1 MSE0.4440±0.0008 0.4968±0.0024 0.5486±0.0031 0.7064±0.0062 MAE0.4400±0.0008 0.4769±0.0017 0.5117±0.0014 0.6099±0.0034 ETTh2 MSE0.2343±0.0025 0.2937±0.0019 0.3411±0.0021 0.4698...

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doi:10.1038/nphoton.2017.93 2017

[5] [2018]

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doi:10.1126/science.aat8084

[6] [2019]

URLhttps://doi.org/10.1016/j.neunet.2019.03.005

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doi:10.1016/j.neunet.2019.03.005 2019

[7] [2020]

URL https://doi.org/10.1038/s41586-020-2973-6

doi: 10.1038/s41586-020-2973-6. URL https://doi.org/10.1038/s41586-020-2973-6. HaixuWu, JiehuiXu, Jianmin Wang, andMingshengLong. Autoformer: Decompositiontransformers withauto-correlationforlong-termseriesforecasting. InAdvances in Neural Information Processing Systems,

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work page doi:10.1038/s41377-021-00623-5