Optical Diffraction Neural Networks (ODNNs)

• Optical Diffraction Neural Networks are all‐optical architectures that use cascaded diffractive layers to encode trainable parameters for statistical inference and task-specific input–output mappings.
• They leverage free-space propagation, diffraction, and interference modeled by scalar diffraction theory (e.g., Fresnel approximation) to implement high-dimensional optical computations.
• Recent implementations achieve high simulation accuracies (up to 98.52%) across tasks like image classification, imaging, and graph learning, highlighting their potential for low-energy, high-speed processing.

Searching arXiv for recent and foundational papers on optical diffraction neural networks and closely related diffractive optical computing architectures. Optical Diffraction Neural Networks (ODNNs), also referred to in the literature as Diffractive Deep Neural Networks (D2NNs) or Diffractive Optical Neural Networks (DONNs), are all-optical architectures that perform statistical inference by encoding trainable parameters into the complex transmission or reflection coefficients of successive diffractive layers, such that free-space propagation, diffraction, and interference collectively implement a task-specific input–output mapping (Lin et al., 2018). In the canonical formulation, the input is encoded into an optical field, each layer applies amplitude and/or phase modulation, and the output is obtained by measuring intensity over designated detector regions (Lin et al., 2018). Across the literature, ODNNs have been developed for classification, imaging, convolutional acceleration, scientific computing, mode sorting, graph learning, and hybrid optical–electronic inference, with designs spanning free-space transmissive stacks, on-chip relief surfaces, digital phase-change implementations, and fiber-based diffractive systems (Shao et al., 2024).

1. Foundational definition and optical forward model

ODNNs are built from cascaded diffractive layers separated by free-space propagation. In a standard phase-only formulation, the field immediately after a layer is

$U_\ell^+(x,y)=U_\ell^-(x,y)e^{j\phi_\ell(x,y)},$

where $\phi_\ell(x,y)$ is the learned phase profile (Lin et al., 2018). More generally, a layer can apply a complex transmission

$t_\ell(x,y)=A_\ell(x,y)e^{i\phi_\ell(x,y)},$

with $|t_\ell(m)|\le 1$ in the discrete-pixel formulation (Filipovich et al., 2023).

Propagation between planes is modeled by scalar diffraction theory. Several equivalent forms recur in the literature. In the angular-spectrum representation,

$$U_{\ell+1}(x,y)=\mathcal{F}^{-1}\left\{\mathcal{F}[U_\ell(x,y)t_\ell(x,y)]\,H(f_x,f_y;z)\right\},$$

with

$$H(f_x,f_y;z)=\exp\!\Bigl(i\,2\pi z\sqrt{\tfrac{1}{\lambda^2}-f_x^2-f_y^2}\Bigr)$$

(Lin et al., 2018). Under the Fresnel approximation, the transfer function is also written as

$H(f_x,f_y)=e^{ikz}e^{-i\pi\lambda z(f_x^2+f_y^2)}$

(Shao et al., 2024). In spatial coordinates, the same layer-to-layer mapping can be expressed by a Rayleigh–Sommerfeld or Fresnel convolution integral (Lin et al., 2018, Filipovich et al., 2023).

This optical forward model is the basis for interpreting ODNNs as linear optical processors whose trainable degrees of freedom reside in diffractive masks, while dense coupling is supplied by diffraction itself. In the original D2NN framework, each neuron is treated as a point secondary source under the Huygens–Fresnel principle, and large arrays of such neurons collectively realize high-dimensional optical mappings (Lin et al., 2018). A consistent feature across later work is that inference within the diffractive stack remains passive once the layers are fixed, and class scores or regression outputs are read from output intensities, detector regions, or balanced detector differences (Li et al., 2019).

2. Architectural families and computational primitives

The most direct ODNN architecture is a multilayer free-space stack of transmissive diffractive surfaces followed by detector regions, as in the five-layer D2NN classifier and imaging lens demonstrations reported in 2018 (Lin et al., 2018). In that setting, classification is performed by concentrating optical energy into one of several detector regions, while imaging is realized by training the diffractive stack to reproduce a target output field (Lin et al., 2018).

Subsequent work broadened the architectural repertoire. Class-specific differential detection assigns a positive and a negative detector to each class and defines a normalized differential score

$S_c=\frac{I_c^+-I_c^-}{I_c^++I_c^-},$

thereby mitigating the non-negativity constraint of intensity measurements (Li et al., 2019). The same work introduced jointly trained optically isolated subnetworks and independently optimized ensembles, improving simulation accuracies to 98.52%, 91.48% and 50.82% for MNIST, Fashion-MNIST and grayscale CIFAR-10 datasets, respectively, in the class-specific differential configuration (Li et al., 2019).

Another major development is the Hybrid Diffraction Neural Network (HDNN), which introduces a matrix-multiplication stage into ODNNs by combining a singular phase modulation layer with an amplitude modulation layer (Shao et al., 2024). In that formulation, a 2D greyscale image is encoded as $U_0(x,y)$, a phase layer produces

$U_1(x,y)=U_0(x,y)e^{i\phi(x,y)},$

free-space propagation yields $\phi_\ell(x,y)$0, and an amplitude mask $\phi_\ell(x,y)$1 generates channel-wise fields

$\phi_\ell(x,y)$2

Detection then implements

$\phi_\ell(x,y)$3

so that stacking all channels yields $\phi_\ell(x,y)$4, described in the paper as exactly a fully-connected layer multiplication (Shao et al., 2024). The on-chip HDNN variant further uses a beam-splitting phase layer to route the post-phase wavefront into distinct sub-regions for independent amplitude masking and detection (Shao et al., 2024).

ODNN principles have also been adapted to convolutional processing. A free-space 4f optical accelerator used DMD #1 as an amplitude-modulated input plane, DMD #2 in the Fourier plane to apply pre-trained Fourier-domain kernels pixel-by-pixel, and a second lens to implement the inverse Fourier transform, thereby realizing

$\phi_\ell(x,y)$5

for optical convolution (Hu et al., 2021). In an integrated-photonic setting, the Optical Convolution Unit (OCU) treated diffraction in a planar silicon slab plus cascaded metalines as a matrix product

$\phi_\ell(x,y)$6

which was then used to emulate arbitrary real-valued convolution kernels through structural re-parameterization (Huang et al., 2022).

The architectural scope has expanded further to reconfigurable digital ODNNs using Sb$\phi_\ell(x,y)$7Se$\phi_\ell(x,y)$8 phase-change material, with three digital diffractive layers of 14,400 neurons on each layer and binary phase states $\phi_\ell(x,y)$9 (Wu et al., 2023); to fiber-based diffractive deep neural networks that replace free-space layers with successively perturbed sections of a graded-index multimode fiber and realize a learned transmission matrix

$t_\ell(x,y)=A_\ell(x,y)e^{i\phi_\ell(x,y)},$0

(Kesgin et al., 17 Feb 2025); and to hybrid, physically composable systems that combine free-space metasurface paths with integrated photonic tensor cores and learn variables such as wavelength, spacing, orientation, placement order, and channel-mixing matrices (Yin et al., 2024).

3. Training, quantization, and hardware-aware codesign

ODNN training is generally performed in simulation by differentiating through propagation and mask modulation. In the original D2NN framework, gradients with respect to phase delays are obtained by reverse-mode autodifferentiation through the diffraction pipeline, and the layer phases are optimized with Adam (Lin et al., 2018). Similar end-to-end training through FFT-based propagation is used in later works, including graph learning in HoloGraph and integrated diffractive tensor processing (Li et al., 7 Feb 2026, Huang et al., 2022).

For classification, cross-entropy-type objectives are common. The 2018 D2NN digit classifier defined class scores from detector-region intensities and used a cross-entropy-style loss over the normalized energies (Lin et al., 2018). Differential-detection ODNNs scale the normalized differential signals by a temperature parameter before softmax and then apply cross-entropy (Li et al., 2019). HoloGraph instead minimizes a mean-squared error loss on the softmax of detector-region intensities,

$t_\ell(x,y)=A_\ell(x,y)e^{i\phi_\ell(x,y)},$1

with Adam and learning rate $t_\ell(x,y)=A_\ell(x,y)e^{i\phi_\ell(x,y)},$2 (Li et al., 7 Feb 2026). In scientific-computing DONNs, the measured intensity in each output region is normalized into a softmax prediction and optimized by cross-entropy plus a phase regularizer (Chen et al., 2023).

Hardware discretization and fabrication constraints have motivated specific codesign strategies. A physics-aware differentiable discrete codesign framework introduced Gumbel-Softmax to map trainable logits at each pixel onto arbitrary experimentally measured discrete device levels $t_\ell(x,y)=A_\ell(x,y)e^{i\phi_\ell(x,y)},$3, thereby supporting non-uniform and non-monotonic hardware responses across layers (Li et al., 2022). That work reported that at 8 discrete levels and 5 layers, the Gumbel-Softmax method achieves $t_\ell(x,y)=A_\ell(x,y)e^{i\phi_\ell(x,y)},$4 on MNIST and $t_\ell(x,y)=A_\ell(x,y)e^{i\phi_\ell(x,y)},$5 on Fashion-MNIST, while post-processing in conventional quantization-based methods can destroy accuracy when enforcing nonnegative hardware levels (Li et al., 2022).

A distinct low-precision route is binary or 1-bit quantization. The on-chip HDNN constrains phase and amplitude weights to two levels through

$t_\ell(x,y)=A_\ell(x,y)e^{i\phi_\ell(x,y)},$6

with the Straight-Through Estimator used for gradients; in practice, phase takes values in $t_\ell(x,y)=A_\ell(x,y)e^{i\phi_\ell(x,y)},$7 and amplitude in $t_\ell(x,y)=A_\ell(x,y)e^{i\phi_\ell(x,y)},$8 (Shao et al., 2024). The same work designed a silicon relief surface with etch depth

$t_\ell(x,y)=A_\ell(x,y)e^{i\phi_\ell(x,y)},$9

giving designed $|t_\ell(m)|\le 1$0 and measured $|t_\ell(m)|\le 1$1 at $|t_\ell(m)|\le 1$2 (Shao et al., 2024). The reconfigurable digital ODNN based on Sb$|t_\ell(m)|\le 1$3Se$|t_\ell(m)|\le 1$4 likewise uses binary phase neurons, a binarization penalty, and a straight-through estimator in training (Wu et al., 2023).

Binning Design (BD) addresses a different hardware bottleneck: the gap between fine simulation sampling and fabricable feature sizes. The HDNN paper explicitly decouples the optical field sampling interval $|t_\ell(m)|\le 1$5 from the physical modulation-unit size $|t_\ell(m)|\le 1$6 by grouping $|t_\ell(m)|\le 1$7 simulation samples into a single modulation pixel so that $|t_\ell(m)|\le 1$8 (Shao et al., 2024). The paper states that larger $|t_\ell(m)|\le 1$9 reduces sensitivity to lateral misalignment, with simulations showing $$U_{\ell+1}(x,y)=\mathcal{F}^{-1}\left\{\mathcal{F}[U_\ell(x,y)t_\ell(x,y)]\,H(f_x,f_y;z)\right\},$$0 improvement in error tolerance as $$U_{\ell+1}(x,y)=\mathcal{F}^{-1}\left\{\mathcal{F}[U_\ell(x,y)t_\ell(x,y)]\,H(f_x,f_y;z)\right\},$$1 grows, while simplifying fabrication by using fewer, larger features (Shao et al., 2024).

4. Optical expressivity, coherence, and interpretability

A recurrent question in ODNN research concerns where effective expressivity comes from in systems whose internal physics is linear. One line of work treats photodetection or hybrid opto-electronic post-processing as the effective source of nonlinearity. The 4f optical convolution accelerator notes that optical-to-electronic conversion at the camera supplies a nonlinear activation through intensity squaring plus A/D, after which max-pooling and fully connected electronic layers complete the network (Hu et al., 2021). HDNN-assisted lesion detection similarly used a standard electronic CNN up to a fully connected layer, followed optically by a 2-channel HDNN (Shao et al., 2024).

Another line of work shows that spatial coherence fundamentally changes ODNN behavior. Under coherent illumination, the input mutual intensity has rank one and the output obeys the standard field-propagation model (Filipovich et al., 2023). Under fully incoherent illumination, the ODNN reduces to a purely linear mapping from input intensity to output intensity,

$$U_{\ell+1}(x,y)=\mathcal{F}^{-1}\left\{\mathcal{F}[U_\ell(x,y)t_\ell(x,y)]\,H(f_x,f_y;z)\right\},$$2

and the paper concludes that an incoherently illuminated ODNN cannot outperform a classical linear classifier (Filipovich et al., 2023). Under partial coherence, nonzero off-diagonal mutual-intensity terms contribute an effective nonlinearity. In the MNIST study, five-layer phase-only ODNNs at $$U_{\ell+1}(x,y)=\mathcal{F}^{-1}\left\{\mathcal{F}[U_\ell(x,y)t_\ell(x,y)]\,H(f_x,f_y;z)\right\},$$3 achieved 89.77% at $$U_{\ell+1}(x,y)=\mathcal{F}^{-1}\left\{\mathcal{F}[U_\ell(x,y)t_\ell(x,y)]\,H(f_x,f_y;z)\right\},$$4, 97.77% at $$U_{\ell+1}(x,y)=\mathcal{F}^{-1}\left\{\mathcal{F}[U_\ell(x,y)t_\ell(x,y)]\,H(f_x,f_y;z)\right\},$$5, and already at $$U_{\ell+1}(x,y)=\mathcal{F}^{-1}\left\{\mathcal{F}[U_\ell(x,y)t_\ell(x,y)]\,H(f_x,f_y;z)\right\},$$6 reached accuracy $$U_{\ell+1}(x,y)=\mathcal{F}^{-1}\left\{\mathcal{F}[U_\ell(x,y)t_\ell(x,y)]\,H(f_x,f_y;z)\right\},$$7 (Filipovich et al., 2023). The same paper therefore argues that the expressive power of diffractive neural networks is not an all-or-nothing property of “laser” versus “lamp” illumination (Filipovich et al., 2023).

Interpretability has also become a subject of direct study. For high-dimensional vortex mode sorting, trained diffractive networks were analyzed layer by layer and found to recover physically meaningful transforms, such as a “log-polar unwrapper,” a “beam-shaper / radial transformer,” and a “corrector + focuser,” depending on task dimensionality and number of masks (Wu et al., 2024). That work reported a “physical transformation division” phenomenon as mask count increases: for $$U_{\ell+1}(x,y)=\mathcal{F}^{-1}\left\{\mathcal{F}[U_\ell(x,y)t_\ell(x,y)]\,H(f_x,f_y;z)\right\},$$8 sorting, field–field correlation $$U_{\ell+1}(x,y)=\mathcal{F}^{-1}\left\{\mathcal{F}[U_\ell(x,y)t_\ell(x,y)]\,H(f_x,f_y;z)\right\},$$9 rose from $$H(f_x,f_y;z)=\exp\!\Bigl(i\,2\pi z\sqrt{\tfrac{1}{\lambda^2}-f_x^2-f_y^2}\Bigr)$$0 for $$H(f_x,f_y;z)=\exp\!\Bigl(i\,2\pi z\sqrt{\tfrac{1}{\lambda^2}-f_x^2-f_y^2}\Bigr)$$1 to $$H(f_x,f_y;z)=\exp\!\Bigl(i\,2\pi z\sqrt{\tfrac{1}{\lambda^2}-f_x^2-f_y^2}\Bigr)$$2 at $$H(f_x,f_y;z)=\exp\!\Bigl(i\,2\pi z\sqrt{\tfrac{1}{\lambda^2}-f_x^2-f_y^2}\Bigr)$$3, then saturated at $$H(f_x,f_y;z)=\exp\!\Bigl(i\,2\pi z\sqrt{\tfrac{1}{\lambda^2}-f_x^2-f_y^2}\Bigr)$$4 for $$H(f_x,f_y;z)=\exp\!\Bigl(i\,2\pi z\sqrt{\tfrac{1}{\lambda^2}-f_x^2-f_y^2}\Bigr)$$5, with additional masks contributing redundant corrections (Wu et al., 2024). This suggests that at least some trained ODNNs can be mapped onto explicit optical transforms rather than being treated as irreducible black boxes.

5. Representative implementations and empirical performance

The original D2NN work demonstrated a five-layer, 3D-printed terahertz classifier with numerical test accuracy 91.75% on 10,000 unseen MNIST digits and experimental match between simulation and experiment of $$H(f_x,f_y;z)=\exp\!\Bigl(i\,2\pi z\sqrt{\tfrac{1}{\lambda^2}-f_x^2-f_y^2}\Bigr)$$6 on 50 printed digits (Lin et al., 2018). That study also trained a separate five-layer diffractive stack to act as an imaging lens, reporting 1.8 mm line resolution at $$H(f_x,f_y;z)=\exp\!\Bigl(i\,2\pi z\sqrt{\tfrac{1}{\lambda^2}-f_x^2-f_y^2}\Bigr)$$7 and depth-of-focus of $$H(f_x,f_y;z)=\exp\!\Bigl(i\,2\pi z\sqrt{\tfrac{1}{\lambda^2}-f_x^2-f_y^2}\Bigr)$$8 (Lin et al., 2018).

Class-specific differential detection systematically improved free-space classification performance. Relative to the standard architecture $$H(f_x,f_y;z)=\exp\!\Bigl(i\,2\pi z\sqrt{\tfrac{1}{\lambda^2}-f_x^2-f_y^2}\Bigr)$$9, which achieved $H(f_x,f_y)=e^{ikz}e^{-i\pi\lambda z(f_x^2+f_y^2)}$0, $H(f_x,f_y)=e^{ikz}e^{-i\pi\lambda z(f_x^2+f_y^2)}$1, and $H(f_x,f_y)=e^{ikz}e^{-i\pi\lambda z(f_x^2+f_y^2)}$2 on MNIST, Fashion-MNIST, and grayscale CIFAR-10, the fully split class-specific differential design $H(f_x,f_y)=e^{ikz}e^{-i\pi\lambda z(f_x^2+f_y^2)}$3 achieved $H(f_x,f_y)=e^{ikz}e^{-i\pi\lambda z(f_x^2+f_y^2)}$4, $H(f_x,f_y)=e^{ikz}e^{-i\pi\lambda z(f_x^2+f_y^2)}$5, and $H(f_x,f_y)=e^{ikz}e^{-i\pi\lambda z(f_x^2+f_y^2)}$6 (Li et al., 2019).

The ensemble-learning extension trained 1,252 D2NNs with diverse passive pre-filters and selected optimized ensembles through pruning. The best ensembles of size $H(f_x,f_y)=e^{ikz}e^{-i\pi\lambda z(f_x^2+f_y^2)}$7 and $H(f_x,f_y)=e^{ikz}e^{-i\pi\lambda z(f_x^2+f_y^2)}$8 achieved blind-testing accuracies of 61.14% and 62.13%, respectively, on CIFAR-10, described as $H(f_x,f_y)=e^{ikz}e^{-i\pi\lambda z(f_x^2+f_y^2)}$9 better than the average performance of the individual D2NNs within each ensemble (Rahman et al., 2020).

The HDNN paper reported 96.39% simulation accuracy and 89.0% experimental accuracy for MNIST 10-digit classification in the spatial-light configuration, and 95.43% simulation accuracy and 73.88% experimental accuracy for the on-chip HDNN on a 4-digit task (Shao et al., 2024). The same work states that the spatial-light HDNN improves over prior DNN diffraction nets such as D2NN $S_c=\frac{I_c^+-I_c^-}{I_c^++I_c^-},$0, and that an HDNN-assisted lesion-detection network achieved simulation versus experiment agreement of 100% on lesion-versus-healthy classification (Shao et al., 2024).

A reconfigurable digital all-optical diffractive neural network based on Sb$S_c=\frac{I_c^+-I_c^-}{I_c^++I_c^-},$1Se$S_c=\frac{I_c^+-I_c^-}{I_c^++I_c^-},$2 phase-change material used three digital diffractive layers with 14,400 neurons on each and 10 photodetectors connected to a resistor network, reaching 94.46% accuracy for handwritten digit recognition (Wu et al., 2023). A scientific-computing DONN system with one amplitude SLM, three phase-only SLMs, and a CMOS camera reported experimental accuracies of approximately 82% for MoS$S_c=\frac{I_c^+-I_c^-}{I_c^++I_c^-},$3 growth prediction, 84%/70%/75% for 2D material stability/bandgap/magnetism, 78–83% for cancer-drug efficacy tasks, 98–100% for photonic splitter ratio prediction, and 98% for 200-step inverted-pendulum reinforcement-learning control (Chen et al., 2023).

Beyond image classification, ODNN concepts have been adapted to non-Euclidean and high-dimensional structured tasks. HoloGraph, described as the first monolithic free-space all-optical graph neural network system, achieved 85.3% on Cora-ML, 77.6% on Citeseer, and 94.8% on Amazon Photo, with ablations showing 83.8% on Cora without skips and gains from optical skip channels (Li et al., 7 Feb 2026). A fiber-based diffractive deep neural network, trained via Trust-Region Bayesian Optimization over nine mechanical fiber controllers, achieved 82.70% on BreastMNIST with ridge readout, 82.43% on full FashionMNIST, and 95.90% on RSSCN7, exceeding the listed ResNet-50, VGG16, and AlexNet baselines on the latter dataset (Kesgin et al., 17 Feb 2025).

6. Applications, invariance, scattering correction, and future directions

ODNN applications have expanded well beyond centered handwritten-digit classification. Scale-, shift-, and rotation-invariant diffractive networks were obtained by stochastically transforming training inputs with uniformly distributed random scale, translation, and rotation parameters (Mengu et al., 2020). In a five-layer network with 200×200-neuron layers and 10 detector regions, training with shifts uniformly sampled in $S_c=\frac{I_c^+-I_c^-}{I_c^++I_c^-},$4 raised centered MNIST accuracy to 98.00% and maintained $S_c=\frac{I_c^+-I_c^-}{I_c^++I_c^-},$5 up to $S_c=\frac{I_c^+-I_c^-}{I_c^++I_c^-},$6 shifts, while rotation training with $S_c=\frac{I_c^+-I_c^-}{I_c^++I_c^-},$7 produced 97.5% at $S_c=\frac{I_c^+-I_c^-}{I_c^++I_c^-},$8 and 96.7% at $S_c=\frac{I_c^+-I_c^-}{I_c^++I_c^-},$9 (Mengu et al., 2020). Wider layers mitigated the trade-off between invariance range and peak accuracy (Mengu et al., 2020).

ODNNs have also been used as front ends for inverse problems and imaging through disorder. In computational ghost imaging through dynamic scattering media, a two-layer phase-only ODNN trained on simulated random phase screens was inserted after the scattering medium and before the object, with the objective that the cascaded response approximate a delta-like imaging kernel (Li et al., 28 Nov 2025). Experiments with rotating single-layer and double-layer ground glass showed that without ODNN no reconstruction is possible, while with ODNN both DGI and un-trained methods recover crisp digits at all five tested pattern sizes from 26×26 to 66×66 (Li et al., 28 Nov 2025). A closely related imaging strategy using fixed optical modulations and the “optical shower-curtain effect” achieved 80 Hz imaging of moving objects in dynamic scattering media with decorrelation times $U_0(x,y)$0, was reported to be immune to speckle decorrelation, and succeeded up to optical depth $U_0(x,y)$1–2 (Li et al., 21 Aug 2025). The same paper states that ODNNs generalized from MNIST training to CIFAR-10, OPT-Aircraft, letters, Chinese characters, and natural textures (Li et al., 21 Aug 2025).

Diffractive processing has also been generalized to logic and tensor operations. Diffraction casting designed a diffractive network for single instruction, multiple data operations and numerically demonstrated all 16 logic operations on two arbitrary 256 bits parallel binary inputs with zero RMSE on 256 blind test pairs using 11 layers (Mashiko et al., 2024). On-chip optical diffractive tensor processing achieved 91.63% on Fashion-MNIST and 86.25% on CIFAR-4 classification, and in denoising reported average PSNR of 31.70 dB, 29.39 dB, and 27.72 dB for Gaussian noise levels $U_0(x,y)$2 (Huang et al., 2022).

A recurring theme in forward-looking ODNN work is reconfigurability. The multi-dimensional reconfigurable hybrid diffractive ONN introduced learnable system variables including wavelength, layer spacing, orientation states, placement order, polarization-combining factor, and pre/post channel-mixing matrices, and reported digital-comparable accuracy on task adaptations with 74x faster speed and 194x lower energy, plus 5x faster training speed relative to prior DONNs (Yin et al., 2024). The paper characterizes the resulting functional space as exponentially larger because of orientation and permutation degrees of freedom (Yin et al., 2024).

Across these directions, several limitations remain explicit in the literature. Fully incoherent ODNNs are limited to linear mappings (Filipovich et al., 2023). Mechanical reconfiguration and free-space alignment can be slow or sensitive (Yin et al., 2024, Li et al., 21 Aug 2025). Dynamic retraining is often unavailable in situ (Li et al., 7 Feb 2026). Many authors therefore identify incorporation of optical nonlinearity, dynamic reconfiguration via tunable phase masks or phase-change materials, hardware-in-the-loop optimization, metasurface miniaturization, and deeper hybrid optical–electronic co-design as major next steps for the field (Shao et al., 2024, Li et al., 2022, Yin et al., 2024).