PRISM: Position-encoded Regressive Inverse Spectral Model for Multilayer Thin-Film Design

Amortized neural inverse design typically remains closed-world: component choices are fixed vocabulary tokens, coordinate grids are frozen at training time, and continuous variables are discretized into sequence tokens. Multilayer optical coatings are an industrially important instance, coupling material sequence, layer thickness and wavelength-dependent response. We present IrisFlow, a query-based, open-vocabulary flow-matching framework instantiated in coatings: the target reflectance/transmittance spectrum, wavelength grid, candidate-material optical constants and layer count are supplied at query time. Candidate materials enter as wavelength-aware optical tokens rather than learned identities; material sequences are sampled by discrete flow matching over the query's candidate bank, thicknesses by continuous flow matching without discretization. A single 136M-parameter model designs 2-100-layer stacks. Across a 224-task benchmark it reconstructs in-distribution targets faithfully and retains same-order accuracy on a 15-material held-out bank without retraining; it reconstructs bands up to 1100 nm beyond its training envelope, designs against analytic application specifications and outperforms an autoregressive baseline on that baseline's material library. With optical constants calibrated to our deposition process, IrisFlow designs four color-displaying coolers, fabricated by ion-assisted evaporation: the three chromatic devices reach a CIEDE2000 color error of 3.1-5.2 while retaining 93-95% solar near-infrared reflectance, demonstrating open-vocabulary design carried through to fabricated coatings.

Generative sequence modeling faces a fundamental tension between the expressivity of Transformers and the efficiency of linear sequence models. Existing efficient architectures are theoretically bounded by shallow, single-step linear updates, while powerful iterative methods like Test-Time Training (TTT) break hardware parallelism due to two dimensions of serial dependency: token-level state reliance and step-level iteration loops. We propose PRISM (Parallel Residual Iterative Sequence Model) to resolve this tension. PRISM explicitly approximates the expressive gate-residual-direction iteration pattern of TTT in a parallelizable form. We employ a Write-Forget Decoupling strategy that isolates non-linearity within the injection operator. To bypass the serial dependency of explicit solvers, PRISM utilizes a two-stage proxy architecture: a short-convolution anchors the initial residual using local history energy, while a learned predictor estimates the refinement updates directly from the input. This design distills structural patterns associated with iterative correction into a parallelizable feedforward operator. Theoretically, we prove that this formulation achieves Rank-$L$ accumulation, structurally expanding the update scheme beyond the single-step Rank-$1$ bottleneck. Empirically, it achieves comparable performance to explicit optimization methods while achieving \textbf{174x higher throughput}. Codes are available in https://github.com/gpr-prism/prism/.

The accurate recovery of constituent-level optical properties from integrating sphere measurements is a central analytical challenge in pharmaceutical analysis, food science, and biomedical diagnostics. Neural network autoencoders can extract spectrally resolved absorption and scattering coefficients for each constituent without prior knowledge, but their fully connected encoders bind learned features to absolute wavelength indices, causing accuracy loss under spectrometer calibration drift or hardware exchange. This work introduces the Bin Latent Transformer (BiLT)-Autoencoder, in which the dense encoder is replaced by a cross-attention scanner: 16 learnable probe vectors query a convolutional feature map, aggregating morphological spectral information independently of absolute wavelength position. A physics-constrained linear decoder with enforced absorption/scattering separation and a three-phase curriculum augmentation strategy complete the architecture. On a liquid phantom benchmark (intralipid and two ink absorbers; 496 samples), the model achieves $R^2 = 0.979$ and $0.975$ for $μ_a(λ)$ and $μ_s'(λ)$, respectively, on held-out test spectra, maintaining $R^2 > 0.90$ for $μ_a$ and $R^2 \approx 0.99$ for $μ_s'$ across the full tested shift range of $\pm 10$ spectral bands. The model generalises to a simulated spectrometer with a broader instrument line shape (${\approx}24$nm FWHM) without retraining, retaining $R^2 \approx 0.96$ and $0.974$ for the two channels. Attention map analysis reveals a physically interpretable two-component probe strategy: sparse anchor probes at absorption-edge wavelengths combined with a diffuse, SNR-driven ensemble at the high-transmittance long-wavelength region, which recruits additional probes dynamically under noise to provide implicit spectral averaging.