When a language model answers, we can usually only estimate why. We build a transformer in which every nonlinearity is a quadratic detection (an interference, a balanced interferometric reading or a camera) and the output is a Born probability: attention $|\langle q|k\rangle|^2$, the form of the Born rule, normalised over each row, a measured product in place of the feed-forward nonlinearity, and a Born readout; between detections a classical controller squares, divides, rescales and re-encodes. With its denominators held at their values for the input, each class probability is a polynomial in the word amplitudes, so its integrated-gradient evidence is computed by a finite quadrature with no quadrature error: the words' contributions sum to the class probability above its no-information share, to $10^{-13}$ or better. On e-SNLI natural language inference the model reaches 77.45 +- 0.91 % test accuracy, level within the spread of three seeds with a softmax transformer of the same size (76.62 +- 0.36 %). Deleting the word its evidence ranks first changes the answer in 44 % of test pairs, out of the 53 % any single deletion can change, against 32 % for the softmax model's integrated gradients and 31 % for the Born Transformer's own attention. The same weights compile exactly to optoelectronic optics (simulated), and its attention overlaps to Hadamard tests on qubits; a separate coherent attention layer becomes one post-selected circuit (852 CNOTs on 23 qubits). On IBM's ibm_kingston, reading only the attention overlaps, the device gave the model's answers on the two shortest test pairs, also when the one word that decides one of them was deleted; with calibration circuits as deep as the overlaps, each word's evidence with the device's attention row sums followed the exact evidence on one pair (correlation 0.997) and on the other less closely (0.962).
Medical images encode intrinsic tissue properties that indicate disease progression, yet these properties remain entangled with the system-dependent physics of image formation. Differentiable inverse rendering asks whether they are recoverable by inverting the imaging system's forward physics rather than through post-hoc correction. We address this in optical coherence tomography (OCT), focusing on the optical attenuation coefficient, a per-pixel marker of pathology and cellular composition. Conventional recovery relies on closed-form inversions limited to simplified light-tissue models, or learned methods coupled to specific imaging configurations. We instead recover per-pixel attenuation from a single OCT image by gradient descent through a differentiable physics-based forward model. We verified the method against analytical solutions, validated it on five in vitro phantoms, and applied it without modification to 29{,}269 clinical intravascular OCT images from 128 patients. The inversion needs no training data or segmentations and is portable across platforms and retrospective archives. Replacing the forward model or recovering another optical parameter leaves the optimization procedure unchanged. We demonstrate per-pixel recovery is tractable because gradient information scales to this high-dimensional problem, where gradient-free methods become intractable. Our work supports quantitative tissue characterization from OCT images and provides a framework for extension across imaging modalities and organ systems.
In situ adjoint training extracts parameter gradients directly from measurement, but has so far been limited to reciprocal or restricted systems. We introduce the physical counterpart of the policy gradient theorem: a stochastic-adjoint gradient estimator that lifts these constraints by trading reciprocity for nondegenerate diffusion. As validation, we train a nonlinear resonator network, whose own dynamics supply the policy, against antagonistic temporal modulations with gradients from measured stochastic trajectories alone, without finite differences or a separate adjoint experiment.
When an image classifier decides, we can usually only estimate why. For quantum and all-optical classifiers that act linearly on amplitude-encoded pictures up to the measurement, with no trained classical network before or after them, each class's Born probability above its no-information share, $P_g - b_g$, splits exactly into contributions of the encoded amplitudes, shown as Born evidence maps (BEM). The split itself follows from known results on quadratic forms: with the transmitted light held fixed, it is what Integrated Gradients from a zero baseline and the Shapley value give. What we add is a way to measure it on the hardware that classifies, from class probabilities on a quantum chip or, in simulation, from camera frames on a lens bench, with no gradient circuit and no light sent backwards; a $g\times g$ map takes $1 + 2g^2$ runs. Deleting the 5% of pixels with the highest evidence drops accuracy from 73% to 9% (one seed), as occlusion and gradient $\times$ input do, while plain gradients remove much less. The classifiers share one architecture, a Fourier-plane mask followed by a brickwall circuit on qubits or by phase plates on a lens bench, read by a fixed Born headroom readout with no trained parameter; centring each picture on its own mean lets dark features count as much as bright ones. In simulation, four phase plates at one wavelength reach 72.3% on Caltech-10 colour photographs. On IBM's ibm_kingston, with the mask computed classically before approximate loading, 300 test pictures were classified at 37.7% against 10% chance (56.3% in exact simulation), and $2\times2$ maps of the filtered input of 30 test pictures drawn at random in advance, measured on the chip, agreed with the exact ones ($r = 0.88$; standard estimator 0.82). The maps also revealed a shortcut in the data; as the trim that removed it was chosen on test pictures, the Caltech-10 results are exploratory.
In single-pixel (ghost) imaging, known illumination patterns probe an object and a detector with no spatial resolution returns one number per pattern. Each measurement costs acquisition time and photons and, for ionizing probes, contributes to delivered dose. Motivated by automated radiographic defect screening, where a class label suffices, we introduce Learning Illumination Patterns for Single-Pixel Classification (LIPS-PC). The patterns are learned end-to-end while the measurement operator remains one fixed linear matrix, identical for every input. We parameterize it as a residual correction to a two-dimensional discrete cosine transform (2D-DCT), $D=D_{\mathrm{base}}+\Delta$, and jointly train the correction and a compact classifier using cross-entropy, without a reconstruction objective. This yields a task-driven linear embedding through optimization. We evaluate LIPS-PC numerically on MNIST and Fashion-MNIST under a controlled protocol, then on RIAWELC, a real industrial X-ray weld-radiograph dataset. Across five budgets, $M\in{8,16,32,64,128}$, corresponding to sampling ratios from below 1% to 12.5%, the learned operator outperforms the best tested fixed transform by 9-15 percentage points at $M=8$ on all three datasets. Its eight-measurement accuracy requires roughly 16-32 measurements with the best fixed transform, indicating a $2\times$ to $4\times$ saving at comparable accuracy. The advantage generally shrinks as $M$ increases, with a small reversal on RIAWELC at higher budgets. These results show that learning what to measure is especially valuable when measurements are scarce.
Quantitative phase imaging (QPI) reveals optical path-length variations in transparent objects but typically relies on spatially resolved intensity measurements. Here we numerically and experimentally demonstrate learned optical compression for single-pixel QPI, jointly optimizing a diffractive encoder and a digital neural decoder to concentrate reconstruction-relevant phase information into a compact measurement vector. A single reconfigurable phase-modulation plane sequentially displays the learned encoding patterns, which are independent of the input object, each yielding one scalar intensity measurement. Operating at a visible wavelength, the experimental system reconstructs quantitative phase images of unknown objects with ~40-fold dimensional compression, using only 2.55% as many intensity measurements as reconstructed pixels. Experimental blind testing on handwritten digits and grating-like phase objects achieves mean Pearson correlation coefficients of 0.945 and 0.848, respectively. Benchmarking under the same measurement budget demonstrates substantially higher reconstruction fidelity than other encoding strategies, highlighting the advantages of learned optical compression. With the optical encoder fixed, decoder-only neural adaptation enables experimental transfer to previously unseen data distributions, extending the utility of the learned measurement representation. These results establish learned optical compression as a measurement-efficient and reusable framework for QPI, integrating phase-information compression into single-pixel intensity measurements while retaining adaptability to new data. This approach paves the way for low-data-rate phase imaging and sensing, with the potential to extend QPI to spectral regions where high-quality detector arrays are costly or unavailable.
A central obstacle in realizing color center cavity-QED-based quantum technologies is inhomogeneity, or disorder, among individual emitters. As the number of emitters increases, so does the complexity of the experimental data, making it difficult to quantify the present physical mechanisms of disorder. Here we introduce an artificial intelligence-driven model discovery framework in which a large language model (LLM)-based agent, equipped with tools and a structured workflow, proposes candidate Hamiltonian and Lindbladian models, generates computational tools, and quantitatively evaluates competing physical hypotheses. We apply the workflow to three previously published experimental cavity-QED datasets collected from color centers in diamond and silicon carbide. Across the experiments, the agent successfully identifies physical models for the system and characterizes the disorder. In assessing reproducibility, we find that run-to-run variability is concentrated primarily in the research plan generation step, while the computational analysis itself is substantially more consistent. Our results suggest that structured LLM agent workflows can support model discovery from quantum optical experimental data while simultaneously allowing for human expert supervision and collaboration.
A spectrum can be given to a model as a table in nanometers or as a plot in photon energy, and the decision should not depend on which one it sees. When the data needed for an answer are missing, the model should say so. We test representation invariance and abstention on measured optical spectra of silicon metasurfaces (MOCLIP) and gold nanoparticles, with labels computed from the data. Each spectrum is shown as four tables (nm, $\mu$m, scientific notation, eV) and two plots (nm, eV), and partial spectra remove data inside or outside the queried range. We evaluate the decision models d3-nano and Jev 1.13, three GPT-6 Luna configurations and the Qwen3.5-2B base model. Changing only the representation moves accuracy by up to 41 percentage points within one model, mostly on photon-energy tables and plots. With the same evidence, asking in photon energy instead of wavelength helps some model-view pairs by 16-50 points and hurts others by up to 25. When the relevant extremum is removed, unadapted models rarely answer "undetermined". LoRA fine-tuning of d3-nano improves comparisons on the trained table formats, but much of its gain on unanswerable questions comes from a shortcut: it abstains whenever the input is truncated. Training with answerable truncations avoids the shortcut in all six seeds, with a 90-100 point gap between abstention after inside and outside cuts on held-out structures; with the same amount of extra original-task data, five of six seeds keep the shortcut. On gold spectra the two training sets perform similarly. Multimodal language models used for scientific decisions should be tested on equivalent representations and on missing evidence, not only on average accuracy. We release the tasks, per-response results and analysis code.
Bound states in the continuum (BIC) metasurfaces are typically described by geometry-specific parameters, hindering cross-geometry comparison, while ultranarrow quasi-BIC (qBIC) features are easily diluted in full-spectrum learning. Here, we map 2,015 samples from seven dielectric metasurface families onto a shared reciprocal-lattice grid. Two fixed low-order Fourier descriptors capture within-branch resonance shifts, with mean $R^2$ values of 0.871-0.999. Field-level analysis of two representative branches shows that these shifts are consistent with the Maxwell-Fourier perturbation picture. A five-channel Fourier-space backbone models the broadband spectrum. A local resonance expert uses complex Fourier coefficients to parameterize the qBIC resonance through a differentiable Fano layer. The expert reduces resonance-position mean absolute error (MAE) from 3.2 to 0.95 nm and reduces the minimum-transmission MAE by a factor of 14 on a geometry-blocked test set. The same coordinate supports spectrum-to-structure reconstruction.
In multiscale systems, nonlocal interactions among spatially distributed constituents can unlock collective, potentially emergent behavior irreducible to individual constituent responses. Beyond characterization, nonlocality in multiscale systems is increasingly viewed as a design element across fracture mechanics, wave physics, and disordered systems. Existing nonlocality theories provide rigorous descriptions and mechanistic insight, but often require prescribed analytic forms, range, symmetries, or periodicity. Machine learning offers a data-driven route to learn interactions, yet principled approaches that tie the network design to physical theory remain nascent. Here we present domain-decomposition attention neural operator (DANO), which learns configuration-dependent interactions in heterogeneous systems governed by linear field equations from field data alone. Through a case study in large-scale optical metasurfaces, we demonstrate DANO's full-field prediction under geometric heterogeneity and across drive conditions, small-to-large domain transfer, and multifunctional inverse design, with learned interactions validated through physics-based interrogation. As an AI-for-Science tool, it supports interaction discovery and scalable, customizable design of nonlocal multiscale systems, including virtual-reality optics.