Programmable k-local Ising Machines and all‑optical Kolmogorov-Arnold Networks on Photonic Platforms

Programmable k-local Ising Machines and all‑optical Kolmogorov-Arnold Networks on Photonic Platforms | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Programmable k-local Ising Machines and all‑optical Kolmogorov-Arnold Networks on Photonic Platforms Natalia Berloff, Nikita Stroev This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8264191/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Photonic computing offers energy-efficient acceleration for optimization and learning, yet combinatorial search and function approximation have typically required different devices and control stacks. We present a unified approach that supports both k-local Ising optimization and optical Kolmogorov–Arnold network (KAN) learning on a single photonic platform. The core is an SLM-centric primitive capable of implementing all-optical k-local Ising interactions and fully optical KAN layers within the same architecture. Our framework maps k-body products to per-window structural nonlinearities, analyzes calibration and training through general Jacobian models, and outlines practical implementation routes on several photonic platforms. The key idea is to exploit the structural nonlinearity of a nominally linear scatterer by adding a second relay pass through the same SLM: a folded 4f relay re-images the Fourier plane so each clique or channel occupies its own window with an independent second-pass phase patch. Optical propagation remains linear, but each window’s measured intensity becomes a programmable polynomial of the clique sum or projection amplitude. This mechanism yields intrinsic k-local couplings without nonlinear media, and simultaneously provides the many independent nonlinearities required for KAN layers, all trainable via in-situ physical gradients using only forward and adjoint frames. We describe implementations on spatial photonic Ising machines, VCSEL arrays, and Microsoft’s analog optical hardware, requiring only one added lens and fold (or an on-chip 4f loop). Our analysis characterizes calibration behavior and noise robustness for broad classes of per-window Jacobians and serves as a blueprint for future experiments. Physical sciences/Optics and photonics/Optical physics Physical sciences/Physics/Information theory and computation Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8264191","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":559541444,"identity":"f3d9473f-a59c-45d2-bb81-bd72a3981063","order_by":0,"name":"Natalia 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