UFO: A Domain-Unification-Free Operator Framework for Generalized Operator Learning
Authors: Hanli Qiao, George Em Karniadakis, Muhammad Muniruzzaman
Summary
arXiv:2605. 12700v1 Announce Type: new Abstract: Neural operators have become an effective framework for learning mappings between function spaces, yet most existing architectures realize operators within a single representational domain, such as physical, spectral, or latent space.
Relevance
Read next because UFO: A Domain-Unification-Free Operator Framework for Generalized Operator Learning overlaps with clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)", clean result "EOS-in-loss was the confound: masking the recipient's EOS from cross-entropy revives within-marker chunk-binding from 1.3% to 23.5% (MODERATE confidence)", clean result "The marker is a representational handle, not a behavioural one — sharing it between a villain persona and the assistant transfers no misalignment (HIGH confidence)". Matching terms: under, training, line, rate, coupling, continuous. Source: arxiv cs.LG (Machine Learning).
Threat model
Potential threat/caveat for clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)": this item discusses benchmark.
Abstract
arXiv:2605.12700v1 Announce Type: new Abstract: Neural operators have become an effective framework for learning mappings between function spaces, yet most existing architectures realize operators within a single representational domain, such as physical, spectral, or latent space. In this work, we introduce UFO (Domain-Unification-Free Operator), a cross-domain neural operator framework that realizes operators through adaptive, jointly conditioned interactions among representations defined on distinct domains. UFO enables discretization decoupling: the input function can be observed at resolutions or locations different from those used during training, while the solution can be queried at arbitrary output resolutions. Across four complementary benchmarks covering discontinuous inputs, irregular sampling with spectral mismatch, nonlinear dynamics, and stochastic high-frequency fields, UFO delivers accurate, robust, and physically coherent predictions under distribution shifts. These results establish cross-domain, phase-modulated realization as a powerful framework for discretization-decoupled neural operator learning.