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First framework to simultaneously learn functions and discover unknown one-parameter Lie symmetry subgroups, with invariance certified by architectural construction. Unifies elliptic, hyperbolic, and parabolic symmetries in a single Lie-theoretic framework.
DPP subset selection traces bias and untruthfulness to specific training samples; PBRF gradient ascent repairs the model. Recovers 21% trustworthiness at <1% perplexity cost. Addresses the practical problem that SFT routinely degrades LLM truthfulness.
Integrates Mamba state-space models with kernel integral operators in latent space, achieving 32.3% improvement over prior PDE solver baselines. Extends neural operator learning with the expressive power of structured state-space models.
Langevin dynamics augmentation bridges source-to-target distribution gaps for robust generalisation in medical image segmentation without any target-domain labels. Demonstrated across heterogeneous imaging sites.
Exploits structural equivalence between the forward diffusion process and segmentation to enable fully self-supervised histopathological segmentation — zero pixel-level annotations required. Outperforms prior methods on two public benchmarks.