Stabilize large-model training by restricting weight updates to curated manifolds that align with desired behaviors and safety envelopes.
Traditional stochastic gradient descent lets weights roam freely throughout parameter space. While flexible, this freedom can amplify instability, catastrophic forgetting, or drift away from safety constraints. Manifold-constrained training introduces mathematical surfaces—subspaces shaped by geometric priors—that guide optimization toward regions exhibiting desirable properties such as robustness, sparsity, or controlled expressiveness. Teams in 2025 use these techniques to make large models easier to align, fine-tune, and certify.