A systematic approach maps any-dimensional invariant functions to a unique function on an infinite-dimensional limit space admitting a topology with compact sets where universality holds, with examples of non-universal architectures and fixes.
Approximation capabilities of multilayer feedforward networks.Neural networks, 4(2):251–257
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Proves first UATs for k-times differentiable nonlinear operators and their derivatives via OL architectures uniformly on compact sets in weighted Bastiani-Sobolev spaces on general Banach spaces.
A framework learns effective multiscale stochastic dynamics from single slow-variable paths by parameterizing the fast process invariant distribution with normalizing flows, trained end-to-end via penalized likelihood from stochastic averaging.
Training transformers with KV sparsification during continued pretraining produces representations that admit better post-hoc KV cache compression, improving quality under memory budgets for long-context tasks.
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Learning stochastic multiscale models through normalizing flows
A framework learns effective multiscale stochastic dynamics from single slow-variable paths by parameterizing the fast process invariant distribution with normalizing flows, trained end-to-end via penalized likelihood from stochastic averaging.