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 by superpositions of a sigmoidal function.Mathematics of control, signals and systems, 2(4):303–314
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Any maximally monotone operator can be approximated in local graph convergence by continuous encoder-decoder networks, with structure-preserving versions that retain maximal monotonicity via resolvent parameterizations.
Parameterizing the temporal derivative in PINNs and reconstructing via Volterra integral yields 100-200x lower errors on advection, Burgers, and Klein-Gordon equations while proving equivalence to the original PDE.
Isotropic activation functions derived from reparameterisation symmetries and SVD diagonalisation enable function-preserving neuron removal and addition in dense networks, supporting up to 50% sparsification and real-time topology adaptation.
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.
Diagonal plus Low-Rank (DLoR) neural networks achieve universal approximation for general activations by additive or multiplicative decompositions of full-rank transformations.
The Neural Basis Method uses a predefined neural basis space and operator residual metric to deliver accurate single solves and fast parametric learning for multiscale Darcian dynamics.
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Training Transformers for KV Cache Compressibility
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.