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
9 Pith papers cite this work. Polarity classification is still indexing.
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Derives MI-LB acquisition function from mutual information in a two-index epistemic-aleatoric framework and shows it outperforms baselines on multimodal regression benchmarks.
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.
A unified structured factorization framework for quantum state tomography that parametrizes the density matrix as FF^dagger, supports multiple priors, provides sample complexity bounds, and introduces projected gradient descent and power-method algorithms.
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.
citing papers explorer
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Any-Dimensional Invariant Universality
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.
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A Mutual Information Lower Bound for Multimodal Regression Active Learning
Derives MI-LB acquisition function from mutual information in a two-index epistemic-aleatoric framework and shows it outperforms baselines on multimodal regression benchmarks.
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Approximation of Maximally Monotone Operators : A Graph Convergence Perspective
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.
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Learning on the Temporal Tangent Bundle for Physics-Informed Neural Networks
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.
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Isotropic Activation Functions Enable Deindividuated Neurons and Adaptive Topologies
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.
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Structured Factorization Approaches for Quantum State Tomography
A unified structured factorization framework for quantum state tomography that parametrizes the density matrix as FF^dagger, supports multiple priors, provides sample complexity bounds, and introduces projected gradient descent and power-method algorithms.
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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.
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Structural Correspondence and Universal Approximation in Diagonal plus Low-Rank Neural Networks
Diagonal plus Low-Rank (DLoR) neural networks achieve universal approximation for general activations by additive or multiplicative decompositions of full-rank transformations.
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Solving and learning advective multiscale Darcian dynamics with the Neural Basis Method
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.