mlsanityData to 7 Oct 2026

Approximation capability of two hidden layer feedforward neural networks with fixed weights

arXiv 2101.09181 ↗First posted 22 Jan 2021cs.NE cs.IT cs.NAcited by 24

Not on the map. Why?

Abstract (arXiv)

We algorithmically construct a two hidden layer feedforward neural network (TLFN) model with the weights fixed as the unit coordinate vectors of the d-dimensional Euclidean space and having 3d+2 number of hidden neurons in total, which can approximate any continuous d-variable function with an arbitrary precision. This result, in particular, shows an advantage of the TLFN model over the single hidden layer feedforward neural network (SLFN) model, since SLFNs with fixed weights do not have the capability of approximating multivariate functions.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Jan 2021.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 2; 2023: 1; 2024: 9; 2025: 3; 2026: 7.

24 papers.

Sort:

By area:

  1. 2021On the approximation of functions by tanh neural networkscited by 81
  2. 2023On the Kolmogorov neural networkscited by 19
  3. 2021The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimationcited by 14
  4. 2024Addressing common misinterpretations of KART and UAT in neural network literaturecited by 9
  5. 2024Robust Weight Initialization for Tanh Neural Networks with Fixed Point Analysiscited by 5
  6. 2022KASAM: Spline Additive Models for Function Approximationcited by 4
  7. 2024Universal approximation theorem for neural networks with inputs from a topological vector spacecited by 4
  8. 2024Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks?cited by 3
  9. 2022Approximation error of single hidden layer neural networks with fixed weightscited by 2
  10. 2025Approximation properties of neural ODEscited by 2
  11. 2025On shallow feedforward neural networks with inputs from a topological spacecited by 2
  12. 2024SGD method for entropy error function with smoothing l0 regularization for neural networkscited by 1
12 more
  1. 2024Numerical Approximation Capacity of Neural Networks with Bounded Parameters: Do Limits Exist, and How Can They Be Measured?cited by 1
  2. 2024Efficient Computation of Confidence Sets Using Classification on Equidistributed Gridscited by 0
  3. 2024Learnability of high-dimensional targets by two-parameter models and gradient flowcited by 0
  4. 2024Fingerprinting web servers through Transformer-encoded HTTP response headerscited by 0
  5. 2025Expressivity of Quadratic Neural ODEscited by 0
  6. 2026Universal Approximation Theorem for Input-Connected Multilayer Perceptronscited by 0
  7. 2026Universality of shallow and deep neural networks on non-Euclidean spacescited by 0
  8. 2026Man, Machine, and Mathematicscited by 0
  9. 2026StreamPhy: Streaming Inference of High-Dimensional Physical Dynamics via State Space Modelscited by 0
  10. 2026On Explicit Super-Expressive Approximation for Neural Networkscited by 0
  11. 2026Solving In-Table Prediction Problems by Deep Neural Networks with Performance Evaluation Using Synthetic Datacited by 0
  12. 2026Arbitrary-Accuracy Neural Approximation with Optimal Neuron Count and Near-Optimal Bit Complexitycited by 0