This is a repository which implements a certain neural network calculus. This neural network calculus, or atleast the version implemented derives itself mainly from <https://doi.org/10.48550/arXiv.2402.01058>, which in turn is a highly modified version of that found in detail in <https://doi.org/10.1007/s10444-022-09970-2> and <https://doi.org/10.48550/arXiv.2310.20360>.

Our neural network calculus envisions neural networks as an ordered tuple of ordered pairs of $W$ and $b$, weight matrices and bias vectors.

We may compose neural networks as in Definition 2.6 in <https://doi.org/10.48550/arXiv.2402.01058>.

We may stack neural networks as in Definition 2.14 in <https://doi.org/10.48550/arXiv.2402.01058>.

We may take the sum of neural networks as in Definition 2.19 in <https://doi.org/10.48550/arXiv.2402.01058>.

We may take squares and products of neural networks as in Definition 2.24 and Definition 2.25 of respectively of <https://doi.org/10.48550/arXiv.2402.01058>.

We may take powers of neural networks as in Definition 2.26 in <https://doi.org/10.48550/arXiv.2402.01058>.

We may take neural network exponential, sines and cosines, as in Definitions 2.28, 2.29, and 2.30 respectively in <https://doi.org/10.48550/arXiv.2402.01058>.

We may implement the 1-D trapezoidal rule for integration as in Definitions 2.31 and 2.33 in <https://doi.org/10.48550/arXiv.2402.01058>.

Finallly, Norms, Maxima, and a maximum convolution type approximation for 1-D continuous functions is possible as in Definitions 2.35, 2.37, and 2.39 respectively in <https://doi.org/10.48550/arXiv.2402.01058>.