Towards an Algebraic Framework For Approximating Functions Using Neural Network Polynomials
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911769595740160 |
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| author | Rafi, Shakil Padgett, Joshua Lee Nakarmi, Ukash |
| author_facet | Rafi, Shakil Padgett, Joshua Lee Nakarmi, Ukash |
| contents | We make the case for neural network objects and extend an already existing neural network calculus explained in detail in Chapter 2 on \cite{bigbook}. Our aim will be to show that, yes, indeed, it makes sense to talk about neural network polynomials, neural network exponentials, sine, and cosines in the sense that they do indeed approximate their real number counterparts subject to limitations on certain of their parameters, $q$, and $\varepsilon$. While doing this, we show that the parameter and depth growth are only polynomial on their desired accuracy (defined as a 1-norm difference over $\mathbb{R}$), thereby showing that this approach to approximating, where a neural network in some sense has the structural properties of the function it is approximating is not entire intractable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01058 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards an Algebraic Framework For Approximating Functions Using Neural Network Polynomials Rafi, Shakil Padgett, Joshua Lee Nakarmi, Ukash Machine Learning Numerical Analysis Neural and Evolutionary Computing Combinatorics 62M45 We make the case for neural network objects and extend an already existing neural network calculus explained in detail in Chapter 2 on \cite{bigbook}. Our aim will be to show that, yes, indeed, it makes sense to talk about neural network polynomials, neural network exponentials, sine, and cosines in the sense that they do indeed approximate their real number counterparts subject to limitations on certain of their parameters, $q$, and $\varepsilon$. While doing this, we show that the parameter and depth growth are only polynomial on their desired accuracy (defined as a 1-norm difference over $\mathbb{R}$), thereby showing that this approach to approximating, where a neural network in some sense has the structural properties of the function it is approximating is not entire intractable. |
| title | Towards an Algebraic Framework For Approximating Functions Using Neural Network Polynomials |
| topic | Machine Learning Numerical Analysis Neural and Evolutionary Computing Combinatorics 62M45 |
| url | https://arxiv.org/abs/2402.01058 |