Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.24271

Build Your Own Neural Network From Scratch

Samantha Donner·Ethan Geary·Peter March·Mathew Umano
View original source ↗Read source document ↗Export metadata ↓

Abstract

These notes are based on our reading of Michael Nielsen's online book neuralnetworksanddeeplearning.com. They represent our effort to elaborate his exposition of neural networks and to provide supporting mathematical detail. Our goal is to provide self-contained instructions for building a basic neural network in the form of pseudocode, so that an interested reader can build a network from scratch and know why it works. No prior knowledge of neural networks or of Python is assumed. Some familiarity with linear algebra, calculus, and probability is helpful but we explain the relevant mathematics in a set of appendices designed to be accessible to newcomers.

Explore related subjects

math.HO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Samantha Donner, Ethan Geary, Peter March, Mathew Umano. 2026-10-16. Build Your Own Neural Network From Scratch. https://arxiv.org/abs/2610.24271

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A century problem related to the Legendre symbol modulo p

The main purpose of this paper is using a very simple constructive method to study an old number theory problem related to the Legendre symbol modulo $p$, and completely solved it. The proving method of the result is purely elementary and has been desired in the literature at least since 1927.

math.HO↗
arXiv2026

Ehrhart Properties under Operations on Lattice Polytopes

This paper investigates the preservation of three classes of Ehrhart properties under various operations on lattice polytopes. These operations include Cartesian products, lattice joins, lattice pyramids, free sums, Minkowski sums, Cayley sums, reflexive polarity, and integral dilations. Specifically, we consider the following properties frequently studied in Ehrhart theory: (i): Positivity of Ehrhart coefficients, including Ehrhart positivity and magic positivity. In particular, we present lattice point counting formulas for the polytopes generated by these operations. (ii): Coefficient properties of the $h^*$-polynomial, including symmetry, unimodality, log-concavity, ultra log-concavity, real-rootedness, and $γ$-positivity. (iii): Geometric properties, including the spanning property, the integer decomposition property, very ampleness, and the existence of unimodular triangulation, regular unimodular triangulation, and quadratic triangulation. We determine which properties are preserved under these eight operations, establishing preservation theorems or constructing explicit counterexamples. Furthermore, when a property is not preserved in general, we investigate sufficient or equivalent conditions for its preservation.

math.HO↗
arXiv2026

From a Student's Question to the Half-Derivative: A Constructivist Teaching Model - Part I

This paper presents a conceptual, cognitive-constructivist model for teaching the half-derivative. The model starts from a student's question and frames it as the problem of generalizing the familiar operation of differentiation. On a suitably chosen space of monomials, under the assumptions of linearity and of lowering the exponent by one half, the requirement that the operator applied twice give the ordinary derivative produces a recurrence for the coefficients. The freedom of normalization becomes visible, and an additional convention yields a formula compatible with the monomial rule of the Riemann-Liouville half-derivative. The domain of the operator and its relation to the Riemann-Liouville and Caputo operators are treated separately. The mathematical results rest on the author's earlier preprints; the contribution of this paper is their transformation into an instructional pathway organized in phases, with diagnostic questions, an analysis of typical errors, and comparative problems. The model is a design proposal: its effectiveness has not yet been established by systematic empirical research. The interactive Socratic implementation and the detailed diagnostics are the subject of Part II.

math.HO↗