\documentclass[12pt, letterpaper]{article}

\usepackage{enumitem}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage[margin=1in]{geometry}
\usepackage{cancel}
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{amstext}
\usepackage{amsthm}
\usepackage{xcolor}
\usepackage{titlesec}
\usepackage{pgfplots}
\usepackage{mdframed}
\usepackage{nicefrac}
\usepackage{dsfont}
\usepackage{tikz}
\usetikzlibrary{trees}
\usepackage{mathdots}
\usepackage{accents}
\usepackage{mathtools}
\usepackage{bbm}

\usepackage{import}

\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lmodern}
\usepackage[hidelinks]{hyperref}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}

\usepackage[english]{babel}
\usepackage{csquotes}

\usepackage{xcolor}

\usepackage[notes,backend=biber]{biblatex-chicago}

% theorem environments
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{corollary}{Corollary}

\theoremstyle{definition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}

\theoremstyle{remark}
\newtheorem*{claim}{Claim}
\newtheorem*{remark}{Remark}
\newtheorem*{note}{Note}

\setlength{\textwidth}{6.0in}
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\setlength{\headheight}{0.25in}
\setlength{\headsep}{0.25in}
\setlength{\textheight}{8.5in}
\setlength{\footskip}{20pt}

\setlength{\topskip}{0in}

\setcounter{secnumdepth}{0}

\setlength{\parindent}{0in}	
\setlength{\parskip}{0.1in}

\newcommand{\vect}[1]{\vec{\mathbf{#1}}}
\newcommand{\sectionbreak}{\clearpage}
\newcommand{\R}{\mathbb{R}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\N}{\mathbb{N}}
\renewcommand{\P}{\mathbb{P}}
\newcommand{\F}{\mathbb{F}}
\newcommand{\modop}{\;\text{mod}\;}
\renewcommand{\mod}[1]{\;(\text{mod}\;#1)}
\newcommand{\Aut}{\text{Aut}}
\newcommand{\id}{\text{id}}
\newcommand{\spn}{\;\text{span}}

\newcommand{\ftntmk}{\textcolor{blue}{\footnotemark}}
\newcommand{\black}[1]{\textcolor{black}{#1}}
\newcommand{\ubcolor}[2]{\color{#1}{\underbrace{\color{black}{#2}}}}
\newcommand*\circled[1]{\tikz[baseline=(char.base)]{
            \node[shape=circle,draw,inner sep=2pt] (char) {#1};}}

\newcommand{\vol}[1]{\text{vol}}

\newcommand{\verteq}{\rotatebox{90}{$\,=$}}
\newcommand{\equalto}[2]{\underset{\scriptstyle\overset{\mkern4mu\verteq}{#2}}{#1}}

\newcommand{\rk}{\text{rk}\,}
\newcommand{\Col}{\text{Col}\,}
\newcommand{\C}{\mathbb{C}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\actson}{\curvearrowright}

\newcommand{\E}{\mathbb{E}}

\renewcommand{\mapsto}{\longmapsto}

% James - Parentheses, brackets, etc.
\newcommand{\ignore}[1]{}  % from Charles
\newcommand{\parens}[1]{\ensuremath{\left( #1 \right)}}
\newcommand{\bracks}[1]{\ensuremath{\left[ #1 \right]}}
\newcommand{\braces}[1]{\ensuremath{\left\{ #1 \right\}}}
\newcommand{\angbrs}[1]{\ensuremath{\langle #1 \rangle}}
\newcommand{\set}[1]{\braces{#1}}
\newcommand{\powset}[1]{\mathcal{P}\parens{#1}}
\newcommand{\vspan}[1]{\angbrs{#1}}  % 4330: Span of a set of vectors

\newcommand{\floor}[1]{\left\lfloor #1 \right\rfloor}
\newcommand{\ceil}[1]{\left\lceil #1 \right\rceil}
\newcommand{\verts}[1]{\left\lvert #1 \right\rvert} % | #1 |
\newcommand{\Verts}[1]{\left\lVert #1 \right\rVert} % || #1 ||
\newcommand{\abs}[1]{\verts{#1}}
\newcommand{\size}[1]{\verts{#1}}
\newcommand{\norm}[1]{\Verts{#1}}

\newcommand{\eps}{\varepsilon}
\newcommand{\vphi}{\varphi}
\renewcommand{\Re}{\mathrm{Re}}
\renewcommand{\Im}{\mathrm{Im}}

\newcommand{\bmat}[1]{\begin{bmatrix} #1 \end{bmatrix}}
\newcommand{\pmat}[1]{\begin{pmatrix} #1 \end{pmatrix}}

\title{Implementing Gradient Descent}
\author{Owen Wetherbee, Ethan Ma, Sylvan Martin}
\date{}

\bibliography{bibliography}

% Body

\pgfplotsset{compat=1.16}
\begin{document}

\maketitle

\include{backprop}
\include{learning_rates}

\end{document}