%% C2S 2026 Keynote — Simon Carrignon
%% Computational Cultural Science Workshop, Paris, 18--19 May 2026
%% École nationale des Chartes -- PSL
%% Compile with: lualatex slides-c2s-2026.tex

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      \textbf{Simon Carrignon} · UCL GEE \hspace{.1cm}\textbf{|}
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      \textbf{C2S Paris · May 2026}
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%% ── Title info ──────────────────────────────────────────────────────────
\title{%
  \textbf{\large Bridging Scales in Cultural Evolution:\\
  Computational Models, Archaeological Data, and Machine Learning}}
\author{%
  \textcolor{white}{%
    Simon Carrignon (\href{mailto:s.carrignon@ucl.ac.uk}{s.carrignon@ucl.ac.uk})\\
    University College London -- Dept.\ of Genetics, Evolution \& Environment\\[4pt]
    ERC COREX Project
  }
}
\institute{}
\date{%
  \textcolor{white}{%
    C2S --- Computational Cultural Science Workshop\\
    École nationale des Chartes -- PSL, Paris\\
    18--19 May 2026
  }
}

%% ═══════════════════════════════════════════════════════════════════════════
\begin{document}

%% ── Title Slide ─────────────────────────────────────────────────────────
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%% ── Plan Slide ──────────────────────────────────────────────────────────
\begin{frame}{Plan}
  \begin{itemize}[<+->]
    \item Introduction --- Cultural Evolution \& Computational Approaches
    \item Computational Models --- ABM, Cultural Transmission, 4-Box Model
    \item Archaeological Evidence --- The Record, Its Biases, What It Gives Us
    \item ML on Archaeological Data --- Autoencoder on Faunal Remains
    \item Approximate Bayesian Computation --- Coupling Data \& Models
    \item Conclusion \pause --- Open Questions \& Connections to CCS
  \end{itemize}
\end{frame}

%% ═══════════════════════════════════════════════════════════════════════════
\section{Introduction}
\sectiondivider{Introduction}

%% ── What is Cultural Evolution? ─────────────────────────────────────────
\begin{frame}{Cultural Change}
  ``Information, traditions, behaviours transmitted socially
  (via direct or indirect interactions with peers)''

  \vspace{6pt}
  \begin{itemize}[<+->]
    \item Languages, technologies, artistic styles, subsistence strategies\ldots
    \item \textbf{Changes of frequencies} of cultural variants over time
    \item Analogous to biological evolution --- but with distinct mechanisms
  \end{itemize}

  \vspace{8pt}
  \uncover<4->{%
  \begin{center}
    \begin{tikzpicture}[
      icon/.style={draw=ifsapurple, rounded corners=3pt, minimum size=1.2cm,
        align=center, font=\scriptsize, fill=purplelight, line width=0.6pt}
    ]
      \node[icon] (a) at (0,0) {words};
      \node[icon] (b) at (2.5,0) {pottery};
      \node[icon] (c) at (5,0) {tools};
      \node[icon] (d) at (7.5,0) {food\\practices};
      \node[icon] (e) at (10,0) {digital\\culture};
    \end{tikzpicture}
  \end{center}
  }
\end{frame}

%% ── Understanding Cultural Change ───────────────────────────────────────
\begin{frame}{Understanding Cultural Change}
  \uncover<+->{What drives these changes?}

  \begin{columns}[t]
    \column{.50\textwidth}
    \vspace{4pt}
    \begin{itemize}[<+->]
      \item Environmental pressures
      \item Social network structure
      \item Cognitive biases \& learning strategies
      \item Demographic processes
    \end{itemize}

    \column{.50\textwidth}
    \uncover<6->{%
      At relatively large geographical \emph{\&} temporal scales:
      \vspace{4pt}
      \begin{itemize}
        \item Limited applicability of general theories
        \item Limited use of experiments
        \item Limited/noisy/biased empirical evidence
      \end{itemize}
      \vspace{6pt}
      \textbf{How to study meso-scale cultural evolution?}
    }
  \end{columns}
\end{frame}

%% ── The COREX Project ───────────────────────────────────────────────────
\begin{frame}{The COREX Project (ERC)}
  \begin{columns}[T]
    \begin{column}{0.55\textwidth}
      \textbf{CO}mputational \textbf{R}esearch on Cultural \textbf{E}volution
      \textbf{X}-disciplinary

      \vspace{8pt}
      \begin{itemize}[<+->]
        \item ERC-funded project at UCL (Dept.\ GEE)
        \item Studying cultural evolution through \textbf{computational}
              and \textbf{archaeological} approaches
        \item Integrating agent-based models, ML, and Bayesian inference
              with large archaeological databases
        \item Focus on subsistence strategies, material culture,
              and demographic dynamics
      \end{itemize}
    \end{column}
    \begin{column}{0.42\textwidth}
      \pause
      \begin{block}{Key Data Sources}
        \small
        Faunal assemblages\\
        Isotope data, ${}^{14}$C dates\\
        Ancient DNA\\
        Material culture typologies
      \end{block}
      \vspace{6pt}
      \begin{exampleblock}{Collaborations}
        \small
        ENCOUNTER (Cambridge)\\
        DySoC (UTK)\\
        BIAD consortium
      \end{exampleblock}
    \end{column}
  \end{columns}
\end{frame}

%% ── Bridging Scales ─────────────────────────────────────────────────────
\begin{frame}{Bridging Scales}
  \begin{center}
    \begin{tikzpicture}[
      box/.style={draw=ifsapurple, rounded corners=5pt, minimum height=1.6cm,
        text width=3cm, align=center, font=\small, line width=0.8pt},
      arr/.style={-{Stealth[length=5pt]}, thick, ifsapurple!60, line width=1pt},
      bigarr/.style={-{Stealth[length=6pt]}, very thick, accentred, line width=1.5pt}
    ]
      % Local
      \node[box, fill=purplelight] (local) at (0,0)
        {\textbf{Local}\\Individual\\interactions\\[2pt]\footnotesize ethnography};

      % Meso
      \node[box, fill=accentgold!25, draw=accentgold!80!black, line width=1.4pt]
        (meso) at (5.5,0)
        {\textbf{Mesoscale}\\Regional dynamics\\over millennia\\[2pt]
         \footnotesize\color{accentred} our target};

      % Global
      \node[box, fill=purplelight] (global) at (11,0)
        {\textbf{Global}\\Cross-cultural\\universals\\[2pt]\footnotesize big data};

      % Arrows
      \draw[arr] (local) -- (meso);
      \draw[arr] (global) -- (meso);

      % Bottom label
      \node[font=\footnotesize\itshape, ifsapurple] at (5.5,-1.6)
        {Primary evidence: the \textbf{archaeological record}};
    \end{tikzpicture}
  \end{center}
  \vspace{4pt}
  \pause
  \begin{block}{The approach}
    Model \textbf{local interactions} (ABM) $\to$
    Generate \textbf{regional patterns} $\to$
    Compare with \textbf{empirical data} $\to$
    Constrain \textbf{transmission processes}
  \end{block}
\end{frame}


%% ═══════════════════════════════════════════════════════════════════════════
\section[Models]{Computational Models}
\sectiondivider{Computational Models}

%% ── Computational Modelling Overview ────────────────────────────────────
\begin{frame}{Computational Modelling}
  \begin{columns}[t]
    \column{.60\textwidth}
    \begin{itemize}[<+->]
      \item Model local interactions to explore hypotheses
            at different scales (\textbf{ABM})
      \item Extract empirical patterns
            (Bayesian stats, ML,\ldots)
      \item Test method robustness
            (`tactical simulation')
    \end{itemize}
    \column{.40\textwidth}
    \uncover<2->{%
      \begin{block}{Epstein (2008)}
        \small ``If you didn't grow it,\\you didn't explain it.''
      \end{block}
    }
  \end{columns}
\end{frame}

%% ── Agent-Based Modelling ───────────────────────────────────────────────
\begin{frame}{Agent-Based Modelling}
  \begin{columns}[t]
    \column{.55\textwidth}
    \begin{itemize}[<+->]
      \item Explicitly describe low-level interactions
      \item Formalise, generate, and explore hypotheses
      \item Reproducible and testable descriptions
      \item Flexible: demography, spatial structure,
            multiple transmission pathways
    \end{itemize}

    \column{.45\textwidth}
    \uncover<2->{%
      \begin{center}
        \begin{tikzpicture}[scale=0.7,
          agent/.style={circle, draw=ifsapurple, fill=purplelight,
            minimum size=5mm, inner sep=0pt, font=\tiny\bfseries},
          link/.style={ifsapurple!40, line width=0.6pt}
        ]
          % Grid of agents
          \foreach \x/\y/\lab in {0/0/a,1.5/0.3/b,3/0/c,0.5/1.5/d,2/1.8/e,
            3.5/1.5/f,0/3/g,1.5/2.8/h,3/3.2/i} {
            \node[agent] (\lab) at (\x,\y) {};
          }
          % Links
          \foreach \a/\b in {a/b,b/c,a/d,b/e,c/f,d/e,e/f,d/g,e/h,f/i,g/h,h/i} {
            \draw[link] (\a) -- (\b);
          }
          % Highlight a transmission event
          \draw[-{Stealth[length=4pt]}, accentred, thick] (e) -- (h)
            node[midway, right, font=\tiny] {copy};
          % Label
          \node[font=\scriptsize, ifsapurple, below] at (1.5,-0.5)
            {agents on a network};
        \end{tikzpicture}
      \end{center}
    }
  \end{columns}
\end{frame}

%% ── The 4-Box Model ────────────────────────────────────────────────────
\begin{frame}{Cultural Transmission --- The 4-Box Model}
  \begin{columns}[t]
    \column{.45\textwidth}
    \textbf{Vidiella et al.\ (2022):}
    \begin{align*}
      \Pr(i,t{+}1) = \frac{1}{Y_t}\, p_i(t)^{\alert{J}}\, e^{\alert{\beta}\, U_i + \psi}
    \end{align*}
    \begin{itemize}[<+->]
      \item $\alert{J}$: social conformity (frequency dependence)
      \item $\alert{\beta}$: transparency of intrinsic utility
    \end{itemize}
    \uncover<3->{A 2D space to classify cultural change:}

    \column{.55\textwidth}
    \uncover<3->{%
      \begin{center}
        \begin{tikzpicture}[scale=0.85,
          box/.style={draw=ifsapurple, rounded corners=3pt,
            minimum height=1.4cm, text width=2.6cm, align=center,
            font=\scriptsize, line width=0.6pt}
        ]
          % Axes
          \draw[-{Stealth[length=5pt]}, thick, ifsapurple]
            (-0.2,0) -- (6.2,0) node[right, font=\small] {$J$ (conformity)};
          \draw[-{Stealth[length=5pt]}, thick, ifsapurple]
            (0,-0.2) -- (0,4.8) node[above, font=\small] {$\beta$ (utility)};

          % Quadrants
          \node[box, fill=purplelight] at (1.5,1.2) {Drift\\(neutral)};
          \node[box, fill=accentgold!20] at (4.5,1.2) {Conformity\\bias};
          \node[box, fill=ifsapurple!12] at (1.5,3.5) {Content\\bias};
          \node[box, fill=accentred!12] at (4.5,3.5) {Guided\\variation};

          % Parameter labels
          \node[font=\tiny, midgray] at (1.5,-0.5) {low $J$};
          \node[font=\tiny, midgray] at (4.5,-0.5) {high $J$};
          \node[font=\tiny, midgray, rotate=90] at (-0.6,1.2) {low $\beta$};
          \node[font=\tiny, midgray, rotate=90] at (-0.6,3.5) {high $\beta$};
        \end{tikzpicture}
      \end{center}
    }
  \end{columns}
\end{frame}

%% ── Cultural Transmission Pathways ──────────────────────────────────────
\begin{frame}{Cultural Transmission Pathways}
  \begin{center}
    \begin{tikzpicture}[
      gen/.style={draw=ifsapurple, rounded corners=2pt, minimum height=0.8cm,
        text width=2.2cm, align=center, font=\scriptsize, fill=purplelight},
      arr/.style={-{Stealth[length=4pt]}, ifsapurple, line width=0.7pt},
      lab/.style={font=\tiny, midgray, align=center}
    ]
      % Parent generation
      \node[gen, fill=ifsapurple!20] (p1) at (0,3) {Parent A};
      \node[gen, fill=ifsapurple!20] (p2) at (3,3) {Parent B};
      \node[gen, fill=ifsapurple!12] (elder) at (6,3) {Elder / Peer};
      \node[gen, fill=accentgold!15] (comm) at (9.5,3) {Community};

      % Child
      \node[gen, fill=accentred!12, text width=2.6cm, minimum height=1cm]
        (child) at (4.5,0) {\textbf{Learner}};

      % Vertical
      \draw[arr, thick] (p1.south) -- (child.north west)
        node[midway, left, lab] {vertical};
      \draw[arr, thick] (p2.south) -- (child.north)
        node[midway, right, lab] {vertical};

      % Oblique
      \draw[arr, dashed] (elder.south) -- (child.north east)
        node[midway, right, lab] {oblique};

      % Horizontal
      \draw[arr, dotted, thick] (comm.south) -- (child.east)
        node[midway, right, lab] {horizontal\\(peers)};

      % Pre/post marital annotation
      \node[font=\scriptsize\itshape, ifsapurple, align=center] at (11.5,1.5)
        {pre- \& post-\\marital pathways};
    \end{tikzpicture}
  \end{center}
  \vspace{4pt}
  \begin{itemize}
    \item<2-> Multiple pathways combine: vertical, oblique, horizontal
    \item<3-> Post-marital resocialisation adds further complexity
    \item<4-> Sex-biased transmission: probability $s$ to copy from female role model
  \end{itemize}
\end{frame}

%% ── Hitchhiking and Migration ───────────────────────────────────────────
\begin{frame}{Cultural Hitchhiking \& Migration}
  \begin{columns}[T]
    \begin{column}{0.52\textwidth}
      \textbf{Analogy with genetic hitchhiking:}
      \begin{itemize}[<+->]
        \item `Neutral traits' spreading alongside advantageous technology
        \item Dispersal of farming:\\
              demographic growth + cultural contact
        \item Marital rules ($\rho$) modulate which traits hitchhike
      \end{itemize}
      \vspace{4pt}
      \uncover<4->{%
        \begin{block}{Model ingredients}
          \small
          Demography (growth, fission)\\
          Adaptive technology (community-level)\\
          Neutral traits (individual-level, multiple pathways)
        \end{block}
      }
    \end{column}
    \begin{column}{0.45\textwidth}
      \uncover<2->{%
        \begin{center}
          \begin{tikzpicture}[scale=0.65,
            comm/.style={circle, draw=ifsapurple, minimum size=8mm,
              font=\tiny\bfseries, line width=0.6pt},
            farr/.style={-{Stealth[length=4pt]}, ifsapurple!50, line width=0.5pt}
          ]
            % Farmer communities
            \node[comm, fill=accentgold!30] (f1) at (0,0) {F};
            \node[comm, fill=accentgold!30] (f2) at (1.5,1) {F};
            % HG communities
            \node[comm, fill=purplelight] (h1) at (3,0) {HG};
            \node[comm, fill=purplelight] (h2) at (4.5,1) {HG};
            \node[comm, fill=purplelight] (h3) at (3,2.2) {HG};
            \node[comm, fill=purplelight] (h4) at (5.5,2.5) {HG};
            % Expansion arrows
            \draw[farr, thick] (f1) -- (h1);
            \draw[farr, thick] (f2) -- (h3);
            \draw[farr, dashed] (h1) -- (h2);
            \draw[farr, dashed] (h3) -- (h4);
            % Label
            \node[font=\tiny\itshape, ifsapurple] at (2.7,-0.8)
              {farming expansion \& cultural contact};
          \end{tikzpicture}
        \end{center}
      }
    \end{column}
  \end{columns}
\end{frame}


%% ═══════════════════════════════════════════════════════════════════════════
\section[Evidence]{Archaeological Evidence}
\sectiondivider{Archaeological Evidence}

%% ── What the Record Gives Us ────────────────────────────────────────────
\begin{frame}{What the Archaeological Record Gives Us}
  \begin{columns}[T]
    \begin{column}{0.50\textwidth}
      \textbf{A unique window into the past:}
      \begin{itemize}
        \item Material traces of human activity
        \item Spatial distributions of artefacts
        \item Typological and technological variation
        \item Covers millennia and all world regions
      \end{itemize}
    \end{column}
    \begin{column}{0.47\textwidth}
      \begin{alertblock}{But deeply imperfect}
        \begin{itemize}
          \item Organic materials lost
          \item Spatial sampling uneven
          \item Temporal resolution coarse
          \item Behaviour $\to$ material $\to$ preservation $\to$ observation
        \end{itemize}
      \end{alertblock}
    \end{column}
  \end{columns}
  \vspace{6pt}
  \pause
  \begin{block}{Key insight}
    Methods must be \textbf{explicitly designed} to account for these filters ---
    not applied naively from other domains
  \end{block}
\end{frame}

%% ── Taphonomic Filter Diagram ───────────────────────────────────────────
\begin{frame}{The Taphonomic Filter}
  \begin{center}
    \begin{tikzpicture}[
      box/.style={draw, rounded corners=4pt, minimum height=1.6cm,
        text width=2.6cm, align=center, font=\small},
      filt/.style={draw, rounded corners=2pt, fill=accentred!15,
        minimum height=1.6cm, text width=2.2cm, align=center,
        font=\small, thick, draw=accentred},
      arr/.style={-{Stealth[length=5pt]}, thick, ifsapurple, line width=1.2pt}
    ]
      % Original signal
      \node[box, fill=ifsapurple!15, draw=ifsapurple] (sig) at (0,0)
        {\textbf{Original}\\cultural\\signal\\[2pt]\footnotesize 100\% diversity};

      % Preservation filter
      \node[filt] (pres) at (4.2,0)
        {\textbf{Preservation}\\filter\\[2pt]\footnotesize decay, erosion,\\chemistry};

      % Sampling filter
      \node[filt] (samp) at (8.4,0)
        {\textbf{Sampling}\\filter\\[2pt]\footnotesize excavation,\\recording};

      % Observed record
      \node[box, fill=accentgold!20, draw=accentgold!80!black] (obs) at (12.6,0)
        {\textbf{Observed}\\record\\[2pt]\footnotesize 5--20\%\\preserved};

      % Arrows
      \draw[arr] (sig) -- (pres);
      \draw[arr] (pres) -- (samp);
      \draw[arr] (samp) -- (obs);

      % Loss annotations
      \draw[accentred, thick,
        decorate, decoration={snake, amplitude=2pt, segment length=6pt}]
        (4.2,-1.5) -- ++(0,-0.4);
      \node[below, font=\footnotesize, accentred] at (4.2,-1.9) {material lost};
      \draw[accentred, thick,
        decorate, decoration={snake, amplitude=2pt, segment length=6pt}]
        (8.4,-1.5) -- ++(0,-0.4);
      \node[below, font=\footnotesize, accentred] at (8.4,-1.9) {information lost};
    \end{tikzpicture}
  \end{center}
  \vspace{4pt}
  \pause
  \begin{exampleblock}{Implication}
    Naive diversity estimates from the archaeological record can be
    \textbf{systematically misleading} --- simulation studies show that
    spatial structure and mobility rates interact with taphonomic loss
  \end{exampleblock}
\end{frame}

%% ── Bronze Age Networks (BIAD) ──────────────────────────────────────────
\begin{frame}{Bronze Age Networks --- The BIAD Project}
  \begin{columns}[T]
    \begin{column}{0.50\textwidth}
      \begin{exampleblock}{Question}
        How were artefacts distributed across Europe, and what does
        network structure tell us about cultural interaction?
      \end{exampleblock}
      \vspace{4pt}
      \begin{itemize}[<+->]
        \item Similarity networks from assemblage data
        \item Community detection $\to$ regional interaction zones
        \item Structure \textbf{not visible} in raw typologies alone
      \end{itemize}
    \end{column}
    \begin{column}{0.47\textwidth}
      \uncover<2->{%
        \begin{center}
          \begin{tikzpicture}[scale=0.7,
            site/.style={circle, draw=ifsapurple, fill=ifsapurple!20,
              minimum size=6mm, font=\tiny\bfseries},
            edge/.style={thick, ifsapurple!50}
          ]
            \node[site] (A) at (0,0) {A};
            \node[site] (B) at (2,1.2) {B};
            \node[site] (C) at (4,0.2) {C};
            \node[site] (D) at (2.5,-1) {D};
            \node[site, fill=accentgold!30, draw=accentgold] (E) at (5.5,1) {E};
            \node[site] (F) at (5,-1) {F};
            \node[site, fill=accentgold!30, draw=accentgold] (G) at (7,0) {G};
            \draw[edge, line width=2pt] (A) -- (B);
            \draw[edge, line width=1.5pt] (B) -- (C);
            \draw[edge] (A) -- (D);
            \draw[edge, line width=2pt] (C) -- (D);
            \draw[edge, line width=1.5pt] (C) -- (E);
            \draw[edge] (D) -- (F);
            \draw[edge, line width=2pt] (E) -- (G);
            \draw[edge, line width=1.5pt] (F) -- (E);
            \draw[edge] (F) -- (G);
            \draw[edge] (B) -- (D);
            % Cluster outlines
            \begin{scope}[on background layer]
              \node[draw=ifsapurple!30, rounded corners=8pt, fill=ifsapurple!5,
                fit=(A)(B)(C)(D), inner sep=4pt] {};
              \node[draw=accentgold!50, rounded corners=8pt, fill=accentgold!5,
                fit=(E)(F)(G), inner sep=4pt] {};
            \end{scope}
          \end{tikzpicture}
        \end{center}
        \vspace{2pt}
        \begin{block}{\small Related projects}
          \footnotesize EPNet (Roman economy)\\
          BIAD (Bronze \& Iron Age Database)\\
          bronze-ssr (R/Shiny visualisation)
        \end{block}
      }
    \end{column}
  \end{columns}
\end{frame}

%% ── Merzbach Valley Case Study ──────────────────────────────────────────
\begin{frame}{Merzbach Valley --- Decorative Motifs}
  \begin{columns}[t]
    \column{.50\textwidth}
    Conformity vs.\ utility-based biases:
    \begin{itemize}[<+->]
      \item LBK pottery decorations in the Merzbach Valley
      \item 8 phases, 36 styles, $\sim$200 years
      \item Can the 4-box model capture the observed patterns?
    \end{itemize}
    \uncover<4->{%
      \vspace{4pt}
      \begin{align*}
        \Pr(i,t{+}1) = \frac{1}{Y_t}\, p_i(t)^{J}\, e^{\beta\, U_i + \psi}
      \end{align*}
      \textit{Where in $(J,\beta)$ space does Merzbach fall?}
    }
    \column{.50\textwidth}
    \uncover<2->{%
      \begin{center}
        \begin{tikzpicture}[scale=0.6]
          % Simplified heatmap-like illustration
          \draw[ifsapurple, thick] (0,0) rectangle (5,4);
          \foreach \y/\lab in {0.5/Phase 1, 1/Phase 2, 1.5/Phase 3,
            2/Phase 4, 2.5/Phase 5, 3/Phase 6, 3.5/Phase 7} {
            \node[font=\tiny, left] at (0,\y) {\lab};
          }
          % Bars representing style frequencies
          \foreach \y/\w in {0.5/3.5, 1/3, 1.5/2.8, 2/2.2, 2.5/1.8, 3/1.5, 3.5/1.2} {
            \fill[ifsapurple!40] (0.1,\y-0.15) rectangle (\w,\y+0.15);
          }
          \foreach \y/\w/\s in {0.5/0.5/0.8, 1/0.8/1.5, 1.5/1.2/2,
            2/1.8/2.8, 2.5/2.2/3, 3/2.5/3.5, 3.5/2.8/4} {
            \fill[accentgold!50] (\w+0.2,\y-0.15) rectangle (\s,\y+0.15);
          }
          \node[font=\scriptsize, ifsapurple] at (2.5,-0.5)
            {style frequency by phase};
        \end{tikzpicture}
      \end{center}
    }
  \end{columns}
\end{frame}


%% ═══════════════════════════════════════════════════════════════════════════
\section[ML]{ML on Archaeological Data}
\sectiondivider{ML on Archaeological Data}

%% ── Autoencoder on Faunal Data ──────────────────────────────────────────
\begin{frame}{Autoencoder on Zooarchaeological Data}
  \begin{columns}[T]
    \begin{column}{0.52\textwidth}
      \textbf{New work (COREX):}
      \begin{itemize}[<+->]
        \item Faunal assemblage data: taxon presence/absence
              or frequency matrices across sites
        \item Apply an \textbf{autoencoder} to learn latent dimensions
        \item Compressed representation reveals
              \textbf{cultural and environmental signatures}
        \item Downstream use: summary statistics for ABC,
              input features for ABM calibration
      \end{itemize}
    \end{column}
    \begin{column}{0.46\textwidth}
      \uncover<2->{%
        \begin{block}{Why autoencoders?}
          \small
          Non-linear dimensionality reduction\\[3pt]
          Learn structure without supervision\\[3pt]
          Latent space amenable to\\
          statistical comparison with\\
          simulated outputs
        \end{block}
      }
    \end{column}
  \end{columns}
\end{frame}

%% ── Autoencoder Architecture Diagram ────────────────────────────────────
\begin{frame}{Autoencoder Architecture}
  \begin{center}
    \begin{tikzpicture}[
      neuron/.style={circle, draw=ifsapurple, minimum size=5mm,
        line width=0.6pt, inner sep=0pt},
      input/.style={neuron, fill=ifsapurple!15},
      hidden/.style={neuron, fill=purplemid!30},
      latent/.style={neuron, fill=accentgold!40, minimum size=7mm,
        line width=1pt, draw=accentgold!80!black},
      output/.style={neuron, fill=ifsapurple!15},
      conn/.style={ifsapurple!30, line width=0.4pt},
      brace/.style={decorate, decoration={brace, amplitude=5pt}, ifsapurple}
    ]
      % Input layer (taxa)
      \foreach \i in {1,...,6} {
        \node[input] (i\i) at (0, 4.2-0.7*\i) {};
      }
      \node[font=\tiny, ifsapurple] at (0, 4.6) {\textbf{Input}};
      \node[font=\tiny, midgray] at (0, 0.3) {$n$ taxa};

      % Encoder hidden
      \foreach \i in {1,...,4} {
        \node[hidden] (e\i) at (2.5, 3.5-0.8*\i) {};
      }
      \node[font=\tiny, ifsapurple] at (2.5, 4.6) {\textbf{Encoder}};

      % Latent
      \foreach \i in {1,...,2} {
        \node[latent] (z\i) at (5, 2.45-0.9*\i) {};
      }
      \node[font=\scriptsize, accentgold!80!black, above] at (5, 2.2)
        {\textbf{Latent $\mathbf{z}$}};

      % Decoder hidden
      \foreach \i in {1,...,4} {
        \node[hidden] (d\i) at (7.5, 3.5-0.8*\i) {};
      }
      \node[font=\tiny, ifsapurple] at (7.5, 4.6) {\textbf{Decoder}};

      % Output layer (reconstruction)
      \foreach \i in {1,...,6} {
        \node[output] (o\i) at (10, 4.2-0.7*\i) {};
      }
      \node[font=\tiny, ifsapurple] at (10, 4.6) {\textbf{Output}};
      \node[font=\tiny, midgray] at (10, 0.3) {$\hat{x} \approx x$};

      % Connections: input -> encoder
      \foreach \i in {1,...,6} {
        \foreach \j in {1,...,4} {
          \draw[conn] (i\i) -- (e\j);
        }
      }
      % encoder -> latent
      \foreach \i in {1,...,4} {
        \foreach \j in {1,...,2} {
          \draw[conn] (e\i) -- (z\j);
        }
      }
      % latent -> decoder
      \foreach \i in {1,...,2} {
        \foreach \j in {1,...,4} {
          \draw[conn] (z\i) -- (d\j);
        }
      }
      % decoder -> output
      \foreach \i in {1,...,4} {
        \foreach \j in {1,...,6} {
          \draw[conn] (d\i) -- (o\j);
        }
      }

      % Braces
      \draw[brace] (-0.5,0.7) -- (-0.5,4) node[midway, left, font=\tiny,
        xshift=-6pt, align=right] {taxa freq.\\per site};
      \draw[brace] (10.5,4) -- (10.5,0.7) node[midway, right, font=\tiny,
        xshift=6pt, align=left] {reconstructed\\frequencies};
    \end{tikzpicture}
  \end{center}
  \vspace{2pt}
  \begin{columns}[t]
    \column{.50\textwidth}
    \footnotesize
    \textbf{Input:} taxon frequency matrix ($n_{\text{sites}} \times n_{\text{taxa}}$)
    \column{.50\textwidth}
    \footnotesize
    \textbf{Latent $z$:} compressed representation usable as summary statistics
  \end{columns}
\end{frame}

%% ── Latent Space Exploration ────────────────────────────────────────────
\begin{frame}{Latent Space --- What It Reveals}
  \begin{columns}[T]
    \begin{column}{0.50\textwidth}
      \textbf{Latent dimensions capture:}
      \begin{itemize}[<+->]
        \item Environmental gradients\\(climate, biome)
        \item Cultural signatures\\(subsistence strategies)
        \item Temporal trends\\(shifts in animal exploitation)
      \end{itemize}
      \vspace{6pt}
      \uncover<4->{%
        \begin{block}{Advantage over PCA}
          \small Non-linear: captures interactions
          between taxa that linear methods miss
        \end{block}
      }
    \end{column}
    \begin{column}{0.47\textwidth}
      \uncover<2->{%
        \begin{center}
          \begin{tikzpicture}[scale=0.75]
            % Axes
            \draw[-{Stealth[length=4pt]}, ifsapurple]
              (-0.3,0) -- (5.5,0) node[right, font=\scriptsize] {$z_1$};
            \draw[-{Stealth[length=4pt]}, ifsapurple]
              (0,-0.3) -- (0,4.5) node[above, font=\scriptsize] {$z_2$};

            % Cluster 1: pastoralist
            \fill[ifsapurple!15, rounded corners=6pt]
              (0.3,2.5) rectangle (2.2,4.2);
            \node[font=\tiny, ifsapurple] at (1.25,4.5) {pastoralist};
            \foreach \x/\y in {0.6/3, 0.9/3.5, 1.3/2.8, 1.5/3.7, 1.8/3.2} {
              \fill[ifsapurple] (\x,\y) circle (2pt);
            }

            % Cluster 2: mixed farming
            \fill[accentgold!15, rounded corners=6pt]
              (2.5,0.5) rectangle (4.5,2.5);
            \node[font=\tiny, accentgold!80!black] at (3.5,2.8) {mixed farming};
            \foreach \x/\y in {2.8/1, 3.2/1.5, 3.5/0.8, 3.8/1.8, 4.1/1.2} {
              \fill[accentgold!80!black] (\x,\y) circle (2pt);
            }

            % Cluster 3: hunter-gatherer
            \fill[accentred!10, rounded corners=6pt]
              (3.5,3) rectangle (5.2,4.3);
            \node[font=\tiny, accentred] at (4.35,4.5) {hunter-gatherer};
            \foreach \x/\y in {3.8/3.3, 4.2/3.8, 4.5/3.5, 4.8/3.9} {
              \fill[accentred] (\x,\y) circle (2pt);
            }
          \end{tikzpicture}
        \end{center}
        \vspace{2pt}
        \footnotesize\itshape Schematic: sites in learned latent space,
        coloured by subsistence strategy
      }
    \end{column}
  \end{columns}
\end{frame}


%% ═══════════════════════════════════════════════════════════════════════════
\section[ABC]{Approximate Bayesian Computation}
\sectiondivider{Approximate Bayesian Computation}

%% ── ABC Overview ────────────────────────────────────────────────────────
\begin{frame}{Approximate Bayesian Computation}
  \textbf{Linking models \& patterns:}
  \begin{itemize}[<+->]
    \item Goal: estimate $P(\theta \mid \text{data})$ --- the posterior
          distribution of model parameters given observed evidence
    \item Likelihood intractable for complex ABMs
    \item ABC: simulate from prior, compare summary statistics,
          accept parameters that produce ``close enough'' output
    \item Computationally costly but \textbf{flexible}
  \end{itemize}
\end{frame}

%% ── ABC Pipeline Diagram ────────────────────────────────────────────────
\begin{frame}{The ABC Pipeline}
  \begin{center}
    \begin{tikzpicture}[
      box/.style={draw=ifsapurple, rounded corners=4pt, minimum height=1.3cm,
        text width=2.4cm, align=center, font=\small, line width=0.7pt},
      arr/.style={-{Stealth[length=5pt]}, thick, ifsapurple, line width=1.2pt},
      decision/.style={draw=accentred, diamond, aspect=1.8, inner sep=1pt,
        font=\scriptsize, fill=accentred!10, line width=0.7pt, align=center}
    ]
      % Empirical data
      \node[box, fill=ifsapurple!15] (data) at (0,0)
        {\textbf{Empirical}\\data\\[2pt]\footnotesize assemblages};

      % Summary stats (observed)
      \node[box, fill=purplelight] (sobs) at (0,-2.8)
        {\textbf{Summary}\\statistics\\[2pt]\footnotesize $S_{\text{obs}}$};

      % Prior
      \node[box, fill=accentgold!20] (prior) at (5,0)
        {\textbf{Prior}\\$\pi(\theta)$\\[2pt]\footnotesize parameter space};

      % Simulation
      \node[box, fill=accentgold!30] (sim) at (5,-2.8)
        {\textbf{Simulate}\\ABM\\[2pt]\footnotesize $S_{\text{sim}}$};

      % Distance
      \node[decision] (dist) at (9,-1.4)
        {$d(S_{\text{obs}}, S_{\text{sim}})$\\$< \epsilon$ ?};

      % Posterior
      \node[box, fill=softgreen!20, draw=softgreen!80!black] (post) at (12.5,-1.4)
        {\textbf{Posterior}\\$P(\theta|\text{data})$};

      % Arrows
      \draw[arr] (data) -- (sobs);
      \draw[arr] (prior) -- (sim);
      \draw[arr] (sobs.east) -- ++(1,0) |- (dist.west);
      \draw[arr] (sim.east) -- ++(0.5,0) |- (dist.west);
      \draw[arr] (dist) -- (post) node[midway, above, font=\tiny] {accept};

      % Rejection loop
      \draw[arr, dashed, midgray] (dist.north) -- ++(0,1)
        -| (prior.north) node[pos=0.3, above, font=\tiny\itshape] {reject: resample};

      % Latent space annotation
      \node[font=\tiny\itshape, ifsapurple, below] at (0,-3.8)
        {or: autoencoder latent $z$};
    \end{tikzpicture}
  \end{center}
\end{frame}

%% ── ABC in Practice ─────────────────────────────────────────────────────
\begin{frame}{ABC in Practice --- Summary Statistics Matter}
  \begin{columns}[T]
    \begin{column}{0.50\textwidth}
      \textbf{Summary statistics for ABC:}
      \begin{enumerate}[<+->]
        \item Number of unique variants per phase
        \item Simpson's diversity index
        \item Disparity (most vs.\ least popular)
        \item Gini coefficient
        \item Turnover rate
        \item Log-normal fit parameters ($\mu$, $\sigma$)
      \end{enumerate}
    \end{column}
    \begin{column}{0.47\textwidth}
      \uncover<3->{%
        \begin{block}{Random Forest Adjustment}
          \small
          Use Random Forest to combine\\
          all summary dimensions\\[3pt]
          $\to$ No need to select metrics\\
          $\to$ Rank/compare metrics\\
          $\to$ Better posterior estimates
        \end{block}
        \vspace{4pt}
        \begin{alertblock}{Key challenge}
          \small Simulated data must be \textbf{transformed}
          to match taphonomic filters before comparison
        \end{alertblock}
      }
    \end{column}
  \end{columns}
\end{frame}

%% ── Tactical Simulation ─────────────────────────────────────────────────
\begin{frame}{Tactical Simulation --- Validating the Pipeline}
  \begin{columns}[T]
    \begin{column}{0.50\textwidth}
      \textbf{Can we recover known parameters?}
      \begin{itemize}[<+->]
        \item Generate artificial data with known $(J, \beta)$
        \item Apply taphonomic transformation
        \item Run ABC pipeline
        \item Check: does the posterior recover the truth?
      \end{itemize}
      \vspace{4pt}
      \uncover<5->{%
        \textbf{Result:} Yes --- under realistic conditions,
        ABC with RF adjustment recovers planted parameters
      }
    \end{column}
    \begin{column}{0.47\textwidth}
      \uncover<3->{%
        \begin{center}
          \begin{tikzpicture}[scale=0.7]
            % Posterior density sketch
            \draw[-{Stealth[length=4pt]}, ifsapurple]
              (-0.3,0) -- (5.5,0) node[right, font=\scriptsize] {$J$};
            \draw[-{Stealth[length=4pt]}, ifsapurple]
              (0,-0.3) -- (0,3.5) node[above, font=\scriptsize] {density};

            % Prior (flat)
            \draw[midgray, dashed, line width=0.8pt] (0.2,0.5) -- (5,0.5)
              node[right, font=\tiny] {prior};

            % Posterior (peaked)
            \draw[ifsapurple, thick, line width=1.2pt]
              plot[smooth, tension=0.7] coordinates
              {(0.2,0.1) (1,0.3) (1.8,1.2) (2.5,2.8) (3.2,1.5) (4,0.4) (5,0.1)};
            \node[font=\tiny, ifsapurple] at (4.2,2) {posterior};

            % True value
            \draw[accentred, thick, dashed] (2.5,0) -- (2.5,3)
              node[above, font=\tiny, accentred] {true $J$};
          \end{tikzpicture}
        \end{center}
        \vspace{2pt}
        \footnotesize\itshape Schematic: posterior distribution
        concentrates around the true parameter value
      }
    \end{column}
  \end{columns}
\end{frame}

%% ── Connecting Autoencoder + ABC ────────────────────────────────────────
\begin{frame}{Connecting ML and ABC}
  \begin{center}
    \begin{tikzpicture}[
      box/.style={draw=ifsapurple, rounded corners=5pt, minimum height=1.4cm,
        text width=2.8cm, align=center, font=\small, line width=0.8pt},
      arr/.style={-{Stealth[length=5pt]}, thick, ifsapurple, line width=1.3pt}
    ]
      % Data
      \node[box, fill=ifsapurple!15] (data) at (0,0)
        {\textbf{Faunal}\\
         \textbf{assemblages}\\[3pt]
         \footnotesize taxa $\times$ sites};

      % Autoencoder
      \node[box, fill=purplelight] (ae) at (4.5,0)
        {\textbf{Autoencoder}\\[3pt]
         \footnotesize latent $z$ =\\
         summary stats};

      % ABM
      \node[box, fill=accentgold!25, draw=accentgold!80!black] (abm) at (9,0)
        {\textbf{ABM}\\
         \textbf{Simulation}\\[3pt]
         \footnotesize cultural\\
         transmission};

      % ABC
      \node[box, fill=softgreen!15, draw=softgreen!70!black] (abc) at (13,0)
        {\textbf{ABC}\\
         \textbf{Inference}\\[3pt]
         \footnotesize posterior on\\
         $\theta$};

      % Arrows
      \draw[arr] (data) -- (ae);
      \draw[arr] (ae) -- (abm);
      \draw[arr] (abm) -- (abc);

      % Feedback
      \draw[arr, dashed, midgray] (abc.south)
        .. controls +(0,-1.5) and +(0,-1.5) .. (abm.south)
        node[midway, below, font=\footnotesize\itshape] {refine};
    \end{tikzpicture}
  \end{center}
  \vspace{6pt}
  \pause
  \begin{block}{The full pipeline}
    Real data $\xrightarrow{\text{autoencoder}}$ latent summary $\xrightarrow{\text{ABC}}$
    posterior on cultural transmission parameters\\[3pt]
    The autoencoder replaces hand-crafted summary statistics
    with \textbf{learned} representations
  \end{block}
\end{frame}


%% ═══════════════════════════════════════════════════════════════════════════
\section{Conclusion}
\sectiondivider{Conclusion}

%% ── Summary ─────────────────────────────────────────────────────────────
\begin{frame}{What We Learned}
  \begin{enumerate}
    \item Cultural evolution at the \textbf{mesoscale} is accessible
          via archaeological evidence + computational methods
    \vspace{5pt}
    \pause
    \item \textbf{Agent-based models} of cultural transmission
          generate testable predictions about drift, selection,
          hitchhiking, and network effects
    \vspace{5pt}
    \pause
    \item \textbf{Machine learning} (autoencoders on faunal data)
          provides summary statistics that capture
          non-linear structure in assemblages
    \vspace{5pt}
    \pause
    \item \textbf{ABC} closes the loop: coupling empirical patterns
          with generative models to estimate transmission parameters
    \vspace{5pt}
    \pause
    \item Taphonomic awareness is \textbf{essential} ---
          methods must account for what the record hides
  \end{enumerate}
\end{frame}

%% ── Open Questions ──────────────────────────────────────────────────────
\begin{frame}{Open Questions}
  \begin{columns}[T]
    \begin{column}{0.48\textwidth}
      \begin{alertblock}{Validation}
        How do we validate models when\\
        \textbf{ground truth} is unavailable?\\[3pt]
        \footnotesize Tactical simulation, posterior\\
        predictive checks, cross-validation
      \end{alertblock}
      \vspace{4pt}
      \pause
      \begin{alertblock}{Data integration}
        Combining \textbf{heterogeneous} sources:\\
        faunal, isotope, aDNA,\\
        material culture, ${}^{14}$C
      \end{alertblock}
    \end{column}
    \begin{column}{0.48\textwidth}
      \begin{alertblock}{Interpretability}
        ML-extracted patterns must be\\
        \textbf{culturally meaningful},\\
        not just statistically significant
      \end{alertblock}
      \vspace{4pt}
      \pause
      \begin{alertblock}{Scalability}
        Extending the pipeline to\\
        \textbf{larger regions} and\\
        \textbf{longer time spans}\\
        within COREX
      \end{alertblock}
    \end{column}
  \end{columns}
\end{frame}

%% ── Connection to CCS ──────────────────────────────────────────────────
\begin{frame}{Connections to Computational Cultural Science}
  \begin{block}{The pipeline generalises}
    \textbf{Patterns} $\xrightarrow{\text{extraction}}$
    \textbf{Mechanisms} $\xrightarrow{\text{simulation}}$
    \textbf{Predictions}
  \end{block}
  \vspace{6pt}
  \begin{columns}[T]
    \begin{column}{0.30\textwidth}
      \centering
      \textbf{Any cultural data}\\[4pt]
      \footnotesize
      artefacts · texts\\
      images · networks\\
      digital traces
    \end{column}
    \begin{column}{0.30\textwidth}
      \centering
      \textbf{Generative models}\\[4pt]
      \footnotesize
      ABM · evolutionary\\
      dynamics · diffusion\\
      models
    \end{column}
    \begin{column}{0.30\textwidth}
      \centering
      \textbf{Testable hypotheses}\\[4pt]
      \footnotesize
      transmission rates\\
      drift vs.\ selection\\
      network effects
    \end{column}
  \end{columns}
  \vspace{10pt}
  \pause
  \begin{exampleblock}{If it works on archaeology\ldots}
    \small
    If methods work on the \textbf{hardest} data type
    (fragmented, biased, indirect), they should
    generalise to richer data --- texts, media, digital culture
  \end{exampleblock}
\end{frame}

%% ── Thank You ───────────────────────────────────────────────────────────
\begingroup
\setbeamertemplate{footline}{}
\setbeamercolor{background canvas}{bg=ifsapurple,fg=white}
\frame[plain,noframenumbering]{%
  \centering
  \textcolor{white}{%
    \vspace{1cm}
    {\Huge\bfseries Thanks!}\\[16pt]
    {\large
      COREX team \& UCL GEE\\[4pt]
      ENCOUNTER team \& McDonald Institute, Cambridge\\[4pt]
      DySoC \& UTK\\[12pt]
    }
    {\normalsize
      \href{mailto:s.carrignon@ucl.ac.uk}{s.carrignon@ucl.ac.uk}\\[6pt]
      \href{https://github.com/simoncarrignon}{github.com/simoncarrignon}\\[12pt]
    }
    {\small\itshape
      C2S --- Computational Cultural Science Workshop\\
      École nationale des Chartes -- PSL · Paris · May 2026
    }
    \vspace{1cm}
  }
}
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\appendix

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\begin{frame}{References}
  \small
  \begin{itemize}
    \item Vidiella, B.\ et al.\ (2022). A cultural evolutionary theory model\ldots
          \textit{Humanities \& Social Sciences Comms.}
    \item Carrignon, S.\ et al.\ (2020). Tableware trade in the Roman East.
          \textit{JASSS} 23(1):3.
    \item Crema, E.R.\ et al.\ (2022). \textit{Rice paddy expansion\ldots}
    \item Epstein, J.M.\ (2008). Why Model? \textit{JASSS} 11(4):12.
    \item Mesoudi, A.\ (2011). \textit{Cultural Evolution.} U.\ Chicago Press.
    \item Bentley, R.A.\ et al.\ (2004). Random drift and culture change.
          \textit{Proc.\ R.\ Soc.\ B} 271:1443--1450.
    \item Deffner, D.\ et al.\ (2024). \textit{Bridging theory and evidence\ldots}
  \end{itemize}
\end{frame}

\end{document}