papers/zoo-species-classification/sections/06-hierarchical-meta-learning.tex

\section{Hierarchical Meta-Learning}

\label{sec:metalearning}
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\subsection{Episode Construction}

Standard meta-learning samples episodes uniformly. We introduce
\textbf{taxonomic episode sampling} that ensures episodes contain
discriminative challenges at each rank.

For each training episode, we:
\begin{enumerate}
  \item Sample a focal family $f$ with probability proportional to its
    species richness.
  \item From $f$, sample 2--4 genera.
  \item From each genus, sample 2--5 species.
  \item Include 1--2 ``distractor'' species from the same order but
    different family.
\end{enumerate}

This ensures the model must discriminate at multiple taxonomic levels
within each episode, unlike uniform sampling which often produces
episodes of distantly related, trivially distinguishable species.

\subsection{Multi-Rank Loss}

The training loss combines classification losses at each rank:
\begin{equation}
  \Loss_{\text{meta}} = \Loss_{\text{CE}}^{(r_S)} + \gamma_G
  \Loss_{\text{CE}}^{(r_G)} + \gamma_F \Loss_{\text{CE}}^{(r_F)}
  + \lambda \Loss_{\text{triplet}}
\end{equation}
where $\Loss_{\text{CE}}^{(r)}$ is the cross-entropy loss for
classification at rank $r$, $\Loss_{\text{triplet}}$ is a taxonomic
triplet loss that pushes apart embeddings of different genera while
pulling together congeneric species, and $\gamma_G = 0.3$, $\gamma_F =
0.1$, $\lambda = 0.2$ are weighting coefficients.

\subsection{Taxonomic Triplet Loss}

We define:
\begin{equation}
  \Loss_{\text{triplet}} = \sum_{(a, p, n)} \max(0,
  \|\phi(x_a) - \phi(x_p)\| - \|\phi(x_a) - \phi(x_n)\| + m(a, n))
\end{equation}
where $(a, p, n)$ is an anchor-positive-negative triplet, and the margin
$m(a, n)$ scales with taxonomic distance:
\begin{equation}
  m(a, n) = m_0 \cdot (1 - \text{sim}_{\text{tax}}(a, n))
\end{equation}
Here $\text{sim}_{\text{tax}}(a, n) \in [0, 1]$ is the fraction of
shared taxonomic ranks, and $m_0 = 0.5$ is the base margin.

\subsection{Training Protocol}

\begin{itemize}
  \item \textbf{Meta-training set}: 8{,}000 species (disjoint from
    evaluation species).
  \item \textbf{Meta-validation set}: 1{,}000 species.
  \item \textbf{Episodes per epoch}: 10{,}000.
  \item \textbf{Optimizer}: AdamW, learning rate $5 \times 10^{-5}$,
    cosine schedule over 100 epochs.
  \item \textbf{Episode configuration}: 10-way $K$-shot, $K \in
    \{1, 5\}$, with 15 queries per class.
\end{itemize}


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