diff --git a/doc/src/learn.md b/doc/src/learn.md
index 8628cb59b7367280d965c1bbe3fb86ae1d1a104f..9a3a7b67995016fde0bae5663839ec3dfbd2bcf3 100644
--- a/doc/src/learn.md
+++ b/doc/src/learn.md
@@ -6,6 +6,46 @@ space is explored to maximize aphid likelihood.
 
 ## Heuristic starting point { #init }
 
+If not every [initial parameter](./use.md#init)
+has been specified by user,
+aphid uses the following procedure to automatically choose initial parameters.
+
+*(this reuses notations from the [likelihood formula](./likelihood.md))*
+
+First, calculate the mean branches lengths among the selected trees:
+\\[
+  <!-- cmdrun cat ./preamble.mathjax-->
+  \begin{align}
+    m_a &= \frac{1}{G}\sum_g{a_g}\qquad\qquad
+    m_b  = \frac{1}{G}\sum_g{b_g}\\\\
+    m_c &= \frac{1}{G}\sum_g{c_g}\qquad\qquad
+    m_d  = \frac{1}{G}\sum_g{d_g}
+  \end{align}
+\\]
+
+Then, calculate the frequency of discordant topologies among the selected trees:
+\\[
+  \begin{align}
+    f_{ac} &= \frac{1}{G}\sum_g{𝟙(T_g = \ACB)}\\\\
+    f_{bc} &= \frac{1}{G}\sum_g{𝟙(T_g = \BCA)}
+  \end{align}
+\\]
+
+Then use these as default starting points:
+
+\\[
+  \begin{align}
+   \tau_1 &=          \theta \times \frac{m_a + m_b}{4} \\\\
+   \tau_2 &= \tau_1 + \theta \times \frac{m_c + m_d}{4} \\\\
+   \pils  &= e^{2\frac{\tau_1 - \tau_2}{\theta}} \\\\
+   \pac   &= f_{ac} - \pils / 3 \\\\
+   \pbc   &= f_{bc} - \pils / 3 \\\\
+   \pab   &= 1 - \pac - \pbc \\\\
+   \po    &= 1 / |gt|
+  \end{align}
+\\]
+
+
 ## Reparametrization { #transform }
 
 Exploring a constrained space is more difficult
@@ -71,3 +111,7 @@ then here is the reparametrization formula:
 Instead of the constrained \\(𝜃\\), \\(𝜏_1\\), \\(𝜏_2\\) *etc.*,
 the concrete optimisation targets for aphid are
 the unconstrained \\(s_𝜃\\), \\(s_{𝜏_1}\\), \\(s_{𝛥𝜏}\\) *etc.*
+
+## Maximizing likelihood
+
+<!-- HERE: into BFGS + Wolfe -->
diff --git a/doc/src/use.md b/doc/src/use.md
index 7125d5cc4a66622404975670dac3f3d1d60c0479..0809ae8a8e0ea99c23f03cd7c6abd108c6b9cfe4 100644
--- a/doc/src/use.md
+++ b/doc/src/use.md
@@ -88,7 +88,7 @@ TODO: clarify
 
 (see the [geometry filter](preprocess.md#geometry))
 
-### The `[init]` table
+### The `[init]` table { #init }
 
 This additional table can be set to specify
 starting point(s) for likelihood exploration.