Algorithm 1.

Construction of PhyNN

Input: Phylogenetic tree T

Bandwidth b

Hyperparameter H for MLP

Divide T into K = ⌈h/b⌉ bands B1, . . ., BK

for k = K to 2 do

for j = 1 to |Bk| do

if A(Nkj) is not NULL then

S(A(Nkj)) ← S(A(Nkj)) ∪ {Nkj}

else

Insert a new (pseudo) node $N_{k-1,\left|B_{k-1}\right|+1}$ to Bk−1 $S\left(N_{k-1,\left|B_{k-1}\right|+1}\right)\leftarrow \left\{N_{kj}\right\}$

end if

end for

for j = 1 to |Bk−1| do

vkj ← NULL vector

for N in S(Nk−1,j) do

if V(N) is not NULL then

vkj ← [vkj, V(N)] (append V(N) to vkj)

end if

end for

if vkj is not NULL vector then

$V\left(N_{k-1,j}\right)\leftarrow f_{kj}^{(H)}\left(v_{kj}\right)$

end if

end for

end for

v11 ← NULL vector

for N in B1 do

if V(N) is not NULL then

v11 ← [v11, V(N)] (append V(N) to v11)

end if

end for

$z\leftarrow f_{11}^{(H)}\left(v_{11}\right)$

Output: The PhyNN model f that accepts the abundances on all leaf nodes as input and yields z as output