diff --git a/src/named_tuple_shape.jl b/src/named_tuple_shape.jl
index 701ab3e5..072d8d94 100644
--- a/src/named_tuple_shape.jl
+++ b/src/named_tuple_shape.jl
@@ -752,6 +752,20 @@ end
 const _AnySNTArray{names} = ShapedAsNTArray{<:Union{NamedTuple{names},ShapedAsNT{names}}}
 
 
+# For accumulation during automatic differentiation:
+function Base.:(+)(A::_AnySNTArray{names}, B::_AnySNTArray{names}) where names
+    @argcheck elshape(A) == elshape(B)
+    ShapedAsNTArray(_data(A) + _data(B), elshape(A))
+end
+
+# For accumulation during automatic differentiation:
+function ChainRulesCore.add!!(A::_AnySNTArray{names}, B::_AnySNTArray{names}) where names
+    @argcheck elshape(A) == elshape(B)
+    ChainRulesCore.add!!(_data(A), _data(B))
+    return A
+end
+
+
 function ChainRulesCore.Tangent(X::T, unshaped_dX::AbstractArray{<:AbstractVector{<:Real}}) where {T<:ShapedAsNTArray}
     vs = elshape(X)
     gs = gradient_shape(vs)
@@ -789,6 +803,11 @@ function _write_snta_col!(data::AbstractArray{<:AbstractVector{<:Real}}, va::Val
     B = view.(data, Ref(va))
     B .= A
 end
+function _write_snta_col!(data::ArrayOfSimilarVectors{<:Real}, va::ValueAccessor, A::_ZeroLike)
+    flat_data = flatview(data)
+    idxs = view_idxs(axes(flat_data, 1), va)
+    fill!(view(flat_data, idxs, :), zero(eltype(flat_data)))
+end
 _write_snta_col!(data::AbstractArray{<:AbstractVector{<:Real}}, va::ConstAccessor, A) = nothing
 
 function _tablecols_tangent(X::_AnySNTArray, dY::NamedTuple{names}) where names