diff --git a/Cargo.lock b/Cargo.lock
index 1e333c7..c30cc64 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -55,7 +55,6 @@ dependencies = [
 name = "little_learner_app"
 version = "0.1.0"
 dependencies = [
- "arrayvec",
  "immutable-chunkmap",
  "little_learner",
  "ordered-float",
diff --git a/little_learner/src/auto_diff.rs b/little_learner/src/auto_diff.rs
index 0b50b4e..97d59b5 100644
--- a/little_learner/src/auto_diff.rs
+++ b/little_learner/src/auto_diff.rs
@@ -7,12 +7,12 @@ use std::{
     ops::{AddAssign, Div, Mul, Neg},
 };
 
-impl<A> Zero for DifferentiableHidden<A>
+impl<A> Zero for Differentiable<A>
 where
     A: Zero,
 {
-    fn zero() -> DifferentiableHidden<A> {
-        DifferentiableHidden::Scalar(Scalar::Number(A::zero(), None))
+    fn zero() -> Differentiable<A> {
+        Differentiable::Scalar(Scalar::Number(A::zero(), None))
     }
 }
 
@@ -25,16 +25,16 @@ where
     }
 }
 
-impl<A> One for DifferentiableHidden<A>
+impl<A> One for Differentiable<A>
 where
     A: One,
 {
-    fn one() -> DifferentiableHidden<A> {
-        DifferentiableHidden::Scalar(Scalar::one())
+    fn one() -> Differentiable<A> {
+        Differentiable::Scalar(Scalar::one())
     }
 }
 
-impl<A> Clone for DifferentiableHidden<A>
+impl<A> Clone for Differentiable<A>
 where
     A: Clone,
 {
@@ -47,19 +47,19 @@ where
 }
 
 #[derive(Debug)]
-enum DifferentiableHidden<A> {
+pub enum Differentiable<A> {
     Scalar(Scalar<A>),
-    Vector(Vec<DifferentiableHidden<A>>),
+    Vector(Vec<Differentiable<A>>),
 }
 
-impl<A> Display for DifferentiableHidden<A>
+impl<A> Display for Differentiable<A>
 where
     A: Display,
 {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
         match self {
-            DifferentiableHidden::Scalar(s) => f.write_fmt(format_args!("{}", s)),
-            DifferentiableHidden::Vector(v) => {
+            Differentiable::Scalar(s) => f.write_fmt(format_args!("{}", s)),
+            Differentiable::Vector(v) => {
                 f.write_char('[')?;
                 for v in v.iter() {
                     f.write_fmt(format_args!("{}", v))?;
@@ -71,32 +71,32 @@ where
     }
 }
 
-impl<A> DifferentiableHidden<A> {
-    fn map<B, F>(&self, f: &mut F) -> DifferentiableHidden<B>
+impl<A> Differentiable<A> {
+    pub fn map<B, F>(&self, f: &mut F) -> Differentiable<B>
     where
         F: FnMut(Scalar<A>) -> Scalar<B>,
         A: Clone,
     {
         match self {
-            DifferentiableHidden::Scalar(a) => DifferentiableHidden::Scalar(f(a.clone())),
-            DifferentiableHidden::Vector(slice) => {
-                DifferentiableHidden::Vector(slice.iter().map(|x| x.map(f)).collect())
+            Differentiable::Scalar(a) => Differentiable::Scalar(f(a.clone())),
+            Differentiable::Vector(slice) => {
+                Differentiable::Vector(slice.iter().map(|x| x.map(f)).collect())
             }
         }
     }
 
-    fn map2<B, C, F>(&self, other: &DifferentiableHidden<B>, f: &F) -> DifferentiableHidden<C>
+    pub fn map2<B, C, F>(&self, other: &Differentiable<B>, f: &F) -> Differentiable<C>
     where
         F: Fn(&Scalar<A>, &Scalar<B>) -> Scalar<C>,
         A: Clone,
         B: Clone,
     {
         match (self, other) {
-            (DifferentiableHidden::Scalar(a), DifferentiableHidden::Scalar(b)) => {
-                DifferentiableHidden::Scalar(f(a, b))
+            (Differentiable::Scalar(a), Differentiable::Scalar(b)) => {
+                Differentiable::Scalar(f(a, b))
             }
-            (DifferentiableHidden::Vector(slice_a), DifferentiableHidden::Vector(slice_b)) => {
-                DifferentiableHidden::Vector(
+            (Differentiable::Vector(slice_a), Differentiable::Vector(slice_b)) => {
+                Differentiable::Vector(
                     slice_a
                         .iter()
                         .zip(slice_b.iter())
@@ -108,20 +108,69 @@ impl<A> DifferentiableHidden<A> {
         }
     }
 
-    fn of_slice(input: &[A]) -> DifferentiableHidden<A>
+    fn of_slice<T>(input: T) -> Differentiable<A>
     where
         A: Clone,
+        T: AsRef<[A]>,
     {
-        DifferentiableHidden::Vector(
+        Differentiable::Vector(
             input
+                .as_ref()
                 .iter()
-                .map(|v| DifferentiableHidden::Scalar(Scalar::Number((*v).clone(), None)))
+                .map(|v| Differentiable::Scalar(Scalar::Number((*v).clone(), None)))
                 .collect(),
         )
     }
+
+    pub fn rank(&self) -> usize {
+        match self {
+            Differentiable::Scalar(_) => 0,
+            Differentiable::Vector(v) => v[0].rank() + 1,
+        }
+    }
+
+    pub fn attach_rank<const RANK: usize>(
+        self: Differentiable<A>,
+    ) -> Option<RankedDifferentiable<A, RANK>> {
+        if self.rank() == RANK {
+            Some(RankedDifferentiable { contents: self })
+        } else {
+            None
+        }
+    }
 }
 
-impl<A> DifferentiableHidden<A>
+impl<A> Differentiable<A> {
+    pub fn into_scalar(self) -> Scalar<A> {
+        match self {
+            Differentiable::Scalar(s) => s,
+            Differentiable::Vector(_) => panic!("not a scalar"),
+        }
+    }
+
+    pub fn into_vector(self) -> Vec<Differentiable<A>> {
+        match self {
+            Differentiable::Scalar(_) => panic!("not a vector"),
+            Differentiable::Vector(v) => v,
+        }
+    }
+
+    pub fn borrow_scalar(&self) -> &Scalar<A> {
+        match self {
+            Differentiable::Scalar(s) => s,
+            Differentiable::Vector(_) => panic!("not a scalar"),
+        }
+    }
+
+    pub fn borrow_vector(&self) -> &Vec<Differentiable<A>> {
+        match self {
+            Differentiable::Scalar(_) => panic!("not a vector"),
+            Differentiable::Vector(v) => v,
+        }
+    }
+}
+
+impl<A> Differentiable<A>
 where
     A: Clone
         + Eq
@@ -134,7 +183,7 @@ where
         + One
         + Neg<Output = A>,
 {
-    fn accumulate_gradients_vec(v: &[DifferentiableHidden<A>], acc: &mut HashMap<Scalar<A>, A>) {
+    fn accumulate_gradients_vec(v: &[Differentiable<A>], acc: &mut HashMap<Scalar<A>, A>) {
         for v in v.iter().rev() {
             v.accumulate_gradients(acc);
         }
@@ -142,33 +191,36 @@ where
 
     fn accumulate_gradients(&self, acc: &mut HashMap<Scalar<A>, A>) {
         match self {
-            DifferentiableHidden::Scalar(y) => {
+            Differentiable::Scalar(y) => {
                 let k = y.clone_link();
                 k.invoke(y, A::one(), acc);
             }
-            DifferentiableHidden::Vector(y) => {
-                DifferentiableHidden::accumulate_gradients_vec(y, acc)
-            }
+            Differentiable::Vector(y) => Differentiable::accumulate_gradients_vec(y, acc),
         }
     }
 
-    fn grad_once(self, wrt: &DifferentiableHidden<A>) -> DifferentiableHidden<A> {
+    fn grad_once<const PARAM_NUM: usize>(
+        self,
+        wrt: [Differentiable<A>; PARAM_NUM],
+    ) -> [Differentiable<A>; PARAM_NUM] {
         let mut acc = HashMap::new();
         self.accumulate_gradients(&mut acc);
 
-        wrt.map(&mut |d| match acc.get(&d) {
-            None => Scalar::Number(A::zero(), None),
-            Some(x) => Scalar::Number(x.clone(), None),
+        wrt.map(|wrt| {
+            wrt.map(&mut |d| match acc.get(&d) {
+                None => Scalar::Number(A::zero(), None),
+                Some(x) => Scalar::Number(x.clone(), None),
+            })
         })
     }
 }
 
 #[derive(Clone, Debug)]
-pub struct Differentiable<A, const RANK: usize> {
-    contents: DifferentiableHidden<A>,
+pub struct RankedDifferentiable<A, const RANK: usize> {
+    contents: Differentiable<A>,
 }
 
-impl<A, const RANK: usize> Display for Differentiable<A, RANK>
+impl<A, const RANK: usize> Display for RankedDifferentiable<A, RANK>
 where
     A: Display,
 {
@@ -177,123 +229,161 @@ where
     }
 }
 
-pub fn of_scalar<A>(s: Scalar<A>) -> Differentiable<A, 0> {
-    Differentiable {
-        contents: DifferentiableHidden::Scalar(s),
-    }
-}
-
-pub fn to_scalar<A>(s: Differentiable<A, 0>) -> Scalar<A> {
-    match s.contents {
-        DifferentiableHidden::Scalar(s) => s,
-        DifferentiableHidden::Vector(_) => panic!("not a vector"),
-    }
-}
-
-pub fn of_slice<A>(input: &[A]) -> Differentiable<A, 1>
-where
-    A: Clone,
-{
-    Differentiable {
-        contents: DifferentiableHidden::of_slice(input),
-    }
-}
-
-impl<A, const RANK: usize> Differentiable<A, RANK> {
-    pub fn of_vector(s: Vec<Differentiable<A, RANK>>) -> Differentiable<A, { RANK + 1 }> {
-        Differentiable {
-            contents: DifferentiableHidden::Vector(s.into_iter().map(|v| v.contents).collect()),
+impl<A> RankedDifferentiable<A, 0> {
+    pub fn to_scalar(self) -> Scalar<A> {
+        match self.contents {
+            Differentiable::Scalar(s) => s,
+            Differentiable::Vector(_) => panic!("not a scalar despite teq that we're a scalar"),
         }
     }
 
-    pub fn map<B, F>(s: Differentiable<A, RANK>, f: &mut F) -> Differentiable<B, RANK>
+    pub fn of_scalar(s: Scalar<A>) -> RankedDifferentiable<A, 0> {
+        RankedDifferentiable {
+            contents: Differentiable::Scalar(s),
+        }
+    }
+}
+
+impl<A> RankedDifferentiable<A, 1> {
+    pub fn of_slice<T>(input: T) -> RankedDifferentiable<A, 1>
+    where
+        A: Clone,
+        T: AsRef<[A]>,
+    {
+        RankedDifferentiable {
+            contents: Differentiable::of_slice(input),
+        }
+    }
+}
+
+impl<A> RankedDifferentiable<A, 2> {
+    pub fn of_slice_2<T, const N: usize>(input: &[T]) -> RankedDifferentiable<A, 2>
+    where
+        A: Clone,
+        T: AsRef<[A]>,
+    {
+        let v = input
+            .iter()
+            .map(|x| Differentiable::of_slice(x))
+            .collect::<Vec<_>>();
+        RankedDifferentiable {
+            contents: Differentiable::Vector(v),
+        }
+    }
+}
+
+impl<A, const RANK: usize> RankedDifferentiable<A, RANK> {
+    pub fn to_unranked(self) -> Differentiable<A> {
+        self.contents
+    }
+
+    pub fn to_unranked_borrow(&self) -> &Differentiable<A> {
+        &self.contents
+    }
+
+    pub fn of_vector(
+        s: Vec<RankedDifferentiable<A, RANK>>,
+    ) -> RankedDifferentiable<A, { RANK + 1 }> {
+        RankedDifferentiable {
+            contents: Differentiable::Vector(s.into_iter().map(|v| v.contents).collect()),
+        }
+    }
+
+    pub fn map<B, F>(
+        self: RankedDifferentiable<A, RANK>,
+        f: &mut F,
+    ) -> RankedDifferentiable<B, RANK>
     where
         F: FnMut(Scalar<A>) -> Scalar<B>,
         A: Clone,
     {
-        Differentiable {
-            contents: DifferentiableHidden::map(&s.contents, f),
+        RankedDifferentiable {
+            contents: Differentiable::map(&self.contents, f),
         }
     }
 
     pub fn map2<B, C, F>(
-        self: &Differentiable<A, RANK>,
-        other: &Differentiable<B, RANK>,
+        self: &RankedDifferentiable<A, RANK>,
+        other: &RankedDifferentiable<B, RANK>,
         f: &F,
-    ) -> Differentiable<C, RANK>
+    ) -> RankedDifferentiable<C, RANK>
     where
         F: Fn(&Scalar<A>, &Scalar<B>) -> Scalar<C>,
         A: Clone,
         B: Clone,
     {
-        Differentiable {
-            contents: DifferentiableHidden::map2(&self.contents, &other.contents, f),
+        RankedDifferentiable {
+            contents: Differentiable::map2(&self.contents, &other.contents, f),
         }
     }
 
-    pub fn to_vector(s: Differentiable<A, { RANK + 1 }>) -> Vec<Differentiable<A, RANK>> {
-        match s.contents {
-            DifferentiableHidden::Scalar(_) => panic!("not a scalar"),
-            DifferentiableHidden::Vector(v) => v
+    pub fn to_vector(
+        self: RankedDifferentiable<A, RANK>,
+    ) -> Vec<RankedDifferentiable<A, { RANK - 1 }>> {
+        match self.contents {
+            Differentiable::Scalar(_) => panic!("not a scalar"),
+            Differentiable::Vector(v) => v
                 .into_iter()
-                .map(|v| Differentiable { contents: v })
+                .map(|v| RankedDifferentiable { contents: v })
                 .collect(),
         }
     }
+}
 
-    pub fn grad<F>(f: F, theta: &Differentiable<A, RANK>) -> Differentiable<A, RANK>
-    where
-        F: Fn(Differentiable<A, RANK>) -> Differentiable<A, RANK>,
-        A: Clone
-            + Hash
-            + AddAssign
-            + Mul<Output = A>
-            + Exp
-            + Div<Output = A>
-            + Zero
-            + One
-            + Neg<Output = A>
-            + Eq,
-    {
-        let mut i = 0usize;
-        let wrt = theta.contents.map(&mut |x| {
+pub fn grad<A, F, const RANK: usize, const PARAM_RANK: usize>(
+    f: F,
+    theta: &[Differentiable<A>; PARAM_RANK],
+) -> [Differentiable<A>; PARAM_RANK]
+where
+    F: Fn(&[Differentiable<A>; PARAM_RANK]) -> RankedDifferentiable<A, RANK>,
+    A: ?Sized
+        + Clone
+        + Hash
+        + AddAssign
+        + Mul<Output = A>
+        + Exp
+        + Div<Output = A>
+        + Zero
+        + One
+        + Neg<Output = A>
+        + Eq,
+{
+    let mut i = 0usize;
+    let wrt = theta.each_ref().map(|theta| {
+        theta.map(&mut |x| {
             let result = Scalar::truncate_dual(x, Some(i));
             i += 1;
             result
-        });
-        let after_f = f(Differentiable {
-            contents: wrt.clone(),
-        });
-        Differentiable {
-            contents: DifferentiableHidden::grad_once(after_f.contents, &wrt),
-        }
-    }
+        })
+    });
+    let after_f = f(&wrt);
+    Differentiable::grad_once(after_f.contents, wrt)
 }
 
 #[cfg(test)]
 mod tests {
     use ordered_float::NotNan;
 
-    use crate::loss::{l2_loss_2, predict_line_2};
+    use crate::loss::{l2_loss_2, predict_line_2_unranked};
 
     use super::*;
 
-    fn extract_scalar<'a, A>(d: &'a DifferentiableHidden<A>) -> &'a A {
+    fn extract_scalar<'a, A>(d: &'a Differentiable<A>) -> &'a A {
         match d {
-            DifferentiableHidden::Scalar(a) => &(a.real_part()),
-            DifferentiableHidden::Vector(_) => panic!("not a scalar"),
+            Differentiable::Scalar(a) => &(a.real_part()),
+            Differentiable::Vector(_) => panic!("not a scalar"),
         }
     }
 
     #[test]
     fn test_map() {
-        let v = DifferentiableHidden::Vector(
+        let v = Differentiable::Vector(
             vec![
-                DifferentiableHidden::Scalar(Scalar::Number(
+                Differentiable::Scalar(Scalar::Number(
                     NotNan::new(3.0).expect("3 is not NaN"),
                     Some(0usize),
                 )),
-                DifferentiableHidden::Scalar(Scalar::Number(
+                Differentiable::Scalar(Scalar::Number(
                     NotNan::new(4.0).expect("4 is not NaN"),
                     Some(1usize),
                 )),
@@ -306,8 +396,8 @@ mod tests {
         });
 
         let v = match mapped {
-            DifferentiableHidden::Scalar(_) => panic!("Not a scalar"),
-            DifferentiableHidden::Vector(v) => v
+            Differentiable::Scalar(_) => panic!("Not a scalar"),
+            Differentiable::Vector(v) => v
                 .iter()
                 .map(|d| extract_scalar(d).clone())
                 .collect::<Vec<_>>(),
@@ -318,26 +408,27 @@ mod tests {
 
     #[test]
     fn test_autodiff() {
-        let input_vec = of_slice(&[NotNan::<f64>::zero(), NotNan::<f64>::zero()]);
+        let input_vec = [
+            RankedDifferentiable::of_scalar(Scalar::<NotNan<f64>>::zero()).contents,
+            RankedDifferentiable::of_scalar(Scalar::<NotNan<f64>>::zero()).contents,
+        ];
         let xs = [2.0, 1.0, 4.0, 3.0].map(|x| NotNan::new(x).expect("not nan"));
         let ys = [1.8, 1.2, 4.2, 3.3].map(|x| NotNan::new(x).expect("not nan"));
-        let grad = Differentiable::grad(
+        let grad = grad(
             |x| {
-                Differentiable::of_vector(vec![of_scalar(l2_loss_2(
-                    predict_line_2,
-                    of_slice(&xs),
-                    of_slice(&ys),
+                RankedDifferentiable::of_vector(vec![RankedDifferentiable::of_scalar(l2_loss_2(
+                    predict_line_2_unranked,
+                    RankedDifferentiable::of_slice(&xs),
+                    RankedDifferentiable::of_slice(&ys),
                     x,
                 ))])
             },
             &input_vec,
         );
 
-        let grad_vec: Vec<f64> = Differentiable::to_vector(grad)
-            .into_iter()
-            .map(to_scalar)
-            .map(|x| f64::from(*x.real_part()))
-            .collect();
-        assert_eq!(grad_vec, vec![-63.0, -21.0]);
+        let grad_vec = grad
+            .map(Differentiable::into_scalar)
+            .map(|x| f64::from(*x.real_part()));
+        assert_eq!(grad_vec, [-63.0, -21.0]);
     }
 }
diff --git a/little_learner/src/const_teq.rs b/little_learner/src/const_teq.rs
new file mode 100644
index 0000000..6952ee2
--- /dev/null
+++ b/little_learner/src/const_teq.rs
@@ -0,0 +1,13 @@
+use std::marker::PhantomData;
+
+pub struct ConstTeq<const A: usize, const B: usize> {
+    phantom_a: PhantomData<[(); A]>,
+    phantom_b: PhantomData<[(); B]>,
+}
+
+pub fn make<const A: usize>() -> ConstTeq<A, A> {
+    ConstTeq {
+        phantom_a: Default::default(),
+        phantom_b: Default::default(),
+    }
+}
diff --git a/little_learner/src/lib.rs b/little_learner/src/lib.rs
index cf17061..3bfa7ab 100644
--- a/little_learner/src/lib.rs
+++ b/little_learner/src/lib.rs
@@ -1,7 +1,9 @@
 #![allow(incomplete_features)]
 #![feature(generic_const_exprs)]
+#![feature(array_methods)]
 
 pub mod auto_diff;
+pub mod const_teq;
 pub mod expr_syntax_tree;
 pub mod loss;
 pub mod scalar;
diff --git a/little_learner/src/loss.rs b/little_learner/src/loss.rs
index b669a18..9bcbe43 100644
--- a/little_learner/src/loss.rs
+++ b/little_learner/src/loss.rs
@@ -4,7 +4,7 @@ use std::{
 };
 
 use crate::{
-    auto_diff::{of_scalar, to_scalar, Differentiable},
+    auto_diff::{Differentiable, RankedDifferentiable},
     scalar::Scalar,
     traits::{One, Zero},
 };
@@ -16,49 +16,61 @@ where
     x.clone() * x.clone()
 }
 
-pub fn dot_2<A, const RANK: usize>(
-    x: &Differentiable<A, RANK>,
-    y: &Differentiable<A, RANK>,
-) -> Differentiable<A, RANK>
+pub fn elementwise_mul<A, const RANK: usize>(
+    x: &RankedDifferentiable<A, RANK>,
+    y: &RankedDifferentiable<A, RANK>,
+) -> RankedDifferentiable<A, RANK>
+where
+    A: Mul<Output = A> + Sum<<A as Mul>::Output> + Clone + Default,
+{
+    RankedDifferentiable::map2(x, y, &|x, y| x.clone() * y.clone())
+}
+
+pub fn dot_unranked<A>(x: &Differentiable<A>, y: &Differentiable<A>) -> Differentiable<A>
 where
     A: Mul<Output = A> + Sum<<A as Mul>::Output> + Clone + Default,
 {
     Differentiable::map2(x, y, &|x, y| x.clone() * y.clone())
 }
 
-fn squared_2<A, const RANK: usize>(x: &Differentiable<A, RANK>) -> Differentiable<A, RANK>
+fn squared_2<A, const RANK: usize>(
+    x: &RankedDifferentiable<A, RANK>,
+) -> RankedDifferentiable<A, RANK>
 where
     A: Mul<Output = A> + Copy + Default,
 {
-    Differentiable::map2(x, x, &|x, y| x.clone() * y.clone())
+    RankedDifferentiable::map2(x, x, &|x, y| x.clone() * y.clone())
 }
 
-fn sum_2<A>(x: Differentiable<A, 1>) -> Scalar<A>
+fn sum_2<A>(x: RankedDifferentiable<A, 1>) -> Scalar<A>
 where
     A: Sum<A> + Clone + Add<Output = A> + Zero,
 {
-    Differentiable::to_vector(x)
+    RankedDifferentiable::to_vector(x)
         .into_iter()
-        .map(to_scalar)
+        .map(|x| x.to_scalar())
         .sum()
 }
 
-fn l2_norm_2<A>(prediction: &Differentiable<A, 1>, data: &Differentiable<A, 1>) -> Scalar<A>
+fn l2_norm_2<A>(
+    prediction: &RankedDifferentiable<A, 1>,
+    data: &RankedDifferentiable<A, 1>,
+) -> Scalar<A>
 where
     A: Sum<A> + Mul<Output = A> + Copy + Default + Neg<Output = A> + Add<Output = A> + Zero + Neg,
 {
-    let diff = Differentiable::map2(prediction, data, &|x, y| x.clone() - y.clone());
+    let diff = RankedDifferentiable::map2(prediction, data, &|x, y| x.clone() - y.clone());
     sum_2(squared_2(&diff))
 }
 
-pub fn l2_loss_2<A, F, Params>(
+pub fn l2_loss_2<A, F, Params, const N: usize>(
     target: F,
-    data_xs: Differentiable<A, 1>,
-    data_ys: Differentiable<A, 1>,
+    data_xs: RankedDifferentiable<A, N>,
+    data_ys: RankedDifferentiable<A, 1>,
     params: Params,
 ) -> Scalar<A>
 where
-    F: Fn(Differentiable<A, 1>, Params) -> Differentiable<A, 1>,
+    F: Fn(RankedDifferentiable<A, N>, Params) -> RankedDifferentiable<A, 1>,
     A: Sum<A> + Mul<Output = A> + Copy + Default + Neg<Output = A> + Add<Output = A> + Zero,
 {
     let pred_ys = target(data_xs, params);
@@ -66,42 +78,143 @@ where
 }
 
 pub fn predict_line_2<A>(
-    xs: Differentiable<A, 1>,
-    theta: Differentiable<A, 1>,
-) -> Differentiable<A, 1>
+    xs: RankedDifferentiable<A, 1>,
+    theta: &[RankedDifferentiable<A, 0>; 2],
+) -> RankedDifferentiable<A, 1>
 where
     A: Mul<Output = A> + Add<Output = A> + Sum<<A as Mul>::Output> + Copy + Default + One + Zero,
 {
-    let xs = Differentiable::to_vector(xs)
+    let xs = RankedDifferentiable::to_vector(xs)
         .into_iter()
-        .map(|v| to_scalar(v));
+        .map(|v| v.to_scalar());
     let mut result = vec![];
     for x in xs {
-        let left_arg = Differentiable::of_vector(vec![
-            of_scalar(x.clone()),
-            of_scalar(<Scalar<A> as One>::one()),
+        let left_arg = RankedDifferentiable::of_vector(vec![
+            RankedDifferentiable::of_scalar(x.clone()),
+            RankedDifferentiable::of_scalar(<Scalar<A> as One>::one()),
         ]);
-        let dotted = of_scalar(
-            Differentiable::to_vector(dot_2(&left_arg, &theta))
-                .iter()
-                .map(|x| to_scalar((*x).clone()))
-                .sum(),
+        let dotted = RankedDifferentiable::of_scalar(
+            RankedDifferentiable::to_vector(elementwise_mul(
+                &left_arg,
+                &RankedDifferentiable::of_vector(theta.to_vec()),
+            ))
+            .iter()
+            .map(|x| (*x).clone().to_scalar())
+            .sum(),
         );
         result.push(dotted);
     }
-    Differentiable::of_vector(result)
+    RankedDifferentiable::of_vector(result)
+}
+
+pub fn predict_line_2_unranked<A>(
+    xs: RankedDifferentiable<A, 1>,
+    theta: &[Differentiable<A>; 2],
+) -> RankedDifferentiable<A, 1>
+where
+    A: Mul<Output = A> + Add<Output = A> + Sum<<A as Mul>::Output> + Copy + Default + One + Zero,
+{
+    let xs = RankedDifferentiable::to_vector(xs)
+        .into_iter()
+        .map(|v| v.to_scalar());
+    let mut result = vec![];
+    for x in xs {
+        let left_arg = RankedDifferentiable::of_vector(vec![
+            RankedDifferentiable::of_scalar(x.clone()),
+            RankedDifferentiable::of_scalar(<Scalar<A> as One>::one()),
+        ]);
+        let dotted = RankedDifferentiable::of_scalar(
+            dot_unranked(
+                left_arg.to_unranked_borrow(),
+                &Differentiable::Vector(theta.to_vec()),
+            )
+            .into_vector()
+            .into_iter()
+            .map(|x| x.into_scalar())
+            .sum(),
+        );
+        result.push(dotted);
+    }
+    RankedDifferentiable::of_vector(result)
 }
 
 pub fn predict_quadratic<A>(
-    xs: Differentiable<A, 1>,
-    theta: Differentiable<A, 1>,
-) -> Differentiable<A, 1>
+    xs: RankedDifferentiable<A, 1>,
+    theta: &[RankedDifferentiable<A, 0>; 3],
+) -> RankedDifferentiable<A, 1>
 where
     A: Mul<Output = A> + Add<Output = A> + Sum + Default + One + Zero + Clone,
 {
-    Differentiable::map(xs, &mut |x| {
+    RankedDifferentiable::map(xs, &mut |x| {
         let x_powers = vec![Scalar::make(A::one()), x.clone(), square(&x)];
-        let x_powers = Differentiable::of_vector(x_powers.into_iter().map(of_scalar).collect());
-        sum_2(dot_2(&x_powers, &theta))
+        let x_powers = RankedDifferentiable::of_vector(
+            x_powers
+                .into_iter()
+                .map(RankedDifferentiable::of_scalar)
+                .collect(),
+        );
+        RankedDifferentiable::to_vector(elementwise_mul(
+            &x_powers,
+            &RankedDifferentiable::of_vector(theta.to_vec()),
+        ))
+        .into_iter()
+        .map(|x| x.to_scalar())
+        .sum()
     })
 }
+
+pub fn predict_quadratic_unranked<A>(
+    xs: RankedDifferentiable<A, 1>,
+    theta: &[Differentiable<A>; 3],
+) -> RankedDifferentiable<A, 1>
+where
+    A: Mul<Output = A> + Add<Output = A> + Sum + Default + One + Zero + Clone,
+{
+    RankedDifferentiable::map(xs, &mut |x| {
+        let x_powers = vec![Scalar::make(A::one()), x.clone(), square(&x)];
+        let x_powers = RankedDifferentiable::of_vector(
+            x_powers
+                .into_iter()
+                .map(RankedDifferentiable::of_scalar)
+                .collect(),
+        );
+        dot_unranked(
+            x_powers.to_unranked_borrow(),
+            &Differentiable::Vector(theta.to_vec()),
+        )
+        .attach_rank::<1>()
+        .expect("wanted a tensor1")
+        .to_vector()
+        .into_iter()
+        .map(|x| x.to_scalar())
+        .sum()
+    })
+}
+
+// The parameters are: a tensor1 of length 2 (to be dotted with the input), and a scalar (to translate).
+pub fn predict_plane<A>(
+    xs: RankedDifferentiable<A, 2>,
+    theta: &[Differentiable<A>; 2],
+) -> RankedDifferentiable<A, 1>
+where
+    A: Mul<Output = A> + Add<Output = A> + Sum + Default + One + Zero + Clone,
+{
+    if theta[0].rank() != 1 {
+        panic!("theta0 must be of rank 1, got: {}", theta[0].rank())
+    }
+    let theta0 = RankedDifferentiable::of_vector(
+        theta[0]
+            .borrow_vector()
+            .iter()
+            .map(|v| RankedDifferentiable::of_scalar(v.borrow_scalar().clone()))
+            .collect::<Vec<_>>(),
+    );
+    let theta1 = theta[1].borrow_scalar().clone();
+    let dotted: Vec<_> = xs
+        .to_vector()
+        .into_iter()
+        .map(|point| sum_2(elementwise_mul(&theta0, &point)))
+        .map(|x| RankedDifferentiable::of_scalar(x + theta1.clone()))
+        .collect();
+    RankedDifferentiable::of_vector(dotted)
+}
diff --git a/little_learner_app/Cargo.toml b/little_learner_app/Cargo.toml
index 721f1e5..93592cb 100644
--- a/little_learner_app/Cargo.toml
+++ b/little_learner_app/Cargo.toml
@@ -9,4 +9,3 @@ edition = "2021"
 immutable-chunkmap = "1.0.5"
 ordered-float = "3.6.0"
 little_learner = { path = "../little_learner" }
-arrayvec = "0.7.2"
diff --git a/little_learner_app/src/main.rs b/little_learner_app/src/main.rs
index a10bb07..da18e8e 100644
--- a/little_learner_app/src/main.rs
+++ b/little_learner_app/src/main.rs
@@ -6,9 +6,9 @@ mod with_tensor;
 use core::hash::Hash;
 use std::ops::{Add, AddAssign, Div, Mul, Neg};
 
-use little_learner::auto_diff::{of_scalar, of_slice, to_scalar, Differentiable};
+use little_learner::auto_diff::{grad, Differentiable, RankedDifferentiable};
 
-use little_learner::loss::{l2_loss_2, predict_quadratic};
+use little_learner::loss::{l2_loss_2, predict_plane};
 use little_learner::scalar::Scalar;
 use little_learner::traits::{Exp, One, Zero};
 use ordered_float::NotNan;
@@ -24,16 +24,16 @@ where
     v
 }
 
-struct GradientDescentHyper<A, const RANK: usize> {
+struct GradientDescentHyper<A> {
     learning_rate: A,
     iterations: u32,
 }
 
-fn gradient_descent_step<A, F, const RANK: usize>(
+fn gradient_descent_step<A, F, const RANK: usize, const PARAM_NUM: usize>(
     f: &F,
-    theta: Differentiable<A, RANK>,
-    params: &GradientDescentHyper<A, RANK>,
-) -> Differentiable<A, RANK>
+    theta: [Differentiable<A>; PARAM_NUM],
+    params: &GradientDescentHyper<A>,
+) -> [Differentiable<A>; PARAM_NUM]
 where
     A: Clone
         + Mul<Output = A>
@@ -46,17 +46,33 @@ where
         + One
         + Eq
         + Exp,
-    F: Fn(Differentiable<A, RANK>) -> Differentiable<A, RANK>,
+    F: Fn(&[Differentiable<A>; PARAM_NUM]) -> RankedDifferentiable<A, RANK>,
 {
-    let delta = Differentiable::grad(f, &theta);
-    Differentiable::map2(&theta, &delta, &|theta, delta| {
-        (*theta).clone() - (Scalar::make((params.learning_rate).clone()) * (*delta).clone())
+    let delta = grad(f, &theta);
+    let mut i = 0;
+    theta.map(|theta| {
+        let delta = &delta[i];
+        i += 1;
+        // For speed, you might want to truncate_dual this.
+        let learning_rate = Scalar::make((params.learning_rate).clone());
+        Differentiable::map2(
+            &theta,
+            &delta.map(&mut |s| s * learning_rate.clone()),
+            &|theta, delta| (*theta).clone() - (*delta).clone(),
+        )
     })
 }
 
 fn main() {
-    let xs = [-1.0, 0.0, 1.0, 2.0, 3.0];
-    let ys = [2.55, 2.1, 4.35, 10.2, 18.25];
+    let plane_xs = [
+        [1.0, 2.05],
+        [1.0, 3.0],
+        [2.0, 2.0],
+        [2.0, 3.91],
+        [3.0, 6.13],
+        [4.0, 8.09],
+    ];
+    let plane_ys = [13.99, 15.99, 18.0, 22.4, 30.2, 37.94];
 
     let hyper = GradientDescentHyper {
         learning_rate: NotNan::new(0.001).expect("not nan"),
@@ -64,48 +80,63 @@ fn main() {
     };
 
     let iterated = {
-        let xs = xs.map(|x| NotNan::new(x).expect("not nan"));
-        let ys = ys.map(|x| NotNan::new(x).expect("not nan"));
+        let xs = plane_xs.map(|x| {
+            [
+                NotNan::new(x[0]).expect("not nan"),
+                NotNan::new(x[1]).expect("not nan"),
+            ]
+        });
+        let ys = plane_ys.map(|x| NotNan::new(x).expect("not nan"));
         iterate(
             &|theta| {
                 gradient_descent_step(
                     &|x| {
-                        Differentiable::of_vector(vec![of_scalar(l2_loss_2(
-                            predict_quadratic,
-                            of_slice(&xs),
-                            of_slice(&ys),
-                            x,
-                        ))])
+                        RankedDifferentiable::of_vector(vec![RankedDifferentiable::of_scalar(
+                            l2_loss_2(
+                                predict_plane,
+                                RankedDifferentiable::of_slice_2::<_, 2>(&xs),
+                                RankedDifferentiable::of_slice(ys),
+                                x,
+                            ),
+                        )])
                     },
                     theta,
                     &hyper,
                 )
             },
-            of_slice(&[
-                NotNan::<f64>::zero(),
-                NotNan::<f64>::zero(),
-                NotNan::<f64>::zero(),
-            ]),
+            [
+                RankedDifferentiable::of_slice([NotNan::zero(), NotNan::zero()]).to_unranked(),
+                Differentiable::Scalar(Scalar::zero()),
+            ],
             hyper.iterations,
         )
     };
 
-    println!(
-        "After iteration: {:?}",
-        Differentiable::to_vector(iterated)
+    let [theta0, theta1] = iterated;
+
+    let theta0 = theta0.attach_rank::<1>().expect("rank 1 tensor");
+    let theta1 = theta1.attach_rank::<0>().expect("rank 0 tensor");
+
+    assert_eq!(
+        theta0
+            .to_vector()
             .into_iter()
-            .map(|x| to_scalar(x).real_part().into_inner())
-            .collect::<Vec<_>>()
+            .map(|x| x.to_scalar().real_part().into_inner())
+            .collect::<Vec<_>>(),
+        [3.97757644609063, 2.0496557321494446]
+    );
+    assert_eq!(
+        theta1.to_scalar().real_part().into_inner(),
+        5.786758464448078
     );
 }
 
 #[cfg(test)]
 mod tests {
     use super::*;
-    use arrayvec::ArrayVec;
     use little_learner::{
-        auto_diff::to_scalar,
-        loss::{predict_line_2, square},
+        auto_diff::grad,
+        loss::{l2_loss_2, predict_line_2, predict_line_2_unranked, predict_quadratic_unranked},
     };
 
     use crate::with_tensor::{l2_loss, predict_line};
@@ -116,9 +147,12 @@ mod tests {
         let ys = [1.8, 1.2, 4.2, 3.3];
         let loss = l2_loss_2(
             predict_line_2,
-            of_slice(&xs),
-            of_slice(&ys),
-            of_slice(&[0.0, 0.0]),
+            RankedDifferentiable::of_slice(&xs),
+            RankedDifferentiable::of_slice(&ys),
+            &[
+                RankedDifferentiable::of_scalar(Scalar::zero()),
+                RankedDifferentiable::of_scalar(Scalar::zero()),
+            ],
         );
 
         assert_eq!(*loss.real_part(), 33.21);
@@ -134,29 +168,39 @@ mod tests {
 
     #[test]
     fn grad_example() {
-        let input_vec = of_slice(&[NotNan::new(27.0).expect("not nan")]);
+        let input_vec = [Differentiable::Scalar(Scalar::make(
+            NotNan::new(27.0).expect("not nan"),
+        ))];
 
-        let grad: Vec<_> = Differentiable::to_vector(Differentiable::grad(
-            |x| Differentiable::map(x, &mut |x| square(&x)),
+        let grad: Vec<_> = grad(
+            |x| {
+                RankedDifferentiable::of_scalar(
+                    x[0].borrow_scalar().clone() * x[0].borrow_scalar().clone(),
+                )
+            },
             &input_vec,
-        ))
+        )
         .into_iter()
-        .map(|x| to_scalar(x).real_part().into_inner())
+        .map(|x| x.into_scalar().real_part().into_inner())
         .collect();
         assert_eq!(grad, [54.0]);
     }
 
     #[test]
     fn loss_gradient() {
-        let input_vec = of_slice(&[NotNan::<f64>::zero(), NotNan::<f64>::zero()]);
+        let zero = Scalar::<NotNan<f64>>::zero();
+        let input_vec = [
+            RankedDifferentiable::of_scalar(zero.clone()).to_unranked(),
+            RankedDifferentiable::of_scalar(zero).to_unranked(),
+        ];
         let xs = [2.0, 1.0, 4.0, 3.0].map(|x| NotNan::new(x).expect("not nan"));
         let ys = [1.8, 1.2, 4.2, 3.3].map(|x| NotNan::new(x).expect("not nan"));
-        let grad = Differentiable::grad(
+        let grad = grad(
             |x| {
-                Differentiable::of_vector(vec![of_scalar(l2_loss_2(
-                    predict_line_2,
-                    of_slice(&xs),
-                    of_slice(&ys),
+                RankedDifferentiable::of_vector(vec![RankedDifferentiable::of_scalar(l2_loss_2(
+                    predict_line_2_unranked,
+                    RankedDifferentiable::of_slice(&xs),
+                    RankedDifferentiable::of_slice(&ys),
                     x,
                 ))])
             },
@@ -164,9 +208,8 @@ mod tests {
         );
 
         assert_eq!(
-            Differentiable::to_vector(grad)
-                .into_iter()
-                .map(|x| *(to_scalar(x).real_part()))
+            grad.into_iter()
+                .map(|x| *(x.into_scalar().real_part()))
                 .collect::<Vec<_>>(),
             [-63.0, -21.0]
         );
@@ -174,13 +217,7 @@ mod tests {
 
     #[test]
     fn test_iterate() {
-        let f = |t: [i32; 3]| {
-            let mut vec = ArrayVec::<i32, 3>::new();
-            for i in t {
-                vec.push(i - 3);
-            }
-            vec.into_inner().unwrap()
-        };
+        let f = |t: [i32; 3]| t.map(|i| i - 3);
         assert_eq!(iterate(&f, [1, 2, 3], 5u32), [-14, -13, -12]);
     }
 
@@ -189,6 +226,8 @@ mod tests {
         let xs = [2.0, 1.0, 4.0, 3.0];
         let ys = [1.8, 1.2, 4.2, 3.3];
 
+        let zero = Scalar::<NotNan<f64>>::zero();
+
         let hyper = GradientDescentHyper {
             learning_rate: NotNan::new(0.01).expect("not nan"),
             iterations: 1000,
@@ -200,24 +239,29 @@ mod tests {
                 &|theta| {
                     gradient_descent_step(
                         &|x| {
-                            Differentiable::of_vector(vec![of_scalar(l2_loss_2(
-                                predict_line_2,
-                                of_slice(&xs),
-                                of_slice(&ys),
-                                x,
-                            ))])
+                            RankedDifferentiable::of_vector(vec![RankedDifferentiable::of_scalar(
+                                l2_loss_2(
+                                    predict_line_2_unranked,
+                                    RankedDifferentiable::of_slice(&xs),
+                                    RankedDifferentiable::of_slice(&ys),
+                                    x,
+                                ),
+                            )])
                         },
                         theta,
                         &hyper,
                     )
                 },
-                of_slice(&[NotNan::<f64>::zero(), NotNan::<f64>::zero()]),
+                [
+                    RankedDifferentiable::of_scalar(zero.clone()).to_unranked(),
+                    RankedDifferentiable::of_scalar(zero).to_unranked(),
+                ],
                 hyper.iterations,
             )
         };
-        let iterated = Differentiable::to_vector(iterated)
+        let iterated = iterated
             .into_iter()
-            .map(|x| to_scalar(x).real_part().into_inner())
+            .map(|x| x.into_scalar().real_part().into_inner())
             .collect::<Vec<_>>();
 
         assert_eq!(iterated, vec![1.0499993623489503, 0.0000018747718457656533]);
@@ -228,6 +272,8 @@ mod tests {
         let xs = [-1.0, 0.0, 1.0, 2.0, 3.0];
         let ys = [2.55, 2.1, 4.35, 10.2, 18.25];
 
+        let zero = Scalar::<NotNan<f64>>::zero();
+
         let hyper = GradientDescentHyper {
             learning_rate: NotNan::new(0.001).expect("not nan"),
             iterations: 1000,
@@ -240,35 +286,104 @@ mod tests {
                 &|theta| {
                     gradient_descent_step(
                         &|x| {
-                            Differentiable::of_vector(vec![of_scalar(l2_loss_2(
-                                predict_quadratic,
-                                of_slice(&xs),
-                                of_slice(&ys),
-                                x,
-                            ))])
+                            RankedDifferentiable::of_vector(vec![RankedDifferentiable::of_scalar(
+                                l2_loss_2(
+                                    predict_quadratic_unranked,
+                                    RankedDifferentiable::of_slice(&xs),
+                                    RankedDifferentiable::of_slice(&ys),
+                                    x,
+                                ),
+                            )])
                         },
                         theta,
                         &hyper,
                     )
                 },
-                of_slice(&[
-                    NotNan::<f64>::zero(),
-                    NotNan::<f64>::zero(),
-                    NotNan::<f64>::zero(),
-                ]),
+                [
+                    RankedDifferentiable::of_scalar(zero.clone()).to_unranked(),
+                    RankedDifferentiable::of_scalar(zero.clone()).to_unranked(),
+                    RankedDifferentiable::of_scalar(zero).to_unranked(),
+                ],
                 hyper.iterations,
             )
         };
-        let iterated = Differentiable::to_vector(iterated)
+        let iterated = iterated
             .into_iter()
-            .map(|x| to_scalar(x).real_part().into_inner())
+            .map(|x| x.into_scalar().real_part().into_inner())
             .collect::<Vec<_>>();
 
-        println!("{:?}", iterated);
-
         assert_eq!(
             iterated,
             [2.0546423148479684, 0.9928606519360353, 1.4787394427094362]
         );
     }
+
+    #[test]
+    fn optimise_plane() {
+        let plane_xs = [
+            [1.0, 2.05],
+            [1.0, 3.0],
+            [2.0, 2.0],
+            [2.0, 3.91],
+            [3.0, 6.13],
+            [4.0, 8.09],
+        ];
+        let plane_ys = [13.99, 15.99, 18.0, 22.4, 30.2, 37.94];
+
+        let hyper = GradientDescentHyper {
+            learning_rate: NotNan::new(0.001).expect("not nan"),
+            iterations: 1000,
+        };
+
+        let iterated = {
+            let xs = plane_xs.map(|x| {
+                [
+                    NotNan::new(x[0]).expect("not nan"),
+                    NotNan::new(x[1]).expect("not nan"),
+                ]
+            });
+            let ys = plane_ys.map(|x| NotNan::new(x).expect("not nan"));
+            iterate(
+                &|theta| {
+                    gradient_descent_step(
+                        &|x| {
+                            RankedDifferentiable::of_vector(vec![RankedDifferentiable::of_scalar(
+                                l2_loss_2(
+                                    predict_plane,
+                                    RankedDifferentiable::of_slice_2::<_, 2>(&xs),
+                                    RankedDifferentiable::of_slice(ys),
+                                    x,
+                                ),
+                            )])
+                        },
+                        theta,
+                        &hyper,
+                    )
+                },
+                [
+                    RankedDifferentiable::of_slice([NotNan::zero(), NotNan::zero()]).to_unranked(),
+                    Differentiable::Scalar(Scalar::zero()),
+                ],
+                hyper.iterations,
+            )
+        };
+
+        let [theta0, theta1] = iterated;
+
+        let theta0 = theta0.attach_rank::<1>().expect("rank 1 tensor");
+        let theta1 = theta1.attach_rank::<0>().expect("rank 0 tensor");
+
+        assert_eq!(
+            theta0
+                .to_vector()
+                .into_iter()
+                .map(|x| x.to_scalar().real_part().into_inner())
+                .collect::<Vec<_>>(),
+            [3.97757644609063, 2.0496557321494446]
+        );
+        assert_eq!(
+            theta1.to_scalar().real_part().into_inner(),
+            5.786758464448078
+        );
+    }
 }