diff --git a/core/src/main/scala/dimwit/autodiff/FloatTree.scala b/core/src/main/scala/dimwit/autodiff/FloatTree.scala
index bf0b1cb..b51ee5f 100644
--- a/core/src/main/scala/dimwit/autodiff/FloatTree.scala
+++ b/core/src/main/scala/dimwit/autodiff/FloatTree.scala
@@ -104,6 +104,13 @@ object FloatTree:
       def **![P](p1: P)(using TensorTree[P], FloatTree[P, V]): P = p1.map([T <: Tuple] => (n: Labels[T]) ?=> (a: Tensor[T, V]) => a *! p2)
       def `//!`[P](p1: P)(using TensorTree[P], FloatTree[P, V]): P = p1.map([T <: Tuple] => (n: Labels[T]) ?=> (a: Tensor[T, V]) => a /! p2)
 
+    // Scalar broadcast extensions (Tensor0 op Tree)
+    extension [V: IsFloating](p2: Double)
+      def ++![P](p1: P)(using TensorTree[P], FloatTree[P, V]): P = Tensor0(VType[V])(p2) ++! p1
+      def --![P](p1: P)(using TensorTree[P], FloatTree[P, V]): P = Tensor0(VType[V])(p2) --! p1
+      def **![P](p1: P)(using TensorTree[P], FloatTree[P, V]): P = Tensor0(VType[V])(p2) **! p1
+      def `//!`[P](p1: P)(using TensorTree[P], FloatTree[P, V]): P = Tensor0(VType[V])(p2) `//!` p1
+
     // Tree extensions (Tree op Tree, Tree op Scalar, and math ops)
     // Excluded for bare Tensor[T, V] to avoid conflicts with tensor's own operators
     extension [P, V](p1: P)(using tt: TensorTree[P], ft: FloatTree[P, V], isF: IsFloating[V], ev: NotGiven[IsFloatingTensor[P, V]])
diff --git a/core/src/main/scala/dimwit/optimizer/GradientOptimizer.scala b/core/src/main/scala/dimwit/optimizer/GradientOptimizer.scala
index 17a2d53..d02672b 100644
--- a/core/src/main/scala/dimwit/optimizer/GradientOptimizer.scala
+++ b/core/src/main/scala/dimwit/optimizer/GradientOptimizer.scala
@@ -1,6 +1,7 @@
 package dimwit.optimizer
 
 import dimwit.*
+import dimwit.Conversions.given
 import dimwit.autodiff.FloatTree.*
 import dimwit.autodiff.FloatTree.ops.*
 import dimwit.autodiff.*
@@ -25,43 +26,43 @@ import dimwit.autodiff.*
   *    }}}
   */
 trait GradientOptimizer:
-  type State[_]
+  type State[_, V]
 
   // Core API
-  def init[Params: TensorTree: FloatTreeFor[Float32]](params: Params): State[Params]
-  def update[Params: TensorTree: FloatTreeFor[Float32]](gradients: Grad[Params], params: Params, state: State[Params]): (Params, State[Params])
+  def init[V, Params: TensorTree: FloatTreeFor[V]](params: Params)(using IsFloating[V]): State[Params, V]
+  def update[V, Params: TensorTree: FloatTreeFor[V]](gradients: Grad[Params], params: Params, state: State[Params, V])(using IsFloating[V]): (Params, State[Params, V])
 
   // Convenience: iterator with fixed gradient function
-  def iterateWithState[Params: TensorTree: FloatTreeFor[Float32]](init: Params)(df: Params => Grad[Params]): Iterator[(Params, State[Params])] =
+  def iterateWithState[V, Params: TensorTree: FloatTreeFor[V]](init: Params)(df: Params => Grad[Params])(using IsFloating[V]): Iterator[(Params, State[Params, V])] =
     Iterator.iterate((init, this.init(init))): (params, state) =>
       val grads = df(params)
       update(grads, params, state)
 
-  def iterate[Params: TensorTree: FloatTreeFor[Float32]](init: Params)(df: Params => Grad[Params]): Iterator[Params] =
+  def iterate[V, Params: TensorTree: FloatTreeFor[V]](init: Params)(df: Params => Grad[Params])(using IsFloating[V]): Iterator[Params] =
     iterateWithState(init)(df).map(_._1)
 
-case class GradientDescent(learningRate: Tensor0[Float32]) extends GradientOptimizer:
+case class GradientDescent(learningRate: Double) extends GradientOptimizer:
 
-  type State[P] = Unit // Stateless optimizer
+  type State[P, V] = Unit // Stateless optimizer
 
-  def init[Params: TensorTree: FloatTreeFor[Float32]](params: Params): Unit = ()
+  def init[V, Params: TensorTree: FloatTreeFor[V]](params: Params)(using IsFloating[V]): Unit = ()
 
-  def update[Params: TensorTree: FloatTreeFor[Float32]](gradients: Grad[Params], params: Params, state: Unit): (Params, Unit) =
+  def update[V, Params: TensorTree: FloatTreeFor[V]](gradients: Grad[Params], params: Params, state: Unit)(using IsFloating[V]): (Params, Unit) =
     val newParams = params -- gradients.value.scale(learningRate)
     (newParams, ())
 
-case class Lion(learningRate: Tensor0[Float32], weightDecay: Tensor0[Float32] = Tensor0(0.0f), beta1: Tensor0[Float32] = Tensor0(0.9f), beta2: Tensor0[Float32] = Tensor0(0.99f)) extends GradientOptimizer:
+case class Lion(learningRate: Double, weightDecay: Double = 0.0f, beta1: Double = 0.9f, beta2: Double = 0.99f) extends GradientOptimizer:
 
-  type State[P] = P // momentum state has same structure as params
+  type State[P, V] = P // momentum state has same structure as params
 
-  def init[Params: TensorTree: FloatTreeFor[Float32]](params: Params): Params =
+  def init[V, Params: TensorTree: FloatTreeFor[V]](params: Params)(using IsFloating[V]): Params =
     params.map([T <: Tuple] =>
       (n: Labels[T]) ?=>
-        (t: Tensor[T, Float32]) =>
+        (t: Tensor[T, V]) =>
           Tensor(t.shape).fill(0f)
     )
 
-  def update[Params: TensorTree: FloatTreeFor[Float32]](gradients: Grad[Params], params: Params, momentums: Params): (Params, Params) =
+  def update[V, Params: TensorTree: FloatTreeFor[V]](gradients: Grad[Params], params: Params, momentums: Params)(using IsFloating[V]): (Params, Params) =
     // the direction (1 or -1)
     // is determined by the sign of the momentum + gradient
     val updateDirection = (momentums **! beta1 ++ gradients.value **! (1f - beta1)).sign
@@ -71,11 +72,11 @@ case class Lion(learningRate: Tensor0[Float32], weightDecay: Tensor0[Float32] =
 
     (updatedParams, newMomentums)
 
-case class AdamState[P](
+case class AdamState[P, V: IsFloating](
     momentums: P, // momentums
     velocities: P, // velocities
-    b1: Tensor0[Float32], // decay rate for momentums mᵗ
-    b2: Tensor0[Float32] // decay rate for velocities vᵗ
+    b1: Tensor0[V], // decay rate for momentums mᵗ
+    b2: Tensor0[V] // decay rate for velocities vᵗ
 )
 
 /** Implements the Adam optimization algorithm.
@@ -83,26 +84,26 @@ case class AdamState[P](
   * @see [[https://arxiv.org/abs/1412.6980 Adam: A Method for Stochastic Optimization]]
   */
 case class Adam(
-    learningRate: Tensor0[Float32], // step size (learning rate)
-    b1: Tensor0[Float32] = Tensor0(0.9f), // decay rate for momentums mᵗ
-    b2: Tensor0[Float32] = Tensor0(0.999f), // decay rate for velocities vᵗ
-    epsilon: Tensor0[Float32] = Tensor0(1e-8f) // small constant to prevent division by zero
+    learningRate: Double, // step size (learning rate)
+    b1: Double = 0.9, // decay rate for momentums mᵗ
+    b2: Double = 0.999, // decay rate for velocities vᵗ
+    epsilon: Double = 1e-8 // small constant to prevent division by zero
 ) extends GradientOptimizer:
 
   private val β1 = b1
   private val β2 = b2
 
-  type State[P] = AdamState[P]
+  type State[P, V] = AdamState[P, V]
 
-  def init[Params: TensorTree: FloatTreeFor[Float32]](params: Params): State[Params] =
+  def init[V, Params: TensorTree: FloatTreeFor[V]](params: Params)(using IsFloating[V]): State[Params, V] =
     def zeros = params.fillCopy(0f)
-    AdamState(zeros, zeros, b1 = Tensor0(1f), b2 = Tensor0(1f))
+    AdamState[Params, V](zeros, zeros, b1 = Tensor0(VType[V])(1f), b2 = Tensor0(VType[V])(1f))
 
-  def update[Params: TensorTree: FloatTreeFor[Float32]](
+  def update[V, Params: TensorTree: FloatTreeFor[V]](
       gradients: Grad[Params],
       params: Params,
-      state: State[Params]
-  ): (Params, State[Params]) =
+      state: State[Params, V]
+  )(using IsFloating[V]): (Params, State[Params, V]) =
     // rename state variables to last time step for clarity
     val `mₜ₋₁` = state.momentums
     val `vₜ₋₁` = state.velocities
@@ -140,18 +141,18 @@ case class Adam(
   */
 case class AdamW(
     val adam: Adam,
-    val weightDecayFactor: Tensor0[Float32]
+    val weightDecayFactor: Double
 ) extends GradientOptimizer:
 
-  type State[P] = adam.State[P]
+  type State[P, V] = adam.State[P, V]
 
-  def init[Params: TensorTree: FloatTreeFor[Float32]](params: Params): State[Params] = adam.init(params)
+  def init[V, Params: TensorTree: FloatTreeFor[V]](params: Params)(using IsFloating[V]): State[Params, V] = adam.init(params)
 
-  def update[Params: TensorTree: FloatTreeFor[Float32]](
+  def update[V, Params: TensorTree: FloatTreeFor[V]](
       gradients: Grad[Params],
       params: Params,
-      state: State[Params]
-  ): (Params, State[Params]) =
+      state: State[Params, V]
+  )(using IsFloating[V]): (Params, State[Params, V]) =
     val α = adam.learningRate
     val `θₜ₋₁` = params
     val `λ'` = weightDecayFactor
diff --git a/examples/src/main/scala/basic/LogisticRegression.scala b/examples/src/main/scala/basic/LogisticRegression.scala
index 1b35cf1..aabda6d 100644
--- a/examples/src/main/scala/basic/LogisticRegression.scala
+++ b/examples/src/main/scala/basic/LogisticRegression.scala
@@ -125,7 +125,7 @@ object LogisticRegression:
     val trainLoss = jit(BinaryLogisticRegression.loss(trainingData, trainLabels))
     val valLoss = jit(BinaryLogisticRegression.loss(valData, valLabels))
     val learningRate = 5e-1f
-    val gd = GradientDescent(Tensor0(learningRate))
+    val gd = GradientDescent(learningRate)
 
     // Training loop
     val numiterations = 1000
diff --git a/examples/src/main/scala/complex/VariationalAutoencoder.scala b/examples/src/main/scala/complex/VariationalAutoencoder.scala
index a075f99..8fba39e 100644
--- a/examples/src/main/scala/complex/VariationalAutoencoder.scala
+++ b/examples/src/main/scala/complex/VariationalAutoencoder.scala
@@ -209,7 +209,7 @@ object VariationalAutoencoderExample:
       losses.sum / batchSize.toFloat
 
     val batches = trainImages.chunk(Axis[TrainSample], numSamples / batchSize)
-    val optimizer = GradientDescent(learningRate = Tensor0(learningRate))
+    val optimizer = GradientDescent(learningRate = learningRate)
     def trainBatch(trainKey: Random.Key, batch: Tensor3[TrainSample, Height, Width, Float32], params: Params): Params =
       val grads = grad(batchLoss(trainKey, batch))(params)
       val (newParams, _) = optimizer.update(grads, params, ())