diff --git a/dev_swift/03_minibatch_training.ipynb b/dev_swift/03_minibatch_training.ipynb
index 6887bfebd..719858553 100644
--- a/dev_swift/03_minibatch_training.ipynb
+++ b/dev_swift/03_minibatch_training.ipynb
@@ -779,7 +779,7 @@
     "    lossFunc: @escaping @differentiable (Opt.Model.Output, @nondiff Label) -> Tensor<Opt.Scalar>\n",
     ") where Opt.Model: Layer,\n",
     "        Opt.Model.Input: TensorGroup,\n",
-    "        Opt.Model.CotangentVector == Opt.Model.AllDifferentiableVariables,\n",
+    "        Opt.Model.TangentVector == Opt.Model.AllDifferentiableVariables,\n",
     "        Opt.Scalar: TensorFlowFloatingPoint\n",
     "{\n",
     "    for batch in ds {\n",
diff --git a/dev_swift/07_batchnorm.ipynb b/dev_swift/07_batchnorm.ipynb
index 4821b0ea5..660827704 100644
--- a/dev_swift/07_batchnorm.ipynb
+++ b/dev_swift/07_batchnorm.ipynb
@@ -236,8 +236,8 @@
     "\n",
     "    @differentiating(forward)\n",
     "    func gradForward(_ input: Input) ->\n",
-    "        (value: Output, pullback: (Self.Output.CotangentVector) ->\n",
-    "            (Self.CotangentVector, Self.Input.CotangentVector)) {\n",
+    "        (value: Output, pullback: (Self.Output.TangentVector) ->\n",
+    "            (Self.TangentVector, Self.Input.TangentVector)) {\n",
     "        switch Context.local.learningPhase {\n",
     "        case .training:\n",
     "            return valueWithPullback(at: input) { $0.forwardTraining ($1) }\n",
@@ -382,9 +382,9 @@
     "    static func _vjpFusedBatchNorm(\n",
     "        _ x : Tensor<Scalar>, scale: Tensor<Scalar>, offset: Tensor<Scalar>, epsilon: Scalar\n",
     "    ) -> (BatchNormResult<Scalar>, \n",
-    "          (BatchNormResult<Scalar>.CotangentVector) -> (Tensor<Scalar>.CotangentVector, \n",
-    "                                                        Tensor<Scalar>.CotangentVector, \n",
-    "                                                        Tensor<Scalar>.CotangentVector)) {\n",
+    "          (BatchNormResult<Scalar>.TangentVector) -> (Tensor<Scalar>.TangentVector, \n",
+    "                                                        Tensor<Scalar>.TangentVector, \n",
+    "                                                        Tensor<Scalar>.TangentVector)) {\n",
     "      let bnresult = fusedBatchNorm(x, scale: scale, offset: offset, epsilon: epsilon)\n",
     "  \n",
     "        return (\n",
diff --git a/dev_swift/07b_batchnorm_lesson.ipynb b/dev_swift/07b_batchnorm_lesson.ipynb
index 5c4bb7d14..63a89c780 100644
--- a/dev_swift/07b_batchnorm_lesson.ipynb
+++ b/dev_swift/07b_batchnorm_lesson.ipynb
@@ -177,8 +177,8 @@
     "\n",
     "    @differentiating(forward)\n",
     "    func gradForward(_ input: Input) ->\n",
-    "        (value: Output, pullback: (Self.Output.CotangentVector) ->\n",
-    "            (Self.CotangentVector, Self.Input.CotangentVector)) {\n",
+    "        (value: Output, pullback: (Self.Output.TangentVector) ->\n",
+    "            (Self.TangentVector, Self.Input.TangentVector)) {\n",
     "        switch Context.local.learningPhase {\n",
     "        case .training:  return valueWithPullback(at: input) { $0.forwardTraining($1)  }\n",
     "        case .inference: return valueWithPullback(at: input) { $0.forwardInference($1) }\n",
@@ -260,7 +260,7 @@
    "source": [
     "//export\n",
     "public struct ConvNorm<NormType: Norm & FALayer>: FALayer\n",
-    "    where NormType.AllDifferentiableVariables == NormType.CotangentVector {\n",
+    "    where NormType.AllDifferentiableVariables == NormType.TangentVector {\n",
     "    public var conv: FANoBiasConv2D<Float>\n",
     "    public var norm: NormType\n",
     "    \n",
@@ -285,7 +285,7 @@
    "source": [
     "//export\n",
     "public struct CnnModelNormed<NormType: Norm & FALayer>: FALayer\n",
-    "    where NormType.AllDifferentiableVariables == NormType.CotangentVector {\n",
+    "    where NormType.AllDifferentiableVariables == NormType.TangentVector {\n",
     "    public var convs: [ConvNorm<NormType>]\n",
     "    public var pool = FAGlobalAvgPool2D<Float>()\n",
     "    public var linear: FADense<Float>\n",
@@ -416,10 +416,10 @@
     "\n",
     "func xlaCompiled<T : Differentiable & TensorGroup, U : Differentiable & TensorGroup>(\n",
     "    _ fn: @escaping @differentiable (T) -> U) -> CompiledFunction<T, U>\n",
-    "    where T.CotangentVector : TensorGroup, U.CotangentVector : TensorGroup {\n",
+    "    where T.TangentVector : TensorGroup, U.TangentVector : TensorGroup {\n",
     "    let xlaCompiledFn: (T) -> U = _graph(fn, useXLA: true)\n",
     "    let xlaCompiledPullback = _graph(\n",
-    "        { (pbArgs: PullbackArgs<T, U.CotangentVector>) in\n",
+    "        { (pbArgs: PullbackArgs<T, U.TangentVector>) in\n",
     "            pullback(at: pbArgs.input, in: fn)(pbArgs.cotangent) },\n",
     "        useXLA: true\n",
     "    )\n",
diff --git a/dev_swift/09_optimizer.ipynb b/dev_swift/09_optimizer.ipynb
index a776ec6a6..a756f6282 100644
--- a/dev_swift/09_optimizer.ipynb
+++ b/dev_swift/09_optimizer.ipynb
@@ -264,7 +264,7 @@
    "source": [
     "//export\n",
     "public class StatefulOptimizer<Model: Layer>\n",
-    "    where Model.AllDifferentiableVariables == Model.CotangentVector {\n",
+    "    where Model.AllDifferentiableVariables == Model.TangentVector {\n",
     "    public typealias ModelKeyPath = WritableKeyPath<Model.AllDifferentiableVariables, TF>\n",
     "    public typealias SplitDict = [ModelKeyPath: Int]\n",
     "    public var hpGroups: [[String:Float]]\n",
@@ -291,7 +291,7 @@
     "        \n",
     "    public func update(\n",
     "        _ variables: inout Model.AllDifferentiableVariables,\n",
-    "        along direction: Model.CotangentVector\n",
+    "        along direction: Model.TangentVector\n",
     "    ) {\n",
     "        for kp in variables.keyPaths {\n",
     "            var 𝛁p = direction[keyPath: kp]\n",
@@ -949,7 +949,7 @@
    "source": [
     "// export\n",
     "extension Learner where Opt.Scalar: BinaryFloatingPoint, \n",
-    "    Opt.Model.AllDifferentiableVariables == Opt.Model.CotangentVector{\n",
+    "    Opt.Model.AllDifferentiableVariables == Opt.Model.TangentVector{\n",
     "    public class ParamScheduler: Delegate {\n",
     "        public override var order: Int { return 1 }\n",
     "        public typealias ScheduleFunc = (Float) -> Float\n",
@@ -1011,7 +1011,7 @@
    "source": [
     "// export\n",
     "extension Learner where Opt.Scalar: BinaryFloatingPoint, \n",
-    "    Opt.Model.AllDifferentiableVariables == Opt.Model.CotangentVector{\n",
+    "    Opt.Model.AllDifferentiableVariables == Opt.Model.TangentVector{\n",
     "\n",
     "    public func addOneCycleDelegates(_ lrMax: Float, pctStart:Float=0.25, divStart: Float = 10, divEnd: Float = 1e5, \n",
     "                               moms: (Float,Float,Float) = (0.95,0.85,0.95)) {\n",
diff --git a/dev_swift/11_imagenette.ipynb b/dev_swift/11_imagenette.ipynb
index ea42ffe35..2d086ae9f 100644
--- a/dev_swift/11_imagenette.ipynb
+++ b/dev_swift/11_imagenette.ipynb
@@ -312,12 +312,12 @@
     "    @differentiating(callAsFunction)\n",
     "    func gradForward(_ input: Input) ->\n",
     "           (value: Input,\n",
-    "            pullback: (Self.Input.CotangentVector) ->\n",
-    "                                  (Self.CotangentVector, Self.Input.CotangentVector)) {\n",
+    "            pullback: (Self.Input.TangentVector) ->\n",
+    "                                  (Self.TangentVector, Self.Input.TangentVector)) {\n",
     "        if isOn {\n",
     "            return valueWithPullback(at: input) { $0.forward($1) } \n",
     "        } else {\n",
-    "            return (input, { (Self.CotangentVector.zero, $0) }) \n",
+    "            return (input, { (Self.TangentVector.zero, $0) }) \n",
     "        }\n",
     "    }\n",
     "}"
diff --git a/dev_swift/FastaiNotebook_07_batchnorm/Sources/FastaiNotebook_07_batchnorm/07_batchnorm.swift b/dev_swift/FastaiNotebook_07_batchnorm/Sources/FastaiNotebook_07_batchnorm/07_batchnorm.swift
index 06bffeef8..69fb13a20 100644
--- a/dev_swift/FastaiNotebook_07_batchnorm/Sources/FastaiNotebook_07_batchnorm/07_batchnorm.swift
+++ b/dev_swift/FastaiNotebook_07_batchnorm/Sources/FastaiNotebook_07_batchnorm/07_batchnorm.swift
@@ -38,8 +38,8 @@ extension LearningPhaseDependent {
 
     @differentiating(forward)
     func gradForward(_ input: Input) ->
-        (value: Output, pullback: (Self.Output.CotangentVector) ->
-            (Self.CotangentVector, Self.Input.CotangentVector)) {
+        (value: Output, pullback: (Self.Output.TangentVector) ->
+            (Self.TangentVector, Self.Input.TangentVector)) {
         switch Context.local.learningPhase {
         case .training:
             return valueWithPullback(at: input) { $0.forwardTraining ($1) }
@@ -154,9 +154,9 @@ public struct TFBatchNorm<Scalar: TensorFlowFloatingPoint>: LearningPhaseDepende
     static func _vjpFusedBatchNorm(
         _ x : Tensor<Scalar>, scale: Tensor<Scalar>, offset: Tensor<Scalar>, epsilon: Scalar
     ) -> (BatchNormResult<Scalar>, 
-          (BatchNormResult<Scalar>.CotangentVector) -> (Tensor<Scalar>.CotangentVector, 
-                                                        Tensor<Scalar>.CotangentVector, 
-                                                        Tensor<Scalar>.CotangentVector)) {
+          (BatchNormResult<Scalar>.TangentVector) -> (Tensor<Scalar>.TangentVector, 
+                                                        Tensor<Scalar>.TangentVector, 
+                                                        Tensor<Scalar>.TangentVector)) {
       let bnresult = fusedBatchNorm(x, scale: scale, offset: offset, epsilon: epsilon)
   
         return (
diff --git a/dev_swift/FastaiNotebook_08_data_block/Sources/FastaiNotebook_08_data_block/07_batchnorm.swift b/dev_swift/FastaiNotebook_08_data_block/Sources/FastaiNotebook_08_data_block/07_batchnorm.swift
index 06bffeef8..69fb13a20 100644
--- a/dev_swift/FastaiNotebook_08_data_block/Sources/FastaiNotebook_08_data_block/07_batchnorm.swift
+++ b/dev_swift/FastaiNotebook_08_data_block/Sources/FastaiNotebook_08_data_block/07_batchnorm.swift
@@ -38,8 +38,8 @@ extension LearningPhaseDependent {
 
     @differentiating(forward)
     func gradForward(_ input: Input) ->
-        (value: Output, pullback: (Self.Output.CotangentVector) ->
-            (Self.CotangentVector, Self.Input.CotangentVector)) {
+        (value: Output, pullback: (Self.Output.TangentVector) ->
+            (Self.TangentVector, Self.Input.TangentVector)) {
         switch Context.local.learningPhase {
         case .training:
             return valueWithPullback(at: input) { $0.forwardTraining ($1) }
@@ -154,9 +154,9 @@ public struct TFBatchNorm<Scalar: TensorFlowFloatingPoint>: LearningPhaseDepende
     static func _vjpFusedBatchNorm(
         _ x : Tensor<Scalar>, scale: Tensor<Scalar>, offset: Tensor<Scalar>, epsilon: Scalar
     ) -> (BatchNormResult<Scalar>, 
-          (BatchNormResult<Scalar>.CotangentVector) -> (Tensor<Scalar>.CotangentVector, 
-                                                        Tensor<Scalar>.CotangentVector, 
-                                                        Tensor<Scalar>.CotangentVector)) {
+          (BatchNormResult<Scalar>.TangentVector) -> (Tensor<Scalar>.TangentVector, 
+                                                        Tensor<Scalar>.TangentVector, 
+                                                        Tensor<Scalar>.TangentVector)) {
       let bnresult = fusedBatchNorm(x, scale: scale, offset: offset, epsilon: epsilon)
   
         return (
diff --git a/dev_swift/FastaiNotebook_08a_heterogeneous_dictionary/Sources/FastaiNotebook_08a_heterogeneous_dictionary/07_batchnorm.swift b/dev_swift/FastaiNotebook_08a_heterogeneous_dictionary/Sources/FastaiNotebook_08a_heterogeneous_dictionary/07_batchnorm.swift
index 06bffeef8..69fb13a20 100644
--- a/dev_swift/FastaiNotebook_08a_heterogeneous_dictionary/Sources/FastaiNotebook_08a_heterogeneous_dictionary/07_batchnorm.swift
+++ b/dev_swift/FastaiNotebook_08a_heterogeneous_dictionary/Sources/FastaiNotebook_08a_heterogeneous_dictionary/07_batchnorm.swift
@@ -38,8 +38,8 @@ extension LearningPhaseDependent {
 
     @differentiating(forward)
     func gradForward(_ input: Input) ->
-        (value: Output, pullback: (Self.Output.CotangentVector) ->
-            (Self.CotangentVector, Self.Input.CotangentVector)) {
+        (value: Output, pullback: (Self.Output.TangentVector) ->
+            (Self.TangentVector, Self.Input.TangentVector)) {
         switch Context.local.learningPhase {
         case .training:
             return valueWithPullback(at: input) { $0.forwardTraining ($1) }
@@ -154,9 +154,9 @@ public struct TFBatchNorm<Scalar: TensorFlowFloatingPoint>: LearningPhaseDepende
     static func _vjpFusedBatchNorm(
         _ x : Tensor<Scalar>, scale: Tensor<Scalar>, offset: Tensor<Scalar>, epsilon: Scalar
     ) -> (BatchNormResult<Scalar>, 
-          (BatchNormResult<Scalar>.CotangentVector) -> (Tensor<Scalar>.CotangentVector, 
-                                                        Tensor<Scalar>.CotangentVector, 
-                                                        Tensor<Scalar>.CotangentVector)) {
+          (BatchNormResult<Scalar>.TangentVector) -> (Tensor<Scalar>.TangentVector, 
+                                                        Tensor<Scalar>.TangentVector, 
+                                                        Tensor<Scalar>.TangentVector)) {
       let bnresult = fusedBatchNorm(x, scale: scale, offset: offset, epsilon: epsilon)
   
         return (
diff --git a/dev_swift/FastaiNotebook_08c_data_block_generic/Sources/FastaiNotebook_08c_data_block_generic/07_batchnorm.swift b/dev_swift/FastaiNotebook_08c_data_block_generic/Sources/FastaiNotebook_08c_data_block_generic/07_batchnorm.swift
index 06bffeef8..69fb13a20 100644
--- a/dev_swift/FastaiNotebook_08c_data_block_generic/Sources/FastaiNotebook_08c_data_block_generic/07_batchnorm.swift
+++ b/dev_swift/FastaiNotebook_08c_data_block_generic/Sources/FastaiNotebook_08c_data_block_generic/07_batchnorm.swift
@@ -38,8 +38,8 @@ extension LearningPhaseDependent {
 
     @differentiating(forward)
     func gradForward(_ input: Input) ->
-        (value: Output, pullback: (Self.Output.CotangentVector) ->
-            (Self.CotangentVector, Self.Input.CotangentVector)) {
+        (value: Output, pullback: (Self.Output.TangentVector) ->
+            (Self.TangentVector, Self.Input.TangentVector)) {
         switch Context.local.learningPhase {
         case .training:
             return valueWithPullback(at: input) { $0.forwardTraining ($1) }
@@ -154,9 +154,9 @@ public struct TFBatchNorm<Scalar: TensorFlowFloatingPoint>: LearningPhaseDepende
     static func _vjpFusedBatchNorm(
         _ x : Tensor<Scalar>, scale: Tensor<Scalar>, offset: Tensor<Scalar>, epsilon: Scalar
     ) -> (BatchNormResult<Scalar>, 
-          (BatchNormResult<Scalar>.CotangentVector) -> (Tensor<Scalar>.CotangentVector, 
-                                                        Tensor<Scalar>.CotangentVector, 
-                                                        Tensor<Scalar>.CotangentVector)) {
+          (BatchNormResult<Scalar>.TangentVector) -> (Tensor<Scalar>.TangentVector, 
+                                                        Tensor<Scalar>.TangentVector, 
+                                                        Tensor<Scalar>.TangentVector)) {
       let bnresult = fusedBatchNorm(x, scale: scale, offset: offset, epsilon: epsilon)
   
         return (
diff --git a/dev_swift/FastaiNotebook_09_optimizer/Sources/FastaiNotebook_09_optimizer/07_batchnorm.swift b/dev_swift/FastaiNotebook_09_optimizer/Sources/FastaiNotebook_09_optimizer/07_batchnorm.swift
index 06bffeef8..69fb13a20 100644
--- a/dev_swift/FastaiNotebook_09_optimizer/Sources/FastaiNotebook_09_optimizer/07_batchnorm.swift
+++ b/dev_swift/FastaiNotebook_09_optimizer/Sources/FastaiNotebook_09_optimizer/07_batchnorm.swift
@@ -38,8 +38,8 @@ extension LearningPhaseDependent {
 
     @differentiating(forward)
     func gradForward(_ input: Input) ->
-        (value: Output, pullback: (Self.Output.CotangentVector) ->
-            (Self.CotangentVector, Self.Input.CotangentVector)) {
+        (value: Output, pullback: (Self.Output.TangentVector) ->
+            (Self.TangentVector, Self.Input.TangentVector)) {
         switch Context.local.learningPhase {
         case .training:
             return valueWithPullback(at: input) { $0.forwardTraining ($1) }
@@ -154,9 +154,9 @@ public struct TFBatchNorm<Scalar: TensorFlowFloatingPoint>: LearningPhaseDepende
     static func _vjpFusedBatchNorm(
         _ x : Tensor<Scalar>, scale: Tensor<Scalar>, offset: Tensor<Scalar>, epsilon: Scalar
     ) -> (BatchNormResult<Scalar>, 
-          (BatchNormResult<Scalar>.CotangentVector) -> (Tensor<Scalar>.CotangentVector, 
-                                                        Tensor<Scalar>.CotangentVector, 
-                                                        Tensor<Scalar>.CotangentVector)) {
+          (BatchNormResult<Scalar>.TangentVector) -> (Tensor<Scalar>.TangentVector, 
+                                                        Tensor<Scalar>.TangentVector, 
+                                                        Tensor<Scalar>.TangentVector)) {
       let bnresult = fusedBatchNorm(x, scale: scale, offset: offset, epsilon: epsilon)
   
         return (
diff --git a/dev_swift/FastaiNotebook_09_optimizer/Sources/FastaiNotebook_09_optimizer/09_optimizer.swift b/dev_swift/FastaiNotebook_09_optimizer/Sources/FastaiNotebook_09_optimizer/09_optimizer.swift
index 205c159b9..3f74b2dcd 100644
--- a/dev_swift/FastaiNotebook_09_optimizer/Sources/FastaiNotebook_09_optimizer/09_optimizer.swift
+++ b/dev_swift/FastaiNotebook_09_optimizer/Sources/FastaiNotebook_09_optimizer/09_optimizer.swift
@@ -58,7 +58,7 @@ public func initState<Model: Layer>(for model: Model, names: [String])
 }
 
 public class StatefulOptimizer<Model: Layer>
-    where Model.AllDifferentiableVariables == Model.CotangentVector {
+    where Model.AllDifferentiableVariables == Model.TangentVector {
     public typealias ModelKeyPath = WritableKeyPath<Model.AllDifferentiableVariables, TF>
     public typealias SplitDict = [ModelKeyPath: Int]
     public var hpGroups: [[String:Float]]
@@ -85,7 +85,7 @@ public class StatefulOptimizer<Model: Layer>
         
     public func update(
         _ variables: inout Model.AllDifferentiableVariables,
-        along direction: Model.CotangentVector
+        along direction: Model.TangentVector
     ) {
         for kp in variables.keyPaths {
             var 𝛁p = direction[keyPath: kp]
@@ -273,7 +273,7 @@ public extension StatefulOptimizer {
 }
 
 extension Learner where Opt.Scalar: BinaryFloatingPoint, 
-    Opt.Model.AllDifferentiableVariables == Opt.Model.CotangentVector{
+    Opt.Model.AllDifferentiableVariables == Opt.Model.TangentVector{
     public class ParamScheduler: Delegate {
         public override var order: Int { return 1 }
         public typealias ScheduleFunc = (Float) -> Float
@@ -312,7 +312,7 @@ public func oneCycleSchedulers(_ lrMax: Float, pctStart:Float=0.25, divStart: Fl
 }
 
 extension Learner where Opt.Scalar: BinaryFloatingPoint, 
-    Opt.Model.AllDifferentiableVariables == Opt.Model.CotangentVector{
+    Opt.Model.AllDifferentiableVariables == Opt.Model.TangentVector{
 
     public func addOneCycleDelegates(_ lrMax: Float, pctStart:Float=0.25, divStart: Float = 10, divEnd: Float = 1e5, 
                                moms: (Float,Float,Float) = (0.95,0.85,0.95)) {
diff --git a/dev_swift/FastaiNotebook_10_mixup_ls/Sources/FastaiNotebook_10_mixup_ls/07_batchnorm.swift b/dev_swift/FastaiNotebook_10_mixup_ls/Sources/FastaiNotebook_10_mixup_ls/07_batchnorm.swift
index 06bffeef8..69fb13a20 100644
--- a/dev_swift/FastaiNotebook_10_mixup_ls/Sources/FastaiNotebook_10_mixup_ls/07_batchnorm.swift
+++ b/dev_swift/FastaiNotebook_10_mixup_ls/Sources/FastaiNotebook_10_mixup_ls/07_batchnorm.swift
@@ -38,8 +38,8 @@ extension LearningPhaseDependent {
 
     @differentiating(forward)
     func gradForward(_ input: Input) ->
-        (value: Output, pullback: (Self.Output.CotangentVector) ->
-            (Self.CotangentVector, Self.Input.CotangentVector)) {
+        (value: Output, pullback: (Self.Output.TangentVector) ->
+            (Self.TangentVector, Self.Input.TangentVector)) {
         switch Context.local.learningPhase {
         case .training:
             return valueWithPullback(at: input) { $0.forwardTraining ($1) }
@@ -154,9 +154,9 @@ public struct TFBatchNorm<Scalar: TensorFlowFloatingPoint>: LearningPhaseDepende
     static func _vjpFusedBatchNorm(
         _ x : Tensor<Scalar>, scale: Tensor<Scalar>, offset: Tensor<Scalar>, epsilon: Scalar
     ) -> (BatchNormResult<Scalar>, 
-          (BatchNormResult<Scalar>.CotangentVector) -> (Tensor<Scalar>.CotangentVector, 
-                                                        Tensor<Scalar>.CotangentVector, 
-                                                        Tensor<Scalar>.CotangentVector)) {
+          (BatchNormResult<Scalar>.TangentVector) -> (Tensor<Scalar>.TangentVector, 
+                                                        Tensor<Scalar>.TangentVector, 
+                                                        Tensor<Scalar>.TangentVector)) {
       let bnresult = fusedBatchNorm(x, scale: scale, offset: offset, epsilon: epsilon)
   
         return (
diff --git a/dev_swift/FastaiNotebook_10_mixup_ls/Sources/FastaiNotebook_10_mixup_ls/09_optimizer.swift b/dev_swift/FastaiNotebook_10_mixup_ls/Sources/FastaiNotebook_10_mixup_ls/09_optimizer.swift
index 205c159b9..3f74b2dcd 100644
--- a/dev_swift/FastaiNotebook_10_mixup_ls/Sources/FastaiNotebook_10_mixup_ls/09_optimizer.swift
+++ b/dev_swift/FastaiNotebook_10_mixup_ls/Sources/FastaiNotebook_10_mixup_ls/09_optimizer.swift
@@ -58,7 +58,7 @@ public func initState<Model: Layer>(for model: Model, names: [String])
 }
 
 public class StatefulOptimizer<Model: Layer>
-    where Model.AllDifferentiableVariables == Model.CotangentVector {
+    where Model.AllDifferentiableVariables == Model.TangentVector {
     public typealias ModelKeyPath = WritableKeyPath<Model.AllDifferentiableVariables, TF>
     public typealias SplitDict = [ModelKeyPath: Int]
     public var hpGroups: [[String:Float]]
@@ -85,7 +85,7 @@ public class StatefulOptimizer<Model: Layer>
         
     public func update(
         _ variables: inout Model.AllDifferentiableVariables,
-        along direction: Model.CotangentVector
+        along direction: Model.TangentVector
     ) {
         for kp in variables.keyPaths {
             var 𝛁p = direction[keyPath: kp]
@@ -273,7 +273,7 @@ public extension StatefulOptimizer {
 }
 
 extension Learner where Opt.Scalar: BinaryFloatingPoint, 
-    Opt.Model.AllDifferentiableVariables == Opt.Model.CotangentVector{
+    Opt.Model.AllDifferentiableVariables == Opt.Model.TangentVector{
     public class ParamScheduler: Delegate {
         public override var order: Int { return 1 }
         public typealias ScheduleFunc = (Float) -> Float
@@ -312,7 +312,7 @@ public func oneCycleSchedulers(_ lrMax: Float, pctStart:Float=0.25, divStart: Fl
 }
 
 extension Learner where Opt.Scalar: BinaryFloatingPoint, 
-    Opt.Model.AllDifferentiableVariables == Opt.Model.CotangentVector{
+    Opt.Model.AllDifferentiableVariables == Opt.Model.TangentVector{
 
     public func addOneCycleDelegates(_ lrMax: Float, pctStart:Float=0.25, divStart: Float = 10, divEnd: Float = 1e5, 
                                moms: (Float,Float,Float) = (0.95,0.85,0.95)) {
diff --git a/dev_swift/FastaiNotebook_11_imagenette/Sources/FastaiNotebook_11_imagenette/07_batchnorm.swift b/dev_swift/FastaiNotebook_11_imagenette/Sources/FastaiNotebook_11_imagenette/07_batchnorm.swift
index 06bffeef8..69fb13a20 100644
--- a/dev_swift/FastaiNotebook_11_imagenette/Sources/FastaiNotebook_11_imagenette/07_batchnorm.swift
+++ b/dev_swift/FastaiNotebook_11_imagenette/Sources/FastaiNotebook_11_imagenette/07_batchnorm.swift
@@ -38,8 +38,8 @@ extension LearningPhaseDependent {
 
     @differentiating(forward)
     func gradForward(_ input: Input) ->
-        (value: Output, pullback: (Self.Output.CotangentVector) ->
-            (Self.CotangentVector, Self.Input.CotangentVector)) {
+        (value: Output, pullback: (Self.Output.TangentVector) ->
+            (Self.TangentVector, Self.Input.TangentVector)) {
         switch Context.local.learningPhase {
         case .training:
             return valueWithPullback(at: input) { $0.forwardTraining ($1) }
@@ -154,9 +154,9 @@ public struct TFBatchNorm<Scalar: TensorFlowFloatingPoint>: LearningPhaseDepende
     static func _vjpFusedBatchNorm(
         _ x : Tensor<Scalar>, scale: Tensor<Scalar>, offset: Tensor<Scalar>, epsilon: Scalar
     ) -> (BatchNormResult<Scalar>, 
-          (BatchNormResult<Scalar>.CotangentVector) -> (Tensor<Scalar>.CotangentVector, 
-                                                        Tensor<Scalar>.CotangentVector, 
-                                                        Tensor<Scalar>.CotangentVector)) {
+          (BatchNormResult<Scalar>.TangentVector) -> (Tensor<Scalar>.TangentVector, 
+                                                        Tensor<Scalar>.TangentVector, 
+                                                        Tensor<Scalar>.TangentVector)) {
       let bnresult = fusedBatchNorm(x, scale: scale, offset: offset, epsilon: epsilon)
   
         return (
diff --git a/dev_swift/FastaiNotebook_11_imagenette/Sources/FastaiNotebook_11_imagenette/09_optimizer.swift b/dev_swift/FastaiNotebook_11_imagenette/Sources/FastaiNotebook_11_imagenette/09_optimizer.swift
index 205c159b9..3f74b2dcd 100644
--- a/dev_swift/FastaiNotebook_11_imagenette/Sources/FastaiNotebook_11_imagenette/09_optimizer.swift
+++ b/dev_swift/FastaiNotebook_11_imagenette/Sources/FastaiNotebook_11_imagenette/09_optimizer.swift
@@ -58,7 +58,7 @@ public func initState<Model: Layer>(for model: Model, names: [String])
 }
 
 public class StatefulOptimizer<Model: Layer>
-    where Model.AllDifferentiableVariables == Model.CotangentVector {
+    where Model.AllDifferentiableVariables == Model.TangentVector {
     public typealias ModelKeyPath = WritableKeyPath<Model.AllDifferentiableVariables, TF>
     public typealias SplitDict = [ModelKeyPath: Int]
     public var hpGroups: [[String:Float]]
@@ -85,7 +85,7 @@ public class StatefulOptimizer<Model: Layer>
         
     public func update(
         _ variables: inout Model.AllDifferentiableVariables,
-        along direction: Model.CotangentVector
+        along direction: Model.TangentVector
     ) {
         for kp in variables.keyPaths {
             var 𝛁p = direction[keyPath: kp]
@@ -273,7 +273,7 @@ public extension StatefulOptimizer {
 }
 
 extension Learner where Opt.Scalar: BinaryFloatingPoint, 
-    Opt.Model.AllDifferentiableVariables == Opt.Model.CotangentVector{
+    Opt.Model.AllDifferentiableVariables == Opt.Model.TangentVector{
     public class ParamScheduler: Delegate {
         public override var order: Int { return 1 }
         public typealias ScheduleFunc = (Float) -> Float
@@ -312,7 +312,7 @@ public func oneCycleSchedulers(_ lrMax: Float, pctStart:Float=0.25, divStart: Fl
 }
 
 extension Learner where Opt.Scalar: BinaryFloatingPoint, 
-    Opt.Model.AllDifferentiableVariables == Opt.Model.CotangentVector{
+    Opt.Model.AllDifferentiableVariables == Opt.Model.TangentVector{
 
     public func addOneCycleDelegates(_ lrMax: Float, pctStart:Float=0.25, divStart: Float = 10, divEnd: Float = 1e5, 
                                moms: (Float,Float,Float) = (0.95,0.85,0.95)) {
diff --git a/dev_swift/FastaiNotebook_11_imagenette/Sources/FastaiNotebook_11_imagenette/11_imagenette.swift b/dev_swift/FastaiNotebook_11_imagenette/Sources/FastaiNotebook_11_imagenette/11_imagenette.swift
index be95b875f..ea9438f45 100644
--- a/dev_swift/FastaiNotebook_11_imagenette/Sources/FastaiNotebook_11_imagenette/11_imagenette.swift
+++ b/dev_swift/FastaiNotebook_11_imagenette/Sources/FastaiNotebook_11_imagenette/11_imagenette.swift
@@ -44,12 +44,12 @@ public extension SwitchableLayer {
     @differentiating(callAsFunction)
     func gradForward(_ input: Input) ->
            (value: Input,
-            pullback: (Self.Input.CotangentVector) ->
-                                  (Self.CotangentVector, Self.Input.CotangentVector)) {
+            pullback: (Self.Input.TangentVector) ->
+                                  (Self.TangentVector, Self.Input.TangentVector)) {
         if isOn {
             return valueWithPullback(at: input) { $0.forward($1) } 
         } else {
-            return (input, { (Self.CotangentVector.zero, $0) }) 
+            return (input, { (Self.TangentVector.zero, $0) }) 
         }
     }
 }
diff --git a/dev_swift/Runnable11/Sources/Runnable11/01a_fastai_layers.swift b/dev_swift/Runnable11/Sources/Runnable11/01a_fastai_layers.swift
index 29fdd341b..b99950c67 100644
--- a/dev_swift/Runnable11/Sources/Runnable11/01a_fastai_layers.swift
+++ b/dev_swift/Runnable11/Sources/Runnable11/01a_fastai_layers.swift
@@ -52,7 +52,7 @@ public extension FALayer {
     }
     
     func callGrad(_ input: Input) ->
-        (Output, (Self.Output.CotangentVector) -> (Self.CotangentVector, Self.Input.CotangentVector)) {
+        (Output, (Self.Output.TangentVector) -> (Self.TangentVector, Self.Input.TangentVector)) {
         return Swift.valueWithPullback(at: self, input) { (m, i) in m.forward(i) }
     }
 }
@@ -288,24 +288,24 @@ extension Array: Layer where Element: Layer, Element.Input == Element.Output {
     }
     
     public func _vjpApplied(_ input: Input)
-        -> (Output, (Output.CotangentVector) -> (Array.CotangentVector, Input.CotangentVector))
+        -> (Output, (Output.TangentVector) -> (Array.TangentVector, Input.TangentVector))
     {
         var activation = input
-        var pullbacks: [(Input.CotangentVector) -> (Element.CotangentVector, Input.CotangentVector)] = []
+        var pullbacks: [(Input.TangentVector) -> (Element.TangentVector, Input.TangentVector)] = []
         for layer in self {
             let (newActivation, newPullback) = layer.valueWithPullback(at: activation) { $0($1) }
             activation = newActivation
             pullbacks.append(newPullback)
         }
-        func pullback(_ v: Input.CotangentVector) -> (Array.CotangentVector, Input.CotangentVector) {
+        func pullback(_ v: Input.TangentVector) -> (Array.TangentVector, Input.TangentVector) {
             var activationGradient = v
-            var layerGradients: [Element.CotangentVector] = []
+            var layerGradients: [Element.TangentVector] = []
             for pullback in pullbacks.reversed() {
                 let (newLayerGradient, newActivationGradient) = pullback(activationGradient)
                 activationGradient = newActivationGradient
                 layerGradients.append(newLayerGradient)
             }
-            return (Array.CotangentVector(layerGradients.reversed()), activationGradient)
+            return (Array.TangentVector(layerGradients.reversed()), activationGradient)
         }
         return (activation, pullback)
     }
diff --git a/dev_swift/Runnable11/Sources/Runnable11/04_callbacks.swift b/dev_swift/Runnable11/Sources/Runnable11/04_callbacks.swift
index 1c7ea127e..5a9c0d4aa 100644
--- a/dev_swift/Runnable11/Sources/Runnable11/04_callbacks.swift
+++ b/dev_swift/Runnable11/Sources/Runnable11/04_callbacks.swift
@@ -115,7 +115,7 @@ public final class Learner<Label: TensorGroup,
     /// The current epoch.
     public private(set) var currentEpoch: Int = .zero
     /// The current gradient.
-    public private(set) var currentGradient: Model.CotangentVector = .zero
+    public private(set) var currentGradient: Model.TangentVector = .zero
     /// The current loss.
     public private(set) var currentLoss: Loss = .zero
     /// In training mode or not
diff --git a/dev_swift/Runnable11/Sources/Runnable11/07_batchnorm.swift b/dev_swift/Runnable11/Sources/Runnable11/07_batchnorm.swift
index 91fa8fd0f..43d538e37 100644
--- a/dev_swift/Runnable11/Sources/Runnable11/07_batchnorm.swift
+++ b/dev_swift/Runnable11/Sources/Runnable11/07_batchnorm.swift
@@ -35,8 +35,8 @@ public extension LearningPhaseDependent {
     }
 
     func gradForward(_ input: Input) ->
-        (Output, (Self.Output.CotangentVector) ->
-            (Self.CotangentVector, Self.Input.CotangentVector)) {
+        (Output, (Self.Output.TangentVector) ->
+            (Self.TangentVector, Self.Input.TangentVector)) {
         switch Context.local.learningPhase {
         case .training:
             return valueWithPullback(at: input) { $0.forwardTraining(to: $1) }
diff --git a/dev_swift/Runnable11/Sources/Runnable11/09_optimizer.swift b/dev_swift/Runnable11/Sources/Runnable11/09_optimizer.swift
index 8d603bc5d..6a8164b4c 100644
--- a/dev_swift/Runnable11/Sources/Runnable11/09_optimizer.swift
+++ b/dev_swift/Runnable11/Sources/Runnable11/09_optimizer.swift
@@ -43,7 +43,7 @@ public extension Tensor where Scalar: Numeric {
 }
 
 public class StatefulOptimizer<Model: Layer>
-    where Model.AllDifferentiableVariables == Model.CotangentVector{
+    where Model.AllDifferentiableVariables == Model.TangentVector{
     public var configs: [HeterogeneousDictionary]
     public var splitFunc: (Int) -> Int
     public var states: [String: Model.AllDifferentiableVariables]
@@ -78,7 +78,7 @@ public class StatefulOptimizer<Model: Layer>
         
     public func update(
         _ model: inout Model.AllDifferentiableVariables,
-        along direction: Model.CotangentVector
+        along direction: Model.TangentVector
     ) {
         for (i,kp) in model.keyPaths.enumerated() {
             var grad = direction[keyPath: kp]
diff --git a/dev_swift/Runnable11/Sources/Runnable11/main.swift b/dev_swift/Runnable11/Sources/Runnable11/main.swift
index 567893e93..546c09f56 100644
--- a/dev_swift/Runnable11/Sources/Runnable11/main.swift
+++ b/dev_swift/Runnable11/Sources/Runnable11/main.swift
@@ -59,10 +59,10 @@ public extension SwitchableLayer {
 
     @differentiating(call)
     func gradForward(_ input: Input) ->
-        (value: Input, pullback: (Self.Input.CotangentVector) ->
-            (Self.CotangentVector, Self.Input.CotangentVector)) {
+        (value: Input, pullback: (Self.Input.TangentVector) ->
+            (Self.TangentVector, Self.Input.TangentVector)) {
         if isOn { return valueWithPullback(at: input) { $0.forward($1) } }
-        else { return (input, {v in return (Self.CotangentVector.zero, v)}) }
+        else { return (input, {v in return (Self.TangentVector.zero, v)}) }
     }
 }
 
diff --git a/dev_swift/audio.ipynb b/dev_swift/audio.ipynb
index 2f3cb0dff..c6d0dbb93 100644
--- a/dev_swift/audio.ipynb
+++ b/dev_swift/audio.ipynb
@@ -597,10 +597,10 @@
     "\n",
     "    @differentiating(call)\n",
     "    func gradForward(_ input: Input) ->\n",
-    "        (value: Input, pullback: (Self.Input.CotangentVector) ->\n",
-    "            (Self.CotangentVector, Self.Input.CotangentVector)) {\n",
+    "        (value: Input, pullback: (Self.Input.TangentVector) ->\n",
+    "            (Self.TangentVector, Self.Input.TangentVector)) {\n",
     "        if isOn { return valueWithPullback(at: input) { $0.forward($1) } }\n",
-    "        else { return (input, {v in return (Self.CotangentVector.zero, v)}) }\n",
+    "        else { return (input, {v in return (Self.TangentVector.zero, v)}) }\n",
     "    }\n",
     "}"
    ]