diff --git a/Sources/TensorFlow/CMakeLists.txt b/Sources/TensorFlow/CMakeLists.txt
index 4644b48fb..cdbd92d83 100644
--- a/Sources/TensorFlow/CMakeLists.txt
+++ b/Sources/TensorFlow/CMakeLists.txt
@@ -37,6 +37,8 @@ add_library(TensorFlow SHARED
   Core/Threading.swift
   Core/Utilities.swift
   Core/EuclideanDifferentiable.swift
+  Core/VectorProtocol.swift
+  Core/PointwiseMultiplicative.swift
   Core/ElementaryFunctions.swift
   
   Epochs/Algorithms.swift
diff --git a/Sources/TensorFlow/Core/EuclideanDifferentiable.swift b/Sources/TensorFlow/Core/EuclideanDifferentiable.swift
index 6a662e931..d5f4fadbc 100644
--- a/Sources/TensorFlow/Core/EuclideanDifferentiable.swift
+++ b/Sources/TensorFlow/Core/EuclideanDifferentiable.swift
@@ -110,4 +110,10 @@ where Element: EuclideanDifferentiable {
     out = Array.DifferentiableView.TangentVector(self.base.map { $0.differentiableVectorView })
   }
 }
+extension RNNCellInput: _EuclideanDifferentiable
+ where Input: EuclideanDifferentiable, State: EuclideanDifferentiable {}
+extension RNNCellOutput: _EuclideanDifferentiable
+ where Output: EuclideanDifferentiable, State: EuclideanDifferentiable {}
+extension Tensor: _EuclideanDifferentiable where Scalar: TensorFlowFloatingPoint {}
+
 #endif
diff --git a/Sources/TensorFlow/Core/PointwiseMultiplicative.swift b/Sources/TensorFlow/Core/PointwiseMultiplicative.swift
new file mode 100644
index 000000000..ef256f928
--- /dev/null
+++ b/Sources/TensorFlow/Core/PointwiseMultiplicative.swift
@@ -0,0 +1,137 @@
+// Copyright 2020 The TensorFlow Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+import _Differentiation
+
+#if TENSORFLOW_USE_STANDARD_TOOLCHAIN
+@_spi(Reflection) import Swift
+
+infix operator .*: MultiplicationPrecedence
+infix operator .*=: AssignmentPrecedence
+
+/// Implementation detail of the reflection default implementation.
+///
+/// Contains versions of functions in PointwiseMultiplicative that
+/// operate over key paths and modify a child of `Root` in-place.
+/// The key paths must all be WritableKeyPath<Root, Self>. This is a workaround
+/// to simulate having Self constraints.
+public protocol _PointwiseMultiplicative {
+  /// lhs[keyPath: kp] .*= rhs[keyPath: kp]
+  static func _pointwiseMult<Root>(_ lhs: inout Root, _ rhs: Root, _ kp: PartialKeyPath<Root>)
+  /// out[keyPath: kp] = Self.one
+  static func _setOne<Root>(_ out: inout Root, _ kp: PartialKeyPath<Root>)
+  /// out[keyPath: kp] = out[keyPath: kp].reciprocal
+  static func _setReciprocal<Root>(_ out: inout Root, _ kp: PartialKeyPath<Root>)
+}
+
+public protocol PointwiseMultiplicative: _PointwiseMultiplicative & AdditiveArithmetic {
+  /// The one value.
+  ///
+  /// One is the identity element for multiplication. For any value,
+  /// `x .* .one == x` and `.one .* x == x`.
+  static var one: Self { get }
+
+  /// The multiplicative inverse of self.
+  ///
+  /// For any value, `x .* x.reciprocal == .one` and
+  /// `x.reciprocal .* x == .one`.
+  var reciprocal: Self { get }
+
+  /// Multiplies two values and produces their product.
+  ///
+  /// - Parameters:
+  ///   - lhs: The first value to multiply.
+  ///   - rhs: The second value to multiply.
+  static func .* (lhs: Self, rhs: Self) -> Self
+
+  /// Multiplies two values and produces their product.
+  ///
+  /// - Parameters:
+  ///   - lhs: The first value to multiply.
+  ///   - rhs: The second value to multiply.
+  static func .*= (lhs: inout Self, rhs: Self)
+}
+
+extension PointwiseMultiplicative {
+  public static func .*= (lhs: inout Self, rhs: Self) {
+    lhs = lhs .* rhs
+  }
+}
+
+extension PointwiseMultiplicative
+where Self: ExpressibleByIntegerLiteral {
+  public static var one: Self {
+    return 1
+  }
+}
+
+extension PointwiseMultiplicative {
+  public static var one: Self {
+    var out = self.zero
+    visitChildren { kp, t in t._setOne(&out, kp) }
+    return out
+  }
+  public var reciprocal: Self {
+    var out = self
+    Self.visitChildren { kp, t in t._setReciprocal(&out, kp) }
+    return out
+  }
+  public static func .* (lhs: Self, rhs: Self) -> Self {
+    var out = lhs
+    visitChildren { kp, t in
+      t._pointwiseMult(&out, rhs, kp)
+    }
+    return out
+  }
+  public static func _pointwiseMult<Root>(
+    _ lhs: inout Root, _ rhs: Root, _ kp: PartialKeyPath<Root>
+  ) {
+    let kp = kp as! WritableKeyPath<Root, Self>
+    lhs[keyPath: kp] .*= rhs[keyPath: kp]
+  }
+  public static func _setOne<Root>(_ out: inout Root, _ kp: PartialKeyPath<Root>) {
+    let kp = kp as! WritableKeyPath<Root, Self>
+    out[keyPath: kp] = Self.one
+  }
+  public static func _setReciprocal<Root>(_ out: inout Root, _ kp: PartialKeyPath<Root>) {
+    let kp = kp as! WritableKeyPath<Root, Self>
+    out[keyPath: kp] = out[keyPath: kp].reciprocal
+  }
+}
+
+extension PointwiseMultiplicative {
+  internal static func visitChildren(
+    _ body: (PartialKeyPath<Self>, _PointwiseMultiplicative.Type) -> Void
+  ) {
+    if !_forEachFieldWithKeyPath(
+      of: Self.self,
+      body: { name, kp in
+        let valueType = type(of: kp).valueType
+        guard let valueType = valueType as? _PointwiseMultiplicative.Type else {
+          fatalError("not PointwiseMultiplicative: \(valueType)")
+        }
+        body(kp, valueType)
+        return true
+      })
+    {
+      fatalError(
+        "Unreflectable member of \(Self.self) while implementing PointwiseMultiplicative.")
+    }
+  }
+}
+
+extension Array.DifferentiableView: _PointwiseMultiplicative
+where Element: Differentiable & PointwiseMultiplicative {}
+extension Tensor: _PointwiseMultiplicative where Scalar: Numeric {}
+#endif
diff --git a/Sources/TensorFlow/Core/VectorProtocol.swift b/Sources/TensorFlow/Core/VectorProtocol.swift
new file mode 100644
index 000000000..554535c29
--- /dev/null
+++ b/Sources/TensorFlow/Core/VectorProtocol.swift
@@ -0,0 +1,128 @@
+// Copyright 2020 The TensorFlow Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+import _Differentiation
+
+#if TENSORFLOW_USE_STANDARD_TOOLCHAIN
+@_spi(Reflection) import Swift
+
+/// Implementation detail for reflection.
+///
+/// This should contain the methods of `VectorProtocol`
+/// that do not require Self constraints.
+public protocol _VectorProtocol {
+  typealias VectorSpaceScalar = Float
+
+  /// Adds the specified scalar to `self`.
+  mutating func add(_ x: VectorSpaceScalar)
+
+  /// Subtracts the specified scalar to `self`.
+  mutating func subtract(_ x: VectorSpaceScalar)
+
+  /// Scales `self` by the specified scalar.
+  mutating func scale(by scalar: VectorSpaceScalar)
+}
+
+extension VectorProtocol {
+  internal static func visitChildren(
+    _ body: (PartialKeyPath<Self>, _VectorProtocol.Type) -> Void
+  ) {
+    if !_forEachFieldWithKeyPath(
+      of: Self.self,
+      body: { name, kp in
+        let valueType = type(of: kp).valueType
+        guard let valueType = valueType as? _VectorProtocol.Type else {
+          fatalError("not VectorProtocol: \(valueType)")
+        }
+        body(kp, valueType)
+        return true
+      })
+    {
+      fatalError("Unreflectable member of \(Self.self) while implementing VectorProtocol.")
+    }
+  }
+}
+
+extension _VectorProtocol {
+  static func add<Root>(_ v: inout Root, _ kp: PartialKeyPath<Root>, _ x: VectorSpaceScalar) {
+    v[keyPath: (kp as! WritableKeyPath<Root, Self>)].add(x)
+  }
+  static func subtract<Root>(_ v: inout Root, _ kp: PartialKeyPath<Root>, _ x: VectorSpaceScalar)
+  {
+    v[keyPath: (kp as! WritableKeyPath<Root, Self>)].subtract(x)
+  }
+  static func scale<Root>(
+    _ v: inout Root, _ kp: PartialKeyPath<Root>, by scalar: VectorSpaceScalar
+  ) {
+    v[keyPath: (kp as! WritableKeyPath<Root, Self>)].scale(by: scalar)
+  }
+}
+
+/// A type that represents an unranked vector space. Values of this type are
+/// elements in this vector space and have either no shape or a static shape.
+public protocol VectorProtocol: _VectorProtocol & AdditiveArithmetic {
+  /// The type of scalars in the vector space.
+  associatedtype VectorSpaceScalar = Float
+
+  func adding(_ x: VectorSpaceScalar) -> Self
+
+  mutating func add(_ x: VectorSpaceScalar)
+
+  func subtracting(_ x: VectorSpaceScalar) -> Self
+
+  mutating func subtract(_ x: VectorSpaceScalar)
+
+  /// Returns `self` multiplied by the given scalar.
+  func scaled(by scalar: VectorSpaceScalar) -> Self
+
+  /// Multiplies `self` by the given scalar.
+  mutating func scale(by scalar: VectorSpaceScalar)
+}
+
+extension VectorProtocol {
+  public mutating func add(_ x: VectorSpaceScalar) {
+    self = adding(x)
+  }
+
+  public mutating func subtract(_ x: VectorSpaceScalar) {
+    self = subtracting(x)
+  }
+
+  public mutating func scale(by scalar: VectorSpaceScalar) {
+    self = scaled(by: scalar)
+  }
+}
+
+extension VectorProtocol {
+  public func adding(_ x: VectorSpaceScalar) -> Self {
+    var out = self
+    Self.visitChildren { kp, t in t.add(&out, kp, x) }
+    return out
+  }
+  public func subtracting(_ x: VectorSpaceScalar) -> Self {
+    var out = self
+    Self.visitChildren { kp, t in t.subtract(&out, kp, x) }
+    return out
+  }
+  public func scaled(by scalar: VectorSpaceScalar) -> Self {
+    var out = self
+    Self.visitChildren { kp, t in t.scale(&out, kp, by: scalar) }
+    return out
+  }
+}
+
+extension Tensor: _VectorProtocol where Scalar: TensorFlowFloatingPoint {}
+extension Array.DifferentiableView: _VectorProtocol
+where Element: Differentiable & VectorProtocol {}
+#endif