update momentum optimizer question to new format

Author: mavleo96

Problems/X_momentum_optimizer/solution.py

@@ -0,0 +1 @@
+Implement the momentum optimizer update step function. Your function should take the current parameter value, gradient, and velocity as inputs, and return the updated parameter value and new velocity. The function should also handle scalar and array inputs.

questions/x_momentum-optimizer/description.md

@@ -0,0 +1,5 @@
+{
+  "input": "parameter = 1.0, grad = 0.1, velocity = 0.1",
+  "output": "(0.909, 0.091)",
+  "reasoning": "The momentum optimizer computes updated values for the parameter and the velocity. With input values parameter=1.0, grad=0.1, and velocity=0.1, the updated parameter becomes 0.909 and the updated velocity becomes 0.091."
+}

questions/x_momentum-optimizer/example.json

@@ -45,7 +45,7 @@ Return tuple: (updated_parameter, updated_velocity)
 # Example usage:
 parameter = 1.0
 grad = 0.1
-velocity = 0.0
+velocity = 0.1
 
 new_param, new_velocity = momentum_optimizer(parameter, grad, velocity)
 ```

Problems/X_momentum_optimizer/learn.md questions/x_momentum-optimizer/learn.mdProblems/X_momentum_optimizer/learn.md renamed to questions/x_momentum-optimizer/learn.md

@@ -0,0 +1,17 @@
+{
+  "id": "X",
+  "title": "Momentum Optimizer",
+  "difficulty": "easy",
+  "category": "Deep Learning",
+  "video": "",
+  "likes": "0",
+  "dislikes": "0",
+  "contributor": [
+    {
+      "profile_link": "https://github.com/mavleo96",
+      "name": "Vijayabharathi Murugan"
+    }
+  ],
+  "tinygrad_difficulty": null,
+  "pytorch_difficulty": null
+}

questions/x_momentum-optimizer/meta.json

@@ -0,0 +1,27 @@
+import numpy as np
+
+def momentum_optimizer(parameter, grad, velocity, learning_rate=0.01, momentum=0.9):
+    """
+    Update parameters using the momentum optimizer.
+    Uses momentum to accelerate learning in relevant directions and dampen oscillations.
+
+    Args:
+        parameter: Current parameter value
+        grad: Current gradient
+        velocity: Current velocity/momentum term
+        learning_rate: Learning rate (default=0.01)
+        momentum: Momentum coefficient (default=0.9)
+
+    Returns:
+        tuple: (updated_parameter, updated_velocity)
+    """
+    assert learning_rate > 0, "Learning rate must be positive"
+    assert 0 <= momentum < 1, "Momentum must be between 0 and 1"
+
+    # Update velocity
+    velocity = momentum * velocity + learning_rate * grad
+    
+    # Update parameters
+    parameter = parameter - velocity
+
+    return np.round(parameter, 5), np.round(velocity, 5)

questions/x_momentum-optimizer/solution.py

@@ -0,0 +1,19 @@
+import numpy as np
+
+def momentum_optimizer(parameter, grad, velocity, learning_rate=0.01, momentum=0.9):
+    """
+    Update parameters using the momentum optimizer.
+    Uses momentum to accelerate learning in relevant directions and dampen oscillations.
+
+    Args:
+        parameter: Current parameter value
+        grad: Current gradient
+        velocity: Current velocity/momentum term
+        learning_rate: Learning rate (default=0.01)
+        momentum: Momentum coefficient (default=0.9)
+
+    Returns:
+        tuple: (updated_parameter, updated_velocity)
+    """
+    # Your code here
+    return np.round(parameter, 5), np.round(velocity, 5)

questions/x_momentum-optimizer/starter_code.py

@@ -0,0 +1,18 @@
+[
+  {
+    "test": "print(momentum_optimizer(1., 0.1, 0.5, 0.01, 0.9))",
+    "expected_output": "(0.549, 0.451)"
+  },
+  {
+    "test": "print(momentum_optimizer(np.array([1., 2.]), np.array([0.1, 0.2]), np.array([0.5, 1.0]), 0.01, 0.9))",
+    "expected_output": "(array([0.549, 1.098]), array([0.451, 0.902]))"
+  },
+  {
+    "test": "print(momentum_optimizer(np.array([1., 2.]), np.array([0.1, 0.2]), np.array([0.5, 1.0]), 0.01, 0.))",
+    "expected_output": "(array([0.999, 1.998]), array([0.001, 0.002]))"
+  },
+  {
+    "test": "print(momentum_optimizer(np.array([1., 2.]), np.array([0., 0.]), np.array([0.5, 0.5]), 0.01, 0.9))",
+    "expected_output": "(array([0.55, 1.55]), array([0.45, 0.45]))"
+  }
+]