2025 USA-NA-AIO Round 1, Problem 2, Part 3

AI Olympiads 2025 USA-NA-AIO Round 1
1

Part 3 (10 points, coding task)

In this part, you are asked to build an affine transformation module from scratch by using NumPy, NOT PyTorch or TensorFlow.

Define such a class as My_Linear_NumPy.

  • Attributes

    • in_features: Number of input features

    • out_features: Number of output features

    • weight: This refers to matrix \mathbf{W} in Part 1. The shape is (out_features, in_features).

    • bias: This refers to vector \mathbf{b} in Part 1. The shape is (out_features,).

    • random_seed: The NumPy random seed number used to generate initial values of weight and bias.

  • Method __init__:

    • To initialize an object in this class, you need to specify in_features and out_features.

    • You may initialize the object by specifying a value for random_seed. If it is not specified, then its default value is 42.

    • The initial values of weight and bias are random that follow standard normal distributions generated with the seed number attributerandom_seed.

  • Method forward:

    • Input x: numpy array with shape (n_0, n_1, ..., n_{d-1}, in_features) with an arbitrary dimension d = 0, 1, \cdots.

    • Output y: numpy array with shape (n_0, n_1, ..., n_{d-1}, out_features).

    • The affine transformation works in a way that given the first d indices in x and y, it does affine transformation along the last axis of x and y.

  • Do not use any loop in your code.

2 
### WRITE YOUR SOLUTION HERE ###

class My_Linear_NumPy:
    def __init__(self, in_features, out_features, random_seed=42):
        self.in_features = in_features
        self.out_features = out_features
        self.random_seed = random_seed
        np.random.seed(self.random_seed)
        self.weight = np.random.randn(self.out_features, self.in_features)
        self.bias = np.random.randn(self.out_features)

    def forward(self, x):
        return np.sum(x[..., np.newaxis] * self.weight.T, axis = -2) + self.bias

""" END OF THIS PART """