Bigram Character-Level Name Generation:

This project demonstrates two methods for generating new Indian names by learning from a list of 53,982 existing names. The first approach is purely statistical, while the second uses a simple neural network. Ultimately, both methods produce the same results, showcasing how a basic neural network can replicate a classical statistical model.

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Approach 1: The Statistical Model

This method relies on directly counting character co-occurrences and normalizing them into probabilities.

• Logic:
  • The model processes each name by adding a start (<S>) and end (<E>) token.
  • It then builds a 28x28 matrix to count the frequency of every possible character pair (bigram). For example, it counts how often 'a' is followed by 'n'.
• Generation:
  • The raw counts in the matrix are converted into probabilities by normalizing each row.
  • To generate a name, the model starts with <S> and iteratively samples the next character based on these learned probabilities until <E> is chosen.
• Evaluation:
  • The model's accuracy is measured by its average Negative Log-Likelihood (NLL), which was 2.1748 on the dataset. A lower NLL is better.
  • As a test, the non-Indian name "roberts" yielded a much higher NLL of 3.5319, confirming the model learned patterns specific to the training data.

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Approach 2: The Neural Network Model

This approach frames the problem as a simple classification task: predicting the next character in a sequence.

• Architecture:
  • A single-layer neural network multiplies a one-hot encoded input character by a 28x28 weight matrix (W).
  • A softmax function is applied to the output to create a probability distribution for the next character.
• Training:
  • The network is trained using gradient descent for 300 epochs.
  • The loss function is the Negative Log-Likelihood (NLL). The network adjusts its weights (W) to minimize this loss, effectively learning the character transition probabilities.
  • The final loss after training was 2.1929.

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Key Insight: The Two Models are Identical

The simple neural network is mathematically equivalent to the statistical model.

• The weight matrix W in the neural network effectively learns the log-counts of the bigrams.
• The softmax function is the neural network's way of normalizing counts into a probability distribution.

By minimizing the NLL loss, the neural network converges to the same probability model derived from direct statistical counting.

Results Comparison

Because the underlying models are the same, both notebooks produce identical outputs when given the same random seed.

Model Approach	Average Negative Log-Likelihood
Statistical	2.1748
Neural Network	2.1929 (Final loss)

Generated Names (from both models):

• mik
• rabal
• maanek
• ishiya
• kahel
• abamathanaeraya
• ka
• savithrnan ...and so on.