ngram

In this module we build the n-gram Language Model. In the process, we learn a lot of the basics of machine learning (training, evaluation, data splits, hyperparameters, overfitting) and the basics of autoregressive language modeling (tokenization, next token prediction, perplexity, sampling). GPT is "just" a very large n-gram model, too. The only difference is that GPT uses a neural network to calculate the probability of the next token, while n-gram uses a simple count-based approach.

Our dataset is that of 32,032 names from ssa.gov for the year 2018, which were split into 1,000 names in the test split, 1,000 in val split, and the rest in the training split, all of them inside the data/ folder. Therefore, our n-gram model will essentially try to learn the statistics of the characters in these names, and then generate new names by sampling from the model.

A great reference for this module is Chapter 3 of "Speech and Language Processing" by Jurafsky and Martin.

Currently, the best "build this repo from scratch" reference is the "The spelled-out intro to language modeling: building makemore" YouTube video, though some of the details have changed around a bit. The major departure is that the video covers a bigram Language Model, which for us is just a special case when n = 2 for the n-gram.

Python version

To run the Python code, ensure you have numpy installed (e.g. pip install numpy), and then run the script:

python ngram.py

You'll see that the script first "trains" a small character-level Tokenizer (the vocab size is 27 for all 26 lowercase English letters and the newline character), then it conducts a small grid search of n-gram models with various hyperparameter settings for the n-gram order n and the smoothing factor, using the validation split. With default settings on our data, the values that turn out to be optimal are n=4, smoothing=0.01. It then takes this best model, samples 200 characters from it, and finally reports the test loss and perplexity. Here is the full output, it should only take a few seconds to produce:

python ngram.py
seq_len 3 | smoothing 0.03 | train_loss 2.1843 | val_loss 2.2443
seq_len 3 | smoothing 0.10 | train_loss 2.1870 | val_loss 2.2401
seq_len 3 | smoothing 0.30 | train_loss 2.1935 | val_loss 2.2404
seq_len 3 | smoothing 1.00 | train_loss 2.2117 | val_loss 2.2521
seq_len 4 | smoothing 0.03 | train_loss 1.8703 | val_loss 2.1376
seq_len 4 | smoothing 0.10 | train_loss 1.9028 | val_loss 2.1118
seq_len 4 | smoothing 0.30 | train_loss 1.9677 | val_loss 2.1269
seq_len 4 | smoothing 1.00 | train_loss 2.1006 | val_loss 2.2114
seq_len 5 | smoothing 0.03 | train_loss 1.4955 | val_loss 2.3540
seq_len 5 | smoothing 0.10 | train_loss 1.6335 | val_loss 2.2814
seq_len 5 | smoothing 0.30 | train_loss 1.8610 | val_loss 2.3210
seq_len 5 | smoothing 1.00 | train_loss 2.2132 | val_loss 2.4903
best hyperparameters: {'seq_len': 4, 'smoothing': 0.1}
felton
jasiel
chaseth
nebjnvfobzadon
brittan
shir
esczsvn
freyanty
aubren
... (truncating) ...
test_loss 2.106370, test_perplexity 8.218358
wrote dev/ngram_probs.npy to disk (for visualization)

As you can see, the 4-gram model sampled some relatively reasonable names like "felton" and "jasiel", but also some weirder ones like "nebjnvfobzadon", but you can't expect too much from a little 4-gram character-level language model. Finally, the test perplexity is reported at ~8.2, so the model is as confused about every character in the test set as if it was choosing randomly from 8.2 equally likely characters.

The Python code also writes out the n-gram probabilities to disk into the dev/ folder, which you can then inspect with the attached Jupyter notebook dev/visualize_probs.ipynb.

C version

The C model is identical in functionality but skips the cross-validation. Instead, it hardcodes n=4, smoothing=0.01, but does the training, sampling, and test perplexity evaluation and achieves the exact same results as the Python version. An example of compiling and running the C code is as follows:

clang -O3 -o ngram ngram.c -lm
./ngram

The C version runs, of course, much faster. You'll see the same samples and test perplexity.

TODOs

• Make better
• Make exercises
• Call for help: nice visualization / webapp that shows and animates the 4-gram language model and how it works.