Lecture 14: Data 2

Stanford CS336 · Spring 2025 · 1:19:12 · Watch on YouTube ↗

TL;DR: * Data preparation for large language models involves filtering and deduplication. * Filtering algorithms aim to select high-quality data similar to a target distribution from a vast raw corpus. * Common filtering techniques include n-gram language models (KenLM), fastText classifiers, and importance resampling (DSIR). * Deduplication removes redundant or near-redundant data to improve training efficiency and mitigate memorization. * Hashing is a fundamental tool for both exact deduplication (e.g., Bloom filters) and approximate deduplication (e.g., MinHash, LSH).

Key Concepts: * Data Filtering Pipeline: Live service -> dump/crawl -> processed data (HTML to text, filtering, deduplication). * Filtering Goal: Given target data $T$ (small, high-quality) and raw data $R$ (large), find subset $T'$ of $R$ similar to $T$. * Filtering Desiderata: Generalize from $T$ (want $T'$ to be different from $T$), extremely fast (to run on $R$). * N-gram Language Models (KenLM): * Maximum Likelihood Estimation (MLE) of $P(w_n | w_{n-1}...w_1)$. * Sparse counts problem. * Kneser-Ney smoothing for unseen n-grams. * Perplexity as a scoring function. * Application: CCNET (filter paragraphs by perplexity). * FastText Classifiers: * Bag-of-words embeddings with hashing trick for n-grams. * Linear classifier (no non-linearity). * Parallelized, asynchronous SGD. * Application: Language identification, quality filtering. * Data Selection for Language Models via Importance Resampling (DSIR): * Estimate importance weights using raw + target data (e.g., simple bag-of-n-grams estimator). * Select data via importance resampling. * Problem: Target data $D_P$ is too small to estimate a good model. * Solution: Use hashed n-grams. * General Filtering Framework: 1. Estimate some model based on $T$ and $R$ and derive a scoring function. 2. Keep examples in $R$ based on their score (stochastically). * Deduplication: * Exact Duplicates: Identical copies (e.g., mirror sites, GitHub forks, Project Gutenberg mirrors). * Near Duplicates: Text differing by a few tokens (e.g., terms of service, licenses, formulaic writing, minor formatting). * Benefits: Train more efficiently (fewer tokens), avoid memorization (mitigate copyright/privacy concerns). * Design Space: What is an item (sentence, paragraph, document)? How to match (exact, fraction of common subitems)? What action to take (remove all, remove all but one)? * Key Challenge: Dduplication is fundamentally about comparing items to other items (pair-wise). Need linear time algorithms to scale. * Hashing: * Maps item to a hash value (integer or string). * Hash value much smaller than item. * Hash collision: $h(x) = h(y)$ for $x \neq y$. * Trade-off between efficiency and collision resistance. * MurmurHash (fast, used for hash tables). * Bloom Filter: * Efficient, approximate data structure for testing set membership. * Features: Memory efficient, can update, but can't delete. * If return 'no', definitely 'no'. If return 'yes', most likely 'yes' but small probability of 'no' (false positive). * False positive rate can be driven down exponentially with more time/compute. * MinHash: * Random hash function $h$ such that $P(h(A)=h(B)) = \text{Jaccard}(A,B)$. * Normally, you want different items to hash to different hashes, but here, you want collision probability to depend on similarity. * Locality Sensitive Hashing (LSH): * Breaks $n$ hash functions into $B$ bands of $R$ hashes ($n = B \times R$). * A and B collide if for some band, all its hashes return the same value. * Sharpens the probability curve around a threshold.

[0:00] Lecture 14: Data 2 - Deep Dive into Data Processing

This lecture builds upon the previous one, which provided an overview of datasets used for training language models. We discussed the journey of data from live services (like GitHub) to processed datasets (like The Stack), involving steps like HTML to text conversion, quality/toxicity filtering, and deduplication.

Today, we will take a deep dive into the mechanics of these processing steps, focusing on: * Algorithms for filtering (e.g., classifiers). * Applications of filtering (e.g., language, quality, toxicity). * Deduplication (e.g., Bloom filters, MinHash, LSH).

This lecture will involve more classical big data processing algorithms and some interesting math.

[0:05] 1. Filtering Algorithms

The fundamental algorithmic building block for filtering is: Given some target data $T$ (which is typically small and high-quality) and lots of raw data $R$ (which is huge, e.g., Common Crawl), find a subset $T'$ of $R$ that is similar to $T$.

Filtering Concept Diagram

Desiderata for a filtering algorithm: * Generalize from the target data: We want $T'$ to be different from $T$. If $T'$ is identical to $T$, there's no point in filtering. * Extremely fast: It must be able to run on $R$, which is massive (e.g., the entire web). If filtering is as expensive as training a large language model, it defeats the purpose.

We will explore three different ways to implement this filtering primitive: 1. Training an n-gram model (using KenLM). 2. Training a classifier (using FastText). 3. Using importance resampling (DSIR).

[2:45] 1.1. N-gram Models with Kneser-Ney Smoothing (KenLM)

0:11 A speaker stands in front of a whiteboard, presenting a lecture with a laptop.

0:47 A slide highlights the processing steps for language model training data: HTML to text, filtering, and deduplication.

2:10 A slide shows desiderata for filtering algorithms, emphasizing generalization from target data and speed.

4:05 A slide explains maximum likelihood estimation for n-gram language models, with an example for n=3.

5:35 A slide displays Python code for downloading a KenLM language model from Hugging Face.

7:20 A slide shows computed score and perplexity values, and a reference to the CCNet paper.

N-gram models are a classic approach in natural language processing. * Kneser-Ney smoothing: A technique used to estimate probabilities of n-grams, especially for unseen n-grams. It's a common choice in statistical NLP. * KenLM: A fast, open-source implementation of n-gram language models, originally developed for machine translation. * Commonly used for data filtering: It's simple, fast, and effective. * Extremely simple / fast: Fitting an n-gram model primarily involves counting n-gram occurrences and then normalizing.

Concepts: The starting point is Maximum Likelihood Estimation (MLE) for n-gram language models. For an n-gram of size $n=3$ (e.g., "the cat"), the probability $P(\text{in} | \text{the cat})$ is estimated as: $$P(\text{in} | \text{the cat}) = \frac{\text{count}(\text{the cat in})}{\text{count}(\text{the cat})}$$ The problem with MLE is sparse counts: many n-grams (especially for large $n$) will have a count of 0, even if they are perfectly reasonable. This is why n-gram models historically struggled with the "curse of dimensionality" as $n$ increased. Solution: Use Kneser-Ney smoothing to handle unseen n-grams. Roughly, if a higher-order n-gram (e.g., $P(\text{in} | \text{the cat})$) has insufficient counts, Kneser-Ney smoothing "backs off" to lower-order n-grams (e.g., $P(\text{in} | \text{cat})$) to estimate the probability.

Let's demonstrate with some code: First, download a pre-trained KenLM language model (trained on Wikipedia):

model_url = "https://huggingface.co/edugp/kenlm/resolve/main/wikipedia/en.arpa.bin"
model_path = "var/en.arpa.bin"
download_file(model_url, model_path)

Then, use the kenlm.Model to compute scores and perplexity. Perplexity is a measure of how well a probability distribution predicts a sample. Lower perplexity means the model predicts the text better (i.e., the text is more "likely" given the model). We normalize perplexity by the number of tokens to avoid favoring short documents.

import kenlm
import math

model = kenlm.Model(model_path)

def compute(content: str):
    # Hacky preprocessing
    content = "<s> " + content.replace(",", " ").replace("\"", " ").replace(".", " ") + " </s>"

    # log p(content)
    score = model.score(content)

    # Perplexity normalizes by number of tokens to avoid favoring short documents
    num_tokens = len(list(model.full_scores(content)))
    perplexity = math.exp(-score / num_tokens)

    return score, perplexity

# Example 1: Wikipedia excerpt
score, perplexity = compute("Stanford University was founded in 1885 by Leland and Jane Stanford Jr.")
# Output: score = -151.73, perplexity = 187.19

The perplexity for the Wikipedia excerpt is around 187. This is a reasonable value, as the text is likely to be found in the Wikipedia-trained model.

# Example 2: Text from a course website
score, perplexity = compute("If you believe that the course staff made an objective error in memory of their only child, Leland Stanford Jr.") # @inspect score, @inspect perplexity
# Output: score = -180.81, perplexity = 204.01

This text, from a course website, has a slightly higher perplexity (204), meaning it's less likely than the Wikipedia excerpt. This makes sense, as course-specific text is less likely to be in a general Wikipedia corpus. However, it's still well-formed English, so the perplexity isn't abnormally high.

# Example 3: Gibberish
score, perplexity = compute("asdf asdf asdf asdf asdf")
# Output: score = -44.88, perplexity = 272.08

Gibberish text yields a higher perplexity (272), indicating it's very unlikely according to the model.

# Example 4: Repetitive text
score, perplexity = compute("the the the the the the the the the the the")
# Output: score = -78.60, perplexity = 62.61

Surprisingly, the perplexity for "the the the..." is quite low (62). This highlights a limitation of simple n-gram models: they capture local word sequences but don't necessarily understand broader semantic coherence.

CCNet [Wenzek+ 2019] The CCNET paper, which we discussed previously, used a similar approach for data filtering. * Items are paragraphs of text. * Sort paragraphs by increasing perplexity. * Keep the top 1/3. * This method was used to create the first LLaMA data set.

Summary: Kneser-Ney n-gram language models (with KenLM implementation) are fast but crude.

[8:39] 1.2. FastText Classifiers

8:20 A slide lists characteristics of CCNet, including sorting paragraphs by perplexity and use in LLaMA.

9:55 A slide presents Python code defining a baseline bag-of-words model with input length, vocabulary, and classes.

11:30 A slide illustrates the hashing trick solution for handling a large number of bigrams with example code.

13:10 A slide discusses using classifiers for quality filtering, noting that fastText is a linear classifier.

14:50 A slide shows Python code for sampling from a proposal distribution 'q' with a given vocabulary.

16:30 A slide outlines the setup for importance resampling, highlighting the problem of small target data.

FastText [Joulin+ 2016] is another popular approach, especially for its efficiency. * Task: Text classification (e.g., sentiment classification). * Goal: Train a fast classifier for text classification. * Finding: It was as good as much slower neural network classifiers.

Baseline: Bag of Words (not what they did) Consider a simple bag-of-words model for text classification. * $L = 32$ (Length of input) * $V = 8192$ (Vocabulary size) * $K = 64$ (Number of classes)

To classify, you might define an embedding layer: W = nn.Embedding(V, K) This represents embedding parameters as a $V \times K$ matrix. Input tokens $x$ (e.g., "the") are then processed. y = softmax(mean(W(x), dim=0)) The problem is that $V \times K$ parameters can be huge, leading to sparsity issues and high memory requirements.

FastText Classifier: Bag of Word Embeddings FastText addresses this by introducing a hidden dimension $H$. * $H = 16$ (Hidden dimension, much smaller than $K$) * U = nn.Embedding(V, H) (Embedding parameters $V \times H$) * W = nn.Linear(H, K) (Head parameters $H \times K$) * y = softmax(mean(W(U(x)), dim=0)) (Output probabilities $K$) Notice that there's no non-linearity between the embedding and the linear layer; it's essentially a linear classifier (or matrix factorization). The number of parameters is greatly reduced: only $H \times (V + K)$ parameters.

Implementation: * Parallelized, asynchronous SGD. * Learning rate: linear interpolation from some number to 0.

Bag of N-grams: FastText extends this concept to n-grams. * Problem: The number of n-grams (e.g., bigrams) can get very large and is unbounded. * Solution: Hashing trick. * Define a fixed number of bins (e.g., 10 million bins in practice, 8 in this example). * Hash each n-gram into one of these bins: hashed_x = [hash(bigram) % num_bins for bigram in x] * This allows handling a potentially infinite vocabulary of n-grams within a fixed memory footprint. * Of course, collisions can occur, but the model learns to account for them during optimization.

Application to Filtering: * For quality filtering, we often have $K=2$ classes (good vs. bad). * In that case, FastText is just a linear classifier ($H=K=2$). * In general, you can use any classifier (e.g., BERT, LLaMA); it's just slower. The trade-off is that if you use a very powerful model for filtering, you might be better off using that compute for training your actual language model. Filtering a huge raw dataset means even a small increase in inference cost per item can lead to massive overall compute.

[1:04:55] 1.3. Data Selection for Language Models via Importance Resampling (DSIR)

DSIR [Xie+ 2023] offers a more principled approach to data selection. * Basic Idea: 1. Estimate importance weights using raw + target data (e.g., simple bag-of-n-grams estimator). 2. Select data via importance resampling.

Let's quickly review importance resampling: Setup: * Target distribution $p$: We want to sample from here. * Proposal distribution $q$: We have samples from here. * Example: * vocabulary = [0, 1, 2, 3] * p = [0.1, 0.2, 0.3, 0.4] (Target distribution) * q = [0.4, 0.3, 0.2, 0.1] (Proposal distribution)

Steps: 1. Sample from $q$: Draw $N$ samples (e.g., $N=100$) from the proposal distribution $q$. ```python samples = np.random.choice(vocabulary, p=q, size=n) # samples = [0, 2, 0, 2, 1, 0, 1, 0, 0, 0, 1, 1, 1, 3, 1, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 1, 0, 1, 3, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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