A Quest to Tame Large Language Models

Statistical language models form the conceptual foundation for understanding modern LLMs. These models process a corpus of text and use statistical patterns to predict subsequent words or tokens. While contemporary LLMs have evolved far beyond these simple approaches, understanding statistical models illuminates the core challenges that advanced architectures address.

A bigram model represents the simplest form of statistical language modeling. It analyzes pairs of consecutive words to build frequency tables that inform predictions.

Consider this example corpus: "The cat sat on the mat. The mat was soft and warm."

The resulting bi-gram frequency table would contain:

When processing the input "The," the model examines all bi-grams beginning with "The":

The model predicts "mat" as the most probable next word based on frequency.

While effective for demonstration, bigram models suffer from severe contextual limitations, because the consider only one preceding word for their predictions.

The n-gram model extends the bi-gram concept by incorporating longer contextual windows. A trigram model, for example, considers two preceding words, while an n-gram model employs n-1 words of context.

Let’s look at the sentence: "Thank you very much for your cooperation. I very much appreciated it. We very much made progress."

A trigram model encountering "you very" would leverage both "you" and "very" to predict "much," using conditional probability P("much" | "you", "very").

The relationship between context length and model performance involves critical trade-offs:

Longer Context (Higher n):

Shorter Context (Lower n):

Data sparsity becomes increasingly problematic as n increases—many n-grams may not appear frequently enough in training data to provide reliable probability estimates.

Transformers convert words and tokens into high-dimensional vectors (embeddings) that capture semantic and syntactic relationships. Unlike sequential models that process text word-by-word, transformers can analyze relationships between all words in a passage simultaneously.

Vector Dimensionality:

Each dimension in an vector space captures different aspects of meaning, enabling the model to represent complex relationships between words and concepts. Vectors occupying similar positions in this space represent semantically related concepts.

An attention mechanism functions as a dynamic spotlight, highlighting relevant information during text processing. For each token, the model calculates attention weights determining how much focus to allocate to every other token in the context.

Key Advantages:

Attention mechanisms operate through three primary components for each token:

Processing Steps:

Attention Weight Properties:

Self-Attention:

Every token in a sequence attends to all others, including itself, capturing comprehensive contextual relationships across the entire sequence.

Mechanisms that enable models to weigh the importance of different input portions relative to each other, focusing on the most relevant information for accurate and coherent output generation.

Statistical models that predict the next word based on the immediately preceding word, analyzing word pair frequencies to determine probability distributions.

An algorithm for creating efficient tokenization by:

The surrounding words or sequences that inform next-word prediction. Context length varies by model type—bigram models use 1 word, trigram models use 2 words, and ngram models use n-1 words of context.

The comprehensive dataset of texts used for model training, typically including diverse sources such as books, articles, websites, and other written materials. Corpus quality and diversity directly impact model performance.

Insufficient coverage of possible inputs or features in training data, where certain patterns may not appear frequently enough to provide reliable probability estimates.

Embeddings transform symbolic language into mathematical forms (the vector) that neural networks can process, with similar concepts positioned closer together in the vector space.

The terms "embedding" and "vector" are often used interchangeably in machine learning contexts, though "embedding" specifically speaks to the process of transforming data into the vector form, whereas "an embedding" likely speaks to a vector—unless a new model is invented that doesn’t use vectors.

One complete pass through the entire training dataset, during which the model processes all examples and updates parameters based on prediction errors.

A configuration setting that influences model behavior but is not learned during training. Examples include learning rate, batch size, and temperature. Hyperparameters are typically set before training begins and can significantly impact model performance.

Relationships between words or phrases separated by significant distances in text, such as pronouns referring to entities in different paragraphs.

A metric measuring prediction accuracy by quantifying the difference between model outputs and correct answers. Training progressively reduces loss through parameter optimization.

Describes the general version of a bigram model. It is a statistical language modeling approach that predicts words based on n-1 previous words in sequence. Common variants include bigrams (n=2), trigrams (n=3).

A condition where models perform exceptionally on training data but fail to generalize to new, unseen inputs—analogous to memorizing without understanding.

The individual weights and biases within a model that are adjusted during training to minimize prediction error. Parameters are learned from the training data and define the model’s behavior.

The multidimensional mathematical domain that encompasses all the weights and biases that the model can learn, which can number in the millions or billions for modern language models.

Data preparation steps including cleaning, transformation, and structuring to optimize datasets for machine learning, such as lowercasing text or removing stop words.

A hyperparameter controlling output randomness:

Not to be confused with the parameter space.

The fundamental unit of text processed by language models, representing a piece of text produced through tokenization. Tokens can be words, subwords, characters, or other linguistic units depending on the tokenization method used.

The process of segmenting text into smaller units (tokens) such as words, subwords, or characters. Effective tokenization increases training examples and enables models to learn morphological patterns.

The process of optimizing the model’s parameter space to maximize prediction accuracy, expressed as f(x|params) where x represents input and params represents learned weights.

A neural network architecture that consists of encoders (for understanding input) and decoders (for generating output), or decoder-only (for generative tasks). Transformers process all tokens in parallel rather than sequentially and better capture long range context.

High-dimensional numerical representations of text or data, capturing semantic and syntactic relationships in mathematical space suitable for computational processing.