Podcast
Questions and Answers
Random vectors initialized with angles ranging from 0 to 180 degrees tend to be closer to ______ degrees.
Random vectors initialized with angles ranging from 0 to 180 degrees tend to be closer to ______ degrees.
90
The ______ lemma explains that the number of nearly perpendicular vectors that can be packed into a space grows exponentially with the number of dimensions.
The ______ lemma explains that the number of nearly perpendicular vectors that can be packed into a space grows exponentially with the number of dimensions.
Johnson-Lindenstrauss
LLMs process text by breaking it into ______, which are then represented by high-dimensional vectors.
LLMs process text by breaking it into ______, which are then represented by high-dimensional vectors.
tokens
Large language models might probe at many more ______ than their dimensions by utilizing nearly perpendicular directions.
Large language models might probe at many more ______ than their dimensions by utilizing nearly perpendicular directions.
The ______ between vectors and specific directions can indicate the presence of a particular feature.
The ______ between vectors and specific directions can indicate the presence of a particular feature.
Key aspects of transformer training include: a specific cost function used for language models, fine-tuning using ______ with human feedback, and scaling laws.
Key aspects of transformer training include: a specific cost function used for language models, fine-tuning using ______ with human feedback, and scaling laws.
In the first step of MLP processing, the input vector is multiplied by a large matrix (W up), where each row represents a ______ for a specific feature.
In the first step of MLP processing, the input vector is multiplied by a large matrix (W up), where each row represents a ______ for a specific feature.
The ______ function converts negative values in the vector to zero, creating activated neurons in the MLP.
The ______ function converts negative values in the vector to zero, creating activated neurons in the MLP.
______ autoencoders are a tool used to extract features even when they are superimposed across neurons.
______ autoencoders are a tool used to extract features even when they are superimposed across neurons.
The concept of ______ explains how LLMs store vast amounts of information efficiently by encoding multiple features using slightly non-orthogonal vectors.
The concept of ______ explains how LLMs store vast amounts of information efficiently by encoding multiple features using slightly non-orthogonal vectors.
Flashcards
Large Language Model (LLM)
Large Language Model (LLM)
A model that predicts the next word based on stored knowledge.
Multi-layer Perceptrons (MLPs)
Multi-layer Perceptrons (MLPs)
Neural networks essential for storing and processing facts in LLMs.
Tokens
Tokens
Pieces of text processed by LLMs, represented as high-dimensional vectors.
Attention
Attention
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Superposition
Superposition
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Johnson-Lindenstrauss Lemma
Johnson-Lindenstrauss Lemma
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Feature Space
Feature Space
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Sparse Autoencoders
Sparse Autoencoders
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Transformer Training
Transformer Training
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Study Notes
How Large Language Models Store Facts
- Large language models (LLMs) correctly predict the next word, demonstrating stored knowledge of individuals and their associated sports.
- Multi-layer Perceptrons (MLPs) are crucial for storing factual information within LLMs.
- LLMs process text by breaking it into tokens, represented as high-dimensional vectors.
- Attention allows vectors to share information, while MLPs store and process this information.
- Vectors exist in high-dimensional space, with different directions representing various meanings.
- Dot products between vectors and specific directions reveal the presence of particular features.
- MLPs encode facts by altering input vectors, such as linking Michael Jordan to basketball.
How MLPs Process Vectors
- Step 1: Input vector multiplied by a large matrix (W up). Each row represents a feature query (e.g., "first name Michael"). Dot products indicate feature presence. A bias vector (B up) is added.
- Step 2: The resulting vector passes through a non-linear function (ReLU), converting negative values to zero. Activated neurons (positive values) correspond to the output of ReLU.
- Step 3: The output vector is multiplied by another matrix (W down), where columns represent features to be added. Activated neurons dictate added columns from W down to the output vector. A bias vector (B down) is added.
- Step 4: The final output vector is combined with the original input vector, incorporating the learned features. Parallel processing for all input vectors.
Understanding MLPs and Superposition
- MLPs have numerous parameters, primarily within these blocks.
- Individual neurons rarely represent a single feature, but rather a combination of overlapping features.
- Superposition implies multiple features are encoded by slightly non-orthogonal vectors, enabling efficient information storage in high-dimensional spaces.
Random Vectors and the Johnson-Lindenstrauss Lemma
- Random vectors, initialized with angles from 0 to 180 degrees, tend towards 90 degrees.
- Optimization processes can make vectors more perpendicular.
- The Johnson-Lindenstrauss lemma suggests exponentially increasing nearly perpendicular vectors in higher dimensions.
- This is significant for LLMs, which benefit from associating independent ideas with nearly perpendicular directions.
Large Language Models and Feature Space
- LLMs potentially store more ideas than their dimensions due to the exponential increase of nearly perpendicular vectors.
- This may explain the model performance scaling with size.
- A space with ten times more dimensions can store more than ten times the independent ideas.
- This principle applies to the embedding space and MLP neuron vectors.
Superposition and Feature Extraction
- LLMs might analyze far more features than their dimensions using nearly perpendicular directions.
- Individual features are not represented by single neurons, but rather combinations of neurons (superposition).
- Sparse autoencoders are tools to extract features even when superimposed.
Transformer Training
- Transformer training heavily relies on backpropagation.
- Key training aspects include the specific cost function used for language models, fine-tuning with RL and human feedback, and scaling laws.
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