Introduction to fact storage in LLMs 00:00:00 The video opens with the question of how LLMs store facts like Michael Jordan playing basketball. 00:00:35 DeepMind research suggests that facts reside in multi-layer perceptrons (MLPs). 00:01:25 The goal is to understand MLP computation and see how it can store a concrete fact like 'Michael Jordan plays basketball.' 00:03:20 Recall that vectors in high-dimensional space can encode meaning and that multiple features can be represented as directions.
Toy example setup and first matrix multiplication 00:04:47 We assume directions for first name Michael, last name Jordan, and basketball, and that a vector encoding the full name aligns with both name directions. 00:06:11 Each vector passes through the MLP independently, and the output is added to the input. 00:07:25 The first step is multiplying the embedding by a big matrix, interpreting each row as a direction. 00:08:28 A row equal to M+J produces a value of 2 when the full name is present, and we add a bias of -1 to make it a clear indicator.
Nonlinearity and down projection 00:10:28 A ReLU nonlinearity clips negative values to zero, turning the combination into an AND gate for the full name. 00:11:36 The intermediate values are called neurons, and they are active if positive, inactive if zero. 00:12:10 The next step is a down projection matrix, where each column can be seen as a direction in the embedding space. 00:13:54 The final output is added to the original vector, so if the name features are present, the basketball direction gets added.
Parameter count and superposition 00:15:41 The up and down projection matrices each have about 604 million parameters, totaling 1.2 billion per MLP. 00:16:29 With 96 MLPs, the total is about 116 billion parameters, which is two-thirds of all GPT-3's parameters. 00:17:05 Real models likely don't have neurons that each represent a single clean feature; instead, features may be superimposed. 00:19:58 Superposition allows many nearly perpendicular directions, and the Johnson-Lindenstrauss lemma shows capacity grows exponentially with dimensions.
Wrap-up and next steps 00:21:40 The next chapter will cover training, including cost functions, fine-tuning with RLHF, and scaling laws.