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State Function from Previous Outputs
The formula represents a function, denoted by , that computes a state or context based on a sequence of the previous outputs. Each is a vector representing the -th output in the sequence. This is a fundamental concept in autoregressive models where the prediction of the next element depends on the context derived from the preceding elements.

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Ch.4 Alignment - Foundations of Large Language Models
Foundations of Large Language Models
Foundations of Large Language Models Course
Computing Sciences
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Query (Attention)
Key (Attention)
Value (Attention)
State Function from Previous Outputs
Value Weight Matrix Formula
Set of Sequential Key-Value Pairs
Query Vector
Key Vector
Value Vector
Implicit Relative Position Modeling in Self-Attention with RoPE
Value Weight Matrix Definition ()
Imagine a system translating the sentence 'The quick brown fox jumps'. When the system is generating the output word corresponding to 'jumps', it needs to determine which words in the input sentence are most relevant. To do this, a vector representing the current translation context (i.e., 'what information do I need to produce the next word?') is compared against a set of searchable 'label' vectors, one for each word in the input sentence. This comparison generates a relevance score for each input word. Finally, a new vector is created by taking a weighted average of the 'content' vectors of the input words, using the relevance scores as weights. How do the three main vector types in this process correspond to their roles?
In a system designed to answer questions based on a provided document, the model first creates a representation of the user's question. It then compares this representation against a set of searchable representations, one for each sentence in the document, to determine relevance scores. Finally, it constructs an answer by creating a weighted combination of the informational content from each sentence, using the relevance scores as weights. Which option correctly assigns the roles of Query, Key, and Value vectors in this scenario?
Context Window of Key Vectors Notation
Key-Value Cache
In a computational mechanism designed to selectively focus on different parts of an input sequence, information is represented by three distinct types of vectors that interact to produce a context-aware output. Match each vector type to its specific role in this process.
Masked QKV Attention Formula
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Analyzing State Function Impact on Sequence Generation
In a model that generates a sequence of items one by one, a function
s(ȳ₁, ..., ȳₖ₋₁)is used to compute a summary, or 'state', from thek-1items that have already been generated. What is the primary purpose of this computed state?Applying the State Function in Sequence Generation