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Set of Remaining Items in a Ranked Sequence
In a sequential ranking process, the notation mathring{Y}_{ge k} represents the set of items that are available for selection at step . This set consists of the item chosen at step and all subsequent items that have not yet been ranked. Formally, it is defined as:
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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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Set of Remaining Items in a Ranked Sequence
Plackett-Luce Loss Function
A model is designed to rank a set of three documents {Doc A, Doc B, Doc C} for a given user query. To calculate the log-probability of the specific ranked sequence 'Doc A > Doc B > Doc C', a developer proposes calculating the total log-probability as the sum of the log-probabilities of each document being chosen first from the full set of three documents. Why is this approach fundamentally flawed for modeling a sequential ranking process?
Ranked Sequence Log-Probability Calculation
Calculating Log-Probability for a Ranked List
Learn After
In a process that sequentially ranks a set of five items {A, B, C, D, E}, the final observed ranking is C > A > E > B > D. At each step k, a selection is made from the set of items that have not yet been ranked, denoted as mathring{Y}{ge k}. What are the elements of the set mathring{Y}{ge 3}?
Relationship Between Consecutive Sets in Sequential Ranking
Consider a sequential process that ranks a set of four documents {D1, D2, D3, D4}, resulting in the final ranked list: D3 > D1 > D4 > D2. The notation mathring{Y}{ge k} represents the set of items available for selection at step k. The statement is: The set of items available at step 3, mathring{Y}{ge 3}, is {D2}.