Equation 11 · Part 1 · Measuring What a RAG System Retrieves, Not Just What It Answers
Symbol k
What this part means
the DCG of the ideal ordering, so the ratio is bounded near one regardless of how many relevant documents exist for a given query.
Its job in the formula
k appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Full expression→Symbol k→Article meaning
Where the article explains it
where is the graded relevance of the result at position i and k is the DCG of the ideal ordering, so the ratio is bounded near one regardless of how many relevant documents exist for a given query.
The passage around this formula
Normalised discounted cumulative gain generalises this to graded relevance and to the whole list rather than only the first hit: . where is the graded relevance of the result at position i and k is the DCG of the ideal ordering, so the ratio is bounded near one regardless of how many relevant documents exist for a given query. The logarithmic discount encodes a specific judgement about attention: a relevant document at position one is worth far more than the same document at position ten, and nDCG is the standard way the information-retrieval literature makes that judgement quantitative. Heterogeneous retrieval benchmarks built to compare…
Learn the underlying idea
A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.
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Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.