Rafael Rafailov

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20112026

most citedDirect Preference Optimization: Your Language Model is Secretly a Reward Model

294 citations · 570 across the 29 of their papers we have counts for

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math.MG2012

On extremums of sums of powered distances to a finite set of points

Nikolai Nikolov, Rafael Rafailov

In this paper we investigate the extremal properties of the sum $i = 1 \sum n ∣ M A_{i} ∣^{λ},$ where $A_{i}$ are vertices of a regular simplex, a cross-polytope (orthoplex) or a cube and…

math.MG2011

On the sum of powered distances to certain sets of points on the circle

Nikolai Nikolov, Rafael Rafailov

In this paper we consider an extremal problem in geometry. Let $λ$ be a real number and $A$ , $B$ and $C$ be arbitrary points on the unit circle $Γ$ . We give full characterization o…