DTS, which generates diverse solution strategies before writing solutions, improves GSM8K by 7.1 points and MATH by 4.2 points over an untuned base model at 1.03x baseline compute.
On widely degenerate \textit{p}-Laplace equations with symmetric data
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abstract
In this paper, we consider the Dirichlet problems with a widely degenerate equation. Through a well-known result by Talenti, we explicitly express the gradient of the solution $u_p$ outside the ball with a radius of $1$, if the datum $f$ is a non-negative radially decreasing function. This allows us to establish some sharp higher regularity results for the weak solutions, assuming that the datum $f$ belongs to a suitable Lorentz space, i.e. under a weaker assumption on the datum with respect to the available literature. Moreover we analyze the behaviour of $u_p$ as $p \to 1^+$.
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Data Diversification Methods In Alignment Enhance Math Performance In LLMs
DTS, which generates diverse solution strategies before writing solutions, improves GSM8K by 7.1 points and MATH by 4.2 points over an untuned base model at 1.03x baseline compute.