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| -rw-r--r-- | marginal.tex | 7 |
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diff --git a/marginal.tex b/marginal.tex index faa45ba..32f1fd5 100644 --- a/marginal.tex +++ b/marginal.tex @@ -119,7 +119,7 @@ continuous spectrum, we enforce the condition that the spectrum has a pseudogap, and is therefore marginal. We demonstrate the method on the spherical spin glasses, where it is unnecessary but instructive, and on extensions of the spherical models where the technique is more useful. -In a companion paper, we compare the marginal complexity with the performance +In a related work, we compare the marginal complexity with the performance of gradient descent and approximate message passing algorithms \cite{Kent-Dobias_2024_Algorithm-independent}. An outline of this paper follows. In Section \ref{sec:eigenvalue} we introduce the technique for conditioning on @@ -1652,7 +1652,7 @@ to determine the marginal stability continue to hold even in non-Gaussian cases where the complexity and the condition to fix the minimum eigenvalue are tangled together. -In our companion paper, we use a sum of squared random functions model to explore the relationship between the marginal +In a related paper, we use a sum of squared random functions model to explore the relationship between the marginal complexity and the performance of two generic algorithms: gradient descent and approximate message passing \cite{Kent-Dobias_2024_Algorithm-independent}. We show that the range of @@ -1678,8 +1678,7 @@ We have introduced a method for conditioning complexity on the marginality of stationary points. This method is general, and permits conditioning without first needing to understand the statistics of the Hessian at stationary points. We used our approach to study marginal complexity in three different models of random landscapes, showing that the method works and can be -applied to models whose marginal complexity was not previously known. In our -companion paper, we further show that marginal complexity in the third +applied to models whose marginal complexity was not previously known. In related work, we further show that marginal complexity in the third model of sums of squared random functions can be used to effectively bound algorithmic performance \cite{Kent-Dobias_2024_Algorithm-independent}. |