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Diffstat (limited to 'referee_response.md')
-rw-r--r-- | referee_response.md | 4 |
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diff --git a/referee_response.md b/referee_response.md index 771f046..78a3276 100644 --- a/referee_response.md +++ b/referee_response.md @@ -126,8 +126,8 @@ Ask for minor revision 3. Ok * The referee is wrong to say that the Euler characteristic of a hypersphere is 2 independent of dimension. The Euler characteristic of all odd-dimensional manifolds is zero. Consider the cell complex on *S*₁ [pictured here](https://kent-dobias.com/files/S_1.png). The Euler characteristic calculated using the alternating sum over the number of cells of increasing dimension is χ(*S*₁) = 1 – 1 = 0. * Ok - 4. Ok - * Ok - discuss planting in manuscript, raise skepticism of results of fear paper. + 4. The referee points out that previous work on gradient descent in the spherical spin glasses studied gradient descent from both uniformly random initial conditions ("infinite" temperature) and initial conditions drawn from a Boltzmann distribution at some finite temperature, and found that the final state of the dynamics reached marginal minima in a range of energies depending on the initial condition. The conjecture in this manuscript seeks only to explain the upper energy of this range, that associated with gradient descent from a uniformly random initial condition. Presumably there are a variety of behaviors observable by choosing initial conditions using a variety of initial distributions, Boltzmann or otherwise, and one day we may hope to address such questions using similar approaches to this paper. However, this is not addressed here. A small discussion of this point has been added to the manuscript. + * A paragraph addressing what might occur in planted models has been added to the manuscript. 5. Make a supplementary materials file * The manuscript has been modified to clarify where a review of superspace methods can be found in the referenced material. * The subscript notation associated with the determinant has been explained in a footnote. |