105& 66& 1\
**Total**& 522&468& 465& 327& 8\
& 3mo & 6mo & 12mo & 24mo & 36mo\
NC$^*$& 172& 142& 159& 122& 3\
MCI$^*$& 257& 230& 202& 149& 4\
AD& 94& 98& 101& 52& 1\
**Total** & 523& 470& 462& 323& 8\

Parameter selection
-------------------

We use the regularization kernel $$K = L^{-1} = (-a \nabla^2 - b\nabla(\nabla \cdot) + c)^{-2}$$ with $[a, b, c]$ set to $[1, 0, 0.1]$. The parameter $\sigma$, from equation , is set to $0.1$. We train our network (using `ADAM` [@adam]) over 10 epochs with a learning rate of $0.0001$.

Efficiency
----------

Once trained, the prediction models allow fast computations of registrations. We use a TITAN X (Pascal) GPU and `PyTorch`[^3] for our implementation of FPIR. For the 3D `ADNI-1` dataset ($220 \times 220 \times 220$ MR images), FPSGR took about one day to predict 2646 pairwise registrations (i.e., 25 \[s\]/prediction) and to compute the regression result. Optimization-based LDDMM[^4] would require $\approx$ 40 days of runtime. Runtime for FPIR on `ADNI-2` is identical to `ADNI-1` as the images have the same spatial dimension.

1ex Compared to the-state-of-art fast geodesic regression model [@hong2017fast], FPSGR is also at least twice as fast. The model in 