[yorwba]

I'm not sure why you think neural networks can't handle variable numbers of inputs. Recurrent networks that ingest whole sequences have been around for a long time, and other structures have their own network topologies. Support for things other than classic RNNs is more limited, but e.g. TensorFlow Fold (https://github.com/tensorflow/fold) was specifically designed for that.

[CuriouslyC]

RNNs are a good model for things that are naturally sequential with limited state transfer. They are not so elegant for things with no defined ordering and a large amount of shared state.

[yorwba]

Can you give an example of a problem where you have "no defined ordering and a large amount of shared state"? What kind of model is typically used in that domain?

[CuriouslyC]

One problem I've been considering is triangle surface meshes. The data is variable in size, with no defined start or end point, where points distant on the surface may share a high amount of mutual information (through symmetry, etc).

One approach I've thought about is applying kernel methods. You can compose kernels, so they scale up cleanly regardless of variations in the input dimension. The sum or product of kernels between each node in the input graph and some basis set is itself a kernel. If your kernels describe covariance between observations (i.e. Gaussian processes) then additional input dimensions have a constraining effect, rather than causing evidence inflation for larger inputs as a typical neural network might.