Dataset Card for FIM-Estimation

Dataset Description

Dataset Summary

In a FIM-Estimation task, the input consists of the following components:

1. A dataset of the form $\mathcal{D}_ {train} = {(\mathbf{\lambda}_ i, x_ i)}_ {i=1}^{\left|\mathcal{D}\right|}$, where $\vlambda_ i$ is a point in the parameter space and $x_ i$ is a sample.
2. The structure of each sample $x_ i$. For example, if $x_ i\in{0,1}^n$ is a bitstring representing a measurement of a quantum system on a lattice with $n$ sites, then the said structure is the lattice and the correspondence between the bitstring bits and the lattice sites.
3. Optionally, additional information about the statistical manifold. This could involve, e.g., the symmetries of the system used to generate the statistical manifold.

The task is to estimate Fisher Information Metric (FIM) as a matrix-valued function of parameter $\mathbf{\lambda}$.

In this dataset we present multiple such tasks (parameterised by task name and random seed). E.g. in order to solve the IsNNN400 task with seed=4 one would download config isnnn_400.seed04, split train, estimate the FIM, and compare the results with isnnn_400.seed04.gt_fim.

Additional information

We (TODO:plan to) present datasets corresponding to 6 statistical manifolds: XXZ300_Z, FIL24, etc. The data is stored as follows: data/xxz300_z contains the data for XXZ300_Z datasets. Within that directory, there are subdirectories of the form seed_?? each containing a dataset describing the same statistical manifold, but generated using a different seed (e.g. seed_05). We have seed_05/d_train.parquet, which is the dataset as described in #1 above. seed_05/d_test.parquet is a hold-out dataset which should not be used in estimation of $\mathbf{\lambda}$ (not even for hyperparameter tuning). data/xxz300_z/meta.json (TODO) represents the metadata (including information listed in #2 and #3 above) data/xxz300_z/fim_ground_truth.json (TODO) represents the ground truth FIM.

An algorithm attempting to solve the FIM-Estimation task XXZ300_Z(seed=05) shall take data/xxz300_z/seed_05/d_train.parquet and data/xxz300_z/meta.json as inputs and produce FIM estimates to be compared with data/xxz300_z/fim_ground_truth.json.