tasks

Tasks for Data Generation

The tasks directory contains (1) an implementation of the generator for our main in-context algebra task, as well as (2) an implementation of various non-group algebraic structures.

(1) mix_group_addition.py contains the main code we use to generate sequences for our in-context algebra task. Specifically, the MixGroupAddition base class generates sequences that simulate a mixture of finite groups, with classes extending it for different group mixtures.

These utility methods are used for generation of algebra sequences:

• sample_run - generates a single sequence (as a string)
• sample_batch - generates a batch of sequences (as a torch tensor)

These utility methods handle "tokenization" of sequences:

• stringify - converts a tensor sequence to its string version
• tensor_from_expression - converts a string to its tensor version

The following code is an example of how to generate a random algebra sequence (from the training distribution).

from src.tasks.mix_group_addition import MixRosetteGroupAddition
task = MixRosetteGroupAddition(num_symbols=16, max_order=10, mix=0.7)

sequence, groups, orders, vocab = task.sample_run(k_shots=200, hold_out=False,commute_out=False, unshuffled=False, fixed_groups=None)

inputs = task.tensor_from_expression([sequence])

(2) magma.py contains our implementations of various non-group algebraic structures such as magmas, semigroups, and quasigroups. They are constructed in a similar manner to PermutationGroup classes found in sympy.combinatorics such as CyclicGroup and DihedralGroup

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Other files that contain data-generation code for specific experiments can be found in src/data_utils.