### GraphLog - Suite of 57 graph worlds built using first-order logic

Koustuv Sinha, Shagun Sodhani, Joelle Pineau and William L. Hamilton

### Motivation

A question that we are highly interested in finding an answer to is how generalizable our learning algorithms are? Human beings are incredibly good at generalization - even at old age, we can learn new concepts and apply them in practice. Critical steps towards building algorithms that think like human beings include Multitask Learning - the ability to learn multiple concepts at once; and Continual Learning - the ability to accumulate new knowledge without forgetting the previous knowledge.

Defining a task that aims at either Multitask Learning or Continual learning is challenging - the task should accurately quantify the “distribution shift” in the data. Having precise control of this shift could allow us to understand the drawbacks of our learning methods, and build systems which can generalize over multiple tasks but still remember the old ones.

Data distributions can be quantified by generating them based on a grammar. First-order logic, even with its basic use-case and restrictions, can be an excellent tool for defining such generalizable distributions - to test how systematic a model is. In our prior work, we leveraged first-order logic to build the CLUTRR dataset, which provides a kinship-relation game in natural language QA setting. A nice property of CLUTRR is that it is designed to be a dynamic dataset - one can always roll out longer kinship relation trees to stress-test the generalizability of their proposed approach. Since it is designed to be diagnostic, it opens up the possibility of investigating the semantic understanding capability of Natural Language Understanding models under microscopic precision.

While CLUTRR primarily investigates the aspect of length generalization, the core semantic rules driving the kinship relations are static. In a real-world scenario, a model may have to adapt to the change in underlying dynamics of the domain (for example, recommender systems trained on one domain being deployed / finetuned on a new domain). In terms of grammar, two domains sharing the same grammar constitute similar domains. We need a task where we can generalize over different grammars and control the amount of distribution shift.

### Introducing GraphLog

In this work, we introduce a new paradigm of testing domain generalization in graph-structure data, named GraphLog. Instead of being a single dataset, GraphLog v1.0 contains 57 datasets, which have their own set of grammar or generation rules.

The Task : We are primarily interested in relation prediction, where given a graph $g_i$, a source node $v_i$, and sink node $v_j$, the task is to predict the type of the edge $r$ between $(v_i, v_j)$. In Graph Neural Network (GNN) world, this task is typically performed by RGCN model on popular relation prediction datasets.

Graphs in GraphLog are generated using rules in first-order logic. These rules are 2-ary Horn clauses in the form of $[r_i, r_j] \rightarrow r_j$, where $r_i$ are the types of relation. Each world is a dataset on its own, which consists of 5000 graphs procedurally generated by their own set of rules, which themselves are generated stochastically. Between multiple worlds, there can be overlap between the rules, which helps us in explicitly quantifying the shift in the data distribution. This enables us to perform Multi-task learning and Continual learning along with supervised learning experiments in graph-structured data, which is one of the first datasets which propose to do so.

Dataset Inspectable Rules Diversity Compositional Generalization Modality S Me Mu CL
CLEVR Vision
Cogent Vision
CLUTRR Text
SCAN Text
SQoOP Vision
TextWorld Text
GraphLog Graph

### Supervised Learning

GraphLog can be used to perform supervised relation prediction tasks in any of its multiple worlds. Due to the stochastic nature of rule generation, certain worlds are more difficult than others. We define the notion of difficulty empirically based on model performance, but we observe a correlation with the number of descriptors or unique walks in the graphs associated with a world.

GraphLog makes it easy to extend the supervised learning framework for multi-task learning by transferring model parameters on the next task. We find the model’s capacity saturates at 20 tasks, however we hypothesize larger capacity with more data points will increase the number of tasks. We use a two-step model that adapts for relations in different worlds, the details of which can be found in our paper.

### Continual Learning

GraphLog enables us to evaluate the generalization capability of graph neural networks in the sequential continual learning setup where the model is trained on a sequence of worlds. Before training on a new world, the model is evaluated on all the worlds that the model has trained on so far. We observe that as the model is trained on different worlds, it performance on the previous worlds degrades rapidly. This observation highlights that the current reasoning models are not suitable for continual learning.

Experiments on sequential continual learning setting. The left image depicts random ordering, and the right image depicts ordering based on world difficulty.

### Using GraphLog

We hope that the above examples got you excited about the possibilities of GraphLog! We have made it easier for you to play with GraphLog v1.0 by releasing an API on PyPi, graphlog, which provides custom dataloaders built on Pytorch Geometric.

We have released the code for the API at https://github.com/facebookresearch/graphlog, which includes basic and advanced use cases, as well as simple examples built on Pytorch Lightning. We will be releasing the code to generate GraphLog soon as well, so you can build your own version of GraphLog and contribute to the repository.

### I want to read more

This blog post provides a summary of the results and basic use cases of GraphLog. Please read more in our paper on arxiv titled Evaluating Logical Generalization in Graph Neural Networks. Our submission is currently under review at ICML 2020. The code for reproducing the main experiments are now available in the GraphLog repository.

If you have any questions regarding the usage of GraphLog, feel free to open an issue, or join our Slack Channel, or send me a mail at koustuv.sinha@mail.mcgill.ca. If you would like to contribute, do open a Pull Request (PR)!.

### Acknowledgements

I would like to thank my collaborator Shagun Sodhani for not only helping in writing this blog post, but for being a constant source of motivation throughout our various adventures in research. I would also like to thank my amazing supervisors, William L. Hamilton and Joelle Pineau, for their constant motivation and support. I am grateful to Facebook AI Research (FAIR) for providing extensive compute resources to make this project possible. I thank my wonderful colleagues at Mila and FAIR for various constructive feedback on the project. This research was supported by the Canada CIFAR Chairs in AI program.