Dataset Card for IsoBench

📚 paper 🌐 website

Introducing IsoBench, a benchmark dataset containing problems from four major areas: math, science, algorithms, and games. Each example is presented with multiple isomorphic representations of inputs, such as visual, textual, and mathematical presentations. Details of IsoBench can be found in our paper or website!

Uses

There are 4 major domains: math, algorithm, game, and science. Each domain has several subtasks.

In tatal there are 1,887 samples in the validation split with ground-truth labels provided.

The test split without labels is coming soon......

We will show how to load the data for each subtask.

TL;DR

There are 10 subtasks in total: math_breakpoint, math_convexity, math_parity, graph_connectivity, graph_maxflow, graph_isomorphism, winner_id, puzzle, chemistry, physics.

You can load a subtask via

from datasets import load_dataset
ds_subtask = load_dataset('isobench/IsoBench', subtask, split='validation')

Direct Use

IsoBench is designed with two objectives, which are:

• Analyzing the behavior difference between language-only and multimodal foundation models, by prompting them with distinct (e.g. mathematical expression and plot of a function) representations of the same input.
• Contributing a language-only/multimodal benchmark in the science domain.

Mathematics

There are three mathematics tasks. Each task is structured as a classification problem and each class contains 128 samples.

• Parity implements a ternary classification problem. A model has to classify an input function into an even function, odd function, or neither.
• Convexity implements a binary classification problem for a model to classify an input function as convex or concave. Note: some functions are only convex (resp. concave) within a certain domain (e.g. x > 0), which is reported in the domain field of each sample. We recommend providing this information as part of the prompt!
• Breakpoint counts the number of breakpoints (i.e. intersections of a piecewise linear function). Each function contains either 2 or 3 breakpoints, which renders this task a binary classification problem.

from datasets import load_dataset

dataset_parity = load_dataset('isobench/IsoBench', 'math_parity', split='validation')
dataset_convexity = load_dataset('isobench/IsoBench', 'math_convexity', split='validation')
dataset_breakpoint = load_dataset('isobench/IsoBench', 'math_breakpoint', split='validation')

Algorithms

There are three algorithmic tasks, with ascending complexity: graph connectivity, graph maximum flow, and graph isomorphism.

You can download the data by

from datasets import load_dataset

dataset_connectivity = load_dataset('isobench/IsoBench', 'graph_connectivity', split='validation')
dataset_maxflow = load_dataset('isobench/IsoBench', 'graph_maxflow', split='validation')
dataset_isomorphism = load_dataset('isobench/IsoBench', 'graph_isomorphism', split='validation')

Each task has 128 dev samples under the validation split.

Games

[More Information Needed]

Science

[More Information Needed]

Data Fields

Mathematics

• image: a PIL Image feature;
• latex: a string feature, containing the LateX definition of a function;
• code: a string feature, containing the sympy definition of a function;
• label: a string feature;
• domain: a string feature or None, denoting the domain of a function. This feature is only used for some of the Convexity problems.
• id: a string feature.

Algorithms

Connectivity

• image: a PIL Image feature
• query_nodes_color: a string feature
• adjacency_matrix: a string feature, a string of an 2d array representing the adjacency matrix of a graph
• query_node_1: a unit32 feature
• query_node_2: a unit32 feature
• label: a bool feature, with possible values including True (query nodes connected) and False (query nodes not connected)
• id: a string feature

Maxflow

• image: a PIL Image feature
• source_node: a unit32 feature, denoting the index of the source node
• source_node_color: a string feature, denoting the color of the source_node rendered in the image
• sink_node: a unit32 feature, denoting the index of the sink node
• sink_node_color: a string feature, denoting the color of the sink_node rendered in the image
• adjacency_matrix: a string feature, a string of an 2d array representing the adjacency matrix of a graph. The value in entry (i,j) denotes the capacity of flowing from node i to node j.
• label: a uint32 feature
• id: a string feature

Isomorphism

• image: a PIL Image feature, consisting of two graphs G and H
• adjacency_matrix_G: a string feature, a string of an 2d array representing the adjacency matrix of graph G
• adjacency_matrix_H: a string feature, a string of an 2d array representing the adjacency matrix of graph H
• label: a bool feature, with possible values including True (graphs G and H are isomorphic) and False (not isomorphic)
• id: a string feature

Games

[More Information Needed]

Science

[More Information Needed]

Citation

BibTeX:

@inproceedings{fu2024isobench,
      title={{I}so{B}ench: Benchmarking Multimodal Foundation Models on Isomorphic Representations}, 
      author={Deqing Fu and Ruohao Guo and Ghazal Khalighinejad and Ollie Liu and Bhuwan Dhingra and Dani Yogatama and Robin Jia and Willie Neiswanger},
      booktitle={First Conference on Language Modeling (COLM)},
      year={2024},
      note={First four authors contributed equally.}
}

Chicago Style: Deqing Fu^*, Ruohao Guo^*, Ghazal Khalighinejad^*, Ollie Liu^*, Bhuwan Dhingra, Dani Yogatama, Robin Jia, and Willie Neiswanger. "IsoBench: Benchmarking Multimodal Foundation Models on Isomorphic Representations." arXiv preprint arXiv:2404.01266 (2024).

Contact

deqingfu@usc.edu, rguo48@gatech.edu, me@ollieliu.com, ghazal.khalighinejad@duke.edu