README.md

metadata

language:
  - en
license: apache-2.0
dataset_info:
  - config_name: graph_connectivity
    features:
      - name: image
        dtype: image
      - name: query_nodes_color
        dtype: string
      - name: adjacency_matrix
        dtype: string
      - name: query_node_1
        dtype: int64
      - name: query_node_2
        dtype: int64
      - name: label
        dtype: bool
      - name: id
        dtype: string
    splits:
      - name: validation
        num_bytes: 62682553
        num_examples: 128
    download_size: 19391513
    dataset_size: 62682553
  - config_name: graph_isomorphism
    features:
      - name: image
        dtype: image
      - name: adjacency_matrix_G
        dtype: string
      - name: adjacency_matrix_H
        dtype: string
      - name: label
        dtype: bool
      - name: id
        dtype: string
    splits:
      - name: validation
        num_bytes: 25082487
        num_examples: 128
    download_size: 8931620
    dataset_size: 25082487
  - config_name: graph_maxflow
    features:
      - name: image
        dtype: image
      - name: source_node
        dtype: int64
      - name: source_node_color
        dtype: string
      - name: sink_node
        dtype: int64
      - name: sink_node_color
        dtype: string
      - name: adjacency_matrix
        dtype: string
      - name: label
        dtype: int64
      - name: id
        dtype: string
    splits:
      - name: validation
        num_bytes: 44530168
        num_examples: 128
    download_size: 16112025
    dataset_size: 44530168
  - config_name: math_breakpoint
    features:
      - name: image
        dtype: image
      - name: domain
        dtype: float64
      - name: latex
        dtype: string
      - name: code
        dtype: string
      - name: label
        dtype: int64
      - name: id
        dtype: string
    splits:
      - name: validation
        num_bytes: 14120119
        num_examples: 256
    download_size: 12531449
    dataset_size: 14120119
  - config_name: math_convexity
    features:
      - name: image
        dtype: image
      - name: domain
        dtype: string
      - name: latex
        dtype: string
      - name: code
        dtype: string
      - name: label
        dtype: string
      - name: id
        dtype: string
    splits:
      - name: validation
        num_bytes: 11176740
        num_examples: 256
    download_size: 9253917
    dataset_size: 11176740
  - config_name: math_parity
    features:
      - name: image
        dtype: image
      - name: domain
        dtype: float64
      - name: latex
        dtype: string
      - name: code
        dtype: string
      - name: label
        dtype: string
      - name: id
        dtype: string
    splits:
      - name: validation
        num_bytes: 17012598
        num_examples: 384
    download_size: 14230745
    dataset_size: 17012598
configs:
  - config_name: graph_connectivity
    data_files:
      - split: validation
        path: graph_connectivity/validation-*
  - config_name: graph_isomorphism
    data_files:
      - split: validation
        path: graph_isomorphism/validation-*
  - config_name: graph_maxflow
    data_files:
      - split: validation
        path: graph_maxflow/validation-*
  - config_name: math_breakpoint
    data_files:
      - split: validation
        path: math_breakpoint/validation-*
  - config_name: math_convexity
    data_files:
      - split: validation
        path: math_convexity/validation-*
  - config_name: math_parity
    data_files:
      - split: validation
        path: math_parity/validation-*

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!

Table of Contents

• Dataset Details
  • Mathematics
  • Algorithms
  • Games
  • Science
• Data Fields
  • Mathematics
    • Convexity
    • Breakpoint
    • Parity
  • Algorithms
    • Connectivity
    • Maxflow
    • Isomorphism
  • Games
    • Winner Identification
    • Chess Puzzle
  • Science
    • Chemistry
    • Physics
• Citation
• Contact

Uses

There are 4 major domains: math, algorithm, game, and science. Each domain has several subtasks. We will show how to load the data for each subtask.

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 xlim 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_connectivity = load_dataset('isobench/IsoBench', 'math_parity', split='validation')
dataset_maxflow = load_dataset('isobench/IsoBench', 'math_convexity', split='validation')
dataset_isomorphism = 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

[More Information Needed]

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

Isomorphism

Games

[More Information Needed]

Science

[More Information Needed]

Citation

BibTeX:

@misc{fu2024isobench,
      title={{I}so{B}ench: Benchmarking Multimodal Foundation Models on Isomorphic Representations}, 
      author={Deqing Fu$^*$ and Ghazal Khalighinejad$^*$ and Ollie Liu$^*$ and Bhuwan Dhingra and Dani Yogatama and Robin Jia and Willie Neiswanger},
      year={2024},
      eprint={2404.01266},
      archivePrefix={arXiv},
      primaryClass={cs.AI}
}

Chicago: Fu, Deqing, 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

[email protected], [email protected], [email protected]