README.md

---
language:
- en
license: apache-2.0
dataset_info:
- config_name: chemistry
  features:
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    dtype: image
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- config_name: graph_connectivity
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    dtype: image
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  - name: adjacency_matrix
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  - name: query_node_2
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- config_name: graph_isomorphism
  features:
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    dtype: image
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  - name: adjacency_matrix_H
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  - name: id
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  - name: id
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- config_name: math_breakpoint
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  - name: domain
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  - name: latex
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  - name: id
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  - name: domain
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  - name: latex
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  - name: code
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- config_name: math_parity
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  - name: domain
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  - name: code
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- config_name: physics
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- config_name: puzzle
  features:
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    dtype: image
  - name: anl
    dtype: string
  - name: pgn
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  - name: fen
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    dtype: float64
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- config_name: winner_id
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configs:
- config_name: chemistry
  data_files:
  - split: validation
    path: chemistry/validation-*
- 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-*
- config_name: physics
  data_files:
  - split: validation
    path: physics/validation-*
- config_name: puzzle
  data_files:
  - split: validation
    path: puzzle/validation-*
- config_name: winner_id
  data_files:
  - split: validation
    path: winner_id/validation-*
task_categories:
- text-classification
- zero-shot-classification
- image-classification
pretty_name: IsoBenc
size_categories:
- 1K<n<10K
---
# Dataset Card for IsoBench

<!-- Provide a quick summary of the dataset. -->

📚 [paper](https://arxiv.org/abs/2404.01266) 🌐 [website](https://isobench.github.io)

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](https://arxiv.org/abs/2404.01266) or [website](https://isobench.github.io)!

## Table of Contents
- [Dataset Details](#dataset-details)
  - [Mathematics](#mathematics)
  - [Algorithms](#algorithms)
  - [Games](#games)
  - [Science](#science)
- [Data Fields](#deta-fields)
  - [Mathematics](#mathematics)
    - [Convexity](#convexity)
    - [Breakpoint](#breakpoint)
    - [Parity](#parity)
  - [Algorithms](#algorithms)
    - [Connectivity](#connectivity)
    - [Maxflow](#maxflow)
    - [Isomorphism](#isomorphism)
  - [Games](#games)
    - [Winner Identification](#winner-identification)
    - [Chess Puzzle](#chess-puzzle)
  - [Science](#science)
    - [Chemistry](#chemistry)
    - [Physics](#physics)
- [Citation](#citation)
- [Contact](#contact)

## Uses

<!-- Address questions around how the dataset is intended to be used. -->
There are 4 major domains: math, algorithm, game, and science. Each domain has several subtasks. 

In tatal there are 1,630 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

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


### Direct Use

<!-- This section describes suitable use cases for the dataset. -->
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.

```python
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
```python
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

<!-- If there is a paper or blog post introducing the dataset, the APA and Bibtex information for that should go in this section. -->

**BibTeX:**

```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 Style:**
Deqing Fu, 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, me@ollieliu.com, ghazal.khalighinejad@duke.edu