--- language: - en license: apache-2.0 dataset_info: - config_name: chemistry features: - name: image dtype: image splits: - name: validation num_bytes: 2583029 num_examples: 75 download_size: 2506649 dataset_size: 2583029 - 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 - config_name: physics features: - name: image dtype: image splits: - name: validation num_bytes: 2329788 num_examples: 75 download_size: 2145939 dataset_size: 2329788 - config_name: puzzle features: - name: image dtype: image - name: anl dtype: string - name: pgn dtype: string - name: fen dtype: string - name: label dtype: string - name: id dtype: float64 splits: - name: validation num_bytes: 5085659 num_examples: 200 download_size: 4787468 dataset_size: 5085659 - config_name: winner_id features: - name: image dtype: image - name: anl dtype: string - name: pgn dtype: string - name: fen dtype: string - name: label dtype: string - name: id dtype: string splits: - name: validation num_bytes: 6486731 num_examples: 257 download_size: 6026970 dataset_size: 6486731 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 📚 [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 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 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 **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