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Which solution has a higher concentration of green particles?
['Solution B', 'neither; their concentrations are the same', 'Solution A']
1
In Solution A and Solution B, the green particles represent the solute. The volume of the solvent in two containers are equal. Solution A and Solution B have the same number of green particles.
isobench/science/chemistry_35
Look at the models of molecules below. Select the elementary substance.
['tetraphosphorus', 'fluoromethane', 'chloromethane']
0
In this model, five chemical elements are described by colors: white for H, black for C, light green for F, yellow for P, and green for Cl. Chloromethane is depicted with white, black, and green atoms. Tetraphosphorus contains yellow atoms only. Fluoromethane is depicted with black, white, and light green atoms.
isobench/science/chemistry_48
Complete the statement. Beryllium is ().
['an elementary substance', 'a compound']
0
The table shows that the green ball represents the chemical element with the atomic symbol Be. You can see from the model that beryllium is composed of green balls only.
isobench/science/chemistry_34
Look at the models of molecules below. Select the elementary substance.
['bromine', 'hydrazine', 'trichlorofluoromethane']
0
In this model, six chemical elements are described by colors: white for H, black for C, blue for N, light green for F, green for Cl, and brown for Br. Trichlorofluoromethane is depicted with green atoms and light green atoms only. Hydrazine has blue and white atoms. Bromine includes red atoms only.
isobench/science/chemistry_32
Complete the statement. Potassium bromide is ().
['an elementary substance', 'a compound']
1
The table shows that the purple ball represents the chemical element with the atomic symbol Ni, and the red ball stands for the atomic symbol Br. You can see that the model of potassium bromide consists of purple balls and red balls.
isobench/science/chemistry_45
Complete the text to describe the diagram. Solute particles moved in both directions across the permeable membrane. But more solute particles moved across the membrane (). When there was an equal concentration on both sides, the particles reached equilibrium.
['to the right than to the left', 'to the left than to the right']
0
Look at the diagram again. It shows you how the solution changed during the process of diffusion. Before the solute particles reached equilibrium, there were 6 solute particles on the left side of the membrane and 2 solute particles on the right side of the membrane. When the solute particles reached equilibrium, there were 4 solute particles on each side of the membrane. There were 2 more solute particles on the right side of the membrane than before.
isobench/science/chemistry_22
Which solution has a higher concentration of yellow particles?
['neither; their concentrations are the same', 'Solution A', 'Solution B']
2
In Solution A and Solution B, the yellow particles represent the solute. The volume of the solvent in two containers are both 25mL. Solution A has 2 particles, and Solution B has 4 particles.
isobench/science/chemistry_11
Which solution has a higher concentration of yellow particles?
['Solution A', 'neither; their concentrations are the same', 'Solution B']
1
In Solution A and Solution B, the yellow particles represent the solute. The volume of the solvent in two containers are both 45mL. Solution A has 11 yellow particles, and Solution B has 11 yellow particles.
isobench/science/chemistry_24
Which solution has a higher concentration of yellow particles?
['Solution B', 'neither; their concentrations are the same', 'Solution A']
1
In Solution A and Solution B, the yellow particles represent the solute. The volume of the solvent in two containers are both 40mL. Solution A has 7 blue particles, and Solution B has 7 blue particles.
isobench/science/chemistry_37
Complete the text to describe the diagram. Solute particles moved in both directions across the permeable membrane. But more solute particles moved across the membrane (). When there was an equal concentration on both sides, the particles reached equilibrium.
['to the left than to the right', 'to the right than to the left']
1
Look at the diagram again. It shows you how the solution changed during the process of diffusion. Before the solute particles reached equilibrium, there were 4 solute particles on the left side of the membrane and 2 solute particles on the right side of the membrane. When the solute particles reached equilibrium, there were 3 solute particles on each side of the membrane. There was 1 more solute particle on the right side of the membrane than before.
isobench/science/chemistry_17
Which solution has a higher concentration of pink particles?
['Solution A', 'Solution B', 'neither; their concentrations are the same']
1
In Solution A and Solution B, the pink particles represent the solute. The volume of the solvent in two containers are both 30mL. Solution A has 3 particles, and Solution B has 6 particles.
isobench/science/chemistry_39
Complete the text to describe the diagram. Solute particles moved in both directions across the permeable membrane. But more solute particles moved across the membrane (). When there was an equal concentration on both sides, the particles reached equilibrium.
['to the left than to the right', 'to the right than to the left']
0
Look at the diagram again. It shows you how the solution changed during the process of diffusion. Before the solute particles reached equilibrium, there were 4 solute particles on the left side of the membrane and 6 solute particles on the right side of the membrane. When the solute particles reached equilibrium, there were 5 solute particles on each side of the membrane. There was 1 more solute particle on the left side of the membrane than before.
isobench/science/chemistry_29
Which solution has a higher concentration of blue particles?
['Solution A', 'Solution B', 'neither; their concentrations are the same']
2
In Solution A and Solution B, the blue particles represent the solute. The volume of the solvent in two containers are equal. Solution A has 4 blue particles, and Solution B has 4 blue particles.
isobench/science/chemistry_8
Complete the statement. Hydrazine is ().
['an elementary substance', 'a compound']
1
The table shows that the white ball represents hydrogen atoms (H) and the blue ball represents nitrogen atoms (N) in the model. You can see from the model that a molecule of hydrazine is composed of four hydrogen atoms and two nitrogen atoms bonded together.
isobench/science/chemistry_19
Look at the models of molecules below. Select the elementary substance.
['oxygen', 'bromomethane', 'methane']
0
In this model, four chemical elements are described by colors: white for H, black for C, red for O, and brown for Br. Methane is depicted with black and white atoms. Bromomethane has white, black and brown atoms. Oxygen consists of two red atoms.
isobench/science/chemistry_42
Which solution has a higher concentration of pink particles?
['Solution A', 'Solution B', 'neither; their concentrations are the same']
2
In Solution A and Solution B, the particles represent the solute. The volume of the solvent in two containers are both 35mL. Solution A has 6 particles, and Solution B has 6 particles.
isobench/science/chemistry_10
Complete the statement. Oxygen is ().
['an elementary substance', 'a compound']
0
In the ball-and-stick model shown, both of the balls are the same color. The legend shows that red represents the chemical element with the atomic symbol O.
isobench/science/chemistry_49
Complete the statement. Silver is ().
['an elementary substance', 'a compound']
0
In the space-filling model of silver, all of the balls are the same color. Light blue represents the chemical element with the atomic symbol Ag.
isobench/science/chemistry_18
Select the chemical formula for this molecule.
['H3S2', 'He2S2', 'H2S', 'H2SN']
2
H is the symbol for hydrogen. S is the symbol for sulfur. This ball-and-stick model shows a molecule with two hydrogen atoms and one sulfur atom.
isobench/science/chemistry_0
Complete the statement. Magnesium is ().
['an elementary substance', 'a compound']
0
The table shows that the green ball represents the chemical element with the atomic symbol Mg. You can see from the model that magnesium is composed of green balls only.
isobench/science/chemistry_28
Which solution has a higher concentration of blue particles?
['neither; their concentrations are the same', 'Solution B', 'Solution A']
1
In Solution A and Solution B, the blue particles represent the solute. The volume of the solvent in two containers are both 40mL. Solution A has fewer blue particles.
isobench/science/chemistry_14
Which solution has a higher concentration of green particles?
['Solution B', 'neither; their concentrations are the same', 'Solution A']
0
In Solution A and Solution B, the green particles represent the solute. The volume of the solvent in two containers are both 45mL. Solution B has more green particles.
isobench/science/chemistry_21
Which solution has a higher concentration of green particles?
['Solution B', 'Solution A', 'neither; their concentrations are the same']
0
In Solution A and Solution B, the green particles represent the solute. The volume of the solvent in two containers are 30mL. Solution A has two green particles, and Solution B has six green particles.
isobench/science/chemistry_31
Look at the models of molecules below. Select the elementary substance.
['acetaldehyde', 'chloroform', 'oxygen']
2
In this model, four chemical elements are described by colors: white for H, black for C, red for O, and green for Cl. Acetaldehyde is depicted with black atoms, white atoms and a red atom. Oxygen has two red atoms. Chloroform includes three green atoms, one white atom and one atom atom.
isobench/science/chemistry_23
Which solution has a higher concentration of green particles?
['neither; their concentrations are the same', 'Solution A', 'Solution B']
1
In Solution A and Solution B, the green particles represent the solute. The volume of the solvent in two containers are both 35mL. Solution A has 7 green particles, and Solution B has 6 green particles.
isobench/science/chemistry_25
Look at the models of molecules below. Select the elementary substance.
['fluoromethanol', 'dichloromethane', 'chlorine']
2
In this model, five chemical elements are described by colors: white for H, black for C, red for O, light green for F, and green for Cl. Fluoromethanol is depicted with one black atom, three white atoms, one red atom, and one green atom. Chlorine consists of two green atoms. Dichloromethane includes one black atom, two white atoms, and two green atoms.
isobench/science/chemistry_13
Complete the statement. Calcium oxide is ().
['an elementary substance', 'a compound']
1
The table shows that the red ball represents the chemical element with the atomic symbol O, and the green ball stands for the atomic symbol Ca. You can see that the model consists of green balls and red balls.
isobench/science/chemistry_46
Look at the models of molecules below. Select the elementary substance.
['cyclopropane', 'chloroform', 'nitrogen']
2
In this model, four chemical elements are described by colors: white for H, black for C, blue for N, and green for Cl. Cyclopropane is depicted with black and white atoms. Nitrogen has blue atoms only. Chloroform includes green, black and white atoms.
isobench/science/chemistry_30
Look at the models of molecules below. Select the elementary substance.
['carbon tetrachloride', 'acetaldehyde', 'bromine']
2
In this model, five chemical elements are described by colors: white for H, black for C, red for O, green for Cl, and brown for Br. Acetaldehyde is depicted with black atoms, white atoms and a red atom. Carbon tetrachloride has green and black atoms. Bromine includes red atoms.
isobench/science/chemistry_26
Which solution has a higher concentration of green particles?
['Solution A', 'neither; their concentrations are the same', 'Solution B']
2
In Solution A and Solution B, the particles represent the solute. The volume of the solvent in two containers are both 40mL. Solution B has more particles.
isobench/science/chemistry_9
Look at the models of molecules below. Select the elementary substance.
['fluoromethanol', 'tetraphosphorus', 'methane']
1
In this model, five chemical elements are described by colors: white for H, black for C, red for O, green for F, and yellow for P. Fluoromethanol is depicted with white, black, red and green atoms. Tetraphosphorus contains yellow atoms only. Methane is depicted with black and white atoms.
isobench/science/chemistry_44
Complete the text to describe the diagram. Solute particles moved in both directions across the permeable membrane. But more solute particles moved across the membrane (). When there was an equal concentration on both sides, the particles reached equilibrium.
['to the right than to the left', 'to the left than to the right']
1
Look at the diagram again. It shows you how the solution changed during the process of diffusion. Before the solute particles reached equilibrium, there were 3 solute particles on the left side of the membrane and 7 solute particles on the right side of the membrane. When the solute particles reached equilibrium, there were 5 solute particles on each side of the membrane. There were 2 more solute particles on the left side of the membrane than before.
isobench/science/chemistry_7
Which solution has a higher concentration of blue particles?
['Solution B', 'Solution A', 'neither; their concentrations are the same']
1
In Solution A and Solution B, the blue particles represent the solute. The volume of the solvent in two containers are equal. Solution A has 8 blue particles, and Solution B has 4 blue particles.
isobench/science/chemistry_1
Which solution has a higher concentration of pink particles?
['Solution B', 'neither; their concentrations are the same', 'Solution A']
2
In Solution A and Solution B, the pink particles represent the solute. The volume of the solvent in two containers are equal. Solution A has 11 pink particles, and Solution B has 8 pink particles.
isobench/science/chemistry_6
Look at the models of molecules below. Select the elementary substance.
['silane', 'nitrogen', 'ethane']
1
In this model, four chemical elements are described by colors: white for H, black for C, blue for N, and yellow for Si. Silane is depicted with white and yellow atoms. Nitrogen has blue atoms only. Ethane includes black and white atoms.
isobench/science/chemistry_27
Which solution has a higher concentration of blue particles?
['Solution B', 'neither; their concentrations are the same', 'Solution A']
0
In Solution A and Solution B, the blue particles represent the solute. The volume of the solvent in two containers are equal. Solution B has more blue particles.
isobench/science/chemistry_33
Which solution has a higher concentration of yellow particles?
['Solution A', 'Solution B', 'neither; their concentrations are the same']
1
In Solution A and Solution B, the yellow particles represent the solute. The volume of the solvent in two containers are equal. Solution B has more yellow particles.
isobench/science/chemistry_38
Which solution has a higher concentration of blue particles?
['neither; their concentrations are the same', 'Solution A', 'Solution B']
1
In Solution A and Solution B, the blue particles represent the solute. The volume of the solvent in two containers are both 30mL. Solution A has 5 blue particles, and Solution B has 3 blue particles.
isobench/science/chemistry_36
Complete the statement. Silicon carbide is ().
['a compound', 'an elementary substance']
0
The table shows that the black ball represents carbon atoms (C) and the yellow ball represents silicon atoms (Si) in the model. You can see from the model that silicon carbide is composed of carbon atoms and silicon atoms bonded together.
isobench/science/chemistry_20
Look at the models of molecules below. Select the elementary substance.
['propane', 'hydrazine', 'iodine']
2
In this model, four chemical elements are described by colors: white for H, black for C, blue for N, and purple for I. Propane is depicted with three black atoms and eight white atoms. Hydrazine has two blue atoms and four white atoms. Iodine includes two purple atoms.
isobench/science/chemistry_15
Complete the text to describe the diagram. Solute particles moved in both directions across the permeable membrane. But more solute particles moved across the membrane (). When there was an equal concentration on both sides, the particles reached equilibrium.
['to the left than to the right', 'to the right than to the left']
0
Look at the diagram again. It shows you how the solution changed during the process of diffusion. Before the solute particles reached equilibrium, there were 4 solute particles on the left side of the membrane and 6 solute particles on the right side of the membrane. When the solute particles reached equilibrium, there were 5 solute particles on each side of the membrane. There was 1 more solute particle on the left side of the membrane than before.
isobench/science/chemistry_5
Which solution has a higher concentration of green particles?
['Solution B', 'neither; their concentrations are the same', 'Solution A']
0
In Solution A and Solution B, the green particles represent the solute. The volume of the solvent in two containers are both 30mL. Solution A has 3 green particles, and Solution B has 5 green particles.
isobench/science/chemistry_16
Complete the statement. Hydrogen is ().
['an elementary substance', 'a compound']
0
In this model, each labeled ball represents one chemical element. The model of hydrogen shows that both balls are labeled with H.
isobench/science/chemistry_40
Complete the statement. Ethane is ().
['an elementary substance', 'a compound']
1
Use the model to determine whether ethane is an elementary substance or a compound. You can see from the model that a molecule of ethane is composed of six hydrogen atoms and two carbon atoms bonded together.
isobench/science/chemistry_4
Select the chemical formula for this molecule.
['BF3', 'BFe3', 'HB3F', 'B2F3']
0
B is the symbol for boron. F is the symbol for fluorine. This ball-and-stick model shows a molecule with one boron atom and three fluorine atoms.
isobench/science/chemistry_41
Complete the text to describe the diagram. Solute particles moved in both directions across the permeable membrane. But more solute particles moved across the membrane (). When there was an equal concentration on both sides, the particles reached equilibrium.
['to the right than to the left', 'to the left than to the right']
0
Look at the diagram again. It shows you how the solution changed during the process of diffusion. Before the solute particles reached equilibrium, there were 6 solute particles on the left side of the membrane and 2 solute particles on the right side of the membrane. When the solute particles reached equilibrium, there were 4 solute particles on each side of the membrane. There were 2 more solute particles on the right side of the membrane than before.
isobench/science/chemistry_3
Complete the statement. Ethane is ().
['an elementary substance', 'a compound']
1
In the model of ethane, each ball is labeled with C for carbon or H for hydrogen. The model is made of two chemical elements bonded together.
isobench/science/chemistry_2
Complete the statement. Nickel is ().
['an elementary substance', 'a compound']
0
The table shows that the blue ball represents the chemical element with the atomic symbol Ni. You can see from the model that all of the balls are the same color.
isobench/science/chemistry_43
Which solution has a higher concentration of pink particles?
['neither; their concentrations are the same', 'Solution B', 'Solution A']
1
In Solution A and Solution B, the purple particles represent the solute. The volume of the solvent in two containers are both 25mL. Solution A has 3 particles, and Solution B has 5 particles.
isobench/science/chemistry_12
Complete the statement. Iodine is ().
['an elementary substance', 'a compound']
0
In this model, both balls are labeled with I. Each ball stands for one chemical element.
isobench/science/chemistry_47
The figure shows a reaction between sodium (Na) and water (H2O). Which best explains why the equation is not balanced?
['There is too much sodium in the reactants.', 'There is not enough water in the reactants.', 'There is too much hydrogen gas in the products.', 'There is not enough sodium hydroxide in the products.']
1
This is a chemical equation representing the reaction between solid sodium (Na) and liquid water (H2O) to form aqueous sodium hydroxide (NaOH) and hydrogen gas (H2). In the reaction, two moles of sodium react with one mole of water to produce two moles of sodium hydroxide and one mole of hydrogen gas.
isobench/science/chemistry_50
Is the given chemical equation balanced?
['Yes, it is balanced.', 'No, it is not balanced.']
0
This is a chemical equation representing the reaction between hydrogen (H2) and oxygen (O2) to form water (H2O). In this reaction, two molecules of hydrogen react with one molecule of oxygen to produce two molecules of water.
isobench/science/chemistry_51
How many nitrogens are in the following organic molecule?
['0', '1', '2', '3']
2
Its SMILES notation is CC1(C#N)CCCC(C)(C)[N](C1)=O.
isobench/science/chemistry_60
How many carbons are in the following organic molecule?
['7', '8', '9', '10']
3
Its SMILES notation is CC1(C#N)CCCC(C)(C)[N](C1)=O.
isobench/science/chemistry_61
How many carbons are in the following organic molecule?
['5', '6', '7', '8']
3
Its molecular formula is C8H7Cl.
isobench/science/chemistry_62
How many chlorine atoms are there in the following organic molecule?
['0', '1', '2', '3']
1
Its molecular formula is C8H7Cl.
isobench/science/chemistry_63
How many carbons are there in the following organic molecule?
['7', '8', '9', '10']
2
Its molecular formula is CH3C(CH3)2CH2CH(CH3)CH2CH3.
isobench/science/chemistry_64
How many hydrogens are there in the following organic molecule?
['17', '18', '19', '20']
3
Its molecular formula is CH3C(CH3)2CH2CH(CH3)CH2CH3.
isobench/science/chemistry_65
How many carbons are there in the following organic compound?
['4', '5', '6', '7']
2
The organic compound is benzene.
isobench/science/chemistry_66
How many carbons are there in the following organic compound?
['4', '5', '6', '7']
2
Its molecular formula is C6H6.
isobench/science/chemistry_67
How many carbons are there in the following organic compound?
['4', '5', '6', '7']
2
Its molecular formula is CH3-O-CH2-CH2-CH(-CH3)-C(=O)-OH.
isobench/science/chemistry_68
How many oxygen atoms are there in the following organic compound?
['1', '2', '3', '4']
2
Its molecular formula is CH3-O-CH2-CH2-CH(-CH3)-C(=O)-OH.
isobench/science/chemistry_69
The physical properties of element X are shown in the table. Which most likely represents the identity of element X?
['carbon', 'copper', 'iodine', 'sulfur']
1
The table lists the properties: malleable, ductile, shiny, conducts heat, and conducts electricity.
isobench/science/chemistry_52
What is the coefficient on sulfur dioxide if the following redox reaction is balanced in an acidic solution?
['2', '4', '5', '3']
3
The redox reaction involves sulfur dioxide (SO2) and dichromate ion (Cr2O7^2-). In this reaction, sulfur dioxide is being oxidized to sulfate ion (SO4^2-), while dichromate ion is being reduced to chromium ion (Cr^3+).
isobench/science/chemistry_70
What is the type of the given reaction?
['Decomposition', 'Double replacement', 'Single-replacement', 'Addition']
1
The reaction is AgNO3 + NaCl -> AgCl + NaNO3.
isobench/science/chemistry_71
Which compound or ion is the oxidizing agent in the given reaction?
['Fe', 'Fe (3+)', 'Al', 'Al (3+)']
3
The reaction is \text{Al}^{3+} + \text{Fe} \rightarrow \text{Al} + \text{Fe}^{3+}.
isobench/science/chemistry_72
What is the precipitate in the given reaction?
['BaCl2', 'Na2SO4', 'BaSO4', 'NaCl']
2
The reaction is BaCl2 + Na2SO4 -> BaSO4 + NaCl.
isobench/science/chemistry_73
Consider the given reaction. If you start with 4mol of potassium bromide, how many moles of bromine are produced?
['2', '4', '6', '8']
0
The reaction is 2KBr + Cl2 -> 2KCl + Br2.
isobench/science/chemistry_74
Is the given chemical equation balanced?
['Yes, it is balanced.', 'No, it is not balanced.']
0
The chemical equation shows the chemical equation for the combustion of propane (C3H8). In this reaction, one molecule of propane reacts with five molecules of oxygen gas to produce three molecules of carbon dioxide and four molecules of water.
isobench/science/chemistry_53
Is the given chemical equation balanced?
['Yes, it is balanced.', 'No, it is not balanced.']
1
The chemical equation shows the chemical equation for the combustion of propane (C3H8). In this reaction, one molecule of propane reacts with one molecule of oxygen gas to produce three molecules of carbon dioxide and four molecules of water.
isobench/science/chemistry_54
Is this a neutralisation reaction?
['Yes.', 'No.']
0
This chemical equation shows the reaction between sodium hydroxide (NaOH) and hydrochloric acid (HCl), producing sodium chloride (NaCl) and water (H2O).
isobench/science/chemistry_55
Which change in state is illustrated?
['melting', 'freezing', 'evaporation', 'condensation']
2
State changes from liquid to gas.
isobench/science/chemistry_56
Is the given chemical equation balanced?
['Yes, it is balanced.', 'No, it is not balanced.']
1
This is a chemical equation representing the reaction between hydrogen (H2) and oxygen (O2) to form water (H2O). In this reaction, one molecule of hydrogen reacts with one molecule of oxygen to produce one molecule of water.
isobench/science/chemistry_57
Is the given chemical equation balanced?
['Yes, it is balanced.', 'No, it is not balanced.']
0
The chemical equation shows the chemical equation for the reaction of iron sulfide (FeS) with oxygen (O2), producing iron (III) oxide (Fe2O3) and sulfur dioxide (SO2). In this reaction, four molecules of iron sulfide react with seven molecules of oxygen to produce two molecules of iron oxide and four molecules of sulfur dioxide.
isobench/science/chemistry_58
Is the given chemical equation balanced?
['Yes, it is balanced.', 'No, it is not balanced.']
1
The chemical equation shows the chemical equation for the reaction of iron sulfide (FeS) with oxygen (O2), producing iron (III) oxide (Fe2O3) and sulfur dioxide (SO2). In this reaction, four molecules of iron sulfide react with seven molecules of oxygen to produce two molecules of iron oxide and two molecules of sulfur dioxide.
isobench/science/chemistry_59

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:

@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

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