Update README.md

README.md

@@ -49,40 +49,38 @@ In all cases the characters are heavily concentrated around 0 with very long tai
 ### Statistics for the three datasets, \\(n = 18,20,22\\)
 
 **Characters of \\(S_{18}\\)**
-
 |  | Number of instances | 
 |----------|----------|
 | Train | 118,580 |
 | Test  | 29,645 |
-
 Maximum character value 16,336,320, minimum character value -1,223,040.
 
 **Characters of \\(S_{20}\\)**
-
 |  | Size | 
 |----------|----------|
 | Train | 298,661 |
 | Test  | 74,819 |
-
 Maximum character value 249,420,600, minimum character value -17,592,960.
 
 **Characters of \\(S_{22}\\)**
-
 |  | Size | 
 |----------|----------|
 | Train | 763,109 |
 | Test  | 190,726 |
-
 Maximum character value 5,462,865,408, minimum character value -279,734,796.
 
 **Math question (solved):** The [Murnaghan–Nakayama rule](https://en.wikipedia.org/wiki/Murnaghan–Nakayama_rule) is an example of an algorithm for calculating the character of an irreducible representation of the symmetric group using only elementary operations on the corresponding pair of partitions.
 
-**ML task:** Train a model that can take two partitions of \\(n\\), \\(\lambda\\) and \\(\mu\\), and predict the corresponding character \\(\chi^{\lambda}\_{\mu}\\).
+**ML task:** Train a model that can take two partitions of \\(n\\), \\(\lambda\\) and \\(\mu\\), 
+and predict the corresponding character \\(\chi^{\lambda}_{\mu}\\).
 
-If a successful model is trained, it would be interesting to understand whether the model has learned an existing algorithm or whether it has discovered something new.
+If a successful model is trained, it would be interesting to understand whether the model has 
+learned an existing algorithm or whether it has discovered something new.
 
 ## Small model performance
 
+We provide some basic baselines for this task framed as regression. Benchmarking details can be found in the associated paper.
+
 | Size | Linear regression | MLP | Transformer | Guessing training label mean | 
 |----------|----------|-----------|------------|------------|
 | \\(n= 18\\) | \\(1.5920 \times 10^{10}\\) | \\(2.7447 \times 10^{8} \pm 8.8602 \times 10^8\\) | \\(2.4913 \times 10^{10} \pm 1.4350 \times 10^7\\)| \\(1.5920 \times 10^{10}\\) |
@@ -100,90 +98,53 @@ The \\(\pm\\) signs indicate 95% confidence intervals from random weight initial
 
 The dataset was generated using [SageMath](https://www.sagemath.org/). Data generation scripts can be found [here](https://github.com/pnnl/ML4AlgComb/tree/master/symmetric_group_character).
 
-- **Repository:** [More Information Needed]
-- **Paper [optional]:** [More Information Needed]
-- **Demo [optional]:** [More Information Needed]
-
+- **Repository:** [ACD Repo](https://github.com/pnnl/ML4AlgComb/tree/master/symmetric_group_character)
+  
 ## Uses
 
-This dataset was generated to study ML models ability to calculate the characters of
+This dataset was generated to study ML model's ability to calculate the characters of
 irreducible representations of the symmetric group.
 
 ### Direct Use
 
-<!-- This section describes suitable use cases for the dataset. -->
-
-[More Information Needed]
+There are a range of tasks that could be performed using this dataset. The one we consider here is
+regression of characters from the two integer partitions that index it. That is, given \\(\lambda\\) 
+and \\(\mu\\), predict the corresponding character \\(\chi^{\lambda}_{\mu}\\).
 
 ### Out-of-Scope Use
 
-<!-- This section addresses misuse, malicious use, and uses that the dataset will not work well for. -->
-
-[More Information Needed]
+None.
 
 ## Dataset Structure
 
-<!-- This section provides a description of the dataset fields, and additional information about the dataset structure such as criteria used to create the splits, relationships between data points, etc. -->
-
-[More Information Needed]
-
-## Dataset Creation
-
-### Curation Rationale
-
-<!-- Motivation for the creation of this dataset. -->
+Within each file, two integer partitions are provided followed by an integer 
+corresponding to the character. For instance, the line
 
-[More Information Needed]
+`[3,1,1],[2,2,1],-2`  
 
-### Source Data
+says that the character \\(\chi^{3,1,1}_{2,2,1} = −2\\). 
 
-<!-- This section describes the source data (e.g. news text and headlines, social media posts, translated sentences, ...). -->
+## Dataset Creation
 
-#### Data Collection and Processing
+The dataset was generated using [SageMath](https://www.sagemath.org/). 
+Data generation scripts can be found 
+[here](https://github.com/pnnl/ML4AlgComb/tree/master/symmetric_group_character).
 
-<!-- This section describes the data collection and processing process such as data selection criteria, filtering and normalization methods, tools and libraries used, etc. -->
+### Curation Rationale
 
-[More Information Needed]
+The dataset was generated because the discovery of algorithms that calculate 
+the characters of irreducible representations of the symmetric group was a breakthrough 
+in algebraic combinatorics and thus it is interesting if ML systems can re-discover this
+result.
 
 #### Who are the source data producers?
 
-<!-- This section describes the people or systems who originally created the data. It should also include self-reported demographic or identity information for the source data creators if this information is available. -->
-
-[More Information Needed]
-
-### Annotations [optional]
-
-<!-- If the dataset contains annotations which are not part of the initial data collection, use this section to describe them. -->
-
-#### Annotation process
-
-<!-- This section describes the annotation process such as annotation tools used in the process, the amount of data annotated, annotation guidelines provided to the annotators, interannotator statistics, annotation validation, etc. -->
-
-[More Information Needed]
-
-#### Who are the annotators?
-
-<!-- This section describes the people or systems who created the annotations. -->
-
-[More Information Needed]
-
-#### Personal and Sensitive Information
-
-<!-- State whether the dataset contains data that might be considered personal, sensitive, or private (e.g., data that reveals addresses, uniquely identifiable names or aliases, racial or ethnic origins, sexual orientations, religious beliefs, political opinions, financial or health data, etc.). If efforts were made to anonymize the data, describe the anonymization process. -->
-
-[More Information Needed]
+Henry Kvinge used [SageMath](https://www.sagemath.org/) to generate this dataset.
 
 ## Bias, Risks, and Limitations
 
-<!-- This section is meant to convey both technical and sociotechnical limitations. -->
-
-[More Information Needed]
-
-### Recommendations
-
-<!-- This section is meant to convey recommendations with respect to the bias, risk, and technical limitations. -->
-
-Users should be made aware of the risks, biases and limitations of the dataset. More information needed for further recommendations.
+We only provide characters for \\(n = 18,20,22\\). These characters exist for any \\(n > 0\\).
+We are happy to generate additional datasets upon request.
 
 ## Citation
 
@@ -202,16 +163,6 @@ Users should be made aware of the risks, biases and limitations of the dataset.
 
 Chau, H., Jenne, H., Brown, D., He, J., Raugas, M., Billey, S., & Kvinge, H. (2025). Machine learning meets algebraic combinatorics: A suite of datasets capturing research-level conjecturing ability in pure mathematics. arXiv preprint arXiv:2503.06366.
 
-## Glossary [optional]
-
-<!-- If relevant, include terms and calculations in this section that can help readers understand the dataset or dataset card. -->
-
-[More Information Needed]
-
-## More Information [optional]
-
-[More Information Needed]
-
 ## Dataset Card Contact
 
 Henry Kvinge, acdbenchdataset@gmail.com