Update README.md

README.md

@@ -5,10 +5,10 @@ pretty_name: Characterizing weaving patterns of size 7 x 6
 
 # Dataset Card for Weaving Patterns of Size \\(7 \times 6\\)
 
-Weaving patterns are \\(n \times n−1\\)-matrices with \\(\{1, 2, . . . , n\}\\)-
+*Weaving patterns* are \\((n \times n−1)\\)-matrices with \\(\{1, 2, \dots , n\}\\)-
 entries introduced by \[1\] to study the number of reduced decompositions of the 
-permutation \\(\sigma = n\; n − 1 \;\dots\; 1\\) up to commutation equivalence. The number
-of such objects also counts the number of parallel sorting
+permutation that swaps \\(n\\) and \\(1\\), \\(n\\) - \\(1\\) and \\(2\\), etc. up to commutation equivalence. The number
+of such objects counts a wide range of combinatorial phenomena, including the number of parallel sorting
 networks, the number of rhombic tilings of regular polygons, and is connected to 
 the study of the higher Bruhat orders \[2\]. An \\(O(n^2)\\) algorithm for determining
 if a given \\(\{1, 2, . . . , n\}\\)-matrix is a valid weaving pattern
@@ -22,21 +22,17 @@ ML models that can detect necessary or sufficient conditions
 for a matrix to be a valid weaving pattern have the potential
 to lead to substantial improvements in the upper bound.
 
-Each dataset is a mixture of enriched weaving patterns and
-non-weaving pattern matrices with \\(\{1, 2, . . . , n\}\\)-entries.
+This dataset is a mixture of enriched weaving patterns and
+non-weaving pattern matrices with \\(\{1, 2, \dots, 7\}\\)-entries.
 
 ## Dataset Details
 
-Weaving patterns of size \\(n \times n − 1\\) are a special type of matrix containing 
-entries in \\(\{1, 2, . . . , n\}\\). They correspond to representations of the 
-longest word permutation of \\(n\\) elements (the permutation that sends 
-\\(1 \mapsto n\\), \\(2 \mapsto n − 1\\), etc.). This
-task involves trying to identify weaving patterns among matrices that look like weaving patterns but are not.
 Each matrix is stored on a single line in row-major format. For instance,
 
-`(0, 1, 2, 3, 3, 2, 3, 4, 2, 3, 2, 1, 5, 4, 3, 2)`
+`(0, 1, 2, 3, 3, 2, 3, 4, 2, 3, 2, 1, 5, 4, 3, 2)`.
+
+Labels are `0` (not a weaving pattern) and `1` (a weaving pattern).
 
-The datasets can also be found [here](https://drive.google.com/file/d/1HsWuHpTkCOtpyTG2dFH49jzkKIZYwKG8/view?usp=sharing).
 Data loaders can be found [here](https://github.com/pnnl/ML4AlgComb/tree/master/weaving_patterns).
 
 **Statistics**
@@ -45,19 +41,14 @@ Data loaders can be found [here](https://github.com/pnnl/ML4AlgComb/tree/master/
 | Train | 17,388 |  96,012 |
 | Test  | 7,310 |  41,290 |
 
-This dataset is small, we encourage users to also look at the dataset for \\(n = 7\\).
-
-**Math question:** Find an algorithm or set of rules that can efficiently distinguish between 
-weaving pattern matrices and non-weaving pattern matrices. This should be more efficient than the 
+**Math question:** Find necessary or sufficient conditions to distinguish between 
+weaving pattern matrices and non-weaving pattern matrices. These should be more efficient than the 
 \\(O(n^2\\) algorithm that can be found in the references above.
 
 **ML task:** Train a model to classify whether a \\(\{1, 2, . . . , n\}\\)-
 matrix is a weaving pattern or not. This task is framed as
 binary classification. Extract mathematical insights from a performant model.
 
-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. Benchmarking details can be found in the associated paper.