Update README.md

README.md

@@ -59,40 +59,25 @@ All structure constants in this case are either 0 or 1 (so the classification pr
 | Train | 851 | 833 | 1,684 |
 | Test  | 201 | 220 | 421 |
 
-
-All structure constants in this case are either 0, 1, or 2. 
-
-|  | 0 | 1 | 2 |  Total number of instances | 
-|----------|----------|----------|----------|----------|
-| Train | 42,831 | 42,619 | 170 | 85,620 |
-| Test  | 10,681 | 10,680 | 44 | 21,405 |
-
-
-All structure constants in this case are either 0, 1, 2, 3, 4, or 5. 
-
-|  | 0 | 1 | 2 | 3 | 4 | 5 |  Total number of instances | 
-|----------|----------|----------|----------|----------|----------|----------|----------|
-| Train | 4,202,040 | 4,093,033 | 109,217 | 2,262 | 9 | 9 | 8,406,564 |
-| Test  | 1,052,062 | 1,021,898 | 27,110 | 568 | 3 | 0 | 2,101,641 |
-
 ## Data generation
 
-The Sage notebook within this directory gives the code used to generate these datasets. 
+The Sage notebook within this [directory](https://github.com/pnnl/ML4AlgComb/tree/master/schubert_polynomial_structure) 
+gives the code used to generate these datasets. 
 The process involves:
-
 - For a chosen \\(n\\), compute the products \\(\mathfrak{S}_{\alpha} \mathfrak{S}_{\beta}\\) for \\(\alpha,\beta \in S_n\\).
-- For each of these pairs, extract and add to the dataset all non-zero structure constants \\(c^{\gamma_1}_{\alpha,\beta}, \dots, c^{\gamma_k}_{\alpha,\beta}\\)
+- For each of these pairs, extract and add to the dataset all non-zero structure constants \\(c^{\gamma_1}_{\alpha,\beta}, \dots, c^{\gamma_k}_{\alpha,\beta}\\).
 - Furthermore, for each \\(c^{\gamma_i}_{\alpha,\beta} \neq 0\\), randomly permute \\(\gamma_i \mapsto \gamma_i'\\) to find \\(c^{\gamma_i'}_{\alpha,\beta} = 0\\) and \\(c^{\gamma_i'}_{\alpha,\beta}\\) is not already in the dataset.
 
 ## Task 
 
 **Math question:** Find a combinatorial interpretation of the structure constants \\(c_{\alpha,\beta}^\gamma\\)
-based on properties of \\(\alpha\\), \\(\beta\\), and \\(\gamma\\).
-
+based on properties of \\(\alpha\\), \\(\beta\\), and \\(\gamma\\).  
 **Narrow ML task:** Train a model that, given three permutations \\(\alpha, \beta, \gamma\\), can 
-predict the associated structure constant \\(c^{\gamma}_{\alpha,\beta}\\).
+predict the associated structure constant \\(c^{\gamma}_{\alpha,\beta}\\). Extract the rules 
+the model uses to make successful predictions.
 
 ## Small model performance
+Model and training details can be found in our paper.
 
 | Size | Logistic regression | MLP | Transformer | Guessing majority class | 
 |----------|----------|-----------|------------|------------|