A convex hull is the smallest convex set containing a given set of points. In a sequence-modeling task, the input is a sequence of two-dimensional points, and the model must select the subset forming their hull. Longer sequences make the task harder because the possible combinations multiply. section 5.4.1
Testing Pointer Networks
On 50-point inputs, an LSTM achieved 1.9% accuracy, an LSTM with attention 38.9%, and a Pointer Network 72.6%. Trained on sequences of 5–50 points and tested on 500, the Pointer Network had 1.3% exact accuracy but 99.2% area performance. section 5.4.1
Table 5.2 Performance of LSTM, LSTM with attention, and Ptr-Net on the convex hull problem
|
Model
|
Trained
|
Tested
|
Accuracy
|
Area
|
|---|---|---|---|---|
|
LSTM
|
50
|
50
|
1.9%
|
FAIL
|
|
LSTM + Attention
|
50
|
50
|
38.9%
|
99.7%
|
|
Ptr-Net
|
50
|
50
|
72.6%
|
99.9%
|
|
Ptr-Net
|
5–50
|
100
|
50.3%
|
99.9%
|
|
Ptr-Net
|
5–50
|
500
|
1.3%
|
99.2%
|
Compare exact accuracy and area performance across models and test sizes. section 5.4.1
