Pointer Networks (Ptr-Nets) are a new neural architecture that learns the conditional probability of an output sequence composed of discrete tokens corresponding to positions in an input sequence. Unlike existing methods such as sequence-to-sequence and Neural Turing Machines, Ptr-Nets address the challenge of variable-sized output dictionaries by using a neural attention mechanism to select input elements as outputs. This approach allows the model to generate approximate solutions to three complex geometric problems: planar convex hulls, Delaunay triangulations, and the planar Travelling Salesman Problem (TSP), using only training examples. The Ptr-Net architecture differs from previous attention-based models by using attention as a pointer to select input elements rather than blending encoder hidden units into a context vector. This enables the model to handle variable-sized output dictionaries and generalize beyond the maximum lengths it was trained on. The model uses a softmax probability distribution as a "pointer" to select input elements, making it effective for problems where the output depends on the input sequence length. The Ptr-Net model was tested on three combinatorial optimization problems. For the convex hull problem, the model achieved high accuracy and area coverage, even for large input sizes. For Delaunay triangulation, the model showed good performance in terms of triangle coverage, with results that improved as the input size increased. For the TSP problem, the model outperformed existing algorithms on small-scale problems and demonstrated the ability to extrapolate to larger input sizes. The model's ability to handle variable-sized outputs and generalize to unseen input sizes is a significant improvement over sequence-to-sequence models with fixed output dictionaries. The Ptr-Net architecture is simple and effective, and it opens up new possibilities for applying neural networks to discrete problems without requiring artificial assumptions. The results demonstrate that a purely data-driven approach can learn approximate solutions to computationally intractable problems.Pointer Networks (Ptr-Nets) are a new neural architecture that learns the conditional probability of an output sequence composed of discrete tokens corresponding to positions in an input sequence. Unlike existing methods such as sequence-to-sequence and Neural Turing Machines, Ptr-Nets address the challenge of variable-sized output dictionaries by using a neural attention mechanism to select input elements as outputs. This approach allows the model to generate approximate solutions to three complex geometric problems: planar convex hulls, Delaunay triangulations, and the planar Travelling Salesman Problem (TSP), using only training examples. The Ptr-Net architecture differs from previous attention-based models by using attention as a pointer to select input elements rather than blending encoder hidden units into a context vector. This enables the model to handle variable-sized output dictionaries and generalize beyond the maximum lengths it was trained on. The model uses a softmax probability distribution as a "pointer" to select input elements, making it effective for problems where the output depends on the input sequence length. The Ptr-Net model was tested on three combinatorial optimization problems. For the convex hull problem, the model achieved high accuracy and area coverage, even for large input sizes. For Delaunay triangulation, the model showed good performance in terms of triangle coverage, with results that improved as the input size increased. For the TSP problem, the model outperformed existing algorithms on small-scale problems and demonstrated the ability to extrapolate to larger input sizes. The model's ability to handle variable-sized outputs and generalize to unseen input sizes is a significant improvement over sequence-to-sequence models with fixed output dictionaries. The Ptr-Net architecture is simple and effective, and it opens up new possibilities for applying neural networks to discrete problems without requiring artificial assumptions. The results demonstrate that a purely data-driven approach can learn approximate solutions to computationally intractable problems.