Learning to Reason with Neural Networks: Generalization, Unseen Data and Boolean Measures
his paper considers the Pointer Value Retrieval (PVR) benchmark introduced in [ZRKB21], where a `reasoning’ function acts on a string of digits to produce the label. More generally, the paper considers the learning of logical functions with gradient descent (GD) on neural networks. It is first shown that in order to learn logical functions with gradient descent on symmetric neural networks, the generalization error can be lower-bounded in terms of the noise-stability of the target function, supporting a conjecture made in [ZRKB21]. It is then shown that in the distribution shift setting, when…
The loss metric is very important for neural networks. As all machine learning models are one optimization problem or another, the loss is the objective function to minimize. In neural networks, the optimization is done with gradient descent and backpropagation. But what are loss functions, and how are they affecting…
This paper considers the learning of logical (Boolean) functions with focus on the generalization on the unseen (GOTU) setting, a strong case of out-of-distribution generalization. This is motivated by the fact that the rich combinatorial nature of data in certain reasoning tasks (e.g., arithmetic/logic) makes representative data sampling challenging, and…