Software-based Automatic Differentiation is Flawed

Various software efforts embrace the idea that object oriented programming enables a convenient implementation of the chain rule, facilitating so-called automatic differentiation via backpropagation. Such frameworks have no mechanism for simplifying the expressions (obtained via the chain rule) before evaluating them. As we illustrate below, the resulting errors tend to be unbounded.

Out-of-Distribution Generalization in Algorithmic Reasoning Through Curriculum Learning

Out-of-distribution generalization (OODG) is a longstanding challenge for neural networks, and is quite apparent in tasks with well-defined variables and rules, where explicit use of the rules can solve problems independently of the particular values of the variables. Large transformer-based language models have pushed the boundaries on how well neural networks can generalize to novel inputs, but their complexity obfuscates they achieve such robustness. As a step toward understanding how transformer-based systems generalize, we explore the question of OODG in smaller scale transformers. Using a reasoning task based on the puzzle Sudoku, we show that OODG can occur on complex problems if the training set includes examples sampled from the whole distribution of simpler component tasks.