Andrew J. Nam

Andrew J. Nam, Mengye Ren, Chelsea Finn et al.

Large language models have recently shown promising progress in mathematical reasoning when fine-tuned with human-generated sequences walking through a sequence of solution steps. However, the solution sequences are not formally structured and the resulting model-generated sequences may not reflect the kind of systematic reasoning we might expect an expert human to produce. In this paper, we study how to build stronger reasoning capability in language models using the idea of relational abstractions. We introduce new types of sequences that more explicitly provide an abstract characterization of the transitions through intermediate solution steps to the goal state. We find that models that are supplied with such sequences as prompts can solve tasks with a significantly higher accuracy, and models that are trained to produce such sequences solve problems better than those that are trained with previously used human-generated sequences and other baselines. Our work thus takes several steps toward elucidating and improving how language models perform on tasks requiring multi-step mathematical reasoning.

Andrew J. Nam, Mustafa Abdool, Trevor Maxfield et al.

Out-of-distribution generalization (OODG) is a longstanding challenge for neural networks. This challenge is quite apparent in tasks with well-defined variables and rules, where explicit use of the rules could solve problems independently of the particular values of the variables, but networks tend to be tied to the range of values sampled in their training data. Large transformer-based language models have pushed the boundaries on how well neural networks can solve previously unseen problems, but their complexity and lack of clarity about the relevant content in their training data obfuscates how they achieve such robustness. As a step toward understanding how transformer-based systems generalize, we explore the question of OODG in small scale transformers trained with examples from a known distribution. Using a reasoning task based on the puzzle Sudoku, we show that OODG can occur on a complex problem if the training set includes examples sampled from the whole distribution of simpler component tasks. Successful generalization depends on carefully managing positional alignment when absolute position encoding is used, but we find that suppressing sensitivity to absolute positions overcomes this limitation. Taken together our results represent a small step toward understanding and promoting systematic generalization in transformers.

Andrew J. Nam, James L. McClelland

Neural networks have long been used to model human intelligence, capturing elements of behavior and cognition, and their neural basis. Recent advancements in deep learning have enabled neural network models to reach and even surpass human levels of intelligence in many respects, yet unlike humans, their ability to learn new tasks quickly remains a challenge. People can reason not only in familiar domains, but can also rapidly learn to reason through novel problems and situations, raising the question of how well modern neural network models capture human intelligence and in which ways they diverge. In this work, we explore this gap by investigating human adults' ability to learn an abstract reasoning task based on Sudoku from a brief instructional tutorial with explanatory feedback for incorrect responses using a narrow range of training examples. We find that participants who master the task do so within a small number of trials and generalize well to puzzles outside of the training range. We also find that most of those who master the task can describe a valid solution strategy, and such participants perform better on transfer puzzles than those whose strategy descriptions are vague or incomplete. Interestingly, fewer than half of our human participants were successful in acquiring a valid solution strategy, and this ability is associated with high school mathematics education. We consider the challenges these findings pose for building computational models that capture all aspects of our findings and point toward a possible role for learning to engage in explanation-based reasoning to support rapid learning and generalization.