Large language models (LLMs) achieve good performance on challenging reasoning benchmarks, yet could also make basic reasoning mistakes. This contrasting behavior is puzzling when it comes to understanding the mechanisms behind LLMs’ reasoning capabilities. One hypothesis is that the increasingly high and nearly saturated performance on common reasoning benchmarks could be due to the memorization of similar problems. In this paper, we systematically investigate this hypothesis with a quantitative measurement of memorization in reasoning tasks, using two dynamically generated logical reasoning benchmarks based on Knights and Knaves (K&K) puzzles and Zebra puzzles (DynamicZebra). We find that LLMs could interpolate and memorize the training puzzles (achieving near-perfect accuracy) after fine-tuning, yet they struggle with slight variations of these puzzles. On the other hand, we show that while fine-tuning leads to heavy memorization, it also consistently improves generalization performance. Through in-depth analyses with perturbation tests, cross difficulty-level transferability, probing model internals, and fine-tuning with wrong answers, we establish that LLMs develop reasoning skills on logical puzzles alongside memorization. Finally, our analysis based on a per-sample memorization score sheds light on how LLMs switch between reasoning and memorization when solving logical puzzles.

In this work, we study the large-scale pretraining of BERT-Large (Devlin et al., 2019) with differentially private SGD (DP-SGD). We show that combined with a careful implementation, scaling up the batch size to millions (i.e., mega-batches) improves the utility of the DP-SGD step for BERT; we also enhance the training efficiency by using an increasing batch size schedule. Our implementation builds on the recent work of Subramani et al (2020), who demonstrated that the overhead of a DP-SGD step is minimized with effective use of JAX (Bradbury et al., 2018; Frostig et al., 2018) primitives in conjunction with the XLA compiler (XLA team and collaborators, 2017). Our implementation achieves a masked language model accuracy of 60.5% at a batch size of 2M, for epsilon=5, which is a reasonable privacy setting. To put this number in perspective, non-private BERT models achieve an accuracy of ∼70%.