On the Empirical Complexity of Reasoning and Planning in LLMs

Large Language Models (LLMs) work surprisingly well for some complex reasoning problems via chain-of-thought (CoT) or tree-of-thought (ToT), but the underlying reasons remain unclear. We seek to understand the performance of these methods by conducting experimental case studies and linking the outcomes to sample and computational complexity in machine learning. We found that if problems can be decomposed into a sequence of reasoning steps and learning to predict the next step has a low sample and computational complexity, explicitly outlining the reasoning chain with all necessary information for predicting the next step may improve performance. Conversely, for problems where predicting the next step is computationally hard, adopting ToT may yield better reasoning outcomes than attempting to formulate a short reasoning chain.

Continual Learning of Numerous Tasks from Long-tail Distributions

Continual learning, an important aspect of artificial intelligence and machine learning research, focuses on developing models that learn and adapt to new tasks while retaining previously acquired knowledge. Existing continual learning algorithms usually involve a small number of tasks with uniform sizes and may not accurately represent real-world learning scenarios. In this paper, we investigate the performance of continual learning algorithms with a large number of tasks drawn from a task distribution that is long-tail in terms of task sizes. We design one synthetic dataset and two real-world continual learning datasets to evaluate the performance of existing algorithms in such a setting. Moreover, we study an overlooked factor in continual learning, the optimizer states, e.g. first and second moments in the Adam optimizer, and investigate how it can be used to improve continual learning performance. We propose a method that reuses the optimizer states in Adam by maintaining a weighted average of the second moments from previous tasks. We demonstrate that our method, compatible with most existing continual learning algorithms, effectively reduces forgetting with only a small amount of additional computational or memory costs, and provides further improvements on existing continual learning algorithms, particularly in a long-tail task sequence.