Convex Compositional Reasoning Models

Compositional reasoning is critical for real-world problem solving: since training data is necessarily limited, models must generalize by composing learned skills in new ways. While post-training methods such as reinforcement learning (RL) have substantially improved the reasoning abilities of language models (LMs), their effects on compositional reasoning remain less well understood. We propose a dependency-graph framework to formalize compositional reasoning, yielding three levels of compositionality with increasing complexity. Empirically, we instantiate this framework with data-structure tasks, which provide deterministic reward computation and clear compositional structure. We find a consistent decomposed-to-composed asymmetry: decomposed-skill training does not reliably transfer to composed tasks, whereas composed-task training transfers more readily back to decomposed tasks. We provide theoretical explanation for this asymmetry, and further evaluate compositional generalization under length extrapolation, structural distribution shift, and transfer to tasks requiring unseen skills. Finally, we present a pilot study on real-world tool-calling benchmarks, showing preliminary evidence that the decomposed-to-composed asymmetry can extend to practical settings.

A common approach for teaching large language models (LLMs) to reason is to train on chain-of-thought (CoT) traces of in-distribution reasoning problems, but such annotated data is costly to obtain for every problem of interest. We want reasoning models to generalize beyond their training distribution, and ideally to generalize compositionally: combine atomic reasoning skills to solve harder, unseen reasoning tasks. We take a step towards compositional generalization of reasoning skills when addressing a target compositional task that has no labeled CoT data. We find that simply training models on CoT data of atomic tasks leads to limited generalization, but minimally modifying CoT formats of constituent atomic tasks to be composable can lead to improvements. We can train "atomic CoT" models on the atomic tasks with Composable CoT data and combine them with multitask learning or model merging for better zero-shot performance on the target compositional task. Such a combined model can be further bootstrapped on a small amount of compositional data using rejection sampling fine-tuning (RFT). Results on string operations and natural language skill compositions show that training LLMs on Composable CoT outperforms multitask learning and continued fine-tuning baselines within a given training data budget.

Identifying and exploiting common features across domains is at the heart of the human ability to make analogies, and is believed to be crucial for the ability to continually learn. To do this successfully, general and flexible computational strategies must be developed. While the extent to which Transformer neural network models can perform compositional reasoning has been the subject of intensive recent investigation, little work has been done to systematically understand how well these models can leverage their representations to learn new, related experiences. To address this gap, we expand the previously developed Learning Equality and Group Operations (LEGO) framework to a continual learning (CL) setting ("continual LEGO"). Using this continual LEGO experimental paradigm, we study the capability of feedforward and recurrent Transformer models to perform CL. We find that BERT, a canonical feedforward Transformer model, learns shortcut solutions that limits its ability to generalize and prevents strong forward transfer to new experiences. In contrast, we find evidence supporting the hypothesis that ALBERT, a recurrent version of BERT, learns a For loop-esque solution, which leads to better CL performance. When applying BERT and ALBERT models to a CL setting that requires composition across experiences, we find that both model families fail. Our investigation suggests that ALBERT models can have their performance drop rescued by use of training strategies that combine data across experiences, but this is not true for BERT models, where a detrimental shortcut solution becomes entrenched with initial training. Our results demonstrate that the recurrent ALBERT model may have an inductive bias better suited for CL and motivate future investigation of the interplay between Transformer architecture and computational solutions that emerge in modern models and tasks.