Peixu Wang

Huanyu Liu, Ge Li, Yihong Dong et al. · pku

Large language models (LLMs) based on the Transformer have demonstrated strong performance across diverse tasks. However, current models still exhibit substantial limitations in out-of-distribution (OOD) generalization compared with humans. We investigate this gap through periodicity, one of the basic OOD scenarios. Periodicity captures invariance amid variation. Periodicity generalization represents a model's ability to extract periodic patterns from training data and generalize to OOD scenarios. We introduce a unified interpretation of periodicity from the perspective of abstract algebra and reasoning, including both single and composite periodicity, to explain why Transformers struggle to generalize periodicity. Then we construct Coper about composite periodicity, a controllable generative benchmark with two OOD settings, Hollow and Extrapolation. Experiments reveal that periodicity generalization in Transformers is limited, where models can memorize periodic data during training, but cannot generalize to unseen composite periodicity. We release the source code to support future research.

Yihong Dong, Jiaru Qian, Haoran Zhang et al.

The automatic synthesis of a program from any form of specification is regarded as a holy grail of computer science. Fueled by LLMs, NL2Code has achieved tremendous success, yet the fundamentally more challenging task of synthesizing programs from input-output behavior, which we refer to as IO2Code, remains largely unsolved. Whereas NL2Code can exploit the semantic alignment between natural language and code acquired during pretraining, IO2Code requires recovering underlying principles from concrete computational behavior, navigating a vast and underspecified hypothesis space. To address this, we propose DIO-Agent, a discovery agent for IO2Code. Our method frames IO2Code as an evolutionary search over discrete program space, in which an LLM serves as the mutation operator and concrete error signals from execution guide each mutation. To prevent the search from wandering into structurally complex yet incorrect dead ends, we introduce the Transformation Priority Premise as a mutation prior that biases the LLM toward the simplest hypothesis consistent with current evidence, progressively escalating from constants to conditionals to iteration only when simpler constructs are insufficient. To facilitate systematic study, we further construct an IO2CodeBench spanning multiple difficulty levels. Extensive experiments show that DIO-Agent consistently outperforms both traditional program-by-example method and SOTA evolution-agent baselines across all difficulty levels and various LLMs, while substantially surpassing test-time scaling strategies with equivalent sampling budgets.