Many contemporary studies utilize grid-based models for neural field representation, but a systematic analysis of grid-based models is still missing, hindering the improvement of those models. Therefore, this paper introduces a theoretical framework for grid-based models. This frame-work points out that these models' approximation and generalization behaviors are determined by grid tangent ker-nels (GTK), which are intrinsic properties of grid-based models. The proposed framework facilitates a consistent and systematic analysis of diverse grid-based models. Furthermore, the introduced framework motivates the development of a novel grid-based model named the Multiplicative Fourier Adaptive Grid (MulFAGrid). The numerical analysis demonstrates that MulFAGrid exhibits a lower generalization bound than its predecessors, indicating its robust generalization performance. Empirical studies reveal that MulFAGrid achieves state-of-the-art performance in various tasks, including 2D image fitting, 3D signed distance field (SDF) reconstruction, and novel view synthesis, demonstrating superior representation ability. The project website is available at this link.

Humans can abstract prior knowledge from very little data and use it to boost skill learning. In this paper, we propose routine-augmented policy learning (RAPL), which discovers routines composed of primitive actions from a single demonstration and uses discovered routines to augment policy learning. To discover routines from the demonstration, we first abstract routine candidates by identifying grammar over the demonstrated action trajectory. Then, the best routines measured by length and frequency are selected to form a routine library. We propose to learn policy simultaneously at primitive-level and routine-level with discovered routines, leveraging the temporal structure of routines. Our approach enables imitating expert behavior at multiple temporal scales for imitation learning and promotes reinforcement learning exploration. Extensive experiments on Atari games demonstrate that RAPL improves the state-of-the-art imitation learning method SQIL and reinforcement learning method A2C. Further, we show that discovered routines can generalize to unseen levels and difficulties on the CoinRun benchmark.

Programs, consisting of semantic and structural information, play an important role in the communication between humans and agents. Towards learning general program executors to unify perception, reasoning, and decision making, we formulate program-guided tasks which require learning to execute a given program on the observed task specification. Furthermore, we propose Program-Guided Transformers (ProTo), which integrates both semantic and structural guidance of a program by leveraging cross-attention and masked self-attention to pass messages between the specification and routines in the program. ProTo executes a program in a learned latent space and enjoys stronger representation ability than previous neural-symbolic approaches. We demonstrate that ProTo significantly outperforms the previous state-of-the-art methods on GQA visual reasoning and 2D Minecraft policy learning datasets. Additionally, ProTo demonstrates better generalization to unseen, complex, and human-written programs.