Recent advancements in implicit 3D reconstruction methods, e.g., neural rendering fields and Gaussian splatting, have primarily focused on novel view synthesis of static or dynamic objects with continuous motion states. However, these approaches struggle to efficiently model a human-interactive object with n movable parts, requiring 2^n separate models to represent all discrete states. To overcome this limitation, we propose Inter3D, a new benchmark and approach for novel state synthesis of human-interactive objects. We introduce a self-collected dataset featuring commonly encountered interactive objects and a new evaluation pipeline, where only individual part states are observed during training, while part combination states remain unseen. We also propose a strong baseline approach that leverages Space Discrepancy Tensors to efficiently modelling all states of an object. To alleviate the impractical constraints on camera trajectories across training states, we propose a Mutual State Regularization mechanism to enhance the spatial density consistency of movable parts. In addition, we explore two occupancy grid sampling strategies to facilitate training efficiency. We conduct extensive experiments on the proposed benchmark, showcasing the challenges of the task and the superiority of our approach.

We address the task of simultaneous part-level reconstruction and motion parameter estimation for articulated objects. Given two sets of multi-view images of an object in two static articulation states, we decouple the movable part from the static part and reconstruct shape and appearance while predicting the motion parameters. To tackle this problem, we present PARIS: a self-supervised, end-to-end architecture that learns part-level implicit shape and appearance models and optimizes motion parameters jointly without any 3D supervision, motion, or semantic annotation. Our experiments show that our method generalizes better across object categories, and outperforms baselines and prior work that are given 3D point clouds as input. Our approach improves reconstruction relative to state-of-the-art baselines with a Chamfer-L1 distance reduction of 3.94 (45.2%) for objects and 26.79 (84.5%) for parts, and achieves 5% error rate for motion estimation across 10 object categories. Video summary at: https://youtu.be/tDSrROPCgUc

Model-based reinforcement learning usually suffers from a high sample complexity in training the world model, especially for the environments with complex dynamics. To make the training for general physical environments more efficient, we introduce Hamiltonian canonical ordinary differential equations into the learning process, which inspires a novel model of neural ordinary differential auto-encoder (NODA). NODA can model the physical world by nature and is flexible to impose Hamiltonian mechanics (e.g., the dimension of the physical equations) which can further accelerate training of the environment models. It can consequentially empower an RL agent with the robust extrapolation using a small amount of samples as well as the guarantee on the physical plausibility. Theoretically, we prove that NODA has uniform bounds for multi-step transition errors and value errors under certain conditions. Extensive experiments show that NODA can learn the environment dynamics effectively with a high sample efficiency, making it possible to facilitate reinforcement learning agents at the early stage. Reinforcement learning has obtained substantial progress in both theoretical foundations (Asadi et al., 2018; Jiang, 2018) and empirical applications (Mnih et al., 2013; 2015; Peters & Schaal, 2006; Johannink et al., 2019). In particular, model-free reinforcement learning (MFRL) can complete complex tasks such as Atari games (Schrittwieser et al., 2020) and robot control (Roveda et al., 2020). However, the MFRL algorithms often need a large amount of interactions with the environment (Langlois et al., 2019) in order to train an agent, which impedes their further applications. Model-based reinforcement learning (MBRL) methods can alleviate this issue by resorting to a model to characterize the environmental dynamics and conduct planning (van Hasselt et al., 2019; Moerland et al., 2020a). In general, MBRL can quench the thirst of massive amounts of real data that may be costly to acquire, by using rollouts from the model (Langlois et al., 2019; Deisenroth & Rasmussen, 2011).

Conservation of energy is at the core of many physical phenomena and dynamical systems. There have been a significant number of works in the past few years aimed at predicting the trajectory of motion of dynamical systems using neural networks while adhering to the law of conservation of energy. Most of these works are inspired by classical mechanics such as Hamiltonian and Lagrangian mechanics as well as Neural Ordinary Differential Equations. While these works have been shown to work well in specific domains respectively, there is a lack of a unifying method that is more generally applicable without requiring significant changes to the neural network architectures. In this work, we aim to address this issue by providing a simple method that could be applied to not just energy-conserving systems, but also dissipative systems, by including a different inductive bias in different cases in the form of a regularisation term in the loss function. The proposed method does not require changing the neural network architecture and could form the basis to validate a novel idea, therefore showing promises to accelerate research in this direction.

Search algorithms often suffer from exploring areas which eventually are not part of the shortest path from the start to a goal. Usually it is the purpose of the heuristic function to guide the search algorithm such that it will ignore as much as possible of these areas. We consider other, non-heuristic methods that can be used to prune the search space to make search even faster. We present two algorithms: one for search in graphs that fit in memory, and in which we will need to perform many searches, and another, which improves the search time of planning problems that contain symmetries.

True distance memory-based heuristics (TDHs) were recently introduced as a way to obtain admissible heuristics for explicit state spaces. In this paper, we introduce a new TDH, the portal-based heuristic. The domain is partitioned into regions and portals between regions are identified. True distances between all pairs of portals are stored and used to obtain admissible heuristics throughout the search. We introduce an A*-based algorithm that takes advantage of the special properties of the new heuristic. We study the advantages and limitations of the new heuristic. Our experimental results show large performance improvements over previously-reported TDHs for commonly used classes of maps.

Pattern Databases (PDBs) are the most common form of memory-based heuristics, and they have been widely used in a variety of permutation puzzles and other domains. We explore the true-distance heuristics (TDHs) (also appeared in  (Sturtevant et al. 2009)) which are a different form of memory-based heuristics, designed to work in problem states where there isn't a fixed goal state. Unlike PDBs, which build a heuristic based on distances in an abstract state space, TDHs store distances which are computed in the actual state space. We look in detail at how TDHs work, providing both theoretical and experimental motivation for their use.

In many scenarios, quickly solving a relatively small search problem with an arbitrary start and arbitrary goal state is important (e.g., GPS navigation). In order to speed this process, we introduce a new class of memory-based heuristics, called true distance heuristics, that store true distances between some pairs of states in the original state space can be used for a heuristic between any pair of states. We provide a number of techniques for using and improving true distance heuristics such that most of the benefits of the all-pairs shortest-path computation can be gained with less than 1% of the memory. Experimental results on a number of domains show a 6-14 fold improvement in search speed compared to traditional heuristics.