According to Alg. 2, in each exploration, at least one leaf node will be expanded. Moreover, the overall size of the belief tree isO((|A|min(Pδmax,Nmax))D), where Nmax is the maximum sample size given by KLD-Sampling,Pδmax = supb,aPδ(Yb,a), and Yb,a is the set of reachable beliefs after executing actiona at belief b. The tree size is limited sinceNmax is finite. The weights are normalized, i.e., There exist bounded functionsα and α0 such that V (b) = R α(s)b(s)ds, and V (b0) = R α0(s)b0(s)ds. Wecan bound the first and third terms, respectively,byλinlight ofthe assumptions.

Accurately predicting experimentally-realizable 3D molecular crystal structures from their 2D chemical graphs is a long-standing open challenge in computational chemistry called crystal structure prediction (CSP). Efficiently solving this problem has implications ranging from pharmaceuticals to organic semiconductors, as crystal packing directly governs the physical and chemical properties of organic solids. In this paper, we introduce OXtal, a large-scale 100M parameter all-atom diffusion model that directly learns the conditional joint distribution over intramolecular conformations and periodic packing. To efficiently scale OXtal, we abandon explicit equivariant architectures imposing inductive bias arising from crystal symmetries in favor of data augmentation strategies. We further propose a novel crystallization-inspired lattice-free training scheme, Stoichiometric Stochastic Shell Sampling ($S^4$), that efficiently captures long-range interactions while sidestepping explicit lattice parametrization -- thus enabling more scalable architectural choices at all-atom resolution. By leveraging a large dataset of 600K experimentally validated crystal structures (including rigid and flexible molecules, co-crystals, and solvates), OXtal achieves orders-of-magnitude improvements over prior ab initio machine learning CSP methods, while remaining orders of magnitude cheaper than traditional quantum-chemical approaches. Specifically, OXtal recovers experimental structures with conformer $\text{RMSD}_1<0.5$ Å and attains over 80\% packing similarity rate, demonstrating its ability to model both thermodynamic and kinetic regularities of molecular crystallization.

In agentic LLM scenarios, an agent's interaction process during a single rollout often exhibits branching behaviors. Due to memory retrieval and concurrent tool executions at certain decision points, the token trajectory of one task evolves into a tree-like structure rather than a linear sequence. However, current training pipelines decompose such tree-structured trajectories into separate linear segments, treating each branch as an independent sequence. As a result, shared prefixes across these branches are repeatedly recomputed during both forward and backward passes. To address this inefficiency, we propose Tree Training, a paradigm that computes each shared prefix only once and reuses its intermediate results across related branches during both forward and backward passes, substantially improving computation efficiency in large-scale agentic training. This is achieved via (i) Tree Packing, which efficiently reuses shared computations across trajectories, and (ii) Gradient Restoration, which ensures correct gradient propagation across reused prefixes. Experiments on multiple open-source models demonstrate up to 3.9x reduction in total training time, enabling more efficient agentic LLM SFT and RL training.

With the rapid development of the warehousing and logistics industries, the packing of goods has gradually attracted the attention of academia and industry. The packing of footwear products is a typical representative paired-item packing task involving irregular shapes and deformable objects. Although studies on shoe packing have been conducted, different initial states due to the irregular shapes of shoes and standard packing placement poses have not been considered. This study proposes a robotic manipulation framework, including a perception module, reorientation planners, and a packing planner, that can complete the packing of pairs of shoes in any initial state. First, to adapt to the large intraclass variations due to the state, shape, and deformation of the shoe, we propose a vision module based on semantic keypoints, which can also infer more information such as size, state, pose, and manipulation points by combining geometric features. Subsequently, we not only proposed primitive-based reorientation methods for different states of a single deformable shoe but also proposed a fast reorientation method for the top state using box edge contact and gravity, which further improved the efficiency of reorientation. Finally, based on the perception module and reorientation methods, we propose a task planner for shoe pair packing in any initial state to provide an optimal packing strategy. Real-world experiments were conducted to verify the robustness of the reorientation methods and the effectiveness of the packing strategy for various types of shoes. In this study, we highlight the potential of semantic keypoint representation methods, introduce new perspectives on the reorientation of 3D deformable objects and multi-object manipulation, and provide a reference for paired object packing.

Online 3D Bin Packing Problem (3D-BPP) has widespread applications in industrial automation. Existing methods usually solve the problem with limited resolution of spatial discretization, and/or cannot deal with complex practical constraints well. We propose to enhance the practical applicability of online 3D-BPP via learning on a novel hierarchical representation, packing configuration tree (PCT). PCT is a full-fledged description of the state and action space of bin packing which can support packing policy learning based on deep reinforcement learning (DRL). The size of the packing action space is proportional to the number of leaf nodes, making the DRL model easy to train and well-performing even with continuous solution space. We further discover the potential of PCT as tree-based planners in deliberately solving packing problems of industrial significance, including large-scale packing and different variations of BPP setting. A recursive packing method is proposed to decompose large-scale packing into smaller sub-trees while a spatial ensemble mechanism integrates local solutions into global. For different BPP variations with additional decision variables, such as lookahead, buffering, and offline packing, we propose a unified planning framework enabling out-of-the-box problem solving. Extensive evaluations demonstrate that our method outperforms existing online BPP baselines and is versatile in incorporating various practical constraints. The planning process excels across large-scale problems and diverse problem variations. We develop a real-world packing robot for industrial warehousing, with careful designs accounting for constrained placement and transportation stability. Our packing robot operates reliably and efficiently on unprotected pallets at 10 seconds per box. It achieves averagely 19 boxes per pallet with 57.4% space utilization for relatively large-size boxes.

According to Alg. 2, in each exploration, at least one leaf node will be expanded. Thus, we have the conclusion that AdaOPS is guaranteed to terminate. First, we will demonstrate that the value of any belief can be formulated as an integral. This lemma is a concentration inequality of self-normalized importance sampling estimator. The ESS threshold µ for adaptive resampling is set to .

In many parts of the world - particularly in developing countries - the demand for electricity exceeds the available supply. In such cases, it is impossible to provide electricity to all households simultaneously. This raises a fundamental question: how should electricity be allocated fairly? In this paper, we explore this question through the lens of egalitarianism - a principle that emphasizes equality by prioritizing the welfare of the worst-off households. One natural rule that aligns with this principle is to maximize the egalitarian welfare - the smallest utility across all households. We show that computing such an allocation is NP-hard, even under strong simplifying assumptions. Leximin is a stronger fairness notion that generalizes the egalitarian welfare: it also requires to maximize the smallest utility, but then, subject to that, the second-smallest, then the third, and so on. The hardness results extends directly to leximin as well. Despite this, we present a Fully Polynomial-Time Approximation Scheme (FPTAS) for leximin in the special case where the network connectivity graph is a tree. This means that we can efficiently approximate leximin - and, in particular, the egalitarian welfare - to any desired level of accuracy.

Robotic bin packing aids in a wide range of real-world scenarios such as e-commerce and warehouses. Yet, existing works focus mainly on considering the shape of objects to optimize packing compactness and neglect object properties such as fragility, edibility, and chemistry that humans typically consider when packing objects. This paper presents OPA-Pack (Object-Property-Aware Packing framework), the first framework that equips the robot with object property considerations in planning the object packing. Technical-wise, we develop a novel object property recognition scheme with retrieval-augmented generation and chain-of-thought reasoning, and build a dataset with object property annotations for 1,032 everyday objects. Also, we formulate OPA-Net, aiming to jointly separate incompatible object pairs and reduce pressure on fragile objects, while compacting the packing. Further, OPA-Net consists of a property embedding layer to encode the property of candidate objects to be packed, together with a fragility heightmap and an avoidance heightmap to keep track of the packed objects. Then, we design a reward function and adopt a deep Q-learning scheme to train OPA-Net. Experimental results manifest that OPA-Pack greatly improves the accuracy of separating incompatible object pairs (from 52% to 95%) and largely reduces pressure on fragile objects (by 29.4%), while maintaining good packing compactness. Besides, we demonstrate the effectiveness of OPA-Pack on a real packing platform, showcasing its practicality in real-world scenarios.

Packing objects efficiently is a fundamental problem in logistics, warehouse automation, and robotics. While traditional packing solutions focus on geometric optimization, packing irregular, 3D objects presents significant challenges due to variations in shape and stability. Reinforcement Learning~(RL) has gained popularity in robotic packing tasks, but training purely from simulation can be inefficient and computationally expensive. In this work, we propose HERB, a human-augmented RL framework for packing irregular objects. We first leverage human demonstrations to learn the best sequence of objects to pack, incorporating latent factors such as space optimization, stability, and object relationships that are difficult to model explicitly. Next, we train a placement algorithm that uses visual information to determine the optimal object positioning inside a packing container. Our approach is validated through extensive performance evaluations, analyzing both packing efficiency and latency. Finally, we demonstrate the real-world feasibility of our method on a robotic system. Experimental results show that our method outperforms geometric and purely RL-based approaches by leveraging human intuition, improving both packing robustness and adaptability. This work highlights the potential of combining human expertise-driven RL to tackle complex real-world packing challenges in robotic systems.

Packing, initially utilized in the pre-training phase, is an optimization technique designed to maximize hardware resource efficiency by combining different training sequences to fit the model's maximum input length. Although it has demonstrated effectiveness during pre-training, there remains a lack of comprehensive analysis for the supervised fine-tuning (SFT) stage on the following points: (1) whether packing can effectively enhance training efficiency while maintaining performance, (2) the suitable size of the model and dataset for fine-tuning with the packing method, and (3) whether packing unrelated or related training samples might cause the model to either excessively disregard or over-rely on the context. In this paper, we perform extensive comparisons between SFT methods using padding and packing, covering SFT datasets ranging from 69K to 1.2M and models from 8B to 70B. This provides the first comprehensive analysis of the advantages and limitations of packing versus padding, as well as practical considerations for implementing packing in various training scenarios. Our analysis covers various benchmarks, including knowledge, reasoning, and coding, as well as GPT-based evaluations, time efficiency, and other fine-tuning parameters. We also open-source our code for fine-tuning and evaluation and provide checkpoints fine-tuned on datasets of different sizes, aiming to advance future research on packing methods. Code is available at: https://github.com/ShuheWang1998/Packing-Analysis?tab=readme-ov-file.