Hao Su

Anpei Chen, Zexiang Xu, Andreas Geiger et al. · eth-zurich

We present TensoRF, a novel approach to model and reconstruct radiance fields. Unlike NeRF that purely uses MLPs, we model the radiance field of a scene as a 4D tensor, which represents a 3D voxel grid with per-voxel multi-channel features. Our central idea is to factorize the 4D scene tensor into multiple compact low-rank tensor components. We demonstrate that applying traditional CP decomposition -- that factorizes tensors into rank-one components with compact vectors -- in our framework leads to improvements over vanilla NeRF. To further boost performance, we introduce a novel vector-matrix (VM) decomposition that relaxes the low-rank constraints for two modes of a tensor and factorizes tensors into compact vector and matrix factors. Beyond superior rendering quality, our models with CP and VM decompositions lead to a significantly lower memory footprint in comparison to previous and concurrent works that directly optimize per-voxel features. Experimentally, we demonstrate that TensoRF with CP decomposition achieves fast reconstruction (<30 min) with better rendering quality and even a smaller model size (<4 MB) compared to NeRF. Moreover, TensoRF with VM decomposition further boosts rendering quality and outperforms previous state-of-the-art methods, while reducing the reconstruction time (<10 min) and retaining a compact model size (<75 MB).

Zhan Ling, Yunhao Fang, Xuanlin Li et al.

Large Language Models (LLMs) significantly benefit from Chain-of-Thought (CoT) prompting in performing various reasoning tasks. While CoT allows models to produce more comprehensive reasoning processes, its emphasis on intermediate reasoning steps can inadvertently introduce hallucinations and accumulated errors, thereby limiting models' ability to solve complex reasoning tasks. Inspired by how humans engage in careful and meticulous deductive logical reasoning processes to solve tasks, we seek to enable language models to perform explicit and rigorous deductive reasoning, and also ensure the trustworthiness of their reasoning process through self-verification. However, directly verifying the validity of an entire deductive reasoning process is challenging, even with advanced models like ChatGPT. In light of this, we propose to decompose a reasoning verification process into a series of step-by-step subprocesses, each only receiving their necessary context and premises. To facilitate this procedure, we propose Natural Program, a natural language-based deductive reasoning format. Our approach enables models to generate precise reasoning steps where subsequent steps are more rigorously grounded on prior steps. It also empowers language models to carry out reasoning self-verification in a step-by-step manner. By integrating this verification process into each deductive reasoning stage, we significantly enhance the rigor and trustfulness of generated reasoning steps. Along this process, we also improve the answer correctness on complex reasoning tasks. Code will be released at https://github.com/lz1oceani/verify_cot.

Yifan Xu, Nicklas Hansen, Zirui Wang et al. · princeton

Reinforcement Learning (RL) algorithms can solve challenging control problems directly from image observations, but they often require millions of environment interactions to do so. Recently, model-based RL algorithms have greatly improved sample-efficiency by concurrently learning an internal model of the world, and supplementing real environment interactions with imagined rollouts for policy improvement. However, learning an effective model of the world from scratch is challenging, and in stark contrast to humans that rely heavily on world understanding and visual cues for learning new skills. In this work, we investigate whether internal models learned by modern model-based RL algorithms can be leveraged to solve new, distinctly different tasks faster. We propose Model-Based Cross-Task Transfer (XTRA), a framework for sample-efficient online RL with scalable pretraining and finetuning of learned world models. By offline multi-task pretraining and online cross-task finetuning, we achieve substantial improvements over a baseline trained from scratch; we improve mean performance of model-based algorithm EfficientZero by 23%, and by as much as 71% in some instances.

Nicklas Hansen, Xiaolong Wang, Hao Su

Data-driven model predictive control has two key advantages over model-free methods: a potential for improved sample efficiency through model learning, and better performance as computational budget for planning increases. However, it is both costly to plan over long horizons and challenging to obtain an accurate model of the environment. In this work, we combine the strengths of model-free and model-based methods. We use a learned task-oriented latent dynamics model for local trajectory optimization over a short horizon, and use a learned terminal value function to estimate long-term return, both of which are learned jointly by temporal difference learning. Our method, TD-MPC, achieves superior sample efficiency and asymptotic performance over prior work on both state and image-based continuous control tasks from DMControl and Meta-World. Code and video results are available at https://nicklashansen.github.io/td-mpc.

Jiayuan Gu, Devendra Singh Chaplot, Hao Su et al.

We study a modular approach to tackle long-horizon mobile manipulation tasks for object rearrangement, which decomposes a full task into a sequence of subtasks. To tackle the entire task, prior work chains multiple stationary manipulation skills with a point-goal navigation skill, which are learned individually on subtasks. Although more effective than monolithic end-to-end RL policies, this framework suffers from compounding errors in skill chaining, e.g., navigating to a bad location where a stationary manipulation skill can not reach its target to manipulate. To this end, we propose that the manipulation skills should include mobility to have flexibility in interacting with the target object from multiple locations and at the same time the navigation skill could have multiple end points which lead to successful manipulation. We operationalize these ideas by implementing mobile manipulation skills rather than stationary ones and training a navigation skill trained with region goal instead of point goal. We evaluate our multi-skill mobile manipulation method M3 on 3 challenging long-horizon mobile manipulation tasks in the Home Assistant Benchmark (HAB), and show superior performance as compared to the baselines.

Quankai Gao, Qiangeng Xu, Hao Su et al.

We propose Strivec, a novel neural representation that models a 3D scene as a radiance field with sparsely distributed and compactly factorized local tensor feature grids. Our approach leverages tensor decomposition, following the recent work TensoRF, to model the tensor grids. In contrast to TensoRF which uses a global tensor and focuses on their vector-matrix decomposition, we propose to utilize a cloud of local tensors and apply the classic CANDECOMP/PARAFAC (CP) decomposition to factorize each tensor into triple vectors that express local feature distributions along spatial axes and compactly encode a local neural field. We also apply multi-scale tensor grids to discover the geometry and appearance commonalities and exploit spatial coherence with the tri-vector factorization at multiple local scales. The final radiance field properties are regressed by aggregating neural features from multiple local tensors across all scales. Our tri-vector tensors are sparsely distributed around the actual scene surface, discovered by a fast coarse reconstruction, leveraging the sparsity of a 3D scene. We demonstrate that our model can achieve better rendering quality while using significantly fewer parameters than previous methods, including TensoRF and Instant-NGP.

Minghua Liu, Yin Zhou, Charles R. Qi et al.

Semantic segmentation of LiDAR point clouds is an important task in autonomous driving. However, training deep models via conventional supervised methods requires large datasets which are costly to label. It is critical to have label-efficient segmentation approaches to scale up the model to new operational domains or to improve performance on rare cases. While most prior works focus on indoor scenes, we are one of the first to propose a label-efficient semantic segmentation pipeline for outdoor scenes with LiDAR point clouds. Our method co-designs an efficient labeling process with semi/weakly supervised learning and is applicable to nearly any 3D semantic segmentation backbones. Specifically, we leverage geometry patterns in outdoor scenes to have a heuristic pre-segmentation to reduce the manual labeling and jointly design the learning targets with the labeling process. In the learning step, we leverage prototype learning to get more descriptive point embeddings and use multi-scan distillation to exploit richer semantics from temporally aggregated point clouds to boost the performance of single-scan models. Evaluated on the SemanticKITTI and the nuScenes datasets, we show that our proposed method outperforms existing label-efficient methods. With extremely limited human annotations (e.g., 0.1% point labels), our proposed method is even highly competitive compared to the fully supervised counterpart with 100% labels.

Yuzhe Qin, Binghao Huang, Zhao-Heng Yin et al.

We propose a sim-to-real framework for dexterous manipulation which can generalize to new objects of the same category in the real world. The key of our framework is to train the manipulation policy with point cloud inputs and dexterous hands. We propose two new techniques to enable joint learning on multiple objects and sim-to-real generalization: (i) using imagined hand point clouds as augmented inputs; and (ii) designing novel contact-based rewards. We empirically evaluate our method using an Allegro Hand to grasp novel objects in both simulation and real world. To the best of our knowledge, this is the first policy learning-based framework that achieves such generalization results with dexterous hands. Our project page is available at https://yzqin.github.io/dexpoint

Zhan Ling, Yunhao Fang, Xuanlin Li et al.

Large Language Models (LLMs) have achieved tremendous progress, yet they still often struggle with challenging reasoning problems. Current approaches address this challenge by sampling or searching detailed and low-level reasoning chains. However, these methods are still limited in their exploration capabilities, making it challenging for correct solutions to stand out in the huge solution space. In this work, we unleash LLMs' creative potential for exploring multiple diverse problem solving strategies by framing an LLM as a hierarchical policy via in-context learning. This policy comprises of a visionary leader that proposes multiple diverse high-level problem-solving tactics as hints, accompanied by a follower that executes detailed problem-solving processes following each of the high-level instruction. The follower uses each of the leader's directives as a guide and samples multiple reasoning chains to tackle the problem, generating a solution group for each leader proposal. Additionally, we propose an effective and efficient tournament-based approach to select among these explored solution groups to reach the final answer. Our approach produces meaningful and inspiring hints, enhances problem-solving strategy exploration, and improves the final answer accuracy on challenging problems in the MATH dataset. Code will be released at https://github.com/lz1oceani/LLM-As-Hierarchical-Policy.

Nicklas Hansen, Yixin Lin, Hao Su et al.

Poor sample efficiency continues to be the primary challenge for deployment of deep Reinforcement Learning (RL) algorithms for real-world applications, and in particular for visuo-motor control. Model-based RL has the potential to be highly sample efficient by concurrently learning a world model and using synthetic rollouts for planning and policy improvement. However, in practice, sample-efficient learning with model-based RL is bottlenecked by the exploration challenge. In this work, we find that leveraging just a handful of demonstrations can dramatically improve the sample-efficiency of model-based RL. Simply appending demonstrations to the interaction dataset, however, does not suffice. We identify key ingredients for leveraging demonstrations in model learning -- policy pretraining, targeted exploration, and oversampling of demonstration data -- which forms the three phases of our model-based RL framework. We empirically study three complex visuo-motor control domains and find that our method is 150%-250% more successful in completing sparse reward tasks compared to prior approaches in the low data regime (100K interaction steps, 5 demonstrations). Code and videos are available at: https://nicklashansen.github.io/modemrl

Nicklas Hansen, Hao Su, Xiaolong Wang

TD-MPC is a model-based reinforcement learning (RL) algorithm that performs local trajectory optimization in the latent space of a learned implicit (decoder-free) world model. In this work, we present TD-MPC2: a series of improvements upon the TD-MPC algorithm. We demonstrate that TD-MPC2 improves significantly over baselines across 104 online RL tasks spanning 4 diverse task domains, achieving consistently strong results with a single set of hyperparameters. We further show that agent capabilities increase with model and data size, and successfully train a single 317M parameter agent to perform 80 tasks across multiple task domains, embodiments, and action spaces. We conclude with an account of lessons, opportunities, and risks associated with large TD-MPC2 agents. Explore videos, models, data, code, and more at https://tdmpc2.com

Zhan Ling, Yunchao Yao, Xuanlin Li et al.

Recent studies on visual reinforcement learning (visual RL) have explored the use of 3D visual representations. However, none of these work has systematically compared the efficacy of 3D representations with 2D representations across different tasks, nor have they analyzed 3D representations from the perspective of agent-object / object-object relationship reasoning. In this work, we seek answers to the question of when and how do 3D neural networks that learn features in the 3D-native space provide a beneficial inductive bias for visual RL. We specifically focus on 3D point clouds, one of the most common forms of 3D representations. We systematically investigate design choices for 3D point cloud RL, leading to the development of a robust algorithm for various robotic manipulation and control tasks. Furthermore, through comparisons between 2D image vs 3D point cloud RL methods on both minimalist synthetic tasks and complex robotic manipulation tasks, we find that 3D point cloud RL can significantly outperform the 2D counterpart when agent-object / object-object relationship encoding is a key factor.

Zhiwei Jia, Vineet Thumuluri, Fangchen Liu et al.

We study generalizable policy learning from demonstrations for complex low-level control (e.g., contact-rich object manipulations). We propose a novel hierarchical imitation learning method that utilizes sub-optimal demos. Firstly, we propose an observation space-agnostic approach that efficiently discovers the multi-step subskill decomposition of the demos in an unsupervised manner. By grouping temporarily close and functionally similar actions into subskill-level demo segments, the observations at the segment boundaries constitute a chain of planning steps for the task, which we refer to as the chain-of-thought (CoT). Next, we propose a Transformer-based design that effectively learns to predict the CoT as the subskill-level guidance. We couple action and subskill predictions via learnable prompt tokens and a hybrid masking strategy, which enable dynamically updated guidance at test time and improve feature representation of the trajectory for generalizable policy learning. Our method, Chain-of-Thought Predictive Control (CoTPC), consistently surpasses existing strong baselines on challenging manipulation tasks with sub-optimal demos.

Zhiwei Jia, Xuanlin Li, Zhan Ling et al.

Generalization in deep reinforcement learning over unseen environment variations usually requires policy learning over a large set of diverse training variations. We empirically observe that an agent trained on many variations (a generalist) tends to learn faster at the beginning, yet its performance plateaus at a less optimal level for a long time. In contrast, an agent trained only on a few variations (a specialist) can often achieve high returns under a limited computational budget. To have the best of both worlds, we propose a novel generalist-specialist training framework. Specifically, we first train a generalist on all environment variations; when it fails to improve, we launch a large population of specialists with weights cloned from the generalist, each trained to master a selected small subset of variations. We finally resume the training of the generalist with auxiliary rewards induced by demonstrations of all specialists. In particular, we investigate the timing to start specialist training and compare strategies to learn generalists with assistance from specialists. We show that this framework pushes the envelope of policy learning on several challenging and popular benchmarks including Procgen, Meta-World and ManiSkill.

Stone Tao, Xiaochen Li, Tongzhou Mu et al.

Training long-horizon robotic policies in complex physical environments is essential for many applications, such as robotic manipulation. However, learning a policy that can generalize to unseen tasks is challenging. In this work, we propose to achieve one-shot task generalization by decoupling plan generation and plan execution. Specifically, our method solves complex long-horizon tasks in three steps: build a paired abstract environment by simplifying geometry and physics, generate abstract trajectories, and solve the original task by an abstract-to-executable trajectory translator. In the abstract environment, complex dynamics such as physical manipulation are removed, making abstract trajectories easier to generate. However, this introduces a large domain gap between abstract trajectories and the actual executed trajectories as abstract trajectories lack low-level details and are not aligned frame-to-frame with the executed trajectory. In a manner reminiscent of language translation, our approach leverages a seq-to-seq model to overcome the large domain gap between the abstract and executable trajectories, enabling the low-level policy to follow the abstract trajectory. Experimental results on various unseen long-horizon tasks with different robot embodiments demonstrate the practicability of our methods to achieve one-shot task generalization.

Shuang Liu, Hao Su

We propose and analyze a kernelized version of Q-learning. Although a kernel space is typically infinite-dimensional, extensive study has shown that generalization is only affected by the effective dimension of the data. We incorporate such ideas into the Q-learning framework and derive regret bounds for arbitrary kernels. In particular, we provide concrete bounds for linear kernels and Gaussian RBF kernels; notably, the latter bound looks almost identical to the former, only that the actual dimension is replaced by a different notion of dimensionality. Finally, we test our algorithm on a suite of classic control tasks; remarkably, under the Gaussian RBF kernel, it achieves reasonably good performance after only 1000 environmental steps, while its neural network counterpart, deep Q-learning, still struggles.

Tongzhou Mu, Hao Su

Although reinforcement learning has seen tremendous success recently, this kind of trial-and-error learning can be impractical or inefficient in complex environments. The use of demonstrations, on the other hand, enables agents to benefit from expert knowledge rather than having to discover the best action to take through exploration. In this survey, we discuss the advantages of using demonstrations in sequential decision making, various ways to apply demonstrations in learning-based decision making paradigms (for example, reinforcement learning and planning in the learned models), and how to collect the demonstrations in various scenarios. Additionally, we exemplify a practical pipeline for generating and utilizing demonstrations in the recently proposed ManiSkill robot learning benchmark.

Sid Bharthulwar, Stone Tao, Hao Su

Massively parallel GPU simulation environments have accelerated reinforcement learning (RL) research by enabling fast data collection for on-policy RL algorithms like Proximal Policy Optimization (PPO). To maximize throughput, it is common to use short rollouts per policy update, increasing the update-to-data (UTD) ra- tio. However, we find that, in this setting, standard synchronous resets introduce harmful nonstationarity, skewing the learning signal and destabilizing training. We introduce staggered resets, a simple yet effective technique where environments are initialized and reset at varied points within the task horizon. This yields training batches with greater temporal diversity, reducing the nonstationarity induced by synchronized rollouts. We characterize dimensions along which RL environments can benefit significantly from staggered resets through illustrative toy environ- ments. We then apply this technique to challenging high-dimensional robotics environments, achieving significantly higher sample efficiency, faster wall-clock convergence, and stronger final performance. Finally, this technique scales better with more parallel environments compared to naive synchronized rollouts.

Isabella Liu, Zhan Xu, Wang Yifan et al.

We present RigAnything, a novel autoregressive transformer-based model, which makes 3D assets rig-ready by probabilistically generating joints and skeleton topologies and assigning skinning weights in a template-free manner. Unlike most existing auto-rigging methods, which rely on predefined skeleton templates and are limited to specific categories like humanoid, RigAnything approaches the rigging problem in an autoregressive manner, iteratively predicting the next joint based on the global input shape and the previous prediction. While autoregressive models are typically used to generate sequential data, RigAnything extends its application to effectively learn and represent skeletons, which are inherently tree structures. To achieve this, we organize the joints in a breadth-first search (BFS) order, enabling the skeleton to be defined as a sequence of 3D locations and the parent index. Furthermore, our model improves the accuracy of position prediction by leveraging diffusion modeling, ensuring precise and consistent placement of joints within the hierarchy. This formulation allows the autoregressive model to efficiently capture both spatial and hierarchical relationships within the skeleton. Trained end-to-end on both RigNet and Objaverse datasets, RigAnything demonstrates state-of-the-art performance across diverse object types, including humanoids, quadrupeds, marine creatures, insects, and many more, surpassing prior methods in quality, robustness, generalizability, and efficiency. It achieves significantly faster performance than existing auto-rigging methods, completing rigging in under a few seconds per shape. Please check our website for more details: https://www.liuisabella.com/RigAnything

Bo Ai, Liu Dai, Nico Bohlinger et al. · stanford

Cross-embodiment generalization underpins the vision of building generalist embodied agents for any robot, yet its enabling factors remain poorly understood. We investigate embodiment scaling laws, the hypothesis that increasing the number of training embodiments improves generalization to unseen ones, using robot locomotion as a test bed. We procedurally generate ~1,000 embodiments with topological, geometric, and joint-level kinematic variations, and train policies on random subsets. We observe positive scaling trends supporting the hypothesis, and find that embodiment scaling enables substantially broader generalization than data scaling on fixed embodiments. Our best policy, trained on the full dataset, transfers zero-shot to novel embodiments in simulation and the real world, including the Unitree Go2 and H1. These results represent a step toward general embodied intelligence, with relevance to adaptive control for configurable robots, morphology co-design, and beyond.

Tongzhou Mu, Minghua Liu, Hao Su

The success of many RL techniques heavily relies on human-engineered dense rewards, which typically demand substantial domain expertise and extensive trial and error. In our work, we propose DrS (Dense reward learning from Stages), a novel approach for learning reusable dense rewards for multi-stage tasks in a data-driven manner. By leveraging the stage structures of the task, DrS learns a high-quality dense reward from sparse rewards and demonstrations if given. The learned rewards can be \textit{reused} in unseen tasks, thus reducing the human effort for reward engineering. Extensive experiments on three physical robot manipulation task families with 1000+ task variants demonstrate that our learned rewards can be reused in unseen tasks, resulting in improved performance and sample efficiency of RL algorithms. The learned rewards even achieve comparable performance to human-engineered rewards on some tasks. See our project page (https://sites.google.com/view/iclr24drs) for more details.

Adrià López Escoriza, Nicklas Hansen, Stone Tao et al.

Long-horizon tasks in robotic manipulation present significant challenges in reinforcement learning (RL) due to the difficulty of designing dense reward functions and effectively exploring the expansive state-action space. However, despite a lack of dense rewards, these tasks often have a multi-stage structure, which can be leveraged to decompose the overall objective into manageable subgoals. In this work, we propose DEMO3, a framework that exploits this structure for efficient learning from visual inputs. Specifically, our approach incorporates multi-stage dense reward learning, a bi-phasic training scheme, and world model learning into a carefully designed demonstration-augmented RL framework that strongly mitigates the challenge of exploration in long-horizon tasks. Our evaluations demonstrate that our method improves data-efficiency by an average of 40% and by 70% on particularly difficult tasks compared to state-of-the-art approaches. We validate this across 16 sparse-reward tasks spanning four domains, including challenging humanoid visual control tasks using as few as five demonstrations.

Piao Hu, Jiashuo Jiang, Guodong Lyu et al.

We consider an online two-stage stochastic optimization with long-term constraints over a finite horizon of $T$ periods. At each period, we take the first-stage action, observe a model parameter realization and then take the second-stage action from a feasible set that depends both on the first-stage decision and the model parameter. We aim to minimize the cumulative objective value while guaranteeing that the long-term average second-stage decision belongs to a set. We develop online algorithms for the online two-stage problem from adversarial learning algorithms. Also, the regret bound of our algorithm can be reduced to the regret bound of embedded adversarial learning algorithms. Based on this framework, we obtain new results under various settings. When the model parameters are drawn from unknown non-stationary distributions and we are given machine-learned predictions of the distributions, we develop a new algorithm from our framework with a regret $O(W_T+\sqrt{T})$, where $W_T$ measures the total inaccuracy of the machine-learned predictions. We then develop another algorithm that works when no machine-learned predictions are given and show the performances.

Nicklas Hansen, Hao Su, Xiaolong Wang

General-purpose control demands agents that act across many tasks and embodiments, yet research on reinforcement learning (RL) for continuous control remains dominated by single-task or offline regimes, reinforcing a view that online RL does not scale. Inspired by the foundation model recipe (large-scale pretraining followed by light RL) we ask whether a single agent can be trained on hundreds of tasks with online interaction. To accelerate research in this direction, we introduce a new benchmark with 200 diverse tasks spanning many domains and embodiments, each with language instructions, demonstrations, and optionally image observations. We then present \emph{Newt}, a language-conditioned multitask world model that is first pretrained on demonstrations to acquire task-aware representations and action priors, and then jointly optimized with online interaction across all tasks. Experiments show that Newt yields better multitask performance and data-efficiency than a set of strong baselines, exhibits strong open-loop control, and enables rapid adaptation to unseen tasks. We release our environments, demonstrations, code for training and evaluation, as well as 200+ checkpoints.

Tongzhou Mu, Yijie Guo, Jie Xu et al. · nvidia

Encouraged by the remarkable achievements of language and vision foundation models, developing generalist robotic agents through imitation learning, using large demonstration datasets, has become a prominent area of interest in robot learning. The efficacy of imitation learning is heavily reliant on the quantity and quality of the demonstration datasets. In this study, we aim to scale up demonstrations in a data-efficient way to facilitate the learning of generalist robotic agents. We introduce AdaDemo (Adaptive Online Demonstration Expansion), a general framework designed to improve multi-task policy learning by actively and continually expanding the demonstration dataset. AdaDemo strategically collects new demonstrations to address the identified weakness in the existing policy, ensuring data efficiency is maximized. Through a comprehensive evaluation on a total of 22 tasks across two robotic manipulation benchmarks (RLBench and Adroit), we demonstrate AdaDemo's capability to progressively improve policy performance by guiding the generation of high-quality demonstration datasets in a data-efficient manner.

Xinyue Wei, Fanbo Xiang, Sai Bi et al.

We present a method for generating high-quality watertight manifold meshes from multi-view input images. Existing volumetric rendering methods are robust in optimization but tend to generate noisy meshes with poor topology. Differentiable rasterization-based methods can generate high-quality meshes but are sensitive to initialization. Our method combines the benefits of both worlds; we take the geometry initialization obtained from neural volumetric fields, and further optimize the geometry as well as a compact neural texture representation with differentiable rasterizers. Through extensive experiments, we demonstrate that our method can generate accurate mesh reconstructions with faithful appearance that are comparable to previous volume rendering methods while being an order of magnitude faster in rendering. We also show that our generated mesh and neural texture reconstruction is compatible with existing graphics pipelines and enables downstream 3D applications such as simulation. Project page: https://sarahweiii.github.io/neumanifold/

Minhyuk Sung, Hao Su, Ronald Yu et al.

Various 3D semantic attributes such as segmentation masks, geometric features, keypoints, and materials can be encoded as per-point probe functions on 3D geometries. Given a collection of related 3D shapes, we consider how to jointly analyze such probe functions over different shapes, and how to discover common latent structures using a neural network --- even in the absence of any correspondence information. Our network is trained on point cloud representations of shape geometry and associated semantic functions on that point cloud. These functions express a shared semantic understanding of the shapes but are not coordinated in any way. For example, in a segmentation task, the functions can be indicator functions of arbitrary sets of shape parts, with the particular combination involved not known to the network. Our network is able to produce a small dictionary of basis functions for each shape, a dictionary whose span includes the semantic functions provided for that shape. Even though our shapes have independent discretizations and no functional correspondences are provided, the network is able to generate latent bases, in a consistent order, that reflect the shared semantic structure among the shapes. We demonstrate the effectiveness of our technique in various segmentation and keypoint selection applications.