Abstract--Visual Imitation learning has achieved remarkable progress in robotic manipulation, yet generalization to unseen objects, scene layouts, and camera viewpoints remains a key challenge. Recent advances address this by using 3D point clouds, which provide geometry-aware, appearance-invariant representations, and by incorporating equivariance into policy architectures to exploit spatial symmetries. However, existing equivariant approaches often lack interpretability and rigor due to unstructured integration of equivariant components. We introduce canonical policy, a principled framework for 3D equiv-ariant imitation learning that unifies 3D point cloud observations under a canonical representation. We first establish a theory of 3D canonical representations, enabling equivariant observation-to-action mappings by grouping both seen and novel point clouds to a canonical representation. We then propose a flexible policy learning pipeline that leverages geometric symmetries from canonical representation and the expressiveness of modern generative models. We validate canonical policy on 12 diverse simulated tasks and 4 real-world manipulation tasks across 16 configurations, involving variations in object color, shape, camera viewpoint, and robot platform. Compared to state-of-the-art imitation learning policies, canonical policy achieves an average improvement of 18.0% in simulation and 39.7% in real-world experiments, demonstrating superior generalization capability and sample efficiency. Imitation learning has made remarkable progress in robotic manipulation in recent years [1]-[5]. However, generalization and sample efficiency remain key challenges. In particular, visual imitation learning policies [1], [2] often struggle to generalize beyond the fixed dataset of human demonstrations on which they are trained. Unseen variations in object types, scene configurations, geometric layouts, or camera viewpoints can significantly degrade policy performance. To improve generalization in visual imitation, recent research has explored the use of 3D point clouds as input observations [3], [5]-[7]. Point clouds encode the geometric structure of the environment and are invariant to visual dis-tractors such as background textures or object appearances. As a result, policies trained on 3D representations can more effectively learn the mapping between geometry of observations and robot actions, thereby improving both generalization and sample efficiency. Since robotic manipulation takes place in 3D Euclidean space and involves tasks that are often equivariant to rotations and translations, incorporating symmetry priors into the policy architecture can significantly improve both sample efficiency and generalization performance. However, existing approaches that aim to achieve equiv-ariant policy learning from 3D point clouds or 2D images often rely on re-designing the entire network using equivariant neural modules [8]-[10].

Counterfactual reasoning aims at answering contrary-to-fact questions like "Would have Alice recovered had she taken aspirin?" and corresponds to the most fine-grained layer of causation. Critically, while many counterfactual statements cannot be falsified--even by randomized experiments--they underpin fundamental concepts like individual-wise fairness. Therefore, providing models to formalize and implement counterfactual beliefs remains a fundamental scientific problem. In the Markovian setting of Pearl's causal framework, we propose an alternative approach to structural causal models to represent counterfactuals compatible with a given causal graphical model. More precisely, we introduce counterfactual models, also called canonical representations of structural causal models. They enable analysts to choose a counterfactual assumption via random-process probability distributions with preassigned marginals and characterize the counterfactual equivalence class of structural causal models. Using these representations, we present a normalization procedure to disentangle the (arbitrary and unfalsifiable) counterfactual choice from the (typically testable) interventional constraints. In contrast to structural causal models, this allows to implement many counterfactual assumptions while preserving interventional knowledge, and does not require any estimation step at the individual-counterfactual layer: only to make a choice. Finally, we illustrate the specific role of counterfactuals in causality and the benefits of our approach on theoretical and numerical examples.

We study metric learning from preference comparisons under the ideal point model, in which a user prefers an item over another if it is closer to their latent ideal item. These items are embedded into $\mathbb{R}^d$ equipped with an unknown Mahalanobis distance shared across users. While recent work shows that it is possible to simultaneously recover the metric and ideal items given $\mathcal{O}(d)$ pairwise comparisons per user, in practice we often have a limited budget of $o(d)$ comparisons. We study whether the metric can still be recovered, even though it is known that learning individual ideal items is now no longer possible. We show that in general, $o(d)$ comparisons reveals no information about the metric, even with infinitely many users. However, when comparisons are made over items that exhibit low-dimensional structure, each user can contribute to learning the metric restricted to a low-dimensional subspace so that the metric can be jointly identified. We present a divide-and-conquer approach that achieves this, and provide theoretical recovery guarantees and empirical validation.

In this paper, a method for generating a map from path information described using natural language (textual path) is proposed. In recent years, robotics research mainly focus on vision-and-language navigation (VLN), a navigation task based on images and textual paths. Although VLN is expected to facilitate user instructions to robots, its current implementation requires users to explain the details of the path for each navigation session, which results in high explanation costs for users. To solve this problem, we proposed a method that creates a map as a topological map from a textual path and automatically creates a new path using this map. We believe that large language models (LLMs) can be used to understand textual path. Therefore, we propose and evaluate two methods, one for storing implicit maps in LLMs, and the other for generating explicit maps using LLMs. The implicit map is in the LLM's memory. It is created using prompts. In the explicit map, a topological map composed of nodes and edges is constructed and the actions at each node are stored. This makes it possible to estimate the path and actions at waypoints on an undescribed path, if enough information is available. Experimental results on path instructions generated in a real environment demonstrate that generating explicit maps achieves significantly higher accuracy than storing implicit maps in the LLMs.

Group equivariance ensures consistent responses to group transformations of the input, leading to more robust models and enhanced generalization capabilities. However, this property can lead to overly constrained models if the symmetries considered in the group differ from those observed in data. While common methods address this by determining the appropriate level of symmetry at the dataset level, they are limited to supervised settings and ignore scenarios in which multiple levels of symmetry co-exist in the same dataset. For instance, pictures of cars and planes exhibit different levels of rotation, yet both are included in the CIFAR-10 dataset. In this paper, we propose a method able to detect the level of symmetry of each input without the need for labels. To this end, we derive a sufficient and necessary condition to learn the distribution of symmetries in the data. Using the learned distribution, we generate pseudo-labels that allow us to learn the levels of symmetry of each input in a self-supervised manner. We validate the effectiveness of our approach on synthetic datasets with different per-class levels of symmetries e.g. MNISTMultiple, in which digits are uniformly rotated within a class-dependent interval. We demonstrate that our method can be used for practical applications such as the generation of standardized datasets in which the symmetries are not present, as well as the detection of out-of-distribution symmetries during inference. By doing so, both the generalization and robustness of non-equivariant models can be improved. Our code is publicly available at https://github.com/aurban0/ssl-sym.

Aggregated curves are common structures in economics and finance, and the most prominent examples are supply and demand curves. In this study, we exploit the fact that all aggregated curves have an intrinsic hierarchical structure, and thus hierarchical reconciliation methods can be used to improve the forecast accuracy. We provide an in-depth theory on how aggregated curves can be constructed or deconstructed, and conclude that these methods are equivalent under weak assumptions. We consider multiple reconciliation methods for aggregated curves, including previously established bottom-up, top-down, and linear optimal reconciliation approaches. We also present a new benchmark reconciliation method called 'aggregated-down' with similar complexity to bottom-up and top-down approaches, but it tends to provide better accuracy in this setup. We conducted an empirical forecasting study on the German day-ahead power auction market by predicting the demand and supply curves, where their equilibrium determines the electricity price for the next day. Our results demonstrate that hierarchical reconciliation methods can be used to improve the forecasting accuracy of aggregated curves.

We present a hierarchical Bayesian model for sets of related, but different, classes of time series data. Our model performs alignment simultaneously across all classes, while detecting and characterizing class-specific differences. During inference the model produces, for each class, a distribution over a canonical representation of the class. These class-specific canonical representations are automatically aligned to one another -- preserving common sub-structures, and highlighting differences. Many practical problems over a wide range of domains require synthesizing information from several noisy examples of one or more categories in order to build a model which captures common structure and also learns the patterns of variability between categories.

In this report, I address auto-formulation of problem description, the task of converting an optimization problem into a canonical representation. I first simplify the auto-formulation task by defining an intermediate representation, then introduce entity tag embedding to utilize a given entity tag information. The ablation study demonstrate the effectiveness of the proposed method, which finally took second place in NeurIPS 2022 NL4Opt competition subtask 2.

We propose the Probabilistic Sentential Decision Diagram (PSDD): A complete and canonical representation of probability distributions defined over the models of a given propositional theory. Each parameter of a PSDD can be viewed as the (conditional) probability of making a decision in a corresponding Sentential Decision Diagram (SDD). The SDD itself is a recently proposed complete and canonical representation of propositional theories. We explore a number of interesting properties of PSDDs, including the independencies that underlie them. We show that the PSDD is a tractable representation. We further show how the parameters of a PSDD can be efficiently estimated, in closed form, from complete data. We empirically evaluate the quality of PSDDs learned from data, when we have knowledge, a priori, of the domain logical constraints.

Recently, category-level 6D object pose estimation has achieved significant improvements with the development of reconstructing canonical 3D representations. However, the reconstruction quality of existing methods is still far from excellent. In this paper, we propose a novel Adversarial Canonical Representation Reconstruction Network named ACR-Pose. ACR-Pose consists of a Reconstructor and a Discriminator. The Reconstructor is primarily composed of two novel sub-modules: Pose-Irrelevant Module (PIM) and Relational Reconstruction Module (RRM). PIM tends to learn canonical-related features to make the Reconstructor insensitive to rotation and translation, while RRM explores essential relational information between different input modalities to generate high-quality features. Subsequently, a Discriminator is employed to guide the Reconstructor to generate realistic canonical representations. The Reconstructor and the Discriminator learn to optimize through adversarial training. Experimental results on the prevalent NOCS-CAMERA and NOCS-REAL datasets demonstrate that our method achieves state-of-the-art performance.