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We consider the problem of learning a function respecting a symmetry from among a class of symmetries. We develop a unified framework that enables symmetry discovery across a broad range of subgroups including locally symmetric, dihedral and cyclic subgroups. At the core of the framework is a novel architecture composed of linear and tensor-valued functions that expresses functions invariant to these subgroups in a principled manner. The structure of the architecture enables us to leverage multi-armed bandit algorithms and gradient descent to efficiently optimize over the linear and the tensor-valued functions, respectively, and to infer the symmetry that is ultimately learnt. We also discuss the necessity of the tensor-valued functions in the architecture. Experiments on image-digit sum and polynomial regression tasks demonstrate the effectiveness of our approach.

Composed image retrieval, a task involving the search for a target image using a reference image and a complementary text as the query, has witnessed significant advancements owing to the progress made in cross-modal modeling. Unlike the general image-text retrieval problem with only one alignment relation, i.e., image-text, we argue for the existence of two types of relations in composed image retrieval. The explicit relation pertains to the reference image & complementary text-target image, which is commonly exploited by existing methods. Besides this intuitive relation, the observations during our practice have uncovered another implicit yet crucial relation, i.e., reference image & target image-complementary text, since we found that the complementary text can be inferred by studying the relation between the target image and the reference image. Regrettably, existing methods largely focus on leveraging the explicit relation to learn their networks, while overlooking the implicit relation. In response to this weakness, We propose a new framework for composed image retrieval, termed dual relation alignment, which integrates both explicit and implicit relations to fully exploit the correlations among the triplets. Specifically, we design a vision compositor to fuse reference image and target image at first, then the resulted representation will serve two roles: (1) counterpart for semantic alignment with the complementary text and (2) compensation for the complementary text to boost the explicit relation modeling, thereby implant the implicit relation into the alignment learning. Our method is evaluated on two popular datasets, CIRR and FashionIQ, through extensive experiments. The results confirm the effectiveness of our dual-relation learning in substantially enhancing composed image retrieval performance.

Robots must make and break contact to interact with the world and perform useful tasks. However, planning and control through contact remains a formidable challenge. In this work, we achieve real-time contact-implicit model predictive control with a surprisingly simple method: inverse dynamics trajectory optimization. While trajectory optimization with inverse dynamics is not new, we introduce a series of incremental innovations that collectively enable fast model predictive control on a variety of challenging manipulation and locomotion tasks. We implement these innovations in an open-source solver, and present a variety of simulation examples to support the effectiveness of the proposed approach. Additionally, we demonstrate contact-implicit model predictive control on hardware at over 100 Hz for a 20 degree-of-freedom bi-manual manipulation task.

To control how a robot moves, motion planning algorithms must compute paths in high-dimensional state spaces while accounting for physical constraints related to motors and joints, generating smooth and stable motions, avoiding obstacles, and preventing collisions. A motion planning algorithm must therefore balance competing demands, and should ideally incorporate uncertainty to handle noise, model errors, and facilitate deployment in complex environments. To address these issues, we introduce a framework for robot motion planning based on variational Gaussian Processes, which unifies and generalizes various probabilistic-inference-based motion planning algorithms. Our framework provides a principled and flexible way to incorporate equality-based, inequality-based, and soft motion-planning constraints during end-to-end training, is straightforward to implement, and provides both interval-based and Monte-Carlo-based uncertainty estimates. We conduct experiments using different environments and robots, comparing against baseline approaches based on the feasibility of the planned paths, and obstacle avoidance quality. Results show that our proposed approach yields a good balance between success rates and path quality.

Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical. This paper addresses this computational challenge through the development of a novel generalised Bayesian inference procedure suitable for discrete intractable likelihood. Inspired by recent methodological advances for continuous data, the main idea is to update beliefs about model parameters using a discrete Fisher divergence, in lieu of the problematic intractable likelihood. The result is a generalised posterior that can be sampled from using standard computational tools, such as Markov chain Monte Carlo, circumventing the intractable normalising constant. The statistical properties of the generalised posterior are analysed, with sufficient conditions for posterior consistency and asymptotic normality established. In addition, a novel and general approach to calibration of generalised posteriors is proposed. Applications are presented on lattice models for discrete spatial data and on multivariate models for count data, where in each case the methodology facilitates generalised Bayesian inference at low computational cost.

Sublinear time complexity is required by the massively parallel computation (MPC) model. Breaking dynamic programs into a set of sparse dynamic programs that can be divided, solved, and merged in sublinear time. The rectangle escape problem (REP) is defined as follows: For $n$ axis-aligned rectangles inside an axis-aligned bounding box $B$, extend each rectangle in only one of the four directions: up, down, left, or right until it reaches $B$ and the density $k$ is minimized, where $k$ is the maximum number of extensions of rectangles to the boundary that pass through a point inside bounding box $B$. REP is NP-hard for $k>1$. If the rectangles are points of a grid (or unit squares of a grid), the problem is called the square escape problem (SEP) and it is still NP-hard. We give a $2$-approximation algorithm for SEP with $k\geq2$ with time complexity $O(n^{3/2}k^2)$. This improves the time complexity of existing algorithms which are at least quadratic. Also, the approximation ratio of our algorithm for $k\geq 3$ is $3/2$ which is tight. We also give a $8$-approximation algorithm for REP with time complexity $O(n\log n+nk)$ and give a MPC version of this algorithm for $k=O(1)$ which is the first parallel algorithm for this problem.

This work presents a study on parallel and distributional deep reinforcement learning applied to the mapless navigation of UAVs. For this, we developed an approach based on the Soft Actor-Critic method, producing a distributed and distributional variant named PDSAC, and compared it with a second one based on the traditional SAC algorithm. In addition, we also embodied a prioritized memory system into them. The UAV used in the study is based on the Hydrone vehicle, a hybrid quadrotor operating solely in the air. The inputs for the system are 23 range findings from a Lidar sensor and the distance and angles towards a desired goal, while the outputs consist of the linear, angular, and, altitude velocities. The methods were trained in environments of varying complexity, from obstacle-free environments to environments with multiple obstacles in three dimensions. The results obtained, demonstrate a concise improvement in the navigation capabilities by the proposed approach when compared to the agent based on the SAC for the same amount of training steps. In summary, this work presented a study on deep reinforcement learning applied to mapless navigation of drones in three dimensions, with promising results and potential applications in various contexts related to robotics and autonomous air navigation with distributed and distributional variants.

Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.

Relation prediction for knowledge graphs aims at predicting missing relationships between entities. Despite the importance of inductive relation prediction, most previous works are limited to a transductive setting and cannot process previously unseen entities. The recent proposed subgraph-based relation reasoning models provided alternatives to predict links from the subgraph structure surrounding a candidate triplet inductively. However, we observe that these methods often neglect the directed nature of the extracted subgraph and weaken the role of relation information in the subgraph modeling. As a result, they fail to effectively handle the asymmetric/anti-symmetric triplets and produce insufficient embeddings for the target triplets. To this end, we introduce a \textbf{C}\textbf{o}mmunicative \textbf{M}essage \textbf{P}assing neural network for \textbf{I}nductive re\textbf{L}ation r\textbf{E}asoning, \textbf{CoMPILE}, that reasons over local directed subgraph structures and has a vigorous inductive bias to process entity-independent semantic relations. In contrast to existing models, CoMPILE strengthens the message interactions between edges and entitles through a communicative kernel and enables a sufficient flow of relation information. Moreover, we demonstrate that CoMPILE can naturally handle asymmetric/anti-symmetric relations without the need for explosively increasing the number of model parameters by extracting the directed enclosing subgraphs. Extensive experiments show substantial performance gains in comparison to state-of-the-art methods on commonly used benchmark datasets with variant inductive settings.

Embedding entities and relations into a continuous multi-dimensional vector space have become the dominant method for knowledge graph embedding in representation learning. However, most existing models ignore to represent hierarchical knowledge, such as the similarities and dissimilarities of entities in one domain. We proposed to learn a Domain Representations over existing knowledge graph embedding models, such that entities that have similar attributes are organized into the same domain. Such hierarchical knowledge of domains can give further evidence in link prediction. Experimental results show that domain embeddings give a significant improvement over the most recent state-of-art baseline knowledge graph embedding models.