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1. Localizing and Amortizing: Efficient Inference for Gaussian Processes

   Liu, Linfeng; Liu, Li-Ping (November 2020, Proceedings of The 12th Asian Conference on Machine Learning)

   null (Ed.)

   The inference of Gaussian Processes concerns the distribution of the underlying function given observed data points. GP inference based on local ranges of data points is able to capture fine-scale correlations and allow fine-grained decomposition of the computation. Following this direction, we propose a new inference model that considers the correlations and observations of the K nearest neighbors for the inference at a data point. Compared with previous works, we also eliminate the data ordering prerequisite to simplify the inference process. Additionally, the inference task is decomposed to small subtasks with several technique innovations, making our model well suits the stochastic optimization. Since the decomposed small subtasks have the same structure, we further speed up the inference procedure with amortized inference. Our model runs efficiently and achieves good performances on several benchmark tasks. 

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2. Learning Reactive Motion Policies in Multiple Task Spaces from Human Demonstrations

   M Asif Rana, Anqi Li (January 2019, Conference on Robot Learning)

   Complex manipulation tasks often require non-trivial and coordinated movements of different parts of a robot. In this work, we address the challenges associated with learning and reproducing the skills required to execute such complex tasks. Specifically, we decompose a task into multiple subtasks and learn to reproduce the subtasks by learning stable policies from demonstrations. By leveraging the RMPflow framework for motion generation, our approach finds a stable global policy in the configuration space that enables simultaneous execution of various learned subtasks. The resulting global policy is a weighted combination of the learned policies such that the motions are coordinated and feasible under the robot's kinematic and environmental constraints. We demonstrate the necessity and efficacy of the proposed approach in the context of multiple constrained manipulation tasks performed by a Franka Emika robot. 

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3. Complex priors and flexible inference in recurrent circuits with dendritic nonlinearities

   Lyo, B; Savin, C (January 2024, International Conference on Learning Representations)

   Despite many successful examples in which probabilistic inference can account for perception, we have little understanding of how the brain represents and uses structured priors that capture the complexity of natural input statistics. Here we construct a recurrent circuit model that can implicitly represent priors over latent variables, and combine them with sensory and contextual sources of information to encode task-specific posteriors. Inspired by the recent success of diffusion models as means of learning and using priors over images, our model uses dendritic nonlinearities optimized for denoising, and stochastic somatic integration with the degree of noise modulated by an oscillating global signal. Combining these elements into a recurrent network yields a stochastic dynamical system that samples from the prior at a rate prescribed by the period of the global oscillator. Additional inputs reflecting sensory or top-down contextual information alter these dynamics to generate samples from the corresponding posterior, with different input gating patterns selecting different inference tasks. We demonstrate that this architecture can sample from low dimensional nonlinear manifolds and multimodal posteriors. Overall, the model provides a new framework for circuit-level representation of probabilistic information, in a format that facilitates flexible inference. 

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4. Balancing between the Local and Global Structures (LGS) in Graph Embedding

   https://doi.org/10.1007/978-3-031-49272-3_18  

   Miller, Jacob; Huroyan, Vahan; Kobourov, Stephen (January 2024, 31st International Symposium on Graph Drawing and Network Visualization (GD))

   We present a method for balancing between the Local and Global Structures ( L G S ) in graph embedding, via a tunable parame- ter. Some embedding methods aim to capture global structures, while others attempt to preserve local neighborhoods. Few methods attempt to do both, and it is not always possible to capture well both local and global information in two dimensions, which is where most graph drawing live. The choice of using a local or a global embedding for visualization depends not only on the task but also on the structure of the underly-ing data, which may not be known in advance. For a given graph, L G S aims to find a good balance between the local and global structure to preserve. We evaluate the performance of L G S with synthetic and real- world datasets and our results indicate that it is competitive with the state-of-the-art methods, using established quality metrics such as stress and neighborhood preservation. We introduce a novel quality metric, cluster distance preservation, to assess intermediate structure capture. All source-code, datasets, experiments and analysis are available online. 

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5. Compositional planning in Markov decision processes: Temporal abstraction meets generalized logic composition

   Liu, Xuan; Fu, Jie (July 2019, Annual American Control Conference)

   In hierarchical planning for Markov decision processes (MDPs), temporal abstraction allows planning with macro-actions that take place at different time scale in the form of sequential composition. In this paper, we propose a novel approach to compositional reasoning and hierarchical planning for MDPs under co-safe temporal logic constraints. In addition to sequential composition, we introduce a composition of policies based on generalized logic composition: Given sub-policies for sub-tasks and a new task expressed as logic compositions of subtasks, a semi-optimal policy, which is optimal in planning with only sub-policies, can be obtained by simply composing sub-polices. Thus, a synthesis algorithm is developed to compute optimal policies efficiently by planning with primitive actions, policies for sub-tasks, and the compositions of sub-policies, for maximizing the probability of satisfying constraints specified in the fragment of co-safe temporal logic. We demonstrate the correctness and efficiency of the proposed method in stochastic planning examples with a single agent and multiple task specifications. 

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