Neural Radiance Fields and Gaussian Splatting have recently transformed computer vision by enabling photo-realistic representations of complex scenes. However, they have seen limited application in real-world robotics tasks such as trajectory optimization. This is due to the difficulty in reasoning about collisions in radiance models and the computational complexity associated with operating in dense models. This paper addresses these challenges by proposing SPLANNING, a risk-aware trajectory optimizer operating in a Gaussian Splatting model. This paper first derives a method to rigorously upper-bound the probability of collision between a robot and a radiance field. Then, this paper introduces a normalized reformulation of Gaussian Splatting that enables efficient computation of this collision bound. Finally, this paper presents a method to optimize trajectories that avoid collisions in a Gaussian Splat. Experiments show that SPLANNING outperforms state-of-the-art methods in generating collision-free trajectories in cluttered environments. The proposed system is also tested on a real-world robot manipulator. A project page is available athttps://roahmlab.github.io/splanning.

Considering various data modalities, such as images, videos, and text, humans perform causal reasoning using high-level causal variables, as opposed to operating at the low, pixel level from which the data comes. In practice, most causal reasoning methods assume that the data is described as granular as the underlying causal generative factors, which is often violated in various AI tasks. This mismatch translates into a lack of guarantees in various tasks such as generative modeling, decision-making, fairness, and generalizability, to cite a few. In this paper, we acknowledge this issue and study the problem of causal disentangled representation learning from a combination of data gathered from various heterogeneous domains and assumptions in the form of a latent causal graph. To the best of our knowledge, the proposed work is the first to consider i) non-Markovian causal settings, where there may be unobserved confounding, ii) arbitrary distributions that arise from multiple domains, and iii) a relaxed version of disentanglement. Specifically, we introduce graphical criteria that allow for disentanglement under various conditions. Building on these results, we develop an algorithm that returns a causal disentanglement map, highlighting which latent variables can be disentangled given the combination of data and assumptions. The theory is corroborated by experiments.

A fundamental problem in many sciences is the learning of causal structure underlying a system, typically through observation and experimentation. Commonly, one even collects data across multiple domains, such as gene sequencing from different labs, or neural recordings from different species. Although there exist methods for learning the equivalence class of causal diagrams from observational and experimental data, they are meant to operate in a single domain. In this paper, we develop a fundamental approach to structure learning in non-Markovian systems (i.e. when there exist latent confounders) leveraging observational and interventional data collected from multiple domains. Specifically, we start by showing that learning from observational data in multiple domains is equivalent to learning from interventional data with unknown targets in a single domain. But there are also subtleties when considering observational and experimental data. Using causal invariances derived from do-calculus, we define a property called S-Markov that connects interventional distributions from multiple-domains to graphical criteria on a selection diagram. Leveraging the S-Markov property, we introduce a new constraint-based causal discovery algorithm, S-FCI, that can learn from observational and interventional data from different domains. We prove that the algorithm is sound and subsumes existing constraint-based causal discovery algorithms.

Google services continuously generate vast amounts of application data. This data provides valuable insights to business users. We need to store and serve these planet-scale data sets under the extremely demanding requirements of scalability, sub-second query response times, availability, and strong consistency; all this while ingesting a massive stream of updates from applications used around the globe. We have developed and deployed in production an analytical data management system, Napa, to meet these requirements. Napa is the backend for numerous clients in Google. These clients have a strong expectation of variance-free, robust query performance. At its core, Napa's principal technologies for robust query performance include the aggressive use of materialized views, which are maintained consistently as new data is ingested across multiple data centers. Our clients also demand flexibility in being able to adjust their query performance, data freshness, and costs to suit their unique needs. Robust query processing and flexible configuration of client databases are the hallmark of Napa design. Most of the related work in this area takes advantage of full flexibility to design the whole system without the need to support a diverse set of preexisting use cases. In comparison, a particular challenge we faced is that Napa needs to deal with hard constraints from existing applications and infrastructure, so we could not do a "green field" system, but rather had to satisfy existing constraints. These constraints led us to make particular design decisions and also devise new techniques to meet the challenges. In this paper, we share our experiences in designing, implementing, deploying, and running Napa in production with some of Google's most demanding applications.