Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps (operators) between infinite dimensional function spaces, these models are able to learn discretization invariant representations of target functions. A common approach is to represent such target functions as linear combinations of basis elements learned from data. However, there are simple scenarios where, even though the target functions form a low dimensional submanifold, a very large number of basis elements is needed for an accurate linear representation.

This paper presents a novel approach to image-goal navigation by integrating 3D Gaussian Splatting (3DGS) with Visual Navigation Models (VNMs), a method we refer to as GSplatVNM. VNMs offer a promising paradigm for image-goal navigation by guiding a robot through a sequence of point-of-view images without requiring metrical localization or environment-specific training. However, constructing a dense and traversable sequence of target viewpoints from start to goal remains a central challenge, particularly when the available image database is sparse. To address these challenges, we propose a 3DGS-based viewpoint synthesis framework for VNMs that synthesizes intermediate viewpoints to seamlessly bridge gaps in sparse data while significantly reducing storage overhead. Experimental results in a photorealistic simulator demonstrate that our approach not only enhances navigation efficiency but also exhibits robustness under varying levels of image database sparsity.

Navigation is a fundamental skill of agents with visual-motor capabilities. We introduce a Navigation World Model (NWM), a controllable video generation model that predicts future visual observations based on past observations and navigation actions. To capture complex environment dynamics, NWM employs a Conditional Diffusion Transformer (CDiT), trained on a diverse collection of egocentric videos of both human and robotic agents, and scaled up to 1 billion parameters. In familiar environments, NWM can plan navigation trajectories by simulating them and evaluating whether they achieve the desired goal. Unlike supervised navigation policies with fixed behavior, NWM can dynamically incorporate constraints during planning. Experiments demonstrate its effectiveness in planning trajectories from scratch or by ranking trajectories sampled from an external policy. Furthermore, NWM leverages its learned visual priors to imagine trajectories in unfamiliar environments from a single input image, making it a flexible and powerful tool for next-generation navigation systems.

Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps (operators) between infinite dimensional function spaces, these models are able to learn discretization invariant representations of target functions. A common approach is to represent such target functions as linear combinations of basis elements learned from data. However, there are simple scenarios where, even though the target functions form a low dimensional submanifold, a very large number of basis elements is needed for an accurate linear representation. We show this method is able to accurately learn low dimensional representations of solution manifolds to partial differential equations while outperforming linear models of larger size.

The fine-tuning of Large Language Models (LLMs) has enabled them to recently achieve milestones in natural language processing applications. The emergence of ever larger LLMs has paved the way for more efficient fine-tuning methods. Among these, the Low-Rank Adaptation (LoRA) method keeps most of the weights of the pre-trained LLM frozen while introducing a low-rank decomposition of the weight matrix, enabling the tuning of only a very small proportion of the network. The performance on downstream tasks of models fine-tuned with LoRA heavily relies on a set of hyperparameters including the rank of the decomposition. In this work, we investigate the choice of these hyperparameters through two main blackbox optimization (BBO) techniques. We examine the whole pipeline of performing fine-tuning and validation on a pre-trained LLM as a blackbox and efficiently explore the space of hyperparameters with the \nomad algorithm, achieving a boost in performance and human alignment of the tuned model.

A major challenge in deploying the smallest of Micro Aerial Vehicle (MAV) platforms (< 100 g) is their inability to carry sensors that provide high-resolution metric depth information (e.g., LiDAR or stereo cameras). Current systems rely on end-to-end learning or heuristic approaches that directly map images to control inputs, and struggle to fly fast in unknown environments. In this work, we ask the following question: using only a monocular camera, optical odometry, and offboard computation, can we create metrically accurate maps to leverage the powerful path planning and navigation approaches employed by larger state-of-the-art robotic systems to achieve robust autonomy in unknown environments? We present MonoNav: a fast 3D reconstruction and navigation stack for MAVs that leverages recent advances in depth prediction neural networks to enable metrically accurate 3D scene reconstruction from a stream of monocular images and poses. MonoNav uses off-the-shelf pre-trained monocular depth estimation and fusion techniques to construct a map, then searches over motion primitives to plan a collision-free trajectory to the goal. In extensive hardware experiments, we demonstrate how MonoNav enables the Crazyflie (a 37 g MAV) to navigate fast (0.5 m/s) in cluttered indoor environments. We evaluate MonoNav against a state-of-the-art end-to-end approach, and find that the collision rate in navigation is significantly reduced (by a factor of 4). This increased safety comes at the cost of conservatism in terms of a 22% reduction in goal completion.

Robotic learning for navigation in unfamiliar environments needs to provide policies for both task-oriented navigation (i.e., reaching a goal that the robot has located), and task-agnostic exploration (i.e., searching for a goal in a novel setting). Typically, these roles are handled by separate models, for example by using subgoal proposals, planning, or separate navigation strategies. In this paper, we describe how we can train a single unified diffusion policy to handle both goal-directed navigation and goal-agnostic exploration, with the latter providing the ability to search novel environments, and the former providing the ability to reach a user-specified goal once it has been located. We show that this unified policy results in better overall performance when navigating to visually indicated goals in novel environments, as compared to approaches that use subgoal proposals from generative models, or prior methods based on latent variable models. We instantiate our method by using a large-scale Transformer-based policy trained on data from multiple ground robots, with a diffusion model decoder to flexibly handle both goal-conditioned and goal-agnostic navigation. Our experiments, conducted on a real-world mobile robot platform, show effective navigation in unseen environments in comparison with five alternative methods, and demonstrate significant improvements in performance and lower collision rates, despite utilizing smaller models than state-of-the-art approaches. For more videos, code, and pre-trained model checkpoints, see https://general-navigation-models.github.io/nomad/

It took a while, and a rather bumpy false start with the Star Wars franchise (his Rogue One was plagued by rumours of studio interference and extensive reshoots), but with The Creator, the British director Gareth Edwards finally gets to make the sci-fi spectacular he was always destined to tackle. And with this ambitious, ideas-driven, expectation-subverting, man-versus-machines showdown, he has co-written and directed one of the finest original science-fiction films of recent years. It can be a little misleading, that word "original", when it comes to science fiction. At its most basic, it just refers to any picture that isn't part of an existing franchise or culled from a recognisable IP – be it a book, video game or television series. But very occasionally the word is fully earned, by a film so distinctive in its world-building, its aesthetic and its unexpected approach to well-worn themes that it becomes a definitive example of the genre.

We consider the problem of learning the structure underlying a Gaussian graphical model when the variables (or subsets thereof) are corrupted by independent noise. A recent line of work establishes that even for tree-structured graphical models, only partial structure recovery is possible and goes on to devise algorithms to identify the structure up to an (unavoidable) equivalence class of trees. We extend these results beyond trees and consider the model selection problem under noise for non tree-structured graphs, as tree graphs cannot model several real-world scenarios. Although unidentifiable, we show that, like the tree-structured graphs, the ambiguity is limited to an equivalence class. This limited ambiguity can help provide meaningful clustering information (even with noise), which is helpful in computer and social networks, protein-protein interaction networks, and power networks. Furthermore, we devise an algorithm based on a novel ancestral testing method for recovering the equivalence class. We complement these results with finite sample guarantees for the algorithm in the high-dimensional regime.