Andrew Davison

Theodore Papamarkou, Pierre Alquier, Matthias Bauer et al.

LLMs excel at predictive tasks and complex reasoning tasks, but many high-value deployments rely on decisions under uncertainty, for example, which tool to call, which expert to consult, or how many resources to invest. While the usefulness and feasibility of Bayesian approaches remain unclear for LLM inference, this position paper argues that the control layer of an agentic AI system (that orchestrates LLMs and tools) is a clear case where Bayesian principles should shine. Bayesian decision theory provides a framework for agentic systems that can help to maintain beliefs over task-relevant latent quantities, to update these beliefs from observed agentic and human-AI interactions, and to choose actions. Making LLMs themselves explicitly Bayesian belief-updating engines remains computationally intensive and conceptually nontrivial as a general modeling target. In contrast, this paper argues that coherent decision-making requires Bayesian principles at the orchestration level of the agentic system, not necessarily the LLM agent parameters. This paper articulates practical properties for Bayesian control that fit modern agentic AI systems and human-AI collaboration, and provides concrete examples and design patterns to illustrate how calibrated beliefs and utility-aware policies can improve agentic AI orchestration.

Andrew Davison, S. Carlyle Morgan, Owen G. Ward

Embedding the nodes of a large network into an Euclidean space is a common objective in modern machine learning, with a variety of tools available. These embeddings can then be used as features for tasks such as community detection/node clustering or link prediction, where they achieve state of the art performance. With the exception of spectral clustering methods, there is little theoretical understanding for commonly used approaches to learning embeddings. In this work we examine the theoretical properties of the embeddings learned by node2vec. Our main result shows that the use of $k$-means clustering on the embedding vectors produced by node2vec gives weakly consistent community recovery for the nodes in (degree corrected) stochastic block models. We also discuss the use of these embeddings for node and link prediction tasks. We demonstrate this result empirically, and examine how this relates to other embedding tools for network data.

Vansh Nagpal, Siva Likitha Valluru, Kausik Lakkaraju et al.

A common decision made by people, whether healthy or with health conditions, is choosing meals like breakfast, lunch, and dinner, comprising combinations of foods for appetizer, main course, side dishes, desserts, and beverages. Often, this decision involves tradeoffs between nutritious choices (e.g., salt and sugar levels, nutrition content) and convenience (e.g., cost and accessibility, cuisine type, food source type). We present a data-driven solution for meal recommendations that considers customizable meal configurations and time horizons. This solution balances user preferences while accounting for food constituents and cooking processes. Our contributions include introducing goodness measures, a recipe conversion method from text to the recently introduced multimodal rich recipe representation (R3) format, learning methods using contextual bandits that show promising preliminary results, and the prototype, usage-inspired, BEACON system.

Ignacio Alzugaray, Riku Murai, Andrew Davison

Images are the standard input for most computer vision algorithms. However, their processing often reduces to parallelizable operations applied locally and independently to individual pixels. Yet, many of these low-level raw pixel readings only provide redundant or noisy information for specific high-level tasks, leading to inefficiencies in both energy consumption during their transmission off-sensor and computational resources in their subsequent processing. As novel sensors featuring advanced in-pixel processing capabilities emerge, we envision a paradigm shift toward performing increasingly complex visual processing directly in-pixel, reducing computational overhead downstream. We advocate for synthesizing high-level cues at the pixel level, enabling their off-sensor transmission to directly support downstream tasks more effectively than raw pixel readings. This paper conceptualizes a novel photometric rotation estimation algorithm to be distributed at pixel level, where each pixel estimates the global motion of the camera by exchanging information with other pixels to achieve global consensus. We employ a probabilistic formulation and leverage Gaussian Belief Propagation (GBP) for decentralized inference using messaging-passing. The proposed proposed technique is evaluated on real-world public datasets and we offer a in-depth analysis of the practicality of applying GBP to distributed rotation estimation at pixel level.

Andrew Davison

A common approach to solving prediction tasks on large networks, such as node classification or link prediction, begin by learning a Euclidean embedding of the nodes of the network, from which traditional machine learning methods can then be applied. This includes methods such as DeepWalk and node2vec, which learn embeddings by optimizing stochastic losses formed over subsamples of the graph at each iteration of stochastic gradient descent. In this paper, we study the effects of adding an $\ell_2$ penalty of the embedding vectors to the training loss of these types of methods. We prove that, under some exchangeability assumptions on the graph, this asymptotically leads to learning a graphon with a nuclear-norm-type penalty, and give guarantees for the asymptotic distribution of the learned embedding vectors. In particular, the exact form of the penalty depends on the choice of subsampling method used as part of stochastic gradient descent. We also illustrate empirically that concatenating node covariates to $\ell_2$ regularized node2vec embeddings leads to comparable, when not superior, performance to methods which incorporate node covariates and the network structure in a non-linear manner.

Andrew Davison, Morgane Austern

Network data are ubiquitous in modern machine learning, with tasks of interest including node classification, node clustering and link prediction. A frequent approach begins by learning an Euclidean embedding of the network, to which algorithms developed for vector-valued data are applied. For large networks, embeddings are learned using stochastic gradient methods where the sub-sampling scheme can be freely chosen. Despite the strong empirical performance of such methods, they are not well understood theoretically. Our work encapsulates representation methods using a subsampling approach, such as node2vec, into a single unifying framework. We prove, under the assumption that the graph is exchangeable, that the distribution of the learned embedding vectors asymptotically decouples. Moreover, we characterize the asymptotic distribution and provided rates of convergence, in terms of the latent parameters, which includes the choice of loss function and the embedding dimension. This provides a theoretical foundation to understand what the embedding vectors represent and how well these methods perform on downstream tasks. Notably, we observe that typically used loss functions may lead to shortcomings, such as a lack of Fisher consistency.

Owen G. Ward, Zhen Huang, Andrew Davison et al.

Embedding nodes of a large network into a metric (e.g., Euclidean) space has become an area of active research in statistical machine learning, which has found applications in natural and social sciences. Generally, a representation of a network object is learned in a Euclidean geometry and is then used for subsequent tasks regarding the nodes and/or edges of the network, such as community detection, node classification and link prediction. Network embedding algorithms have been proposed in multiple disciplines, often with domain-specific notations and details. In addition, different measures and tools have been adopted to evaluate and compare the methods proposed under different settings, often dependent of the downstream tasks. As a result, it is challenging to study these algorithms in the literature systematically. Motivated by the recently proposed Veridical Data Science (VDS) framework, we propose a framework for network embedding algorithms and discuss how the principles of predictability, computability and stability apply in this context. The utilization of this framework in network embedding holds the potential to motivate and point to new directions for future research.

Edgar Sucar, Kentaro Wada, Andrew Davison

The choice of scene representation is crucial in both the shape inference algorithms it requires and the smart applications it enables. We present efficient and optimisable multi-class learned object descriptors together with a novel probabilistic and differential rendering engine, for principled full object shape inference from one or more RGB-D images. Our framework allows for accurate and robust 3D object reconstruction which enables multiple applications including robot grasping and placing, augmented reality, and the first object-level SLAM system capable of optimising object poses and shapes jointly with camera trajectory.

Zoe Landgraf, Fabian Falck, Michael Bloesch et al.

Generally capable Spatial AI systems must build persistent scene representations where geometric models are combined with meaningful semantic labels. The many approaches to labelling scenes can be divided into two clear groups: view-based which estimate labels from the input view-wise data and then incrementally fuse them into the scene model as it is built; and map-based which label the generated scene model. However, there has so far been no attempt to quantitatively compare view-based and map-based labelling. Here, we present an experimental framework and comparison which uses real-time height map fusion as an accessible platform for a fair comparison, opening up the route to further systematic research in this area.

Guillermo Gallego, Tobi Delbruck, Garrick Orchard et al.

Event cameras are bio-inspired sensors that differ from conventional frame cameras: Instead of capturing images at a fixed rate, they asynchronously measure per-pixel brightness changes, and output a stream of events that encode the time, location and sign of the brightness changes. Event cameras offer attractive properties compared to traditional cameras: high temporal resolution (in the order of microseconds), very high dynamic range (140 dB vs. 60 dB), low power consumption, and high pixel bandwidth (on the order of kHz) resulting in reduced motion blur. Hence, event cameras have a large potential for robotics and computer vision in challenging scenarios for traditional cameras, such as low-latency, high speed, and high dynamic range. However, novel methods are required to process the unconventional output of these sensors in order to unlock their potential. This paper provides a comprehensive overview of the emerging field of event-based vision, with a focus on the applications and the algorithms developed to unlock the outstanding properties of event cameras. We present event cameras from their working principle, the actual sensors that are available and the tasks that they have been used for, from low-level vision (feature detection and tracking, optic flow, etc.) to high-level vision (reconstruction, segmentation, recognition). We also discuss the techniques developed to process events, including learning-based techniques, as well as specialized processors for these novel sensors, such as spiking neural networks. Additionally, we highlight the challenges that remain to be tackled and the opportunities that lie ahead in the search for a more efficient, bio-inspired way for machines to perceive and interact with the world.

Binbin Xu, Wenbin Li, Dimos Tzoumanikas et al.

We propose a new multi-instance dynamic RGB-D SLAM system using an object-level octree-based volumetric representation. It can provide robust camera tracking in dynamic environments and at the same time, continuously estimate geometric, semantic, and motion properties for arbitrary objects in the scene. For each incoming frame, we perform instance segmentation to detect objects and refine mask boundaries using geometric and motion information. Meanwhile, we estimate the pose of each existing moving object using an object-oriented tracking method and robustly track the camera pose against the static scene. Based on the estimated camera pose and object poses, we associate segmented masks with existing models and incrementally fuse corresponding colour, depth, semantic, and foreground object probabilities into each object model. In contrast to existing approaches, our system is the first system to generate an object-level dynamic volumetric map from a single RGB-D camera, which can be used directly for robotic tasks. Our method can run at 2-3 Hz on a CPU, excluding the instance segmentation part. We demonstrate its effectiveness by quantitatively and qualitatively testing it on both synthetic and real-world sequences.

Jan Czarnowski, Stefan Leutenegger, Andrew Davison

We argue that robust dense SLAM systems can make valuable use of the layers of features coming from a standard CNN as a pyramid of `semantic texture' which is suitable for dense alignment while being much more robust to nuisance factors such as lighting than raw RGB values. We use a straightforward Lucas-Kanade formulation of image alignment, with a schedule of iterations over the coarse-to-fine levels of a pyramid, and simply replace the usual image pyramid by the hierarchy of convolutional feature maps from a pre-trained CNN. The resulting dense alignment performance is much more robust to lighting and other variations, as we show by camera rotation tracking experiments on time-lapse sequences captured over many hours. Looking towards the future of scene representation for real-time visual SLAM, we further demonstrate that a selection using simple criteria of a small number of the total set of features output by a CNN gives just as accurate but much more efficient tracking performance.

John McCormac, Ankur Handa, Andrew Davison et al.

Ever more robust, accurate and detailed mapping using visual sensing has proven to be an enabling factor for mobile robots across a wide variety of applications. For the next level of robot intelligence and intuitive user interaction, maps need extend beyond geometry and appearence - they need to contain semantics. We address this challenge by combining Convolutional Neural Networks (CNNs) and a state of the art dense Simultaneous Localisation and Mapping (SLAM) system, ElasticFusion, which provides long-term dense correspondence between frames of indoor RGB-D video even during loopy scanning trajectories. These correspondences allow the CNN's semantic predictions from multiple view points to be probabilistically fused into a map. This not only produces a useful semantic 3D map, but we also show on the NYUv2 dataset that fusing multiple predictions leads to an improvement even in the 2D semantic labelling over baseline single frame predictions. We also show that for a smaller reconstruction dataset with larger variation in prediction viewpoint, the improvement over single frame segmentation increases. Our system is efficient enough to allow real-time interactive use at frame-rates of approximately 25Hz.

Ankur Handa, Michael Bloesch, Viorica Patraucean et al.

We introduce gvnn, a neural network library in Torch aimed towards bridging the gap between classic geometric computer vision and deep learning. Inspired by the recent success of Spatial Transformer Networks, we propose several new layers which are often used as parametric transformations on the data in geometric computer vision. These layers can be inserted within a neural network much in the spirit of the original spatial transformers and allow backpropagation to enable end-to-end learning of a network involving any domain knowledge in geometric computer vision. This opens up applications in learning invariance to 3D geometric transformation for place recognition, end-to-end visual odometry, depth estimation and unsupervised learning through warping with a parametric transformation for image reconstruction error.

Michael Milford, Hanme Kim, Michael Mangan et al.

Event-based cameras offer much potential to the fields of robotics and computer vision, in part due to their large dynamic range and extremely high "frame rates". These attributes make them, at least in theory, particularly suitable for enabling tasks like navigation and mapping on high speed robotic platforms under challenging lighting conditions, a task which has been particularly challenging for traditional algorithms and camera sensors. Before these tasks become feasible however, progress must be made towards adapting and innovating current RGB-camera-based algorithms to work with event-based cameras. In this paper we present ongoing research investigating two distinct approaches to incorporating event-based cameras for robotic navigation: the investigation of suitable place recognition / loop closure techniques, and the development of efficient neural implementations of place recognition techniques that enable the possibility of place recognition using event-based cameras at very high frame rates using neuromorphic computing hardware.