Erik Bodin

Erik Bodin, Alexandru Stere, Dragos D. Margineantu et al.

Sampling from generative models has become a crucial tool for applications like data synthesis and augmentation. Diffusion, Flow Matching and Continuous Normalising Flows have shown effectiveness across various modalities, and rely on latent variables for generation. For experimental design or creative applications that require more control over the generation process, it has become common to manipulate the latent variable directly. However, existing approaches for performing such manipulations (e.g. interpolation or forming low-dimensional representations) only work well in special cases or are network or data-modality specific. We propose Latent Optimal Linear combinations (LOL) as a general-purpose method to form linear combinations of latent variables that adhere to the assumptions of the generative model. As LOL is easy to implement and naturally addresses the broader task of forming any linear combinations, e.g. the construction of subspaces of the latent space, LOL dramatically simplifies the creation of expressive low-dimensional representations of high-dimensional objects.

Samuel Willis, Alexandru I. Stere, Dragos D. Margineantu et al.

Modern generative AI models such as diffusion and flow matching can sample from rich data distributions, but many downstream tasks -- such as experimental design or creative content generation -- require a higher level of control than unconstrained sampling. The challenge is to efficiently identify outputs that are both probable under the model and satisfy task-specific constraints. We address this by introducing surrogate latent spaces: non-parametric, low-dimensional Euclidean embeddings that can be extracted from any generative model without additional training. The axes in the Euclidean space can be defined via examples, providing a simple and interpretable approach to define custom latent spaces that both express intended features and are convenient to use in downstream tasks. The representation is Euclidean and has controllable dimensionality, permitting direct application of standard optimisation algorithms to traverse the outputs of generative models. Our approach is architecture-agnostic, incurs almost no additional computational cost, and generalises across modalities, including images, audio, videos, and structured objects like proteins.

Erik Bodin, Federico Tomasi, Zhenwen Dai

Neural architecture search (NAS) is a recent methodology for automating the design of neural network architectures. Differentiable neural architecture search (DARTS) is a promising NAS approach that dramatically increases search efficiency. However, it has been shown to suffer from performance collapse, where the search often leads to detrimental architectures. Many recent works try to address this issue of DARTS by identifying indicators for early stopping, regularising the search objective to reduce the dominance of some operations, or changing the parameterisation of the search problem. In this work, we hypothesise that performance collapses can arise from poor local optima around typical initial architectures and weights. We address this issue by developing a more global optimisation scheme that is able to better explore the space without changing the DARTS problem formulation. Our experiments show that our changes in the search algorithm allow the discovery of architectures with both better test performance and fewer parameters.

Erik Bodin, Zhenwen Dai, Neill D. F. Campbell et al.

We present a novel approach to Bayesian inference and general Bayesian computation that is defined through a sequential decision loop. Our method defines a recursive partitioning of the sample space. It neither relies on gradients nor requires any problem-specific tuning, and is asymptotically exact for any density function with a bounded domain. The output is an approximation to the whole density function including the normalisation constant, via partitions organised in efficient data structures. Such approximations may be used for evidence estimation or fast posterior sampling, but also as building blocks to treat a larger class of estimation problems. The algorithm shows competitive performance to recent state-of-the-art methods on synthetic and real-world problems including parameter inference for gravitational-wave physics.

Ivan Ustyuzhaninov, Ieva Kazlauskaite, Markus Kaiser et al.

Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a posterior distribution of compositions of multiple functions giving rise to the observations. However, exact Bayesian inference is intractable for DGPs, motivating the use of various approximations. We show that the application of simplifying mean-field assumptions across the hierarchy leads to the layers of a DGP collapsing to near-deterministic transformations. We argue that such an inference scheme is suboptimal, not taking advantage of the potential of the model to discover the compositional structure in the data. To address this issue, we examine alternative variational inference schemes allowing for dependencies across different layers and discuss their advantages and limitations.

Erik Bodin, Markus Kaiser, Ieva Kazlauskaite et al.

Bayesian optimization (BO) methods often rely on the assumption that the objective function is well-behaved, but in practice, this is seldom true for real-world objectives even if noise-free observations can be collected. Common approaches, which try to model the objective as precisely as possible, often fail to make progress by spending too many evaluations modeling irrelevant details. We address this issue by proposing surrogate models that focus on the well-behaved structure in the objective function, which is informative for search, while ignoring detrimental structure that is challenging to model from few observations. First, we demonstrate that surrogate models with appropriate noise distributions can absorb challenging structures in the objective function by treating them as irreducible uncertainty. Secondly, we show that a latent Gaussian process is an excellent surrogate for this purpose, comparing with Gaussian processes with standard noise distributions. We perform numerous experiments on a range of BO benchmarks and find that our approach improves reliability and performance when faced with challenging objective functions.

Alessandro Di Martino, Erik Bodin, Carl Henrik Ek et al.

The shape of an object is an important characteristic for many vision problems such as segmentation, detection and tracking. Being independent of appearance, it is possible to generalize to a large range of objects from only small amounts of data. However, shapes represented as silhouette images are challenging to model due to complicated likelihood functions leading to intractable posteriors. In this paper we present a generative model of shapes which provides a low dimensional latent encoding which importantly resides on a smooth manifold with respect to the silhouette images. The proposed model propagates uncertainty in a principled manner allowing it to learn from small amounts of data and providing predictions with associated uncertainty. We provide experiments that show how our proposed model provides favorable quantitative results compared with the state-of-the-art while simultaneously providing a representation that resides on a low-dimensional interpretable manifold.

Erik Bodin, Iman Malik, Carl Henrik Ek et al.

We would like to learn latent representations that are low-dimensional and highly interpretable. A model that has these characteristics is the Gaussian Process Latent Variable Model. The benefits and negative of the GP-LVM are complementary to the Variational Autoencoder, the former provides interpretable low-dimensional latent representations while the latter is able to handle large amounts of data and can use non-Gaussian likelihoods. Our inspiration for this paper is to marry these two approaches and reap the benefits of both. In order to do so we will introduce a novel approximate inference scheme inspired by the GP-LVM and the VAE. We show experimentally that the approximation allows the capacity of the generative bottle-neck (Z) of the VAE to be arbitrarily large without losing a highly interpretable representation, allowing reconstruction quality to be unlimited by Z at the same time as a low-dimensional space can be used to perform ancestral sampling from as well as a means to reason about the embedded data.

Erik Bodin, Neill D. F. Campbell, Carl Henrik Ek

We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a latent variable that is used to modulate the covariance function over the training data. We show how our approach can be used to model multi-modal and non-stationary processes. We exemplify the approach on a set of synthetic data and provide results on real data from motion capture and geostatistics.