34 accepted papers
The Schrödinger Bridge provides a principled framework for modeling stochastic processes between distributions; however, existing methods are limited by energy-conservation assumptions, which constrains the bridge's shape preventing it from model varying-energy phenomena. To overcome this, we introd…
Euclidean representations distort data with intrinsic non-Euclidean structure. While Riemannian representation learning offers a solution by embedding data onto matching manifolds, it typically relies on an encoder to estimate densities on chosen manifolds. This involves optimizing numerically britt…
We present a novel geometric perspective on the latent space of diffusion models. We first show that the standard pullback approach, utilizing the deterministic probability flow ODE decoder, is fundamentally flawed. It provably forces geodesics to decode as straight segments in data space, effective…
Bayesian deep learning all too often underfits so that the Bayesian prediction is less accurate than a simple point estimate. Uncertainty quantification then comes at the cost of accuracy. For linearized models, the null space of the generalized Gauss-Newton matrix corresponds to parameters that pre…
Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different representations, even when learning the same task on the same dat…
Accurately modeling and predicting complex dynamical systems, particularly those involving force exchange and dissipation, is crucial for applications ranging from fluid dynamics to robotics, but presents significant challenges due to the intricate interplay of geometric constraints and energy trans…
Deep latent variable models learn condensed representations of data that, hopefully, reflect the inner workings of the studied phenomena. Unfortunately, these latent representations are not statistically identifiable, meaning they cannot be uniquely determined. Domain experts, therefore, need to tre…
Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches ignore the underlying geometric constraints or fail to provi…
Variational mean field approximations tend to struggle with contemporary overparametrized deep neural networks. Where a Bayesian treatment is usually associated with high-quality predictions and uncertainties, the practical reality has been the opposite, with unstable training, poor predictive power…
Optimizing discrete black-box functions is key in several domains, e.g. protein engineering and drug design. Due to the lack of gradient information and the need for sample efficiency, Bayesian optimization is an ideal candidate for these tasks. Several methods for high-dimensional continuous and ca…
Tuning scientific and probabilistic machine learning models - for example, partial differential equations, Gaussian processes, or Bayesian neural networks - often relies on evaluating functions of matrices whose size grows with the data set or the number of parameters. While the state-of-the-art for…
Generative models have shown strong generation ability while efficient likelihood estimation is less explored. Energy-based models (EBMs) define a flexible energy function to parameterize unnormalized densities efficiently but are notorious for being difficult to train. Adversarial EBMs introduce a…
Stability guarantees are crucial when ensuring that a fully autonomous robot does not take undesirable or potentially harmful actions. Unfortunately, global stability guarantees are hard to provide in dynamical systems learned from data, especially when the learned dynamics are governed by neural ne…
Current approximate posteriors in Bayesian neural networks (BNNs) exhibit a crucial limitation: they fail to maintain invariance under reparameterization, i.e. BNNs assign different posterior densities to different parametrizations of identical functions. This creates a fundamental flaw in the appli…
Current uncertainty quantification is memory and compute expensive, which hinders practical uptake. To counter, we develop Sketched Lanczos Uncertainty (SLU): an architecture-agnostic uncertainty score that can be applied to pre-trained neural networks with minimal overhead. Importantly, the memory…
We propose a Bayesian encoder for metric learning. Rather than relying on neural amortization as done in prior works, we learn a distribution over the network weights with the Laplace Approximation. We first prove that the contrastive loss is a negative log-likelihood on the spherical space. We prop…
We present WineSensed, a large multimodal wine dataset for studying the relations between visual perception, language, and flavor. The dataset encompasses 897k images of wine labels and 824k reviews of wines curated from the Vivino platform. It has over 350k unique bottlings, annotated with year, re…
Masked pre-training removes random input dimensions and learns a model that can predict the missing values. Empirical results indicate that this intuitive form of self-supervised learning yields models that generalize very well to new domains. A theoretical understanding is, however, lacking. This p…
Bayesian neural networks often approximate the weight-posterior with a Gaussian distribution. However, practical posteriors are often, even locally, highly non-Gaussian, and empirical performance deteriorates. We propose a simple parametric approximate posterior that adapts to the shape of the true…
Place recognition and visual localization are particularly challenging in wide baseline configurations. In this letter, we contribute with the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Danish Airs and Grounds</i> (DAG) dataset, a large collecti
Established methods for unsupervised representation learning such as variational autoencoders produce none or poorly calibrated uncertainty estimates making it difficult to evaluate if learned representations are stable and reliable. In this work, we present a Bayesian autoencoder for unsupervised r…
Spatial Transformer Networks (STNs) estimate image transformations that can improve downstream tasks by ‘zooming in’ on relevant regions in an image. However, STNs are hard to train and sensitive to mis-predictions of transformations. To circumvent these limitations, we propose a probabilistic exten…
Decoders built on Gaussian processes (GPs) are enticing due to the marginalisation over the non-linear function space. Such models (also known as GP-LVMs) are often expensive and notoriously difficult to train in practice, but can be scaled using variational inference and inducing points. In this pa…
Uncertainty quantification in image retrieval is crucial for downstream decisions, yet it remains a challenging and largely unexplored problem. Current methods for estimating uncertainties are poorly calibrated, computationally expensive, or based on heuristics. We present a new method that views im…
Energy-based models (EBMs) provide an elegant framework for density estimation, but they are notoriously difficult to train. Recent work has established links to generative adversarial networks, where the EBM is trained through a minimax game with a variational value function. We propose a bidirecti…
Deep generative models have been demonstrated as state-of-the-art density estimators. Yet, recent work has found that they often assign a higher likelihood to data from outside the training distribution. This seemingly paradoxical behavior has caused concerns over the quality of the attained density…
For robots to work alongside humans and perform in unstructured environments; they must learn new motion skills and adapt them to unseen situations on the fly. This demands learning models that capture relevant motion patterns; while offering enough flexibility to adapt the encoded skills to new req…
Disentangled representation learning finds compact, independent and easy-to-interpret factors of the data. Learning such has been shown to require an inductive bias, which we explicitly encode in a generative model of images. Specifically, we propose a model with two latent spaces: one that represen…
Latent variable models (LVMs) learn probabilistic models of data manifolds lying in an ambient Euclidean space. In a number of applications, a priori known spatial constraints can shrink the ambient space into a considerably smaller manifold. Additionally, in these applications the Euclidean geomet…
We propose and investigate new complementary methodologies for estimating predictive variance networks in regression neural networks. We derive a locally aware mini-batching scheme that results in sparse robust gradients, and we show how to make unbiased weight updates to a variance network. Further…
Spatial Transformer layers allow neural networks, at least in principle, to be invariant to large spatial transformations in image data. The model has, however, seen limited uptake as most practical implementations support only transformations that are too restricted, e.g. affine or homographic maps…
Deep generative models provide a systematic way to learn nonlinear data distributions through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator implies that the latent space gives a distorted view of the inp…
The multivariate normal density is a monotonic function of the distance to the mean, and its ellipsoidal shape is due to the underlying Euclidean metric. We suggest to replace this metric with a locally adaptive, smoothly changing (Riemannian) metric that favors regions of high local density. The re…
Data augmentation is a key element in training high-dimensional models. In this approach, one synthesizes new observations by applying pre-specified transformations to the original training data; e.g. new images are formed by rotating old ones. Current augmentation schemes, however, rely on ma…