arXiv subjects

Carl Henrik Ek

Publications and source records attributed to Carl Henrik Ek.

At least 19 recordsLinked to original sources

arXiv2026

Sample-Efficient Optimisation over the Outputs of Generative Models

Modern generative AI models, such as diffusion and flow matching models, can sample from rich data distributions. However, many applications, especially in science and engineering, require more than drawing samples from the model distribution: they require searching within this distribution for samples that optimise task-specific criteria. In this work, we propose O3 (Optimisation Over the Outputs of Generative Models), a method for sample-efficient black-box optimisation over continuous-variable diffusion and flow-matching models. O3 is built around surrogate latent spaces: low-dimensional Euclidean embeddings that can be extracted from a generative model without additional training. The resulting representations have controllable dimensionality and support the direct application of standard optimisation algorithms. We show, on image and protein design tasks, that surrogate-space optimisation finds substantially higher-scoring samples than standard sampling or optimisation in the original latent space. Our method is model- and optimiser-agnostic, incurs negligible additional cost over standard generation, and requires no retraining or fine-tuning of the generative model.

stat.ML↗

arXiv2026

Discovering mathematical concepts through a multi-agent system

Mathematical concepts emerge through an interplay of processes, including experimentation, efforts at proof, and counterexamples. In this paper, we present a new multi-agent model for computational mathematical discovery based on this observation. Our system, conceived with research in mind, poses its own conjectures and then attempts to prove them, making decisions informed by this feedback and an evolving data distribution. Inspired by the history of Euler's conjecture for polyhedra and an open challenge in the literature, we benchmark with the task of autonomously recovering the concept of homology from polyhedral data and knowledge of linear algebra. Our system completes this learning problem. Most importantly, the experiments are ablations, statistically testing the value of the complete dynamic and controlling for experimental setup. They support our main claim: that the optimisation of the right combination of local processes can lead to surprisingly well-aligned notions of mathematical interestingness.

cs.AI↗

arXiv2026

Calabi-Yau metrics through Grassmannian learning and Donaldson's algorithm

Motivated by recent progress in the problem of numerical Kähler metrics, we survey machine learning techniques in this area, discussing both advantages and drawbacks. We then revisit the algebraic ansatz pioneered by Donaldson. Inspired by his work, we present a novel approach to obtaining Ricci-flat approximations to Kähler metrics, applying machine learning within a `principled' framework. In particular, we use gradient descent on the Grassmannian manifold to identify an efficient subspace of sections for calculation of the metric. We combine this approach with both Donaldson's algorithm and learning on the $h$-matrix itself (the latter method being equivalent to gradient descent on the fibre bundle of Hermitian metrics on the tautological bundle over the Grassmannian). We implement our methods on the Dwork family of threefolds, commenting on the behaviour at different points in moduli space. In particular, we observe the emergence of nontrivial local minima as the moduli parameter is increased.

hep-th↗

arXiv2025

Linear combinations of latents in generative models: subspaces and beyond

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.

stat.ML↗

arXiv2025

VIKING: Deep variational inference with stochastic projections

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, and subpar calibration. Building upon recent work on reparametrizations of neural networks, we propose a simple variational family that considers two independent linear subspaces of the parameter space. These represent functional changes inside and outside the support of training data. This allows us to build a fully-correlated approximate posterior reflecting the overparametrization that tunes easy-to-interpret hyperparameters. We develop scalable numerical routines that maximize the associated evidence lower bound (ELBO) and sample from the approximate posterior. Empirically, we observe state-of-the-art performance across tasks, models, and datasets compared to a wide array of baseline methods. Our results show that approximate Bayesian inference applied to deep neural networks is far from a lost cause when constructing inference mechanisms that reflect the geometry of reparametrizations.

stat.ML↗

arXiv2025

No-Regret Thompson Sampling for Finite-Horizon Markov Decision Processes with Gaussian Processes

Thompson sampling (TS) is a powerful and widely used strategy for sequential decision-making, with applications ranging from Bayesian optimization to reinforcement learning (RL). Despite its success, the theoretical foundations of TS remain limited, particularly in settings with complex temporal structure such as RL. We address this gap by establishing no-regret guarantees for TS using models with Gaussian marginal distributions. Specifically, we consider TS in episodic RL with joint Gaussian process (GP) priors over rewards and transitions. We prove a regret bound of $\mathcal{\tilde{O}}(\sqrt{KHΓ(KH)})$ over $K$ episodes of horizon $H$, where $Γ(\cdot)$ captures the complexity of the GP model. Our analysis addresses several challenges, including the non-Gaussian nature of value functions and the recursive structure of Bellman updates, and extends classical tools such as the elliptical potential lemma to multi-output settings. This work advances the understanding of TS in RL and highlights how structural assumptions and model uncertainty shape its performance in finite-horizon Markov Decision Processes.

cs.LG↗

arXiv2025

Bayesian Nonparametric Dynamical Clustering of Time Series

We present a method that models the evolution of an unbounded number of time series clusters by switching among an unknown number of regimes with linear dynamics. We develop a Bayesian non-parametric approach using a hierarchical Dirichlet process as a prior on the parameters of a Switching Linear Dynamical System and a Gaussian process prior to model the statistical variations in amplitude and temporal alignment within each cluster. By modeling the evolution of time series patterns, the method avoids unnecessary proliferation of clusters in a principled manner. We perform inference by formulating a variational lower bound for off-line and on-line scenarios, enabling efficient learning through optimization. We illustrate the versatility and effectiveness of the approach through several case studies of electrocardiogram analysis using publicly available databases.

stat.ML↗

arXiv2025

Beyond Quantification: Navigating Uncertainty in Professional AI Systems

The growing integration of large language models across professional domains transforms how experts make critical decisions in healthcare, education, and law. While significant research effort focuses on getting these systems to communicate their outputs with probabilistic measures of reliability, many consequential forms of uncertainty in professional contexts resist such quantification. A physician pondering the appropriateness of documenting possible domestic abuse, a teacher assessing cultural sensitivity, or a mathematician distinguishing procedural from conceptual understanding face forms of uncertainty that cannot be reduced to percentages. This paper argues for moving beyond simple quantification toward richer expressions of uncertainty essential for beneficial AI integration. We propose participatory refinement processes through which professional communities collectively shape how different forms of uncertainty are communicated. Our approach acknowledges that uncertainty expression is a form of professional sense-making that requires collective development rather than algorithmic optimization.

cs.HC↗

arXiv2025

Learning from Preferences and Mixed Demonstrations in General Settings

Reinforcement learning is a general method for learning in sequential settings, but it can often be difficult to specify a good reward function when the task is complex. In these cases, preference feedback or expert demonstrations can be used instead. However, existing approaches utilising both together are often ad-hoc, rely on domain-specific properties, or won't scale. We develop a new framing for learning from human data, \emph{reward-rational partial orderings over observations}, designed to be flexible and scalable. Based on this we introduce a practical algorithm, LEOPARD: Learning Estimated Objectives from Preferences And Ranked Demonstrations. LEOPARD can learn from a broad range of data, including negative demonstrations, to efficiently learn reward functions across a wide range of domains. We find that when a limited amount of preference and demonstration feedback is available, LEOPARD outperforms existing baselines by a significant margin. Furthermore, we use LEOPARD to investigate learning from many types of feedback compared to just a single one, and find that combining feedback types is often beneficial.

cs.LG↗

arXiv2025

Efficient Model-Based Reinforcement Learning Through Optimistic Thompson Sampling

Learning complex robot behavior through interactions with the environment necessitates principled exploration. Effective strategies should prioritize exploring regions of the state-action space that maximize rewards, with optimistic exploration emerging as a promising direction aligned with this idea and enabling sample-efficient reinforcement learning. However, existing methods overlook a crucial aspect: the need for optimism to be informed by a belief connecting the reward and state. To address this, we propose a practical, theoretically grounded approach to optimistic exploration based on Thompson sampling. Our model structure is the first that allows for reasoning about joint uncertainty over transitions and rewards. We apply our method on a set of MuJoCo and VMAS continuous control tasks. Our experiments demonstrate that optimistic exploration significantly accelerates learning in environments with sparse rewards, action penalties, and difficult-to-explore regions. Furthermore, we provide insights into when optimism is beneficial and emphasize the critical role of model uncertainty in guiding exploration.

cs.LG↗

arXiv2025

Reparameterization invariance in approximate Bayesian inference

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 application of Bayesian principles as it breaks the correspondence between uncertainty over the parameters with uncertainty over the parametrized function. In this paper, we investigate this issue in the context of the increasingly popular linearized Laplace approximation. Specifically, it has been observed that linearized predictives alleviate the common underfitting problems of the Laplace approximation. We develop a new geometric view of reparametrizations from which we explain the success of linearization. Moreover, we demonstrate that these reparameterization invariance properties can be extended to the original neural network predictive using a Riemannian diffusion process giving a straightforward algorithm for approximate posterior sampling, which empirically improves posterior fit.

cs.LG↗

arXiv2024

Variance reduction of diffusion model's gradients with Taylor approximation-based control variate

Score-based models, trained with denoising score matching, are remarkably effective in generating high dimensional data. However, the high variance of their training objective hinders optimisation. We attempt to reduce it with a control variate, derived via a $k$-th order Taylor expansion on the training objective and its gradient. We prove an equivalence between the two and demonstrate empirically the effectiveness of our approach on a low dimensional problem setting; and study its effect on larger problems.

cs.LG↗

arXiv2023

Identifying latent distances with Finslerian geometry

Riemannian geometry provides us with powerful tools to explore the latent space of generative models while preserving the underlying structure of the data. The latent space can be equipped it with a Riemannian metric, pulled back from the data manifold. With this metric, we can systematically navigate the space relying on geodesics defined as the shortest curves between two points. Generative models are often stochastic, causing the data space, the Riemannian metric, and the geodesics, to be stochastic as well. Stochastic objects are at best impractical, and at worst impossible, to manipulate. A common solution is to approximate the stochastic pullback metric by its expectation. But the geodesics derived from this expected Riemannian metric do not correspond to the expected length-minimising curves. In this work, we propose another metric whose geodesics explicitly minimise the expected length of the pullback metric. We show this metric defines a Finsler metric, and we compare it with the expected Riemannian metric. In high dimensions, we prove that both metrics converge to each other at a rate of $O\left(\frac{1}{D}\right)$. This convergence implies that the established expected Riemannian metric is an accurate approximation of the theoretically more grounded Finsler metric. This provides justification for using the expected Riemannian metric for practical implementations.

cs.LG↗

arXiv2023

A locally time-invariant metric for climate model ensemble predictions of extreme risk

Adaptation-relevant predictions of climate change are often derived by combining climate model simulations in a multi-model ensemble. Model evaluation methods used in performance-based ensemble weighting schemes have limitations in the context of high-impact extreme events. We introduce a locally time-invariant method for evaluating climate model simulations with a focus on assessing the simulation of extremes. We explore the behaviour of the proposed method in predicting extreme heat days in Nairobi and provide comparative results for eight additional cities.

physics.ao-ph↗

arXiv2021

Deep Neural Networks as Point Estimates for Deep Gaussian Processes

Neural networks and Gaussian processes are complementary in their strengths and weaknesses. Having a better understanding of their relationship comes with the promise to make each method benefit from the strengths of the other. In this work, we establish an equivalence between the forward passes of neural networks and (deep) sparse Gaussian process models. The theory we develop is based on interpreting activation functions as interdomain inducing features through a rigorous analysis of the interplay between activation functions and kernels. This results in models that can either be seen as neural networks with improved uncertainty prediction or deep Gaussian processes with increased prediction accuracy. These claims are supported by experimental results on regression and classification datasets.

stat.ML↗

arXiv2021

Aligned Multi-Task Gaussian Process

Multi-task learning requires accurate identification of the correlations between tasks. In real-world time-series, tasks are rarely perfectly temporally aligned; traditional multi-task models do not account for this and subsequent errors in correlation estimation will result in poor predictive performance and uncertainty quantification. We introduce a method that automatically accounts for temporal misalignment in a unified generative model that improves predictive performance. Our method uses Gaussian processes (GPs) to model the correlations both within and between the tasks. Building on the previous work by Kazlauskaiteet al. [2019], we include a separate monotonic warp of the input data to model temporal misalignment. In contrast to previous work, we formulate a lower bound that accounts for uncertainty in both the estimates of the warping process and the underlying functions. Also, our new take on a monotonic stochastic process, with efficient path-wise sampling for the warp functions, allows us to perform full Bayesian inference in the model rather than MAP estimates. Missing data experiments, on synthetic and real time-series, demonstrate the advantages of accounting for misalignments (vs standard unaligned method) as well as modelling the uncertainty in the warping process(vs baseline MAP alignment approach).

stat.ML↗

arXiv2021

Black-box density function estimation using recursive partitioning

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.

stat.ML↗

arXiv2020

Modulating Surrogates for Bayesian Optimization

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.

stat.ML↗