arXiv subjects

Henry Moss

Publications and source records attributed to Henry Moss.

At least 19 recordsLinked to original sources

arXiv2026

Conditioning Gaussian Processes on Almost Anything

Gaussian processes (GPs) offer a principled probabilistic model over functions, but exact inference is restricted to the linear-Gaussian regime. We establish an explicit equivalence between GPs and a class of linear diffusion models, recasting predictive sampling as an ODE with closed-form Gaussian dynamics and a likelihood-dependent guidance term that admits a simple Monte Carlo approximation. In the linear-Gaussian setting, we recover standard GP conditioning exactly; beyond conjugacy, the same machinery handles any conditioning statement admitting point-wise likelihood evaluation - including non-linear physics, and, for the first time, natural language via large language models. Whitening isolates the irreducible non-Gaussian dynamics, minimising Wasserstein-2 transport cost and eliminating numerical stiffness. The result is a general-purpose GP inference scheme requiring no bespoke derivations. Together, these results provide a general mechanism for incorporating the full richness of real-world knowledge as conditioning information, opening a new frontier for the probabilistic modelling of real-world problems.

stat.ML↗

arXiv2026

SABLE: Scalable Affine Bayesian Latent-space Exploration

Complex objects such as engineering designs and proteins are often difficult to optimise because their design spaces exhibit high-dimensional structure and objective evaluations are expensive. Generative models provide continuous latent representations, but their latent spaces can have thousands to tens of thousands of dimensions, creating a regime where the latent dimension $D$ greatly exceeds the evaluation budget. We introduce SABLE, a Bayesian optimisation method for high-dimensional latent spaces with an isotropic distribution and limited budget. SABLE uses a Bayesian affine surrogate for prediction and acquisition, treating higher-order structure as surrogate discrepancy. After $N$ observations, the slope update has dimension at most $N-1$, yielding a decomposition of each query into an in-span component optimised by expected improvement (EI) in at most $N$ dimensions and an off-span component governed by a scalar norm. We show that the off-span norm implicitly selected by affine EI can lead to underexploration, and SABLE instead prescribes it using a finite-horizon schedule, without restricting search to a learned subspace. A recompression scheme reduces information to $\mathcal O(M)$ pseudo-observations, bounding refitting cost by $\mathcal O(M^2D+M^3)$ while keeping parameter inference, prediction, and acquisition decisions to tens of milliseconds. Across synthetic benchmarks and latent-space optimisation tasks, SABLE achieves high sample efficiency and reduces decision time by several orders of magnitude at large budgets.

cs.LG↗

arXiv2026

Fast Bayesian Optimization Through Linear Models

Bayesian optimization (BO) is typically used only for problems where the underlying function is deemed "expensive" (e.g. in time or money), with the speed of the BO algorithm being of little importance. In the real world, however, problems span a continuous range of values, going from cheap to expensive. In this paper, we present BO algorithms through the lens of a speed-performance Pareto frontier: we compare BO against faster algorithms like CMA-ES, and highlight how certain regions of the Pareto frontier are currently empty. As a solution, we propose a new set of fast BO methods that exploit the linear structure in existing BO algorithms, for both continuous and combinatorial inputs (from ~10 to 6000+ dimensions). Our methods achieve performance similar to state-of-the-art BO, while being more than $10^2\times$ to $10^3\times$ faster, opening the field of BO to an entirely new class of problems.

cs.LG↗

arXiv2026

Acquisition Function-Guided Generation for Bayesian Optimization over Discrete Spaces

Bayesian optimization (BO) over discrete spaces is challenging due to missing gradients and the sparsity of valid solutions. Latent-space BO sidesteps both issues by fitting a surrogate in the latent space of a generative model, which however substantially complicates the direct incorporation of domain knowledge that is naturally expressed in the original discrete space. In this work, we instead combine a pretrained generative model with a surrogate defined directly in data space, where inductive biases such as domain-specific kernels can be readily incorporated. Rather than maximizing the acquisition function over the discrete design space, our method samples candidates from the generative model under a distribution tilted by the acquisition function. To recover useful gradients for sampling, we embed this tilted distribution into a diffusion bridge that yields a smooth, posterior-averaged acquisition function. This leads to \emph{acquisition function guided generation} (AFGG), which we instantiate with a categorical diffusion model and an autoregressive normalizing flow. Across a broad suite of molecular benchmarks, the diffusion model variant performs on par with leading BO methods, while the flow model variant outperforms state-of-the-art methods in most cases and remains highly competitive otherwise. Our implementation is available at https://anonymous.4open.science/r/afgg.

cs.LG↗

arXiv2026

Generative Models as Adaptive Trust Regions for Discrete Bayesian Optimisation

Bayesian optimisation (BO) is a powerful framework for sample-efficient optimisation of expensive black-box functions, but its application to high-dimensional discrete scientific design remains challenging. Local trust-region BO methods such as TuRBO address high dimensionality by restricting search to adaptively sized neighbourhoods. However, a direct discrete analogue based on edit distance can be poorly suited to structured discrete objects: neighbourhoods grow combinatorially, and metric proximity does not capture the dependencies that determine whether a design is plausible or useful. Motivated by the growing availability of pretrained generative models, we introduce GenTuRBO, which replaces the geometric trust region with an adaptively scaled proposal distribution defined by a pretrained generator. The generator provides a learned prior over discrete transformations, encoding coordinated changes without explicitly enumerating edit-distance neighbourhoods. GenTuRBO performs strongly across all three domains and achieves the highest mean final scores on Ehrlich sequence optimisation and Sokoban coordination.

cs.LG↗

arXiv2026

A Critical Look at Power Sampling when Test Time Sharpening LLMs

Reinforcement learning with verifiable rewards (RLVR) has substantially improved LLM reasoning, yet growing evidence suggests it mainly performs distribution sharpening: concentrating probability mass on reasoning paths the base model already produces. Recent work therefore seeks RLVR's gains without needing reward signals, by sampling from the power distribution $π_α\propto π_{\text{base}}^α$ via Markov chain Monte Carlo or sequential Monte Carlo. We show that these samplers fail to converge to $π_α$ under realistic compute budgets, and that their gains are largely recreated via simple Best-of-$N$ with appropriate grading . This suggests they succeed by selecting high-probability sequences, not by approximating $π_α$, raising a natural question: is the power distribution itself a worthwhile target? We test this hypothesis directly by fine-tuning the base model to match $π_α$, sidestepping sampler convergence issues entirely. Despite approximating the target far more faithfully than existing samplers, this strategy yields gains that are noisy and specific to certain models and sampling tasks. Together, our results suggest that the value of power sampling lies not in faithfully targeting $π_α$, but in the simpler goal of extracting sequences the base model already deems likely.

stat.ML↗

arXiv2026

Feature Space Adaptation for Effortless Gaussian Process Flows

Outside the linear-Gaussian regime, conditional sampling from Gaussian processes (GPs) is challenging. Recent methods such as FlowGP (Moss et al., (2026)) can condition on arbitrary non-linear and non-Gaussian statements, but at considerable cost: an expensive iterative and high-dimensional diffusion that requires hand-specified kernel hyperparameters. In this paper, we alleviate two significant drawbacks of FlowGP by (1) introducing kernel approximations that enable scaling to high-resolution domains and (2) proposing a way to obtain the marginal likelihood by measuring the work needed to steer the diffusion towards conditioning statements. We enable, for the first time, hyperparameter optimisation within FlowGP and demonstrate our approach on probabilistic downscaling from areal summary statistics, PDE solution inference on irregular domains, and recovery of sea level anomaly fields from non-Gaussian satellite observations.

stat.ML↗

arXiv2026

$C_4$-Equivariant Flow Matching on Anisotropic Power-Diagram Graphs for Microstructure Generation

Acquiring realistic microstructure data through Electron Backscatter Diffraction (EBSD) is costly and time consuming, often relying on specialised equipment. As microstructures strongly influence material properties, generating realistic samples is essential for modelling the behaviour of polycrystalline materials. We introduce a generative model for synthesising realistic polycrystalline microstructures using flow matching and graph neural networks. By representing microstructures as anisotropic power diagrams, our model learns a compact geometric parametrisation and can render generated samples at arbitrary pixel resolution. A $C_4$-equivariant architecture incorporates rotational symmetry directly into the model, ensuring that rotations of the input noise produce corresponding rotations of the generated microstructure. We also demonstrate how training-free guidance can be used to generate complex microstructures, based on user defined objective function. In particular, we generate microstructures resembling a copper weld, cast metal slab, 3D-printed stainless steel and heterogeneous lamella titanium.

cs.LG↗

arXiv2026

Don't Get Your Kroneckers in a Twist: Gaussian Processes on High-Dimensional Incomplete Grids

We introduce CUTS-GPR, a new method for performing numerically exact GPR in high-dimensional settings. The key component of CUTS-GPR is an extremely fast kernel matrix-vector product, which exhibits near-linear or even linear scaling with the amount of training data, $N$, and low-order polynomial scaling with dimensionality, $D$. This is obtained by combining an additive kernel with an incomplete grid and exploiting the resulting structure of the kernel matrix. The scalability of the matrix-vector product is verified by benchmarks with billions of data points and thousands of dimensions. We demonstrate the end-to-end scalability of CUTS-GPR by running full GPR calculations, including hyperparameter optimization, on synthetic datasets with up to $N = 4\,494\,001$ and $D = 500$. As a realistic and challenging test, we finally apply CUTS-GPR to a set of ten potential energy surfaces (PESs) with $N = 447\,265$ and $D = 24$. The calculations are completed in a matter of hours, showing that CUTS-GPR enables Bayesian modelling of high-dimensional PESs - a longstanding challenge in computational chemistry.

cs.LG↗

arXiv2026

Search at the Cost of Sampling: Nearly-Instant Latent Space Bayesian Optimization

Generative models are increasingly central to many de novo discovery pipelines, in which designs are generated at scale and filtered through virtual screens to determine a set of candidates to experimentally validate. While Bayesian optimization (BO) is a natural fit for this setting, as it uses past evaluations to guide future proposals, the computational overhead required for its sequential decision-making becomes a bottleneck when virtual screens are relatively cheap. We make BO practical in this regime by exploiting the unique combination of a linear model constrained to a spherical domain where high-dimensional latents concentrate. We build off recent work justifying the use of linear surrogates, while deriving nearly closed-form solutions to the surrogate modelling and acquisition problems that exploit spherical symmetry. The result is at least a 100x speedup over state-of-the art baselines, with matching or improved performance across molecular and image generation benchmarks. Altogether, our method makes BO a practical drop-in for de novo pipelines where it was previously too slow to consider.

cs.LG↗

arXiv2026

Replacing Tunable Parameters in Weather and Climate Models with State-Dependent Functions using Reinforcement Learning

Weather and climate models rely on parametrisations to represent unresolved sub-grid processes. Traditional schemes rely on fixed coefficients that are weakly constrained and tuned offline, contributing to persistent biases that limit their ability to adapt to underlying physics. This study presents a framework that learns components of parametrisation schemes online as a function of the evolving model state using reinforcement learning (RL) and evaluates policy-driven parameter updates across idealised testbeds spanning a simple climate bias correction (SCBC), a radiative-convective equilibrium (RCE), and a zonal mean energy balance model (EBM) with single-agent and federated multi-agent settings. Across nine RL algorithms, Truncated Quantile Critics (TQC), Deep Deterministic Policy Gradient (DDPG), and Twin Delayed DDPG (TD3) achieved the highest skill and stable convergence, with performance assessed against a static baseline using area-weighted RMSE, temperature and pressure-level diagnostics. For the EBM, single-agent RL outperformed static parameter tuning with the strongest gains in tropical and mid-latitude bands, while federated RL on multi-agent setups enabled specialised control and faster convergence, with a six-agent DDPG configuration using frequent aggregation yielding the lowest area-weighted RMSE across the tropics and mid-latitudes. The learnt corrections were also physically meaningful as agents modulated EBM radiative parameters to reduce meridional biases, adjusted RCE lapse rates to match vertical temperature errors, and stabilised heating increments to limit drift. Overall, results show that RL can learn skilful state-dependent parametrisation components in idealised settings, offering a scalable pathway for online learning within numerical models and a starting point for evaluation in weather and climate models.

cs.LG↗

arXiv2026

How to Spend Your Oracle Budget: Practical Guidance for Protein Structure Prediction Models

Foundation models for protein structure prediction remain unreliable on certain targets. External oracles can flag and correct these failures, but biological oracles are expensive, making oracle budget a critical constraint. Existing guidance methods, such as FK-steering, DPO, and Best K-of-N sampling, differ in how they spend this budget, yet no systematic comparison exists to guide method selection. To bridge this gap, we benchmark these methods alongside the recently proposed Optimisation Over Outputs (O3), which applies off-the-shelf optimisers within a generative model's latent subspace. We extend the usage of O3 to protein structure prediction models. Overall, our work provides the first practical reference for oracle budget-aware guidance. Our evaluation on two protein targets, calmodulin (1CLL) and E. coli aspartate transcarbamoylase (9EEH), reveals that no single method consistently dominates across all budgets and oracles. Specifically, O3 proves most effective at low oracle budgets, while FK-steering and DPO demonstrate improved performance as the budget increases. We distil these findings into actionable recommendations for practitioners operating under real-world oracle-budget constraints.

cs.AI↗

arXiv2026

LatentFlow: A General Framework for Conditioning Stochastic Processes

Stochastic-process models are, as a rule, far easier to simulate than to condition. Non-linear observations, non-Gaussian likelihoods, black-box information, and global constraints all induce intractable conditional laws, requiring bespoke, model-specific constructions. We introduce LatentFlow, a single framework for conditioning stochastic processes, with no learned neural approximations and no training. Our starting point is to write the stochastic process as the deterministic image of a tractable latent innovation, $f_0 = T_{\vartheta}(ξ_0)$, with $ξ_0$ sampled from a simple reference distribution. This reduces process-level conditioning to latent-space inference: pull the likelihood back through $T_{\vartheta}$, sample the resulting latent law with a tractable guided probability flow, and push the samples forward. This construction is provably exact at the level of the target law; in practice, approximation enters only through finite terminal noising, Monte Carlo guidance, and time discretisation of the continuous-time dynamics, each of which is explicit and systematically reducible. As LatentFlow is training-free, conditioning reduces to solving a single reverse-time SDE. This enables conditional sampling in seconds on a single desktop CPU across model classes that have never shared a scalable method: classical spatial priors, nonlinear stochastic dynamics, mechanistic models from the physical and life sciences, stochastic PDEs, heavy-tails and extremes, point and discrete-state processes, and neural or simulator-defined processes.

stat.ML↗

arXiv2026

Dynamic Gaussian Processes and the Vanilla-SPDE Exchange

Gaussian process inference is often limited by cubic computational costs, a challenge that becomes more pronounced in spatio-temporal settings where posterior inference is required over dense grids. While state-space SPDE formulations enable linear complexity in time, exact inference remains cubic in space and deteriorates further when observation locations are disjoint from the prediction locations, which inflates the number of considered spatial points. To address this, we propose the Vanilla-SPDE Exchange, which exploits an equivalence between the standard and SPDE formulations of GP inference to construct a hybrid scheme with improved computational cost. We demonstrate these gains through complexity analysis and numerical experiments.

stat.ML↗

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

Active Learning for Gaussian Process Regression Under Self-Induced Boltzmann Weights

We consider the active learning problem where the goal is to learn an unknown function with low prediction error under an unknown Boltzmann distribution induced by the function itself. This self-induced weighting arises naturally in problems such as potential energy surface (PES) modeling in computational chemistry, yet poses unique challenges as the target distribution is unknown and its partition function is intractable. We propose \texttt{AB-SID-iVAR}, a Gaussian Process-based acquisition function that approximates the intractable Bayesian target distribution in closed form while avoiding partition function estimation, and is applicable to both discrete and continuous input domains. We also analyze a Thompson sampling alternative (\texttt{TS-SID-iVAR}) as a higher variance Monte Carlo variant. Despite the unknown target, under mild conditions, we establish that the terminal prediction error vanishes with high probability, and provide a tighter average-case guarantee. We demonstrate consistent improvements over existing approaches in this setting on synthetic benchmarks and real-world PES modeling and drug discovery tasks.

cs.LG↗

arXiv2026

We Still Don't Understand High-Dimensional Bayesian Optimization

Existing high-dimensional Bayesian optimization (BO) methods aim to overcome the curse of dimensionality by carefully encoding structural assumptions, from locality to sparsity to smoothness, into the optimization procedure. Surprisingly, we demonstrate that these approaches are outperformed by arguably the simplest method imaginable: Bayesian linear regression. After applying a geometric transformation to avoid boundary-seeking behavior, Gaussian processes with linear kernels match state-of-the-art performance on tasks with 60- to 6,000-dimensional search spaces. Linear models offer numerous advantages over their non-parametric counterparts: they afford closed-form sampling and their computation scales linearly with data, a fact we exploit on molecular optimization tasks with >20,000 observations. Coupled with empirical analyses, our results suggest the need to depart from past intuitions about BO methods in high-dimensions.

cs.LG↗

arXiv2025

RF-Squad: A radiofrequency simulator for quantum dot arrays

Spins in semiconductor quantum dots offer a scalable approach to quantum computing; however, precise control and efficient readout of large quantum dot arrays remain challenging, mainly due to the hyperdimensional voltage space required for tuning multiple gates per dot. To automate this process, large datasets are required for testing and training autotuning algorithms. To address the demand for such large datasets, we introduce RF-Squad, a physics-based simulator designed to realistically replicate radiofrequency (RF) reflectometry measurements of quantum dot arrays, with the ability to go beyond the Constant Interaction Model (CIM) and simulate physical phenomena such as tunnel coupling, tunnel rates, and quantum confinement. Implemented in JAX, an accelerated linear algebra library, RF-Squad achieves high computational speed, enabling the simulation of a 100x100 pixel charge stability diagram of a double quantum dot (DQD) in 52.1 $\pm$0.2 milliseconds at the CIM level. Using optimization algorithms, combined with it's layered architecture, RF-Squad allows users to balance physical accuracy with computational speed, scaling from simple to highly detailed models.

cond-mat.mes-hall↗