The performance of flow matching and diffusion models can be greatly improved at inference time using reward adaptation algorithms, yet efficiency remains a major limitation. While several algorithms were proposed, we demonstrate that a common bottleneck is the *sampling* method these algorithms rely on: many algorithms require to sample Markov transitions via SDE sampling, which is significantly less efficient and often less performant than ODE sampling. To remove this bottleneck, we introduce GLASS Flows, a new sampling paradigm that simulates a ''flow matching model within a flow matching model'' to sample Markov transitions. As we show in this work, this ''inner'' flow matching model can be retrieved from any pre-trained model without any re-training, effectively combining the efficiency of ODEs with the stochastic evolution of SDEs. On large-scale text-to-image models, we show that GLASS Flows eliminate the trade-off between stochastic evolution and efficiency. GLASS Flows improve state-of-the-art performance in text-to-image generation, making it a simple, drop-in solution for inference-time scaling of flow and diffusion models.

Flow and diffusion models produce high-quality samples, but adapting them to user preferences or constraints post-training remains costly and brittle, a challenge commonly called reward alignment. We argue that efficient reward alignment should be a property of the generative model itself, not an afterthought, and redesign the model for adaptability. We propose Diamond Maps, a stochastic flow-map model that enables efficient and accurate alignment to arbitrary rewards at inference time. Diamond Maps amortize many simulation steps into a single-step sampler, like flow maps, while preserving the stochasticity required for optimal reward adaptation. This design makes search, Sequential Monte Carlo, and guidance scalable by enabling efficient and consistent estimation of the value function. Our experiments show that Diamond Maps can be learned efficiently via distillation from GLASS Flows, achieve stronger reward-alignment performance, and scale better than existing alignment methods. Overall, our results point toward a practical route to generative models that can be rapidly adapted to arbitrary preferences and constraints at inference time.

We propose "LEAPS", an algorithm to sample from discrete distributions known up to normalization by learning a rate matrix of a continuous-time Markov chain (CTMC). LEAPS can be seen as a continuous-time formulation of annealed importance sampling and sequential Monte Carlo methods, extended so that the variance of the importance weights is offset by the inclusion of the CTMC. To derive these importance weights, we introduce a set of Radon-Nikodym derivatives of CTMCs over their path measures. Because the computation of these weights is intractable with standard neural network parameterizations of rate matrices, we devise a new compact representation for rate matrices via what we call "locally equivariant" functions. To parameterize them, we introduce a family of locally equivariant multilayer perceptrons, attention layers, and convolutional networks, and provide an approach to make deep networks that preserve the local equivariance. This property allows us to propose a scalable training algorithm for the rate matrix such that the variance of the importance weights associated to the CTMC are minimal. We demonstrate the efficacy of LEAPS on problems in statistical physics.

A major problem in the application of machine learning to neuroimaging is the technological variability of MRI scanners and differences in the subject populations across studies. Transfer learning (TL) attempts to alleviate this problem. TL refers to a family of methods which acquire knowledge from related tasks to improve generalization in the tasks of interest. In this work, we pre-train a deep neural network on UK Biobank MRI data on age and sex prediction, and study the predictions of the network on three small MRI data sets. We find that the neural networks can extract meaningful features from unseen data sets under the necessary but also sufficient condition that the network was pre-trained to predict the label of interest (e.g. pre-trained on age prediction if age prediction is the task of interest). Based on this, we propose a transfer learning pipeline which relies on the re-use of deep neural network features across data sets for the same tasks. We find that our method outperforms classical regression methods and training a network from scratch. In particular, we improve state-of-the-art results on age and sex prediction. Our transfer learning method may therefore provide a simple and efficient pipeline to achieve high performance on small MRI data sets. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This study was funded by the Rhodes Trust in support of Peter Holderrieth. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: The study used (or will use) ONLY openly available human data that were originally located at - http://www.ukbiobank.ac.uk - https://fcon_1000.projects.nitrc.org/indi/abide/ - https://brain-development.org/ixi-dataset/ - https://www.oasis-brains.org/ I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes All data produced are available online at - http://www.ukbiobank.ac.uk - https://fcon_1000.projects.nitrc.org/indi/abide/ - https://brain-development.org/ixi-dataset/ - https://www.oasis-brains.org/ <http://www.ukbiobank.ac.uk> <https://fcon_1000.projects.nitrc.org/indi/abide/> <https://brain-development.org/ixi-dataset/> <https://www.oasis-brains.org/>

AbstractA major problem in the application of machine learning to neuroimaging is the technological variability of MRI scanners and differences in the subject populations across studies. Transfer learning (TL) attempts to alleviate this problem. TL refers to a family of methods which acquire knowledge from related tasks to improve generalization in the tasks of interest. In this work, we pre-train a deep neural network on UK Biobank MRI data on age and sex prediction, and study the predictions of the network on three small MRI data sets. We find that the neural networks can extract meaningful features from unseen data sets under the necessary but also sufficient condition that the network was pre-trained to predict the label of interest (e.g. pre-trained on age prediction if age prediction is the task of interest). Based on this, we propose a transfer learning pipeline which relies on the re-use of deep neural network features across data sets for the same tasks. We find that our method outperforms classical regression methods and training a network from scratch. In particular, we improve state-of-the-art results on age and sex prediction. Our transfer learning method may therefore provide a simple and efficient pipeline to achieve high performance on small MRI data sets.

We show fundamental properties of the Markov semigroup of recently proposed MCMC algorithms based on Piecewise-deterministic Markov processes (PDMPs) such as the Bouncy Particle Sampler, the Zig-Zag process or the Randomized Hamiltonian Monte Carlo method. Under assumptions typically satisfied in MCMC settings, we prove that PDMPs are Feller and that their generator admits the space of infinitely differentiable functions with compact support as a core. As we illustrate via martingale problems and a simplified proof of the invariance of target distributions, these results provide a fundamental tool for the rigorous analysis of these algorithms and corresponding stochastic processes.

PURPOSE:Drug resistant epilepsy (DRE) affects approximately 30 percent of individuals with epilepsy worldwide. Surgery remains the most effective treatment for individuals with DRE, but referral to surgery is low and only about 60 percent of individuals who undergo surgery experience seizure control postoperatively. The present paper evaluates the evidence for using computational models in the prediction of surgical resection sites and surgical outcomes for patients with DRE.METHODS:We conducted a search in the Medline data base using the terms "refractory epilepsy", "drug-resistant epilepsy", "surgery", "computational model", and "artificial intelligence". Inclusion: original articles in English and case reports from 2000 to 2020. Reviews were excluded.RESULTS:Clinical applications of computational models may lead to increased utilisation of surgical services through improving our ability to predict outcomes and by improving surgical outcomes outright. The identification and optimisation of nodes that are crucial for the genesis and propagation of epileptiform activity offers the most promising clinical applications of computational models discussed herein.CONCLUSION:Advances in computational models may in the future significantly increase the application and efficacy of surgery for patients with DRE by optimising the site and amount of cortex to resect, but more research is needed before it achieves therapeutic utility.

We demonstrate that after pre-training a deep neural network using the big UK Biobank neuroimaging dataset, the model can be transferred to new datasets via a simple transfer learning framework, and achieve state-of-the-art results in brain age prediction in different small datasets. Compared to models trained from scratch, we found that the performance gain in transfer learning comes from feature re-usage, and relies on the similarity of population distribution and the task. Our results show that simple transfer learning can help apply deep learning for future neuroimaging studies even for small numbers of subjects.

Motivated by objects such as electric fields or fluid streams, we study the problem of learning stochastic fields, i.e. stochastic processes whose samples are fields like those occurring in physics and engineering. Considering general transformations such as rotations and reflections, we show that spatial invariance of stochastic fields requires an inference model to be equivariant. Leveraging recent advances from the equivariance literature, we study equivariance in two classes of models. Firstly, we fully characterise equivariant Gaussian processes. Secondly, we introduce Steerable Conditional Neural Processes (SteerCNPs), a new, fully equivariant member of the Neural Process family. In experiments with Gaussian process vector fields, images, and real-world weather data, we observe that SteerCNPs significantly improve the performance of previous models and equivariance leads to improvements in transfer learning tasks.

We introduce Equivariant Conditional Neural Processes (EquivCNPs), a new member of the Neural Process family that models vector-valued data in an equivariant manner with respect to isometries of $\mathbb{R}^n$. In addition, we look at multi-dimensional Gaussian Processes (GPs) under the perspective of equivariance and find the sufficient and necessary constraints to ensure a GP over $\mathbb{R}^n$ is equivariant. We test EquivCNPs on the inference of vector fields using Gaussian process samples and real-world weather data. We observe that our model significantly improves the performance of previous models. By imposing equivariance as constraints, the parameter and data efficiency of these models are increased. Moreover, we find that EquivCNPs are more robust against overfitting to local conditions of the training data.