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While the evaluation of multimodal English-centric models is an active area of research with numerous benchmarks, there is a profound lack of benchmarks or evaluation suites for low- and mid-resource languages. We introduce ZNO-Vision, a comprehensive multimodal Ukrainian-centric benchmark derived from standardized university entrance examination (ZNO). The benchmark consists of over 4,300 expert-crafted questions spanning 12 academic disciplines, including mathematics, physics, chemistry, and humanities. We evaluated the performance of both open-source models and API providers, finding that only a handful of models performed above baseline. Alongside the new benchmark, we performed the first evaluation study of multimodal text generation for the Ukrainian language: we measured caption generation quality on the Multi30K-UK dataset, translated the VQA benchmark into Ukrainian, and measured performance degradation relative to original English versions. Lastly, we tested a few models from a cultural perspective on knowledge of national cuisine. We believe our work will advance multimodal generation capabilities for the Ukrainian language and our approach could be useful for other low-resource languages.

This study investigates gender bias in large language models (LLMs) by comparing their gender perception to that of human respondents, U.S. Bureau of Labor Statistics data, and a 50% no-bias benchmark. We created a new evaluation set using occupational data and role-specific sentences. Unlike common benchmarks included in LLM training data, our set is newly developed, preventing data leakage and test set contamination. Five LLMs were tested to predict the gender for each role using single-word answers. We used Kullback-Leibler (KL) divergence to compare model outputs with human perceptions, statistical data, and the 50% neutrality benchmark. All LLMs showed significant deviation from gender neutrality and aligned more with statistical data, still reflecting inherent biases., Comment: under review for Coling conference

We consider the problem of designing typed concurrent calculi with non-deterministic choice in which types leverage linearity for controlling resources, thereby ensuring strong correctness properties for processes. This problem is constrained by the delicate tension between non-determinism and linearity. Prior work developed a session-typed {\pi}-calculus with standard non-deterministic choice; well-typed processes enjoy type preservation and deadlock-freedom. Central to this typed calculus is a lazy semantics that gradually discards branches in choices. This lazy semantics, however, is complex: various technical elements are needed to describe the non-deterministic behavior of typed processes. This paper develops an entirely new approach, based on an eager semantics, which more directly represents choices and commitment. We present a {\pi}-calculus in which non-deterministic choices are governed by this eager semantics and session types. We establish its key correctness properties, including deadlock-freedom, and demonstrate its expressivity by correctly translating a typed resource {\lambda}-calculus., Comment: Presented at MFPS 2024

Recent technological advances in healthcare have led to unprecedented growth in patient data quantity and diversity. While artificial intelligence (AI) models have shown promising results in analyzing individual data modalities, there is increasing recognition that models integrating multiple complementary data sources, so-called multimodal AI, could enhance clinical decision-making. This scoping review examines the landscape of deep learning-based multimodal AI applications across the medical domain, analyzing 432 papers published between 2018 and 2024. We provide an extensive overview of multimodal AI development across different medical disciplines, examining various architectural approaches, fusion strategies, and common application areas. Our analysis reveals that multimodal AI models consistently outperform their unimodal counterparts, with an average improvement of 6.2 percentage points in AUC. However, several challenges persist, including cross-departmental coordination, heterogeneous data characteristics, and incomplete datasets. We critically assess the technical and practical challenges in developing multimodal AI systems and discuss potential strategies for their clinical implementation, including a brief overview of commercially available multimodal AI models for clinical decision-making. Additionally, we identify key factors driving multimodal AI development and propose recommendations to accelerate the field's maturation. This review provides researchers and clinicians with a thorough understanding of the current state, challenges, and future directions of multimodal AI in medicine., Comment: 28 pages

This study investigates the spatial evolution of a zero pressure gradient turbulent boundary layer (TBL) imposed by a square-wave (SqW) of steady spanwise wall-forcing, which varies along the streamwise direction ($x$). The SqW wall-forcing is imposed experimentally via a series of streamwise periodic belts running in opposite spanwise directions, following the methodology of Knoop et al., (Exp Fluids, vol 65, 2024), with the streamwise extent increased to beyond $\sim 11$ times the boundary layer thickness (${\delta}_o$) in the present study. This unique setup is leveraged to investigate the influence of viscous-scaled wavelength of SqW wall-forcing on the turbulent drag reduction (DR) efficacy, for $\lambda^+_x = $ 471 (sub-optimal), 942 (near-optimal), and 1884 (post-optimal conditions), at fixed viscous-scaled wall-forcing amplitude, $A^+ = 12$, and friction Reynolds number, $Re_\tau = 960$. The DR mechanisms associated with SqW wall-forcing are elucidated by comparing against established DR mechanisms for traditionally studied sinusoidal forcing (SinW), based on analysis of the streamwise-phase variation of the Stokes strain rate (SSR). The analysis reveals SqW forcing to be a combination of two distinctly different/decoupled SSR states: (i) strong impulses of SSR at half- ($\lambda_x$/2) and full-phase ($\lambda_x$) locations associated with reversal in spanwise forcing directions leading to significant turbulence attenuation, and (ii) near-zero SSR over the remainder of forcing phase that enables turbulence recovery (when wall-forcing magnitudes and direction remain constant). While present experiments are limited to low Reynolds number TBLs, the results are extrapolated to depict a conceptual picture of SqW forcing efficacy in high Reynolds number TBLs (corresponding to a broader scale hierarchy).

In this paper we present a multi-criteria classification of Vocational and Educational Programs in Extremadura (Spain) during the period 2009-2016. This ranking has been carried out through the integration into a complete database of the detailed information of individuals finishing such studies together with their labor data. The multicriteria method used is TOPSIS together with a new decision support method for assessing the influence of each criterion and its dependence on the weights assigned to them. This new method is based on a worst-best case scenario analysis and it is compared to a well known global sensitivity analysis technique based on the Pearson's correlation ratio., Comment: 18 pages, 7 figures

Quantitative magnetic resonance imaging (qMRI) allows images to be compared across sites and time points, which is particularly important for assessing long-term conditions or for longitudinal studies. The multiparametric mapping (MPM) protocol is used to acquire images with conventional clinical contrasts, namely PD-, T1-, and MT-weighted volumes. Through multi-echo acquisition for each contrast and variations in flip angles between PD- and T1-weighted contrasts, parameter maps, such as proton density (PD), longitudinal relaxation rate (R1), apparent transverse relaxation rate (R2$^*$), and magnetization transfer saturation (MT$_{sat}$), can be estimated. Various algorithms have been employed to estimate these parameters from the acquired volumes. This paper extends an existing maximum a posteriori approach, which uses joint total variation regularization, by transitioning from a Gaussian noise approximation to a more physically plausible model that assumes noncentral chi-distributed noise.

We announce the release of EPT-1.5, the latest iteration in our Earth Physics Transformer (EPT) family of foundation AI earth system models. EPT-1.5 demonstrates substantial improvements over its predecessor, EPT-1. Built specifically for the European energy industry, EPT-1.5 shows remarkable performance in predicting energy-relevant variables, particularly 10m & 100m wind speed and solar radiation. Especially in wind prediction, it outperforms existing AI weather models like GraphCast, FuXi, and Pangu-Weather, as well as the leading numerical weather model, IFS HRES by the European Centre for Medium-Range Weather Forecasts (ECMWF), setting a new state of the art.

This paper introduces a novel approach that integrates future closest point predictions into the distance constraints of a collision avoidance controller, leveraging convex hulls with closest point distance calculations. By addressing abrupt shifts in closest points, this method effectively reduces collision risks and enhances controller performance. Applied to an Image Guided Therapy robot and validated through simulations and user experiments, the framework demonstrates improved distance prediction accuracy, smoother trajectories, and safer navigation near obstacles.

Fingerprints, otherwise known as dermatoglyphs, are most commonly thought of in the context of identification, but have myriad other roles in human biology. They are formed by the restricted ability of ridges and furrows of the epidermis to flatten. The patterns these ridges and furrows make can be represented as 2D fingerprints, but also as 3D structures with cross-sectional shapes that may add new levels of detail to identification, forensic, and behavioral uses/studies. Surface metrology techniques better allow for the quantification of these features, though it is unclear what tool and what scale is most appropriate. A Sensofar S Neox white light reflectance confocal microscope and a Gelsight Mobile 2 were used to independently measure the surface roughness of the fingerprints of four individuals from preserved cadaveric remains. Scale-sensitive fractal analyses (SSFA) were performed on the data from the S Neox (a small area), Gelsight (a larger area), and the same Gelsight datasets cropped down to the size of the S Neox scan size. Though fewer SSFA parameters identified differences between individuals from the smaller, extracted Gelsight area, all three forms of measurement found significant differences between some individuals from the study. No significant differences were found that differ between fingers themselves. Though only an initial step, these data suggest that a variety of surface metrology techniques may be useful in differentiating individuals., Comment: 20 pages, 5 figures

Fidelity estimation for entangled states constitutes an essential building block for quality control and error detection in quantum networks. Nonetheless, quantum networks often encounter heterogeneous and correlated noise, leading to excessive uncertainty in the estimated fidelity. In this paper, the uncertainty associated with the estimated fidelity under conditions of general noise is constrained by jointly employing random sampling, a thought experiment, and Bayesian inference, resulting in a credible interval for fidelity that is valid in the presence of general noise. The proposed credible interval incorporates all even moments of the posterior distribution to enhance estimation accuracy. Factors influencing the estimation accuracy are identified and analyzed. Specifically, the issue of excessive measurements is addressed, emphasizing the necessity of properly determining the measurement ratio for fidelity estimation under general noise conditions.

We obtain distribution-free bounds for various fundamental quantities used in probability theory by solving optimization problems that search for extreme distributions among all distributions with the same mean and dispersion. These sharpest possible bounds depend only on the mean and dispersion of the driving random variable. We solve the optimization problems by a novel yet elementary technique that reduces the set of all candidate solutions to two-point distributions. We consider a general dispersion measure, with variance, mean absolute deviation and power moments as special cases. We apply the bounds to robust newsvendor stocking and monopoly pricing, generalizing foundational mean-variance works. This shows how pricing and order decisions respond to increased demand uncertainty, including scenarios where dispersion information allows for heavy-tailed demand distributions.

Pulse profile modelling (PPM) is a technique for inferring mass, radius and hotspot properties of millisecond pulsars. PPM is now regularly used for analysis of rotation-powered millisecond pulsars (RMPs) with data from the Neutron Star Interior Composition ExploreR (NICER). Extending PPM to accreting millisecond pulsars (AMPs) is attractive, because they are a different source class featuring bright X-ray radiation from hotspots powered by accretion. In this paper, we present a modification of one of the PPM codes, X-PSI, so that it can be used for AMPs. In particular, we implement a model of an accretion disc and atmosphere model appropriate for the hotspots of AMPs, and improve the overall computational efficiency. We then test parameter recovery with synthetic NICER data in two scenarios with reasonable parameters for AMPs. We find in the first scenario, where the hotspot is large, that we are able to tightly and accurately constrain all parameters including mass and radius. In the second scenario, which is a high inclination system with a smaller hotspot, we find degeneracy between a subset of model parameters and a slight bias in the inferred mass and radius. This analysis of synthetic data lays the ground work for future analysis of AMPs with NICER data. Such an analysis could be complemented by future (joint) analysis of polarization data from the Imaging X-ray Polarimetry Explorer (IXPE)., Comment: 14 pages, 5 figures, 3 tables. Paper submitted to MNRAS

We construct the universal central extension of the Lie algebra of exact divergence-free vector fields, proving a conjecture by Claude Roger from 1995. The proof relies on the analysis of a Leibniz algebra that underlies these vector fields. As an application, we construct the universal central extension of the (infinite-dimensional) Lie group of exact divergence-free diffeomorphisms of a compact 3-dimensional manifold., Comment: 25 pages

Despite advancements in splicing detection, practitioners still struggle to fully leverage forensic tools from the literature due to a critical issue: deep learning-based detectors are extremely sensitive to their trained instances. Simple post-processing applied to evaluation images can easily decrease their performances, leading to a lack of confidence in splicing detectors for operational contexts. In this study, we show that a deep splicing detector behaves differently against unknown post-processes for different learned weights, even if it achieves similar performances on a test set from the same distribution as its training one. We connect this observation to the fact that different learnings create different latent spaces separating training samples differently. Our experiments reveal a strong correlation between the distributions of latent margins and the ability of the detector to generalize to post-processed images. We thus provide to the practitioner a way to build deep detectors that are more robust than others against post-processing operations, suggesting to train their architecture under different conditions and picking the one maximizing the latent space margin.

At the intersection of creative text generation and literary theory, this study explores the role of literary metaphor and its capacity to generate a range of meanings. In this regard, literary metaphor is vital to the development of any particular language. To investigate whether the inclusion of original figurative language improves textual quality, we trained an LSTM-based language model in Afrikaans. The network produces phrases containing compellingly novel figures of speech. Specifically, the emphasis falls on how AI might be utilised as a defamiliarisation technique, which disrupts expected uses of language to augment poetic expression. Providing a literary perspective on text generation, the paper raises thought-provoking questions on aesthetic value, interpretation and evaluation., Comment: Accepted as oral presentation to Workshop on Artificial Intelligence and Creativity (CREAI) at ECAI 2024

Given a JPEG pipeline (compression or decompression), this paper shows how to find the antecedent of a 8 x 8 block. If it exists, the block is compatible with the pipeline. For unaltered images, all blocks are always compatible with the original pipeline; however, for manipulated images, this is not always the case. This article demonstrates the potential of compatibility concepts for JPEG image forensics. It presents a solution to the main challenge of finding a block antecedent in a high-dimensional space. This solution relies on a local search algorithm with restrictions on the search space. We show that inpainting, copy-move, or splicing applied after a JPEG compression can be turned into three different mismatch problems and be detected. In particular, when the image is re-compressed after the modification, we can detect the manipulation if the quality factor of the second compression is higher than the first one. Our method can pinpoint forgeries down to the JPEG block with great detection power and without False Positive. We compare our method with two state-of-the-art models on localizing inpainted forgeries after a simple or a double compression. We show that under our working assumptions, it outperforms those models for most experiments.

Cell motility in dense cell collectives is pivotal in various diseases like cancer metastasis and asthma. A central aspect in these phenomena is the heterogeneity in cell motility, but identifying the motility of individual cells is challenging. Previous work has established the importance of the average cell shape in predicting cell dynamics. Here, we aim to identify the importance of individual cell shape features, rather than collective features, to distinguish between high-motility (active) and low-motility (passive) cells in heterogeneous cell layers. Employing the Cellular Potts Model, we generate simulation snapshots and extract static features as inputs for a simple machine-learning model. Our results show that when the passive cells are non-motile, this machine-learning model can accurately predict whether a cell is passive or active using only single-cell shape features. Furthermore, we explore scenarios where passive cells also exhibit some degree of motility, albeit less than active cells. In such cases, our findings indicate that a neural network trained on shape features can accurately classify cell motility, particularly when the number of active cells is low, and the motility of active cells is significantly higher compared to passive cells. This work offers potential for physics-inspired predictions of single-cell properties with implications for inferring cell dynamics from static histological images.

Microscopic levitated objects are a promising platform for inertial sensing, testing gravity at small scales, optomechanics in the quantum regime, and large-mass superpositions. However, existing levitation techniques harnessing optical and electrical fields suffer from noise induced by elevated internal temperatures and charge noise, respectively. Meissner-based magnetic levitation circumvents both sources of decoherence but requires cryogenic environments. Here we characterize a sub-mg ferromagnetic cube levitated in an alternating-current planar magnetic Paul trap at room temperature. We show behavior in line with the Mathieu equations and quality factors of up to 2500 for the librational modes. Besides technological sensing applications, this technique sets out a path for MHz librational modes in the micron-sized particle limit, allowing for magnetic coupling to superconducting circuits and spin-based quantum systems., Comment: 12 pages, 7 figures

Graphs are crucial for representing interrelated data and aiding predictive modeling by capturing complex relationships. Achieving high-quality graph representation is important for identifying linked patterns, leading to improvements in Graph Neural Networks (GNNs) to better capture data structures. However, challenges such as data scarcity, high collection costs, and ethical concerns limit progress. As a result, generative models and data augmentation have become more and more popular. This study explores using generated graphs for data augmentation, comparing the performance of combining generated graphs with real graphs, and examining the effect of different quantities of generated graphs on graph classification tasks. The experiments show that balancing scalability and quality requires different generators based on graph size. Our results introduce a new approach to graph data augmentation, ensuring consistent labels and enhancing classification performance.

When verifying liveness properties on a transition system, it is often necessary to discard spurious violating paths by making assumptions on which paths represent realistic executions. Capturing that some property holds under such an assumption in a logical formula is challenging and error-prone, particularly in the modal $\mu$-calculus. In this paper, we present template formulae in the modal $\mu$-calculus that can be instantiated to a broad range of liveness properties. We consider the following assumptions: progress, justness, weak fairness, strong fairness, and hyperfairness, each with respect to actions. The correctness of these formulae has been proven.

We report Bayesian inference of the mass, radius and hot X-ray emitting region properties - using data from the Neutron Star Interior Composition ExploreR (NICER) - for the brightest rotation-powered millisecond X-ray pulsar PSR J0437$\unicode{x2013}$4715. Our modeling is conditional on informative tight priors on mass, distance and binary inclination obtained from radio pulsar timing using the Parkes Pulsar Timing Array (PPTA) (Reardon et al. 2024), and we use NICER background models to constrain the non-source background, cross-checking with data from XMM-Newton. We assume two distinct hot emitting regions, and various parameterized hot region geometries that are defined in terms of overlapping circles; while simplified, these capture many of the possibilities suggested by detailed modeling of return current heating. For the preferred model identified by our analysis we infer a mass of $M = 1.418 \pm 0.037$ M$_\odot$ (largely informed by the PPTA mass prior) and an equatorial radius of $R = 11.36^{+0.95}_{-0.63}$ km, each reported as the posterior credible interval bounded by the 16% and 84% quantiles. This radius favors softer dense matter equations of state and is highly consistent with constraints derived from gravitational wave measurements of neutron star binary mergers. The hot regions are inferred to be non-antipodal, and hence inconsistent with a pure centered dipole magnetic field., Comment: 27 pages, 16 figures, + appendices. Accepted in ApJL. Data files and reproduction package available in Zenodo

Sim2real, that is, the transfer of learned control policies from simulation to real world, is an area of growing interest in robotics due to its potential to efficiently handle complex tasks. The sim2real approach faces challenges due to mismatches between simulation and reality. These discrepancies arise from inaccuracies in modeling physical phenomena and asynchronous control, among other factors. To this end, we introduce EAGERx, a framework with a unified software pipeline for both real and simulated robot learning. It can support various simulators and aids in integrating state, action and time-scale abstractions to facilitate learning. EAGERx's integrated delay simulation, domain randomization features, and proposed synchronization algorithm contribute to narrowing the sim2real gap. We demonstrate (in the context of robot learning and beyond) the efficacy of EAGERx in accommodating diverse robotic systems and maintaining consistent simulation behavior. EAGERx is open source and its code is available at https://eagerx.readthedocs.io., Comment: For an introductory video, see http://www.youtube.com/watch?v=D0CQNnTT010 . The documentation, tutorials, and our open-source code can be found at http://eagerx.readthedocs.io

Protection of confidential data is an important security consideration of today's applications. Of particular concern is to guard against unintentional leakage to a (malicious) observer, who may interact with the program and draw inference from made observations. Information flow control (IFC) type systems address this concern by statically ruling out such leakage. This paper contributes an IFC type system for message-passing concurrent programs, the computational model of choice for many of today's applications such as cloud computing and IoT applications. Such applications typically either implicitly or explicitly codify protocols according to which message exchange must happen, and to statically ensure protocol safety, behavioral type systems such as session types can be used. This paper marries IFC with session typing and contributes over prior work in the following regards: (1) support of realistic cyclic process networks as opposed to the restriction to tree-shaped networks, (2) more permissive, yet entirely secure, IFC control, exploiting cyclic process networks, and (3) considering deadlocks as another form of side channel, and asserting deadlock-sensitive noninterference (DSNI) for well-typed programs. To prove DSNI, the paper develops a novel logical relation that accounts for cyclic process networks. The logical relation is rooted in linear logic, but drops the tree-topology restriction imposed by prior work., Comment: Extended version of ECOOP24 paper

We present a framework for simulating the open dynamics of spin-boson systems by combining variational non-Gaussian states with a quantum trajectories approach. We apply this method to a generic spin-boson Hamiltonian that has both Tavis-Cummings and Holstein type couplings, and which has broad applications to a variety of quantum simulation platforms, polaritonic physics, and quantum chemistry. Additionally, we discuss how the recently developed truncated Wigner approximation for open quantum systems can be applied to the same Hamiltonian. We benchmark the performance of both methods and identify the regimes where each method is best suited to. Finally we discuss strategies to improve each technique., Comment: 21+3 pages, 12+2 figures. Final version

The large spatial/temporal/frequency scale of geoscience and remote-sensing datasets causes memory issues when using convolutional neural networks for (sub-) surface data segmentation. Recently developed fully reversible or fully invertible networks can mostly avoid memory limitations by recomputing the states during the backward pass through the network. This results in a low and fixed memory requirement for storing network states, as opposed to the typical linear memory growth with network depth. This work focuses on a fully invertible network based on the telegraph equation. While reversibility saves the major amount of memory used in deep networks by the data, the convolutional kernels can take up most memory if fully invertible networks contain multiple invertible pooling/coarsening layers. We address the explosion of the number of convolutional kernels by combining fully invertible networks with layers that contain the convolutional kernels in a compressed form directly. A second challenge is that invertible networks output a tensor the same size as its input. This property prevents the straightforward application of invertible networks to applications that map between different input-output dimensions, need to map to outputs with more channels than present in the input data, or desire outputs that decrease/increase the resolution compared to the input data. However, we show that by employing invertible networks in a non-standard fashion, we can still use them for these tasks. Examples in hyperspectral land-use classification, airborne geophysical surveying, and seismic imaging illustrate that we can input large data volumes in one chunk and do not need to work on small patches, use dimensionality reduction, or employ methods that classify a patch to a single central pixel., Comment: 22 pages, 13 figures

This study focuses on inverting time-domain airborne electromagnetic data in 2D by training a neural-network to understand the relationship between data and conductivity, thereby removing the need for expensive forward modeling during the inversion process. Instead the forward modeling is completed in the training stage, where training models are built before calculating 3D forward modeling training data. The method relies on training data being similar to the field dataset of choice, therefore, the field data was first inverted in 1D to get an idea of the expected conductivity distribution. With this information, $ 10,000 $ training models were built with similar conductivity ranges, and the research shows that this provided enough information for the network to produce realistic 2D inversion models over an aquifer-bearing region in California. Once the training was completed, the actual inversion time took only a matter of seconds on a generic laptop, which means that if future data was collected in this region it could be inverted in near real-time. Better results are expected by increasing the number of training models and eventually the goal is to extend the method to 3D inversion., Comment: 4 pages, 5 figures, conference submission

Research in the food domain is at times limited due to data sharing obstacles, such as data ownership, privacy requirements, and regulations. While important, these obstacles can restrict data-driven methods such as machine learning. Federated learning, the approach of training models on locally kept data and only sharing the learned parameters, is a potential technique to alleviate data sharing obstacles. This systematic review investigates the use of federated learning within the food domain, structures included papers in a federated learning framework, highlights knowledge gaps, and discusses potential applications. A total of 41 papers were included in the review. The current applications include solutions to water and milk quality assessment, cybersecurity of water processing, pesticide residue risk analysis, weed detection, and fraud detection, focusing on centralized horizontal federated learning. One of the gaps found was the lack of vertical or transfer federated learning and decentralized architectures.

The proliferation of image manipulation for unethical purposes poses significant challenges in social networks. One particularly concerning method is Image Steganography, allowing individuals to hide illegal information in digital images without arousing suspicions. Such a technique pose severe security risks, making it crucial to develop effective steganalysis methods enabling to detect manipulated images for clandestine communications. Although significant advancements have been achieved with machine learning models, a critical issue remains: the disparity between the controlled datasets used to train steganalysis models against real-world datasets of forensic practitioners, undermining severely the practical effectiveness of standardized steganalysis models. In this paper, we address this issue focusing on a realistic scenario where practitioners lack crucial information about the limited target set of images under analysis, including details about their development process and even whereas it contains manipulated images or not. By leveraging geometric alignment and distribution matching of source and target residuals, we develop TADA (Target Alignment through Data Adaptation), a novel methodology enabling to emulate sources aligned with specific targets in steganalysis, which is also relevant for highly unbalanced targets. The emulator is represented by a light convolutional network trained to align distributions of image residuals. Experimental validation demonstrates the potential of our strategy over traditional methods fighting covariate shift in steganalysis.

We consider the solution of nonlinear inverse problems where the forward problem is a discretization of a partial differential equation. Such problems are notoriously difficult to solve in practice and require minimizing a combination of a data-fit term and a regularization term. The main computational bottleneck of typical algorithms is the direct estimation of the data misfit. Therefore, likelihood-free approaches have become appealing alternatives. Nonetheless, difficulties in generalization and limitations in accuracy have hindered their broader utility and applicability. In this work, we use a paired autoencoder framework as a likelihood-free estimator for inverse problems. We show that the use of such an architecture allows us to construct a solution efficiently and to overcome some known open problems when using likelihood-free estimators. In particular, our framework can assess the quality of the solution and improve on it if needed. We demonstrate the viability of our approach using examples from full waveform inversion and inverse electromagnetic imaging., Comment: 18 pages, 6 figures

Linearity of Koopman operators and simplicity of their estimators coupled with model-reduction capabilities has lead to their great popularity in applications for learning dynamical systems. While nonparametric Koopman operator learning in infinite-dimensional reproducing kernel Hilbert spaces is well understood for autonomous systems, its control system analogues are largely unexplored. Addressing systems with control inputs in a principled manner is crucial for fully data-driven learning of controllers, especially since existing approaches commonly resort to representational heuristics or parametric models of limited expressiveness and scalability. We address the aforementioned challenge by proposing a universal framework via control-affine reproducing kernels that enables direct estimation of a single operator even for control systems. The proposed approach, called control-Koopman operator regression (cKOR), is thus completely analogous to Koopman operator regression of the autonomous case. First in the literature, we present a nonparametric framework for learning Koopman operator representations of nonlinear control-affine systems that does not suffer from the curse of control input dimensionality. This allows for reformulating the infinite-dimensional learning problem in a finite-dimensional space based solely on data without apriori loss of precision due to a restriction to a finite span of functions or inputs as in other approaches. For enabling applications to large-scale control systems, we also enhance the scalability of control-Koopman operator estimators by leveraging random projections (sketching). The efficacy of our novel cKOR approach is demonstrated on both forecasting and control tasks.

Motivated by asymptotic symmetry groups in general relativity, we consider projective unitary representations $(\overline{\rho}, \mathcal{H})$ of the Lie group $\mathrm{Diff}_c(M)$ of compactly supported diffeomorphisms of a smooth manifold $M$ that satisfy a so-called generalized positive energy condition. In particular, this captures representations that are in a suitable sense compatible with a KMS state on the von Neumann algebra generated by $\overline{\rho}$. We show that if $M$ is connected and $\dim(M) > 1$, then any such representation is necessarily trivial on the identity component $\mathrm{Diff}_c(M)_0$. As an intermediate step towards this result, we determine the continuous second Lie algebra cohomology $H^2_{\mathrm{ct}}(\mathcal{X}_c(M), \mathbb{R})$ of the Lie algebra of compactly supported vector fields (which is subtly different from Gelfand--Fuks cohomology).

We study the effectiveness of subagging, or subsample aggregating, on regression trees, a popular non-parametric method in machine learning. First, we give sufficient conditions for pointwise consistency of trees. We formalize that (i) the bias depends on the diameter of cells, hence trees with few splits tend to be biased, and (ii) the variance depends on the number of observations in cells, hence trees with many splits tend to have large variance. While these statements for bias and variance are known to hold globally in the covariate space, we show that, under some constraints, they are also true locally. Second, we compare the performance of subagging to that of trees across different numbers of splits. We find that (1) for any given number of splits, subagging improves upon a single tree, and (2) this improvement is larger for many splits than it is for few splits. However, (3) a single tree grown at optimal size can outperform subagging if the size of its individual trees is not optimally chosen. This last result goes against common practice of growing large randomized trees to eliminate bias and then averaging to reduce variance.