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A common way to learn and analyze statistical models is to consider operations in the model parameter space. But what happens if we optimize in the parameter space and there is no one-to-one mapping between the parameter space and the underlying statistical model space? Such cases frequently occur for hierarchical models which include statistical mixtures or stochastic neural networks, and these models are said to be singular. Singular models reveal several important and well-studied problems in machine learning like the decrease in convergence speed of learning trajectories due to attractor behaviors. In this work, we propose a relative reparameterization technique of the parameter space, which yields a general method for extracting regular submodels from singular models. Our method enforces model identifiability during training and we study the learning dynamics for gradient descent and expectation maximization for Gaussian Mixture Models (GMMs) under relative parameterization, showing faster experimental convergence and a improved manifold shape of the dynamics around the singularity. Extending the analysis beyond GMMs, we furthermore analyze the Fisher information matrix under relative reparameterization and its influence on the generalization error, and show how the method can be applied to more complex models like deep neural networks.

Scanning transmission electron microscopy (STEM) has a broad range of applications in materials characterization, including real-space imaging, spectroscopy, and diffraction, at length scales from the micron to sub-{\AA}ngstr\"om. The recent development and adoption of high-speed, direct electron STEM detectors has enabled diffraction patterns to be collected at each probe position, generating four-dimensional STEM (4D-STEM) datasets and opening new imaging modalities. However, the limited pixel numbers in these detectors enforce a tradeoff between angular resolution and maximum collection angle. In this paper, we describe a straightforward method for quantifying 4D-STEM data by utilizing the full flux of the electron beam, including electrons scattered beyond the limits of the detector. This enables significantly increased experimental flexibility, including the synthesis of quantitative, high-contrast complementary annular dark field (cADF) STEM images from low-angle diffraction patterns whilst maintaining high angular resolution; as well as the optimization of electron dose and the more effective use of low dynamic range detectors.

Many video editing tasks such as rotoscoping or object removal require the propagation of context across frames. While transformers and other attention-based approaches that aggregate features globally have demonstrated great success at propagating object masks from keyframes to the whole video, they struggle to propagate high-frequency details such as textures faithfully. We hypothesize that this is due to an inherent bias of global attention towards low-frequency features. To overcome this limitation, we present a two-stream approach, where high-frequency features interact locally and low-frequency features interact globally. The global interaction stream remains robust in difficult situations such as large camera motions, where explicit alignment fails. The local interaction stream propagates high-frequency details through deformable feature aggregation and, informed by the global interaction stream, learns to detect and correct errors of the deformation field. We evaluate our two-stream approach for inpainting tasks, where experiments show that it improves both the propagation of features within a single frame as required for image inpainting, as well as their propagation from keyframes to target frames. Applied to video inpainting, our approach leads to 44% and 26% improvements in FID and LPIPS scores. Code at https://github.com/runwayml/guided-inpainting, Comment: CVPRW 2022 - AI for Content Creation Workshop. Code at https://github.com/runwayml/guided-inpainting

We study the H\"olderian regularity of Gaussian wavelets series and show that they display, almost surely, three types of points: slow, ordinary and rapid. In particular, this fact holds for the Fractional Brownian Motion. We also show that this property is satisfied for a multifractal extension of Gaussian wavelet series. Finally, we remark that the existence of slow points is specific to these functions., Comment: 33 pages

Electrospray ion-beam deposition (ES-IBD) is a versatile tool to study structure and reactivity of molecules from small metal clusters to large protein assemblies. It brings molecules gently into the gas phase where they can be accurately manipulated and purified, followed by controlled deposition onto various substrates. In combination with imaging techniques, direct structural information of well-defined molecules can be obtained, which is essential to test and interpret results from indirect mass spectrometry techniques. To date, ion-beam deposition experiments are limited to a small number of custom instruments worldwide, and there are no commercial alternatives. Here we present a module that adds ion-beam deposition capabilities to a popular commercial MS platform (Thermo Scientific$^{\mathrm{TM}}$ Q Exactive$^{\mathrm{TM}}$ UHMR). This combination significantly reduces the overhead associated with custom instruments, while benefiting from established high performance and reliability. We present current performance characteristics including beam intensity, landing-energy control, and deposition spot size for a broad range of molecules. In combination with atomic force microscopy (AFM) and transmission electron microscopy (TEM), we distinguish near-native from unfolded proteins and show retention of native shape of protein assemblies after dehydration and deposition. Further, we use an enzymatic assay to quantify activity of an non-covalent protein complex after deposition an a dry surface. Together, these results indicate a great potential of ES-IBD for applications in structural biology, but also outline the challenges that need to be solved for it to reach its full potential.

Perovskite SrRuO$_3$ is a prototypical itinerant ferromagnet which allows interface engineering of its electronic and magnetic properties. We report synthesis and investigation of atomically flat artificial multilayers of SrRuO$_3$ with the spin-orbit semimetal SrIrO$_3$ in combination with band-structure calculations with a Hubbard $U$ term and topological analysis. They reveal an electronic reconstruction and emergence of flat Ru-4d$_{xz}$ bands near the interface, ferromagnetic interlayer coupling and negative Berry-curvature contribution to the anomalous Hall effect. We analyze the Hall effect and magnetoresistance measurements as a function of the field angle from out of plane towards in-plane orientation (either parallel or perpendicular to the current direction) by a two-channel model. The magnetic easy direction is tilted by about $20^\circ$ from the sample normal for low magnetic fields, rotating towards the out-of-plane direction by increasing fields. Fully strained epitaxial growth enables a strong anisotropy of magnetoresistance. An additional Hall effect contribution, not accounted for by the two-channel model is compatible with stable skyrmions only up to a critical angle of roughly $45^\circ$ from the sample normal. Within about $20^\circ$ from the thin film plane an additional peak-like contribution to the Hall effect suggests the formation of a non-trivial spin structure., Comment: to be published in Phys. Rev. B

Let $n\geq 2$ be any integer. We study the optimal lower bound $v_{n, n-i}$ of the canonical volume and the optimal upper bound $r_{n,n-i}$ of the canonical stability index for minimal projective $n$-folds of general type, which are canonically fibered by $i$-folds ($i=0,1$). The results for $i = 0$, $v_{n,n}=2$ and $r_{n, n}=n+2$, are known to experts. In this article, we show that $v_{n,n-1}=\frac{6}{2n+(n \bmod 3)}$ and $r_{n,n-1}=\frac{1}{3}(5n+ 3 + (n \bmod 3))$. The machinery is applicable to all canonical dimensions $n-i$., Comment: 16 pages, comments are welcome

A database is under construction to provide a complete collection of published basic properties of hypernuclei such as {\Lambda} binding energies, lifetimes, or excitation energies. From these values, averages with related errors are computed in a systematic way. For each property, the overall experimental situation is depicted in form of an ideogram showing the combined probability density function of the measurements. The database is accessible via a dynamic website at https://hypernuclei.kph.uni-mainz.de with an user interface offering customizable visualizations, selections, or unit conversions. The capabilities of the database are demonstrated for the puzzling and disputed data situation of the hypertriton., Comment: 6 pages, 3 figures, HADRON 2021 Proceeding

We consider a stochastic individual-based model of adaptive dynamics on a finite trait graph $G=(V,E)$. The evolution is driven by a linear birth rate, a density dependent logistic death rate an the possibility of mutations along the (possibly directed) edges in $E$. We study the limit of small mutation rates for a simultaneously diverging population size. Closing the gap between the works of Bovier, Coquille and Smadi (2019) and Coquille, Kraut and Smadi (2021), we give a precise description of transitions between evolutionary stable conditions (ESC), where multiple mutations are needed to cross a valley in the fitness landscape. The system shows a metastable behaviour on several divergent time scales associated to a degree of stability. We develop the framework of a meta graph that is constituted of ESCs and possible metastable transitions between those. This allows for a concise description of the multi-scale jump chain arising from concatenating several jumps. Finally, for each of the various time scale, we prove the convergence of the population process to a Markov jump process visiting only ESCs of sufficiently high stability., Comment: 47 pages, 14 figures; Revised version with changed proof structure and reformulation of lemmata therein

By decomposing the image formation process into a sequential application of denoising autoencoders, diffusion models (DMs) achieve state-of-the-art synthesis results on image data and beyond. Additionally, their formulation allows for a guiding mechanism to control the image generation process without retraining. However, since these models typically operate directly in pixel space, optimization of powerful DMs often consumes hundreds of GPU days and inference is expensive due to sequential evaluations. To enable DM training on limited computational resources while retaining their quality and flexibility, we apply them in the latent space of powerful pretrained autoencoders. In contrast to previous work, training diffusion models on such a representation allows for the first time to reach a near-optimal point between complexity reduction and detail preservation, greatly boosting visual fidelity. By introducing cross-attention layers into the model architecture, we turn diffusion models into powerful and flexible generators for general conditioning inputs such as text or bounding boxes and high-resolution synthesis becomes possible in a convolutional manner. Our latent diffusion models (LDMs) achieve a new state of the art for image inpainting and highly competitive performance on various tasks, including unconditional image generation, semantic scene synthesis, and super-resolution, while significantly reducing computational requirements compared to pixel-based DMs. Code is available at https://github.com/CompVis/latent-diffusion ., Comment: CVPR 2022

We perform a systematic study of the $\alpha$-particle excitation from its ground state $0_1^+$ to the $0_2^+$ resonance. The so-called monopole transition form factor is investigated via an electron scattering experiment in a broad $Q^2$-range (from $0.5$ to $5.0$ fm$^{-2}$). The precision of the new data dramatically superseeds that of older sets of data, each covering only a portion of the $Q^2$-range. The new data allow the determination of two coefficients in a low-momentum expansion leading to a new puzzle. By confronting experiment to state-of-the-art theoretical calculations we observe that modern nuclear forces, including those derived within chiral effective field theory which are well tested on a variety of observables, fail to reproduce the excitation of the $\alpha$-particle.

The Extreme Universe Space Observatory Supper Pressure Balloon 2 (EUSO-SPB2) is under development, and will prototype instrumentation for future satellite-based missions, including the Probe of Extreme Multi-Messenger Astrophysics (POEMMA). EUSO-SPB2 will consist of two telescopes. The first is a Cherenkov telescope (CT) being developed to identify and estimate the background sources for future below-the-limb very high energy (E>10 PeV) astrophysical neutrino observations, as well as above-the-limb cosmic ray induced signals (E>1 PeV). The second is a fluorescence telescope (FT) being developed for detection of Ultra High Energy Cosmic Rays (UHECRs). In preparation for the expected launch in 2023, extensive simulations tuned by preliminary laboratory measurements have been preformed to understand the FT capabilities. The energy threshold has been estimated at $10^{18.2}$ eV, and results in a maximum detection rate at $10^{18.6}$ eV when taking into account the shape of the UHECR spectrum. In addition, onboard software has been developed based on the simulations as well as experience with previous EUSO missions. This includes a level 1 trigger to be run on the computationally limited flight hardware, as well as a deep learning based prioritization algorithm in order to accommodate the balloon's telemetry budget. These techniques could also be used later for future, space-based missions., Comment: ICRC 2021

The security of code based constructions is usually assessed by Information Set Decoding (ISD) algorithms. In the quantum setting, amplitude amplification yields an asymptotic square root gain over the classical analogue. However, it is still unclear whether a real quantum circuit could yield actual improvements or suffer an enormous overhead due to its implementation. This leads to different considerations of these quantum attacks in the security analysis of code based proposals. In this work we clarify this doubt by giving the first quantum circuit design of the fully-fledged ISD procedure, an implementation in the quantum simulation library Qibo as well as precise estimates of its complexities. We show that against common belief, Prange's ISD algorithm can be implemented rather efficiently on a quantum computer, namely with only a logarithmic overhead in circuit depth compared to a classical implementation. As another major contribution, we leverage the idea of classical co-processors to design hybrid classical-quantum trade-offs, that allow to tailor the necessary qubits to any available amount, while still providing quantum speedups. Interestingly, when constraining the width of the circuit instead of its depth we are able to overcome previous optimality results on constraint quantum search., Comment: 30+2 pages, 12 figure, code available on Github

In recent years, several results in the supervised learning setting suggested that classical statistical learning-theoretic measures, such as VC dimension, do not adequately explain the performance of deep learning models which prompted a slew of work in the infinite-width and iteration regimes. However, there is little theoretical explanation for the success of neural networks beyond the supervised setting. In this paper we argue that, under some distributional assumptions, classical learning-theoretic measures can sufficiently explain generalization for graph neural networks in the transductive setting. In particular, we provide a rigorous analysis of the performance of neural networks in the context of transductive inference, specifically by analysing the generalisation properties of graph convolutional networks for the problem of node classification. While VC Dimension does result in trivial generalisation error bounds in this setting as well, we show that transductive Rademacher complexity can explain the generalisation properties of graph convolutional networks for stochastic block models. We further use the generalisation error bounds based on transductive Rademacher complexity to demonstrate the role of graph convolutions and network architectures in achieving smaller generalisation error and provide insights into when the graph structure can help in learning. The findings of this paper could re-new the interest in studying generalisation in neural networks in terms of learning-theoretic measures, albeit in specific problems., Comment: 35th Conference on Neural Information Processing Systems (NeurIPS 2021)

When analyzing parametric statistical models, a useful approach consists in modeling geometrically the parameter space. However, even for very simple and commonly used hierarchical models like statistical mixtures or stochastic deep neural networks, the smoothness assumption of manifolds is violated at singular points which exhibit non-smooth neighborhoods in the parameter space. These singular models have been analyzed in the context of learning dynamics, where singularities can act as attractors on the learning trajectory and, therefore, negatively influence the convergence speed of models. We propose a general approach to circumvent the problem arising from singularities by using stratifolds, a concept from algebraic topology, to formally model singular parameter spaces. We use the property that specific stratifolds are equipped with a resolution method to construct a smooth manifold approximation of the singular space. We empirically show that using (natural) gradient descent on the smooth manifold approximation instead of the singular space allows us to avoid the attractor behavior and therefore improve the convergence speed in learning., Comment: A preliminary version of this work was presented at NeurIPS 2021 as a Spotlight in the 13th Annual Workshop on Optimization for Machine Learning (OPT2021)