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Time-resolved X-ray absorption spectroscopy (tr-XAS) has been shown to be a versatile measurement technique for investigating non-equilibrium dynamics. Novel X-ray free electron laser (XFEL) facilities like the European XFEL offer increased repetition rates for stroboscopic XAS experiments through a burst operation mode, which enables measurements with up to 4.5 MHz. These higher repetition rates lead to higher data acquisition rates but can also introduce long-lived excitations that persist and thus build up during each burst. Here, we report on such long-lived effects in Ni and NiO thin film samples that were measured at the European XFEL. We disentangle the long-lived excitations from the initial pump-induced change and perform a detailed modelling-based analysis of how they modify transient X-ray spectra. As a result, we link the long-lived effects in Ni to a local temperature increase, as well as the effects in NiO to excited charge carrier trapping through polaron formation. In addition, we present possible correction methods, as well as discuss ways in which the effects of these long-lived excitations could be minimized for future time-resolved X-ray absorption spectroscopy measurements.

Manipulating magnetism at the THz timescale in atomically thin ferromagnets by exploiting the interactions of spins with optical phonon modes presents an innovative idea for THz spintronics. Spin-phonon coupling raises an important question about the flow of spin angular momentum possibly to chiral phonons. We use femtosecond optical pulses to generate bound electron-hole pairs (excitons) in the 2D ferromagnet CrI3, and probe the subsequent charge and spin dynamics. The observed change in the optical signal during temporal pump-probe overlap represents the buildup of the exciton population. This is accompanied by the excitation of coherent optical phonon modes with 2.4 and 3.9 THz frequencies, corresponding to the bending and stretching of the Cr-I bonds. We observe both modes in the magnetism channel which agrees with first-principles calculations that identify changes in the exchange coupling due to the lattice displacements for both phonon modes., Comment: 10 pages, 3 figures

Private optimization is a topic of major interest in machine learning, with differentially private stochastic gradient descent (DP-SGD) playing a key role in both theory and practice. Furthermore, DP-SGD is known to be a powerful tool in contexts beyond privacy, including robustness, machine unlearning, etc. Existing analyses of DP-SGD either make relatively strong assumptions (e.g., Lipschitz continuity of the loss function, or even convexity) or prove only first-order convergence (and thus might end at a saddle point in the non-convex setting). At the same time, there has been progress in proving second-order convergence of the non-private version of ``noisy SGD'', as well as progress in designing algorithms that are more complex than DP-SGD and do guarantee second-order convergence. We revisit DP-SGD and show that ``noise is all you need'': the noise necessary for privacy already implies second-order convergence under the standard smoothness assumptions, even for non-Lipschitz loss functions. Hence, we get second-order convergence essentially for free: DP-SGD, the workhorse of modern private optimization, under minimal assumptions can be used to find a second-order stationary point., Comment: 30 pages

Contrastive learning is a highly successful technique for learning representations of data from labeled tuples, specifying the distance relations within the tuple. We study the sample complexity of contrastive learning, i.e. the minimum number of labeled tuples sufficient for getting high generalization accuracy. We give tight bounds on the sample complexity in a variety of settings, focusing on arbitrary distance functions, both general $\ell_p$-distances, and tree metrics. Our main result is an (almost) optimal bound on the sample complexity of learning $\ell_p$-distances for integer $p$. For any $p \ge 1$ we show that $\tilde \Theta(\min(nd,n^2))$ labeled tuples are necessary and sufficient for learning $d$-dimensional representations of $n$-point datasets. Our results hold for an arbitrary distribution of the input samples and are based on giving the corresponding bounds on the Vapnik-Chervonenkis/Natarajan dimension of the associated problems. We further show that the theoretical bounds on sample complexity obtained via VC/Natarajan dimension can have strong predictive power for experimental results, in contrast with the folklore belief about a substantial gap between the statistical learning theory and the practice of deep learning.

Identifying the microscopic nature of non-equilibrium energy transfer mechanisms among electronic, spin and lattice degrees of freedom is central for understanding ultrafast phenomena such as manipulating magnetism on the femtosecond timescale. Here we use time and angle-resolved photoemission spectroscopy to go beyond the often-employed ensemble-averaged view of non-equilibrium dynamics in terms of quasiparticle temperature evolutions. We show for ferromagnetic Ni that the non-equilibrium electron and spin dynamics display pronounced variations with electron momentum whereas the magnetic exchange interaction remains isotropic. This highlights the influence of lattice-mediated scattering processes and opens a pathway towards unraveling the still elusive microscopic mechanism of spin-lattice angular momentum transfer.

Photo-doped states in strongly correlated charge transfer insulators are characterized by $d$-$d$ and $d$-$p$ interactions and the resulting intertwined dynamics of charge excitations and local multiplets. Here we use femtosecond x-ray absorption spectroscopy in combination with dynamical mean-field theory to disentangle these contributions in NiO. Upon resonant optical excitation across the charge transfer gap, the Ni $L_3$ and O $K$ absorption edges red-shift for $>10$ ps, associated with photo-induced changes in the screening environment. An additional signature below the Ni $L_3$ edge is identified for $<1$ ps, reflecting a transient nonthermal population of local many-body multiplets. We employ a nonthermal generalization of the multiplet ligand field theory to show that the feature originates from $d$-$d$ transitions. Overall, the photo-doped state differs significantly from a chemically doped state. Our results demonstrate the ability to reveal excitation pathways in correlated materials by x-ray spectroscopies, which is relevant for ultrafast materials design.

Resonant absorption of a photon by bound electrons in a solid can promote an electron to another orbital state or transfer it to a neighboring atomic site. Such a transition in a magnetically ordered material could affect the magnetic order. While this process is an obvious road map for optical control of magnetization, experimental demonstration of such a process remains challenging. Exciting a significant fraction of magnetic ions requires a very intense incoming light beam, as orbital resonances are often weak compared to above-band-gap excitations. In the latter case, a sizeable reduction of the magnetization occurs as the absorbed energy increases the spin temperature, masking the non-thermal optical effects. Here, using ultrafast x-ray spectroscopy, we were able to resolve changes in the magnetization state induced by resonant absorption of infrared photons in Co-doped yttrium iron garnet, with negligible thermal effects. We found that the optical excitation of the Co ions affects the two distinct magnetic Fe sublattices differently, resulting in a transient non-collinear magnetic state. The present results indicate that the all-optical magnetization switching most likely occurs due to the creation of a transient, non-collinear magnetic state followed by coherent spin rotations of the Fe moments.

We study the problem of learning a hierarchical tree representation of data from labeled samples, taken from an arbitrary (and possibly adversarial) distribution. Consider a collection of data tuples labeled according to their hierarchical structure. The smallest number of such tuples required in order to be able to accurately label subsequent tuples is of interest for data collection in machine learning. We present optimal sample complexity bounds for this problem in several learning settings, including (agnostic) PAC learning and online learning. Our results are based on tight bounds of the Natarajan and Littlestone dimensions of the associated problem. The corresponding tree classifiers can be constructed efficiently in near-linear time.

The pulse intensity from X-ray free-electron lasers (FELs) can create extreme excitation densities in solids, entering the regime of non-linear X-ray-matter interactions. We show L3-edge absorption spectra of metallic nickel thin films with fluences entering a regime where several X-ray photons are incident per absorption cross-section. Main features of the observed non-linear spectral changes are described with a predictive rate model for electron population dynamics during the pulse, utilizing a fixed density of states and tabulated ground-state properties., Comment: The main text contains 5 pages and 4 figures, the total length including supplement is 14 pages, 7 figures and one table. See also the simultaneously submitted paper about the rate model

Femtosecond transient soft X-ray Absorption Spectroscopy (XAS) is a very promising technique that can be employed at X-ray Free Electron Lasers (FELs) to investigate out-of-equilibrium dynamics for material and energy research. Here we present a dedicated setup for soft X-rays available at the Spectroscopy & Coherent Scattering (SCS) instrument at the European X-ray Free Electron Laser (EuXFEL). It consists of a beam-splitting off-axis zone plate (BOZ) used in transmission to create three copies of the incoming beam, which are used to measure the transmitted intensity through the excited and unexcited sample, as well as to monitor the incoming intensity. Since these three intensity signals are detected shot-by-shot and simultaneously, this setup allows normalized shot-by-shot analysis of the transmission. For photon detection, the DSSC imaging detector, which is capable of recording up to 800 images at 4.5 MHz frame rate during the FEL burst, is employed and allows approaching the photon shot-noise limit. We review the setup and its capabilities, as well as the online and offline analysis tools provided to users., Comment: 11 figures

The complex electronic structure of metallic ferromagnets is determined by a balance between exchange interaction, electron hopping leading to band formation, and local Coulomb repulsion. The interplay between the respective terms of the Hamiltonian is of fundamental interest, since it produces most, if not all, of the exotic phenomena observed in the solid state. By combining high energy and temporal resolution in femtosecond time-resolved X-ray absorption spectroscopy with ab initio time-dependent density functional theory we analyze the electronic structure in fcc Ni on the time scale of these interactions in a pump-probe experiment. We distinguish transient broadening and energy shifts in the absorption spectra, which we demonstrate to be caused by electron repopulation and correlation-induced modifications of the electronic structure, respectively. Importantly, the theoretical description of this experimental result hence requires to take the local Coulomb interaction into account, revealing a temporal interplay between band formation, exchange interaction, and Coulomb repulsion.

The SASE3 soft X-ray beamline at the European XFEL has been designed and built to provide experiments with pink or monochromatic beam in the photon energy range 250 eV - 3000 eV. Here, we focus on the monochromatic operation of the SASE3 beamline and report on design and performance of the SASE3 grating monochromator. The unique capability of an FEL source to produce short femtosecond pulses of high degree of coherence challenges the monochromator design by a demand to control both photon energy and temporal resolution. The aim to transport close to transform-limited pulses poses very high demands on the optics quality, in particular on the grating. The current realization of the SASE3 monochromator is discussed in comparison with optimal design performance. Presently, the monochromator operates with two gratings: the low-resolution grating is optimized for time-resolved experiments and allows for moderate resolving power of about 2000 - 5000 along with pulse stretching of few to few tens of femtoseconds RMS, and the high-resolution grating reaches resolving power of 10000 at a cost of larger pulse stretching.

We give the first polynomial time algorithms for escaping from high-dimensional saddle points under a moderate number of constraints. Given gradient access to a smooth function $f \colon \mathbb R^d \to \mathbb R$ we show that (noisy) gradient descent methods can escape from saddle points under a logarithmic number of inequality constraints. This constitutes the first tangible progress (without reliance on NP-oracles or altering the definitions to only account for certain constraints) on the main open question of the breakthrough work of Ge et al. who showed an analogous result for unconstrained and equality-constrained problems. Our results hold for both regular and stochastic gradient descent.

Wide-band-gap insulators such as NiO offer the exciting prospect of coherently manipulating electronic correlations with strong optical fields. Contrary to metals where rapid dephasing of optical excitation via electronic processes occurs, the sub-gap excitation in charge-transfer insulators has been shown to couple to low-energy bosonic excitations. However, it is currently unknown if the bosonic dressing field is composed of phonons or magnons. Here we use the prototypical charge-transfer insulator NiO to demonstrate that 1.5 eV sub-gap optical excitation leads to a renormalised NiO band-gap in combination with a significant reduction of the antiferromagnetic order. We employ element-specific X-ray reflectivity at the FLASH free-electron laser to demonstrate the reduction of the upper band-edge at the O 1s-2p core-valence resonance (K-edge) whereas the antiferromagnetic order is probed via X-ray magnetic linear dichroism (XMLD) at the Ni 2p-3d resonance (L2-edge). Comparing the transient XMLD spectral line shape to ground-state measurements allows us to extract a spin temperature rise of 65 +/- 5 K for time delays longer than 400 fs while at earlier times a non-equilibrium spin state is formed. We identify transient mid-gap states being formed during the first 200 fs accompanied by a band-gap reduction lasting at least up to the maximum measured time delay of 2.4 ps. Electronic structure calculations indicate that magnon excitations significantly contribute to the reduction of the NiO band gap.

Magnetic nanoparticles such as FePt in the L10-phase are the bedrock of our current data storage technology. As the grains become smaller to keep up with technological demands, the superparamagnetic limit calls for materials with higher magneto-crystalline anisotropy. This in turn reduces the magnetic exchange length to just a few nanometers enabling magnetic structures to be induced within the nanoparticles. Here we describe the existence of spin-wave solitons, dynamic localized bound states of spin-wave excitations, in FePt nanoparticles. We show with time-resolved X-ray diffraction and micromagnetic modeling that spin-wave solitons of sub-10 nm sizes form out of the demagnetized state following femtosecond laser excitation. The measured soliton spin-precession frequency of 0.1 THz positions this system as a platform to develop miniature devices capable of filling the THz gap., Comment: 32 pages, please check the "attachemnts" tab in the pdf file in order to see the movie

A change of orbital state alters the coupling between ions and their surroundings drastically. Orbital excitations are hence key to understand and control interaction of ions. Rare-earth (RE) elements with strong magneto-crystalline anisotropy (MCA) are important ingredients for magnetic devices. Thus, control of their localized 4f magnetic moments and anisotropy is one major challenge in ultrafast spin physics. With time-resolved X-ray absorption and resonant inelastic scattering experiments, we show for Tb metal that 4f-electronic excitations out of the ground state multiplet occur after optical pumping. These excitations are driven by inelastic 5d-4f-electron scattering, alter the 4f-orbital state and consequently the MCA with important implications for magnetization dynamics in 4f-metals, and more general for the excitation of localized electronic states in correlated materials., Comment: Manuscript (23 pages, 5 figures) and Supplementary Information (32 pages, 10 figures)

Stochastic gradient descent (SGD) is a prevalent optimization technique for large-scale distributed machine learning. While SGD computation can be efficiently divided between multiple machines, communication typically becomes a bottleneck in the distributed setting. Gradient compression methods can be used to alleviate this problem, and a recent line of work shows that SGD augmented with gradient compression converges to an $\varepsilon$-first-order stationary point. In this paper we extend these results to convergence to an $\varepsilon$-second-order stationary point ($\varepsilon$-SOSP), which is to the best of our knowledge the first result of this type. In addition, we show that, when the stochastic gradient is not Lipschitz, compressed SGD with RandomK compressor converges to an $\varepsilon$-SOSP with the same number of iterations as uncompressed SGD [Jin et al.,2021] (JACM), while improving the total communication by a factor of $\tilde \Theta(\sqrt{d} \varepsilon^{-3/4})$, where $d$ is the dimension of the optimization problem. We present additional results for the cases when the compressor is arbitrary and when the stochastic gradient is Lipschitz.

Second-order intensity interferometry was employed to study the spatial and temporal properties of the European X-ray Free-Electron Laser (EuXFEL). Measurements were performed at the soft X-ray SASE3 undulator beamline at a photon energy of 1.2 keV in the Self-Amplified Spontaneous Emission (SASE) mode. Two high-power regimes of the SASE3 undulator settings, i.e. linear and quadratic tapering at saturation, were studied in detail and compared with the linear gain regime. The statistical analysis showed an exceptionally high degree of spatial coherence up to 90% for the linear undulator tapering. Analysis of the measured data in spectral and spatial domains provided an average pulse duration of about 10 fs in our measurements. The obtained results will be valuable for the experiments requiring and exploiting short pulse duration and utilizing high coherence properties of the EuXFEL., Comment: 12 pages, 6 figures, 2 tables

Stabilization and sufficient conditions for mixing by stochastic transport are shown. More precisely, given a second order linear operator with possibly unstable eigenvalues on a smooth compact Riemannian manifold, it is shown that the inclusion of transport noise can imply global asymptotic stability. Moreover, it is shown that an arbitrary large exponential rate of convergence can be reached, implying enhanced dissipation. The sufficient conditions are shown to be satisfied by the so-called Kraichnan model for stochastic transport of passive scalars in turbulent fluids. In addition, an example is given showing that it can be sufficient to force four modes in order to induce stabilization., Comment: Minor revision

We initiate a comprehensive experimental study of objective-based hierarchical clustering methods on massive datasets consisting of deep embedding vectors from computer vision and NLP applications. This includes a large variety of image embedding (ImageNet, ImageNetV2, NaBirds), word embedding (Twitter, Wikipedia), and sentence embedding (SST-2) vectors from several popular recent models (e.g. ResNet, ResNext, Inception V3, SBERT). Our study includes datasets with up to $4.5$ million entries with embedding dimensions up to $2048$. In order to address the challenge of scaling up hierarchical clustering to such large datasets we propose a new practical hierarchical clustering algorithm B++&C. It gives a 5%/20% improvement on average for the popular Moseley-Wang (MW) / Cohen-Addad et al. (CKMM) objectives (normalized) compared to a wide range of classic methods and recent heuristics. We also introduce a theoretical algorithm B2SAT&C which achieves a $0.74$-approximation for the CKMM objective in polynomial time. This is the first substantial improvement over the trivial $2/3$-approximation achieved by a random binary tree. Prior to this work, the best poly-time approximation of $\approx 2/3 + 0.0004$ was due to Charikar et al. (SODA'19).

Hierarchical Clustering is an unsupervised data analysis method which has been widely used for decades. Despite its popularity, it had an underdeveloped analytical foundation and to address this, Dasgupta recently introduced an optimization viewpoint of hierarchical clustering with pairwise similarity information that spurred a line of work shedding light on old algorithms (e.g., Average-Linkage), but also designing new algorithms. Here, for the maximization dual of Dasgupta's objective (introduced by Moseley-Wang), we present polynomial-time .4246 approximation algorithms that use Max-Uncut Bisection as a subroutine. The previous best worst-case approximation factor in polynomial time was .336, improving only slightly over Average-Linkage which achieves 1/3. Finally, we complement our positive results by providing APX-hardness (even for 0-1 similarities), under the Small Set Expansion hypothesis.

A function $f : \mathbb{F}_2^n \to \mathbb{R}$ is $s$-sparse if it has at most $s$ non-zero Fourier coefficients. Motivated by applications to fast sparse Fourier transforms over $\mathbb{F}_2^n$, we study efficient algorithms for the problem of approximating the $\ell_2$-distance from a given function to the closest $s$-sparse function. While previous works (e.g., Gopalan et al. SICOMP 2011) study the problem of distinguishing $s$-sparse functions from those that are far from $s$-sparse under Hamming distance, to the best of our knowledge no prior work has explicitly focused on the more general problem of distance estimation in the $\ell_2$ setting, which is particularly well-motivated for noisy Fourier spectra. Given the focus on efficiency, our main result is an algorithm that solves this problem with query complexity $\mathcal{O}(s)$ for constant accuracy and error parameters, which is only quadratically worse than applicable lower bounds.