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Astronomical spectrographs require frequency calibration through sources like hollow-cathode lamps or absorption-gas cells. Laser frequency combs (LFCs) provide highest accuracy but are facing operational challenges. We aim to provide a precise and accurate frequency solution for the spectrum of molecular iodine absorption by referencing to an LFC that does not cover the same frequency range. We used a Fourier Transform Spectrometer (FTS) to produce a consistent frequency scale for the combined spectrum from an iodine absorption cell at 5200--6200\AA and an LFC at 8200\AA. We used 17,807 comb lines to determine the FTS frequency offset and compared the calibrated iodine spectrum to a synthetic spectrum computed from a molecular potential model. In a single scan, the frequency offset was determined from the comb spectrum with an uncertainty of $\sim$1 cm s$^{-1}$. The distribution of comb line frequencies is consistent with no deviation from linearity. The iodine observation matches the model with an offset of smaller than the model uncertainties of $\sim$1 m s$^{-1}$, which confirms that the FTS zero point is valid outside the range covered by the LFC, and that the frequencies of the iodine absorption model are accurate. We also report small systematic effects regarding the iodine model's energy scale. We conclude that Fourier Transform Spectrometry can transfer LFC accuracy into frequency ranges not originally covered by the comb. This allows us to assign accurate frequency scales to the spectra of customized wavelength calibrators. The calibrators can be optimized for individual spectrograph designs regarding resolution and spectral bandwidth, and requirements on their long-term stability are relaxed because FTS monitoring can be performed during operation. This provides flexibility for the design and operation of calibration sources for high-precision Doppler experiments., Comment: 10 pages, accepted for publication in A&A, abstract shortened for arXiv version

We study nonnegative and sums of squares symmetric (and even symmetric) functions of fixed degree. We can think of these as limit cones of symmetric nonnegative polynomials and symmetric sums of squares of fixed degree as the number of variables goes to infinity. We compare these cones, including finding explicit examples of nonnegative polynomials which are not sums of squares for any sufficiently large number of variables, and compute the tropicalizations of their dual cones in the even symmetric case. We find that the tropicalization of the dual cones is naturally understood in terms of the overlooked superdominance order on partitions. The power sum symmetric functions obey this same partial order (analogously to how term-normalized power sums obey the dominance order).

Quantum one-class support vector machines leverage the advantage of quantum kernel methods for semi-supervised anomaly detection. However, their quadratic time complexity with respect to data size poses challenges when dealing with large datasets. In recent work, quantum randomized measurements kernels and variable subsampling were proposed, as two independent methods to address this problem. The former achieves higher average precision, but suffers from variance, while the latter achieves linear complexity to data size and has lower variance. The current work focuses instead on combining these two methods, along with rotated feature bagging, to achieve linear time complexity both to data size and to number of features. Despite their instability, the resulting models exhibit considerably higher performance and faster training and testing times., Comment: Submitted to Springer Nature CS

The first generation of ELT instruments includes an optical-infrared high-resolution spectrograph, indicated as ELT-HIRES and recently christened ANDES (ArmazoNes high Dispersion Echelle Spectrograph). ANDES consists of three fibre-fed spectrographs ([U]BV, RIZ, YJH) providing a spectral resolution of $\sim$100,000 with a minimum simultaneous wavelength coverage of 0.4-1.8 $\mu$m with the goal of extending it to 0.35-2.4 $\mu$m with the addition of a U arm to the BV spectrograph and a separate K band spectrograph. It operates both in seeing- and diffraction-limited conditions and the fibre feeding allows several, interchangeable observing modes including a single conjugated adaptive optics module and a small diffraction-limited integral field unit in the NIR. Modularity and fibre-feeding allow ANDES to be placed partly on the ELT Nasmyth platform and partly in the Coud\'e room. ANDES has a wide range of groundbreaking science cases spanning nearly all areas of research in astrophysics and even fundamental physics. Among the top science cases, there are the detection of biosignatures from exoplanet atmospheres, finding the fingerprints of the first generation of stars, tests on the stability of Nature's fundamental couplings, and the direct detection of the cosmic acceleration. The ANDES project is carried forward by a large international consortium, composed of 35 Institutes from 13 countries, forming a team of almost 300 scientists and engineers which include the majority of the scientific and technical expertise in the field that can be found in ESO member states., Comment: SPIE astronomical telescope and instrumentation 2024, in press

Transformers have recently gained prominence in long time series forecasting by elevating accuracies in a variety of use cases. Regrettably, in the race for better predictive performance the overhead of model architectures has grown onerous, leading to models with computational demand infeasible for most practical applications. To bridge the gap between high method complexity and realistic computational resources, we introduce the Residual Cyclic Transformer, ReCycle. ReCycle utilizes primary cycle compression to address the computational complexity of the attention mechanism in long time series. By learning residuals from refined smoothing average techniques, ReCycle surpasses state-of-the-art accuracy in a variety of application use cases. The reliable and explainable fallback behavior ensured by simple, yet robust, smoothing average techniques additionally lowers the barrier for user acceptance. At the same time, our approach reduces the run time and energy consumption by more than an order of magnitude, making both training and inference feasible on low-performance, low-power and edge computing devices. Code is available at https://github.com/Helmholtz-AI-Energy/ReCycle, Comment: 9 pages, 3 figures, to be published at IEEE CAI 2024, Associated code available at https://github.com/Helmholtz-AI-Energy/ReCycle

Communication bottlenecks severely hinder the scalability of distributed neural network training, particularly in high-performance computing (HPC) environments. We introduce AB-training, a novel data-parallel method that leverages low-rank representations and independent training groups to significantly reduce communication overhead. Our experiments demonstrate an average reduction in network traffic of approximately 70.31\% across various scaling scenarios, increasing the training potential of communication-constrained systems and accelerating convergence at scale. AB-training also exhibits a pronounced regularization effect at smaller scales, leading to improved generalization while maintaining or even reducing training time. We achieve a remarkable 44.14 : 1 compression ratio on VGG16 trained on CIFAR-10 with minimal accuracy loss, and outperform traditional data parallel training by 1.55\% on ResNet-50 trained on ImageNet-2012. While AB-training is promising, our findings also reveal that large batch effects persist even in low-rank regimes, underscoring the need for further research into optimized update mechanisms for massively distributed training.

Quantum computing (QC) seems to show potential for application in machine learning (ML). In particular quantum kernel methods (QKM) exhibit promising properties for use in supervised ML tasks. However, a major disadvantage of kernel methods is their unfavorable quadratic scaling with the number of training samples. Together with the limits imposed by currently available quantum hardware (NISQ devices) with their low qubit coherence times, small number of qubits, and high error rates, the use of QC in ML at an industrially relevant scale is currently impossible. As a small step in improving the potential applications of QKMs, we introduce QUACK, a quantum kernel algorithm whose time complexity scales linear with the number of samples during training, and independent of the number of training samples in the inference stage. In the training process, only the kernel entries for the samples and the centers of the classes are calculated, i.e. the maximum shape of the kernel for n samples and c classes is (n, c). During training, the parameters of the quantum kernel and the positions of the centroids are optimized iteratively. In the inference stage, for every new sample the circuit is only evaluated for every centroid, i.e. c times. We show that the QUACK algorithm nevertheless provides satisfactory results and can perform at a similar level as classical kernel methods with quadratic scaling during training. In addition, our (simulated) algorithm is able to handle high-dimensional datasets such as MNIST with 784 features without any dimensionality reduction., Comment: Accepted to IEEE International Conference on Quantum Computing and Engineering (QCE) 2024

We explore the possibility of accelerating the formal verification of classical programs with a quantum computer. A common source of security flaws stems from the existence of common programming errors like use after free, null-pointer dereference, or division by zero. To aid in the discovery of such errors, we try to verify that no such flaws exist. In our approach, for some code snippet and undesired behaviour, a SAT instance is generated, which is satisfiable precisely if the behavior is present in the code. It is in turn converted to an optimization problem, that is solved on a quantum computer. This approach holds the potential of an asymptotically polynomial speedup. Minimal examples of common errors, like out-of-bounds and overflows, but also synthetic instances with special properties, specific number of solutions, or structure, are tested with different solvers and tried on a quantum device. We use the near-standard Quantum Approximation Optimisation Algorithm, an application of the Grover algorithm, and the Quantum Singular Value Transformation to find the optimal solution, and with it a satisfying assignment.

Quantum machine learning (QML) continues to be an area of tremendous interest from research and industry. While QML models have been shown to be vulnerable to adversarial attacks much in the same manner as classical machine learning models, it is still largely unknown how to compare adversarial attacks on quantum versus classical models. In this paper, we show how to systematically investigate the similarities and differences in adversarial robustness of classical and quantum models using transfer attacks, perturbation patterns and Lipschitz bounds. More specifically, we focus on classification tasks on a handcrafted dataset that allows quantitative analysis for feature attribution. This enables us to get insight, both theoretically and experimentally, on the robustness of classification networks. We start by comparing typical QML model architectures such as amplitude and re-upload encoding circuits with variational parameters to a classical ConvNet architecture. Next, we introduce a classical approximation of QML circuits (originally obtained with Random Fourier Features sampling but adapted in this work to fit a trainable encoding) and evaluate this model, denoted Fourier network, in comparison to other architectures. Our findings show that this Fourier network can be seen as a "middle ground" on the quantum-classical boundary. While adversarial attacks successfully transfer across this boundary in both directions, we also show that regularization helps quantum networks to be more robust, which has direct impact on Lipschitz bounds and transfer attacks., Comment: submitted to IEEE QCE24

A symmetric ideal is an ideal in a polynomial ring which is stable under all permutations of the variables. In this paper we initiate a global study of zero-dimensional symmetric ideals. By this we mean a geometric study of the invariant Hilbert schemes $\mathrm{Hilb}_{\rho}^{S_n}(\mathbb{C}^n)$ parametrizing symmetric subschemes of $\mathbb{C}^n$ whose coordinate rings, as $S_n$-modules, are isomorphic to a given representation $\rho$. In the case that $\rho = M^\lambda$ is a permutation module corresponding to certain special types of partitions $\lambda$ of $n$, we prove that $\mathrm{Hilb}_{\rho}^{S_n}(\mathbb{C}^n)$ is irreducible or even smooth. We also prove irreducibility whenever $\dim \rho \leq 2n$ and the invariant Hilbert scheme is non-empty. In this same range, we classify all homogeneous symmetric ideals and decide which of these define singular points of $\mathrm{Hilb}_{\rho}^{S_n}(\mathbb{C}^n)$. A central tool is the combinatorial theory of higher Specht polynomials., Comment: Comments welcome!

Univariate polynomials are called stable with respect to a circular region $\mathcal{A}$, if all of their roots are in $\mathcal{A}$. We consider the special case where $\mathcal{A}$ is a half-plane and investigate affine slices of the set of stable polynomials. In this setup, we show that an affine slice of codimension $k$ always contains a stable polynomial that possesses at most $2(k+2)$ distinct roots on the boundary and at most $(k+2)$ distinct roots in the interior of $\mathcal{A}$. This result also extends to affine slices of weakly Hurwitz polynomials, i.e. real, univariate, left half-plane stable polynomials. Subsequently, we apply these results to symmetric polynomials and varieties. Here we show that a variety described by polynomials in few multiaffine polynomials has no root in $\mathcal{A}^n$, if and only if it has no root in $\mathcal{A}^n$ with few distinct coordinates. This is at the same time a generalization of the degree principle to stable polynomials and a generalization of Grace-Walsh-Szeg\H{o}'s coincidence theorem., Comment: 13 pages

The equivariant nonnegativity versus sums of squares question has been solved for any infinite series of essential reflection groups but type A. As a first step to a classification, we analyse $A_n$-invariant quartics. We prove that the cones of invariant sums of squares and nonnegative forms are equal if and only if the number of variables is at most 3 or odd.

This study explores the learning dynamics of neural networks by analyzing the singular value decomposition (SVD) of their weights throughout training. Our investigation reveals that an orthogonal basis within each multidimensional weight's SVD representation stabilizes during training. Building upon this, we introduce Orthogonality-Informed Adaptive Low-Rank (OIALR) training, a novel training method exploiting the intrinsic orthogonality of neural networks. OIALR seamlessly integrates into existing training workflows with minimal accuracy loss, as demonstrated by benchmarking on various datasets and well-established network architectures. With appropriate hyperparameter tuning, OIALR can surpass conventional training setups, including those of state-of-the-art models.

Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for its classically challenging representational capacity, notable improvements in average precision compared to classical counterparts were observed in previous studies. Conventional calculations of these kernels, however, present a quadratic time complexity concerning data size, posing challenges in practical applications. To mitigate this, we explore two distinct approaches: utilizing randomized measurements to evaluate the quantum kernel and implementing the variable subsampling ensemble method, both targeting linear time complexity. Experimental results demonstrate a substantial reduction in training and inference times by up to 95\% and 25\% respectively, employing these methods. Although unstable, the average precision of randomized measurements discernibly surpasses that of the classical Radial Basis Function kernel, suggesting a promising direction for further research in scalable, efficient quantum computing applications in machine learning., Comment: Accepted at ICAART 2024

The IAG solar observatory is producing high-fidelity, ultra-high-resolution spectra (R>500000) of the spatially resolved surface of the Sun using a Fourier Transform spectrometer (FTS). The radial velocity (RV) calibration of these spectra is currently performed using absorption lines from Earth's atmosphere, limiting the precision and accuracy. To improve the frequency calibration precision and accuracy we plan to use a Fabry-Perot etalon (FP) setup that is an evolution of the CARMENES FP design and an iodine cell in combination. To create an accurate wavelength solution, the iodine cell is measured in parallel with the FP. The FP can then be used to transfer the accurate wavelength solution provided by the iodine via simultaneous calibration of solar observations. To verify the stability and precision of the FTS we perform parallel measurements of the FP and an iodine cell. The measurements show an intrinsic stability of the FTS of a level of 1 m/s over 90 hours. The difference between the FP RVs and the iodine cell RVs show no significant trends during the same time span. The RMS of the RV difference between FP and iodine cell is 10.7 cm/s, which can be largely attributed to the intrinsic RV precisions of the iodine cell and the FP (10.2 cm/s and 1.0 cm/s, respectively). This shows that we can calibrate the FTS to a level of 10 cm/s, competitive with current state-of-the-art precision RV instruments. Based on these results we argue that the spectrum of iodine can be used as an absolute reference to reach an RV accuracy of 10 cm/s., Comment: 13 pages, 9 figures, to be published in Journal of Astronomical Telescopes, Instruments, and Systems (JATIS)

Machine-learning (ML) shortcuts or spurious correlations are artifacts in datasets that lead to very good training and test performance but severely limit the model's generalization capability. Such shortcuts are insidious because they go unnoticed due to good in-domain test performance. In this paper, we explore the influence of different shortcuts and show that even simple shortcuts are difficult to detect by explainable AI methods. We then exploit this fact and design an approach to defend online databases against crawlers: providers such as dating platforms, clothing manufacturers, or used car dealers have to deal with a professionalized crawling industry that grabs and resells data points on a large scale. We show that a deterrent can be created by deliberately adding ML shortcuts. Such augmented datasets are then unusable for ML use cases, which deters crawlers and the unauthorized use of data from the internet. Using real-world data from three use cases, we show that the proposed approach renders such collected data unusable, while the shortcut is at the same time difficult to notice in human perception. Thus, our proposed approach can serve as a proactive protection against illegitimate data crawling., Comment: Published at BMVC 2023

We present EZ, a novel current deposition algorithm for particle-in-cell (PIC) simulations. EZ calculates the current density on the electromagnetic grid due to macro-particle motion within a time step by solving the continuity equation of electrodynamics. Being a charge conserving hybridization of Esirkepov's method and ZigZag, we refer to it as ``EZ'' as shorthand for ``Esirkepov meets ZigZag''. Simulations of a warm, relativistic plasma with PIConGPU show that EZ achieves the same level of charge conservation as the commonly used method by Esirkepov, yet reaches higher performance for macro-particle assignment-functions up to third-order. In addition to a detailed description of the functioning of EZ, reasons for the expected and observed performance increase are given, and guidelines for its implementation aiming at highest performance on GPUs are provided.

Anomaly detection (AD) involves identifying observations or events that deviate in some way from the rest of the data. Machine learning techniques have shown success in automating this process by detecting hidden patterns and deviations in large-scale data. The potential of quantum computing for machine learning has been widely recognized, leading to extensive research efforts to develop suitable quantum machine learning (QML) algorithms. In particular, the search for QML algorithms for near-term NISQ devices is in full swing. However, NISQ devices pose additional challenges due to their limited qubit coherence times, low number of qubits, and high error rates. Kernel methods based on quantum kernel estimation have emerged as a promising approach to QML on NISQ devices, offering theoretical guarantees, versatility, and compatibility with NISQ constraints. Especially support vector machines (SVM) utilizing quantum kernel estimation have shown success in various supervised learning tasks. However, in the context of AD, semisupervised learning is of great relevance, and yet there is limited research published in this area. This paper introduces an approach to semisupervised AD based on the reconstruction loss of a support vector regression (SVR) with quantum kernel. This novel model is an alternative to the variational quantum and quantum kernel one-class classifiers, and is compared to a quantum autoencoder as quantum baseline and a SVR with radial-basis-function (RBF) kernel as well as a classical autoencoder as classical baselines. The models are benchmarked extensively on 10 real-world AD data sets and one toy data set, and it is shown that our SVR model with quantum kernel performs better than the SVR with RBF kernel as well as all other models, achieving highest mean AUC over all data sets. In addition, our QSVR outperforms the quantum autoencoder on 9 out of 11 data sets., Comment: Accepted to IEEE International Conference on Quantum Computing and Engineering (QCE) 2023

Backpropagation has long been criticized for being biologically implausible, relying on concepts that are not viable in natural learning processes. This paper proposes an alternative approach to solve two core issues, i.e., weight transport and update locking, for biological plausibility and computational efficiency. We introduce Feed-Forward with delayed Feedback (F$^3$), which improves upon prior work by utilizing delayed error information as a sample-wise scaling factor to approximate gradients more accurately. We find that F$^3$ reduces the gap in predictive performance between biologically plausible training algorithms and backpropagation by up to 96%. This demonstrates the applicability of biologically plausible training and opens up promising new avenues for low-energy training and parallelization.

We study the geometry of the image of the nonnegative orthant under the power-sum map and the elementary symmetric polynomials map. After analyzing the image in finitely many variables, we concentrate on the limit as the number of variables approaches infinity. We explain how the geometry of the limit plays a crucial role in undecidability results in nonnegativity of symmetric polynomials, deciding validity of trace inequalities in linear algebra, and extremal combinatorics - recently observed by Blekherman, Raymond, and F. Wei. We verify the experimental observation that the image has the combinatorial geometry of a cyclic polytope made by Mel\'anov\'a, Sturmfels, and Winter, and generalize results of Choi, Lam, and Reznick on nonnegative even symmetric polynomials. We also show that undecidability does not hold for the normalized power sum map., Comment: 29 pages