Search

Realizing universal fault-tolerant quantum computation is a key goal in quantum information science. By encoding quantum information into logical qubits utilizing quantum error correcting codes, physical errors can be detected and corrected, enabling substantial reduction in logical error rates. However, the set of logical operations that can be easily implemented on such encoded qubits is often constrained, necessitating the use of special resource states known as 'magic states' to implement universal, classically hard circuits. A key method to prepare high-fidelity magic states is to perform 'distillation', creating them from multiple lower fidelity inputs. Here we present the experimental realization of magic state distillation with logical qubits on a neutral-atom quantum computer. Our approach makes use of a dynamically reconfigurable architecture to encode and perform quantum operations on many logical qubits in parallel. We demonstrate the distillation of magic states encoded in d=3 and d=5 color codes, observing improvements of the logical fidelity of the output magic states compared to the input logical magic states. These experiments demonstrate a key building block of universal fault-tolerant quantum computation, and represent an important step towards large-scale logical quantum processors., Comment: 8+11 pages, 4+4 figures

We introduce an efficient open-source python package for the inverse design of three-dimensional photonic nanostructures using the Finite-Difference Time-Domain (FDTD) method. Leveraging a flexible reverse-mode automatic differentiation implementation, our software enables gradient-based optimization over large simulation volumes. Gradient computation is implemented within the JAX framework and based on the property of time reversibility in Maxwell's equations. This approach significantly reduces computational time and memory requirements compared to traditional FDTD methods. Gradient-based optimization facilitates the automatic creation of intricate three-dimensional structures with millions of design parameters, which would be infeasible to design manually. We demonstrate the scalability of the solver from single to multiple GPUs through several inverse design examples, highlighting its robustness and performance in large-scale photonic simulations. In addition, the package features an object-oriented and user-friendly API that simplifies the specification of materials, sources, and constraints. Specifically, it allows for intuitive positioning and sizing of objects in absolute or relative coordinates within the simulation scene. By rapid specification of the desired design properties and rapid optimization within the given user constraints, this open-source framework aims to accelerate innovation in photonic inverse design. It yields a powerful and accessible computational tool for researchers, applicable in a wide range of use cases, including but not limited to photonic waveguides, active devices, and photonic integrated circuits.

In this paper, we consider the application of exponential integrators to problems that are advection dominated, either on the entire or on a subset of the domain. In this context, we compare Leja and Krylov based methods to compute the action of exponential and related matrix functions. We set up a performance model by counting the different operations needed to implement the considered algorithms. This model assumes that the evaluation of the right-hand side is memory bound and allows us to evaluate performance in a hardware independent way. We find that exponential integrators perform comparably to explicit Runge-Kutta schemes for problems that are advection dominated in the entire domain. Moreover, they are able to outperform explicit methods in situations where small parts of the domain are diffusion dominated. We generally observe that Leja based methods outperform Krylov iterations in the problems considered. This is in particular true if computing inner products is expensive.

This paper aims to delve into the rate-distortion-complexity trade-offs of modern neural video coding. Recent years have witnessed much research effort being focused on exploring the full potential of neural video coding. Conditional autoencoders have emerged as the mainstream approach to efficient neural video coding. The central theme of conditional autoencoders is to leverage both spatial and temporal information for better conditional coding. However, a recent study indicates that conditional coding may suffer from information bottlenecks, potentially performing worse than traditional residual coding. To address this issue, recent conditional coding methods incorporate a large number of high-resolution features as the condition signal, leading to a considerable increase in the number of multiply-accumulate operations, memory footprint, and model size. Taking DCVC as the common code base, we investigate how the newly proposed conditional residual coding, an emerging new school of thought, and its variants may strike a better balance among rate, distortion, and complexity., Comment: Accepted to MMSP 2024

Contextualized embeddings based on large language models (LLMs) are available for various languages, but their coverage is often limited for lower resourced languages. Using LLMs for such languages is often difficult due to a high computational cost; not only during training, but also during inference. Static word embeddings are much more resource-efficient ("green"), and thus still provide value, particularly for very low-resource languages. There is, however, a notable lack of comprehensive repositories with such embeddings for diverse languages. To address this gap, we present GrEmLIn, a centralized repository of green, static baseline embeddings for 87 mid- and low-resource languages. We compute GrEmLIn embeddings with a novel method that enhances GloVe embeddings by integrating multilingual graph knowledge, which makes our static embeddings competitive with LLM representations, while being parameter-free at inference time. Our experiments demonstrate that GrEmLIn embeddings outperform state-of-the-art contextualized embeddings from E5 on the task of lexical similarity. They remain competitive in extrinsic evaluation tasks like sentiment analysis and natural language inference, with average performance gaps of just 5-10\% or less compared to state-of-the-art models, given a sufficient vocabulary overlap with the target task, and underperform only on topic classification. Our code and embeddings are publicly available at https://huggingface.co/DFKI., Comment: Long paper, preview

The dual phosphorylation network provides an essential component of intracellular signaling, affecting the expression of phenotypes and cell metabolism. For particular choices of kinetic parameters, this system exhibits multistationarity, a property that is relevant in the decision-making of cells. Determining which reaction rate constants correspond to monostationarity and which produce multistationarity is an open problem. The system's monostationarity is linked to the nonnegativity of a specific polynomial. A previous study by Feliu et al. provides a sufficient condition for monostationarity via a decomposition of this polynomial into nonnegative circuit polynomials. However, this decomposition is not unique. We extend their work by a systematic approach to classifying such decompositions in the dual phosphorylation network. Using this result classification, we provide a qualitative comparison of the decompositions into nonnegative circuit polynomials via empirical experiments and improve on previous conditions for the region of monostationarity., Comment: 20 pages, 9 figures, 2 tables

We consider corotational wave maps from Minkowski spacetime into the sphere and the equivariant Yang-Mills equation for all energy-supercritical dimensions. Both models have explicit self-similar finite time blowup solutions, which continue to exist even past the singularity. We prove the nonlinear asymptotic stability of these solutions in spacetime regions that approach the future light cone of the singularity. For this, we develop a general functional analytic framework in adapted similarity coordinates that allows to evolve the stable wave flow near a self-similar blowup solution in such spacetime regions., Comment: 68 pages, 2 figures

In the era of high performing Large Language Models, researchers have widely acknowledged that contextual word representations are one of the key drivers in achieving top performances in downstream tasks. In this work, we investigate the degree of contextualization encoded in the fine-grained sub-layer representations of a Pre-trained Language Model (PLM) by empirical experiments using linear probes. Unlike previous work, we are particularly interested in identifying the strength of contextualization across PLM sub-layer representations (i.e. Self-Attention, Feed-Forward Activation and Output sub-layers). To identify the main contributions of sub-layers to contextualisation, we first extract the sub-layer representations of polysemous words in minimally different sentence pairs, and compare how these representations change through the forward pass of the PLM network. Second, by probing on a sense identification classification task, we try to empirically localize the strength of contextualization information encoded in these sub-layer representations. With these probing experiments, we also try to gain a better understanding of the influence of context length and context richness on the degree of contextualization. Our main conclusion is cautionary: BERT demonstrates a high degree of contextualization in the top sub-layers if the word in question is in a specific position in the sentence with a shorter context window, but this does not systematically generalize across different word positions and context sizes.

Natural language explanations (NLEs) are vital for elucidating the reasoning behind large language model (LLM) decisions. Many techniques have been developed to generate NLEs using LLMs. However, like humans, LLMs might not always produce optimal NLEs on first attempt. Inspired by human learning processes, we introduce Cross-Refine, which employs role modeling by deploying two LLMs as generator and critic, respectively. The generator outputs a first NLE and then refines this initial explanation using feedback and suggestions provided by the critic. Cross-Refine does not require any supervised training data or additional training. We validate Cross-Refine across three NLP tasks using three state-of-the-art open-source LLMs through automatic and human evaluation. We select Self-Refine (Madaan et al., 2023) as the baseline, which only utilizes self-feedback to refine the explanations. Our findings from automatic evaluation and a user study indicate that Cross-Refine outperforms Self-Refine. Meanwhile, Cross-Refine can perform effectively with less powerful LLMs, whereas Self-Refine only yields strong results with ChatGPT. Additionally, we conduct an ablation study to assess the importance of feedback and suggestions. Both of them play an important role in refining explanations. We further evaluate Cross-Refine on a bilingual dataset in English and German., Comment: Accepted at COLING 2025; long paper

Prompt tuning is an efficient solution for training large language models (LLMs). However, current soft-prompt-based methods often sacrifice multi-task modularity, requiring the training process to be fully or partially repeated for each newly added task. While recent work on task vectors applied arithmetic operations on full model weights to achieve the desired multi-task performance, a similar approach for soft-prompts is still missing. To this end, we introduce Task Prompt Vectors, created by element-wise difference between weights of tuned soft-prompts and their random initialization. Experimental results on 12 NLU datasets show that task prompt vectors can be used in low-resource settings to effectively initialize prompt tuning on similar tasks. In addition, we show that task prompt vectors are independent of the random initialization of prompt tuning on 2 different language model architectures. This allows prompt arithmetics with the pre-trained vectors from different tasks. In this way, we provide a competitive alternative to state-of-the-art baselines by arithmetic addition of task prompt vectors from multiple tasks.

Active atomic clocks are predicted to provide far better short-term stability and robustness against thermal fluctuations than typical feedback-based optical atomic clocks. However, continuous laser operation using an ensemble of clock atoms still remains an experimentally challenging task. We study spatial self-organization in a transversely driven ensemble of clock atoms inside an optical resonator and coherent light emission from the cavity. We focus on the spectral properties of the emitted light in the narrow atomic linewidth regime, where the phase coherence providing frequency stability is stored in the atomic dipoles rather than the cavity field. The atoms are off-resonantly driven by a standing-wave coherent laser transversely to the cavity axis allowing for atomic motion along the cavity axis as well as along the pump. In order to treat larger atom numbers we employ a second-order cumulant expansion which allows us to calculate the spectrum of the cavity light field. We identify the self-organization threshold where the atoms align themselves in a checkerboard pattern thus maximizing light scattering into the cavity which simultaneously induces cooling. For a larger driving intensity, more atoms are transferred to the excited state, reducing cooling but increasing light emission from the excited atoms. This can be enhanced via a second cavity mode at the atomic frequency spatially shifted by a quarter wavelength. For large enough atom numbers we observe laser-like emission close to the bare atomic transition frequency., Comment: 8 pages, 8 figures

Long-range dipole-dipole interactions in subwavelength arrays of quantum emitters involve virtual photon exchange processes that impart forces on the emitters due to the imposed photon recoil. We perform a semi-classical analysis of the dynamics of an impurity allowed to freely move through a subwavelength array of atoms in different parameter regimes. We numerically solve the coupled set of equations between motional and spin degrees of freedom to elucidate the possible impurity trajectories realizable in this system. We find that the impurity can maintain quasi-stable orbits within the plaquette for long times. The regions through which these orbits pass are strongly dependent on the chosen atomic transition dipole moment. We further provide intuition for our findings based on a simplified model, where the lattice dynamics is adiabatically eliminated. As a final point of analysis, we also take the motional degrees of freedom of the lattice atoms into account, and study the polaron-like excitation induced in the kinetic state of the lattice by the impurity., Comment: 11 pages, 7 figures

The inverse design of photonic integrated circuits (PICs) presents distinctive computational challenges, including their large memory requirements. Advancements in the two-photon polymerization (2PP) fabrication process introduce additional complexity, necessitating the development of more flexible optimization algorithms to enable the creation of multi-material 3D structures with unique properties. This paper presents a memory efficient reverse-mode automatic differentiation framework for finite-difference time-domain (FDTD) simulations that is able to handle complex constraints arising from novel fabrication methods. Our method is based on straight-through gradient estimation that enables non-differentiable shape parametrizations. We demonstrate the effectiveness of our approach by creating increasingly complex structures to solve the coupling problem in PICs. The results highlight the potential of our method for future PIC design and practical applications., Comment: 26 pages, 11 figures

Prompt injection (both direct and indirect) and jailbreaking are now recognized as significant issues for large language models (LLMs), particularly due to their potential for harm in application-integrated contexts. This extended abstract explores a novel approach to protecting LLMs from such attacks, termed "soft begging." This method involves training soft prompts to counteract the effects of corrupted prompts on the LLM's output. We provide an overview of prompt injections and jailbreaking, introduce the theoretical basis of the "soft begging" technique, and discuss an evaluation of its effectiveness.

The dissemination of false information on online platforms presents a serious societal challenge. While manual fact-checking remains crucial, Large Language Models (LLMs) offer promising opportunities to support fact-checkers with their vast knowledge and advanced reasoning capabilities. This survey explores the application of generative LLMs in fact-checking, highlighting various approaches and techniques for prompting or fine-tuning these models. By providing an overview of existing methods and their limitations, the survey aims to enhance the understanding of how LLMs can be used in fact-checking and to facilitate further progress in their integration into the fact-checking process.

Cross-lingual knowledge transfer, especially between high- and low-resource languages, remains challenging in natural language processing (NLP). This study offers insights for improving cross-lingual NLP applications through the combination of parameter-efficient fine-tuning methods. We systematically explore strategies for enhancing cross-lingual transfer through the incorporation of language-specific and task-specific adapters and soft prompts. We present a detailed investigation of various combinations of these methods, exploring their efficiency across 16 languages, focusing on 10 mid- and low-resource languages. We further present to our knowledge the first use of soft prompts for language transfer, a technique we call soft language prompts. Our findings demonstrate that in contrast to claims of previous work, a combination of language and task adapters does not always work best; instead, combining a soft language prompt with a task adapter outperforms most configurations in many cases.

This paper explores the integration of graph knowledge from linguistic ontologies into multilingual Large Language Models (LLMs) using adapters to improve performance for low-resource languages (LRLs) in sentiment analysis (SA) and named entity recognition (NER). Building upon successful parameter-efficient fine-tuning techniques, such as K-ADAPTER and MAD-X, we propose a similar approach for incorporating knowledge from multilingual graphs, connecting concepts in various languages with each other through linguistic relationships, into multilingual LLMs for LRLs. Specifically, we focus on eight LRLs -- Maltese, Bulgarian, Indonesian, Nepali, Javanese, Uyghur, Tibetan, and Sinhala -- and employ language-specific adapters fine-tuned on data extracted from the language-specific section of ConceptNet, aiming to enable knowledge transfer across the languages covered by the knowledge graph. We compare various fine-tuning objectives, including standard Masked Language Modeling (MLM), MLM with full-word masking, and MLM with targeted masking, to analyse their effectiveness in learning and integrating the extracted graph data. Through empirical evaluation on language-specific tasks, we assess how structured graph knowledge affects the performance of multilingual LLMs for LRLs in SA and NER, providing insights into the potential benefits of adapting language models for low-resource scenarios., Comment: 9 pages, KaLLM workshop

We analyze the driven-dissipative dynamics of subwavelength periodic atomic arrays in free space, where atoms interact via light-induced dipole-dipole interactions. We find that depending on the system parameters, the underlying mean-field model allows four different types of dynamics at late times: a single monostable steady state solution, bistability (where two stable steady state solutions exist), limit cycles and chaotic dynamics. We provide conditions on the parameters required to realize the different solutions in the thermodynamic limit. In this limit, only the monostable or bistable regime can be accessed for the parameter values accessible via light-induced dipole-dipole interactions. For finite size periodic arrays, however, we find that the mean-field dynamics of the many-body system also exhibit limit cycles and chaotic behavior. Notably, the emergence of chaotic dynamics does not rely on the randomness of an external control parameter but arises solely due to the interplay of coherent drive and dissipation., Comment: 11 pages, 7 figures

The sequent calculus is a proof system which was designed as a more symmetric alternative to natural deduction. The {\lambda}{\mu}{\mu}-calculus is a term assignment system for the sequent calculus and a great foundation for compiler intermediate languages due to its first-class representation of evaluation contexts. Unfortunately, only experts of the sequent calculus can appreciate its beauty. To remedy this, we present the first introduction to the {\lambda}{\mu}{\mu}-calculus which is not directed at type theorists or logicians but at compiler hackers and programming-language enthusiasts. We do this by writing a compiler from a small but interesting surface language to the {\lambda}{\mu}{\mu}-calculus as a compiler intermediate language., Comment: Preprint of the paper accepted at ICFP '24

Conversational explainable artificial intelligence (ConvXAI) systems based on large language models (LLMs) have garnered significant interest from the research community in natural language processing (NLP) and human-computer interaction (HCI). Such systems can provide answers to user questions about explanations in dialogues, have the potential to enhance users' comprehension and offer more information about the decision-making and generation processes of LLMs. Currently available ConvXAI systems are based on intent recognition rather than free chat, as this has been found to be more precise and reliable in identifying users' intentions. However, the recognition of intents still presents a challenge in the case of ConvXAI, since little training data exist and the domain is highly specific, as there is a broad range of XAI methods to map requests onto. In order to bridge this gap, we present CoXQL, the first dataset in the NLP domain for user intent recognition in ConvXAI, covering 31 intents, seven of which require filling multiple slots. Subsequently, we enhance an existing parsing approach by incorporating template validations, and conduct an evaluation of several LLMs on CoXQL using different parsing strategies. We conclude that the improved parsing approach (MP+) surpasses the performance of previous approaches. We also discover that intents with multiple slots remain highly challenging for LLMs., Comment: EMNLP 2024 Findings (short paper); camera-ready version

We propose a versatile quantum sensing protocol based on two dissipatively coupled distant atoms embedded as impurities in a two-dimensional sub-wavelength atomic array. The array acts as a waveguide for the emitter light, creating cooperative enhancement that allows for more efficient population transfer. By monitoring the population of one of the impurity atoms, it is possible to detect frequency shifts in the emitters' resonance frequencies. We analytically estimate achievable sensitivities as well as the dependence on various system parameters. The proposed protocol is robust against various environmental factors and perturbations, which enhances its applicability in real-world scenarios.

Subwavelength atomic arrays in free space are becoming a leading platform for exploring emergent many-body quantum phenomena. These arrays feature strong light-induced dipole-dipole interactions, resulting in subradiant collective resonances characterized by narrowed linewidths. In this work, we present a sideband cooling scheme for atoms trapped in subwavelength arrays that utilizes these narrow collective resonances. We derive an effective master equation for the atomic motion by adiabatically eliminating the internal degrees of freedom of the atoms, and validate its prediction with numerical simulations of the full system. Our results demonstrate that subradiant resonances enable the cooling of ensembles of atoms to temperatures lower than those achievable without dipole interactions, provided the atoms have different trap frequencies. Remarkably, narrow collective resonances can be sideband-resolved even when the individual atomic transition is not. In such scenarios, ground state cooling becomes feasible solely due to light-induced dipole-dipole interactions. This approach could be utilized for future quantum technologies based on dense ensembles of emitters, and paves the way towards harnessing many-body cooperative decay for enhanced motional control., Comment: 10 pages of main text and appendix, with 4 figures. 9 pages of Supplemental Material, with 4 figures

In contrast to free space, in waveguides the dispersive and dissipative dipole-dipole interactions among quantum emitters exhibit a periodic behavior over remarkably long distances. We propose a novel setup exploiting this long-range periodicity in order to create highly excited subradiant states and facilitate fast controlled collective energy transport amongst far-apart ensembles coupled to a waveguide. For sufficiently large ensembles collective superradiant emission into the fiber modes dominates over its free space counterpart. We show that for a large number of emitters a fast transverse coherent pulse can create almost perfect subradiant states with up to $50\%$ excitation. On the other hand, for a coherent excitation of one sub-ensemble above an overall excitation fraction of $50\%$ we find a nearly lossless and fast energy transfer to the ground state sub-ensemble. This transport can be enhanced or suppressed by controlling the positions of the ensembles relative to each other, while it can also be realized with a random position distribution. In the optimally enhanced case this fast transfer appears as superradiant emission with subsequent superabsorption, yet, without a superradiant decay after the absorption. The highly excited subradiant states as well as the superradiant excitation transfer appear as suitable building blocks in applications like active atomic clocks, quantum batteries, quantum information protocols and quantum metrology procedures such as fiber-based Ramsey schemes., Comment: 9 pages, 7 figures

Nonlinear diffusion-reaction systems model a multitude of physical phenomena. A common situation is biological development modeling where such systems have been widely used to study spatiotemporal phenomena in cell biology. Systems of coupled diffusion-reaction equations are usually subject to some complicated features directly related to their multiphysics nature. Moreover, the presence of advection is source of numerical instabilities, in general, and adds another challenge to these systems. In this study, we propose a NURBS-based isogeometric analysis (IgA) combined with a second-order Strang operator splitting to deal with the multiphysics nature of the problem. The advection part is treated in a semi-Lagrangian framework and the resulting diffusion-reaction equations are then solved using an efficient time-stepping algorithm based on operator splitting. The accuracy of the method is studied by means of a advection-diffusion-reaction system with analytical solution. To further examine the performance of the new method on complex geometries, the well-known Schnakenberg-Turing problem is considered with and without advection. Finally, a Gray-Scott system on a circular domain is also presented. The results obtained demonstrate the efficiency of our new algorithm to accurately reproduce the solution in the presence of complex patterns on complex geometries. Moreover, the new method clarifies the effect of geometry on Turing patterns.

Understanding quantum phenomena which go beyond classical concepts is a focus of modern quantum physics. Here, we show how the theory of nonnegative polynomials emerging around Hilbert's 17th problem, can be used to optimally exploit data capturing the nonclassical nature of light. Specifically, we show that nonnegative polynomials can reveal nonclassicality in data even when it is hidden from standard detection methods up to now. Moreover, the abstract language of nonnegative polynomials also leads to a unified mathematical approach to nonclassicality for light and spin systems, allowing us to map methods for one to the other. Conversely, the physical problems arising also inspire several mathematical insights into characterisation of nonnegative polynomials., Comment: 16 pages, 5 figures, comments are welcome!

The expression problem describes how most types can easily be extended with new ways to produce the type or new ways to consume the type, but not both. When abstract syntax trees are defined as an algebraic data type, for example, they can easily be extended with new consumers, such as print or eval, but adding a new constructor requires the modification of all existing pattern matches. The expression problem is one way to elucidate the difference between functional or data-oriented programs (easily extendable by new consumers) and object-oriented programs (easily extendable by new producers). This difference between programs which are extensible by new producers or new consumers also exists for dependently typed programming, but with one core difference: Dependently-typed programming almost exclusively follows the functional programming model and not the object-oriented model, which leaves an interesting space in the programming language landscape unexplored. In this paper, we explore the field of dependently-typed object-oriented programming by deriving it from first principles using the principle of duality. That is, we do not extend an existing object-oriented formalism with dependent types in an ad-hoc fashion, but instead start from a familiar data-oriented language and derive its dual fragment by the systematic use of defunctionalization and refunctionalization. Our central contribution is a dependently typed calculus which contains two dual language fragments. We provide type- and semantics-preserving transformations between these two language fragments: defunctionalization and refunctionalization. We have implemented this language and these transformations and use this implementation to explain the various ways in which constructions in dependently typed programming can be explained as special instances of the phenomenon of duality., Comment: This extended version contains additional appendices not contained in the published version. The published version will be available in the ACM DL as part of the PACMPL issue for OOPSLA 2024

The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point iteration, making its implementation straightforward. Second-order convergence in time is shown in an abstract Hilbert space framework under reasonable assumptions on the problem. Numerical experiments illustrate the proven order of convergence.

Light-harvesting via the transport and trapping of optically-induced electronic excitations is of fundamental interest to the design of new energy efficient quantum technologies. Using a paradigmatic quantum optical model, we study the influence of coherence, entanglement, and cooperative dissipation on the transport and capture of excitation energy. In particular, we demonstrate that the rate of energy extraction is optimized under conditions that minimize the quantum coherence and entanglement of the system. We show that this finding is not limited to disordered or high temperature systems but is instead a fundamental consequence of spontaneous parity time-reversal symmetry breaking associated with the quantum-to-classical transition. We then examine the effects of vibrational fluctuations, revealing a strong dephasing assisted transport enhancement for delocalized excitations in the presence of cooperative interactions. Our results highlight the rich, emergent behavior associated with decoherence and may be relevant to the study of biological photosynthetic antenna complexes or to the design of room-temperature quantum devices., Comment: Updated acknowledgements

We present a model describing the transmission of light through atomic media with a vanishing index of refraction. Zero index materials are of particular interest as the infinite phase velocity of light within the material offers the potential to manipulate electromagnetic waves to mediate dipole-dipole interactions over extended distances. We focus on the preparation of zero-index conditions based on atomic coherence using two distinct atomic media as exemplary of generic zero-index materials. We establish a model based on the Maxwell-Bloch equations to describe the propagation of a light pulse through these media. To investigate the sustainability of the zero index under minimal light conditions, we assume single-photon intensity of the propagating pulse. Specifically, we examine whether the spatial phase change of the photon remains zero as it traverses the medium. We employ a finite-element numerical approach to solve the coupled Maxwell-Bloch equations describing the photon propagation. Our results indicate that the presence of a photon within the medium will disrupt the zero-index state, thus disallowing the establishment of enhanced dipole-dipole interactions over large distances., Comment: 15 pages, 29 figures

We investigate a filtered Lie-Trotter splitting scheme for the ``good" Boussinesq equation and derive an error estimate for initial data with very low regularity. Through the use of discrete Bourgain spaces, our analysis extends to initial data in $H^{s}$ for $01/2$ imposed by the bilinear estimate in smooth Sobolev spaces. We establish convergence rates of order $\tau^{s/2}$ in $L^2$ for such levels of regularity. Our analytical findings are supported by numerical experiments., Comment: 3 figures

The Traveling Salesman Problem (TSP) is one of the most extensively researched and widely applied combinatorial optimization problems. It is NP-hard even in the symmetric and metric case. Building upon elaborate research, state-of-the-art exact solvers such as CONCORDE can solve TSP instances with several ten thousand vertices. A key ingredient for these integer programming approaches are fast heuristics to find a good initial solution, in particular the Lin-Kernighan-Helsgaun (LKH) heuristic. For instances with few hundred vertices heuristics like LKH often find an optimal solution. In this work we develop variations of LKH that perform significantly better on large instances. LKH repeatedly improves an initially random tour by exchanging edges along alternating circles. Thereby, it respects several criteria designed to quickly find alternating circles that give a feasible improvement of the tour. Among those criteria, the positive gain criterion stayed mostly untouched in previous research. It requires that, while constructing an alternating circle, the total gain has to be positive after each pair of edges. We relax this criterion carefully leading to improvement steps hitherto undiscovered by LKH. We confirm this improvement experimentally via extensive simulations on various benchmark libraries for TSP. Our computational study shows that for large instances our method is on average 13% faster than the latest version of LKH., Comment: 25 pages, 23 pages appendix, 7 figures, 27 tables

Conditional coding has lately emerged as the mainstream approach to learned video compression. However, a recent study shows that it may perform worse than residual coding when the information bottleneck arises. Conditional residual coding was thus proposed, creating a new school of thought to improve on conditional coding. Notably, conditional residual coding relies heavily on the assumption that the residual frame has a lower entropy rate than that of the intra frame. Recognizing that this assumption is not always true due to dis-occlusion phenomena or unreliable motion estimates, we propose a masked conditional residual coding scheme. It learns a soft mask to form a hybrid of conditional coding and conditional residual coding in a pixel adaptive manner. We introduce a Transformer-based conditional autoencoder. Several strategies are investigated with regard to how to condition a Transformer-based autoencoder for inter-frame coding, a topic that is largely under-explored. Additionally, we propose a channel transform module (CTM) to decorrelate the image latents along the channel dimension, with the aim of using the simple hyperprior to approach similar compression performance to the channel-wise autoregressive model. Experimental results confirm the superiority of our masked conditional residual transformer (termed MaskCRT) to both conditional coding and conditional residual coding. On commonly used datasets, MaskCRT shows comparable BD-rate results to VTM-17.0 under the low delay P configuration in terms of PSNR-RGB and outperforms VTM-17.0 in terms of MS-SSIM-RGB. It also opens up a new research direction for advancing learned video compression., Comment: Accepted for Publication in IEEE Transactions on Circuits and Systems for Video Technology (TCSVT)

The filtered Lie splitting scheme is an established method for the numerical integration of the periodic nonlinear Schr\"{o}dinger equation at low regularity. Its temporal convergence was recently analyzed in a framework of discrete Bourgain spaces in one and two space dimensions for initial data in $H^s$ with $0

Pre-trained Language Models (PLMs) have shown to be consistently successful in a plethora of NLP tasks due to their ability to learn contextualized representations of words (Ethayarajh, 2019). BERT (Devlin et al., 2018), ELMo (Peters et al., 2018) and other PLMs encode word meaning via textual context, as opposed to static word embeddings, which encode all meanings of a word in a single vector representation. In this work, we present a study that aims to localize where exactly in a PLM word contextualization happens. In order to find the location of this word meaning transformation, we investigate representations of polysemous words in the basic BERT uncased 12 layer architecture (Devlin et al., 2018), a masked language model trained on an additional sentence adjacency objective, using qualitative and quantitative measures., Comment: EMNLP 2023 BlackBloxNLP 2023 Workshop

We show that the performance of critical quantum metrology protocols, counter-intuitively, can be enhanced by finite temperature. We consider a toy-model squeezing Hamiltonian, the Lipkin-Meshkov-Glick model and the paradigmatic Ising model. We show that the temperature enhancement of the quantum Fisher information can be achieved by adiabatic preparation of the critical state and by preparing it directly in the proximity of the critical point. We also find a relatively simple, however, non-optimal measurement capable of harnessing finite temperature to increase the parameter estimation sensitivity. Therefore, we argue that temperature can be considered as a resource in critical quantum metrology., Comment: 6 pages, 2 figures, improved presentation and discussions