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Image inpainting, the process of restoring missing or corrupted regions of an image by reconstructing pixel information, has recently seen considerable advancements through deep learning-based approaches. In this paper, we introduce a novel deep learning-based pre-processing methodology for image inpainting utilizing the Vision Transformer (ViT). Our approach involves replacing masked pixel values with those generated by the ViT, leveraging diverse visual patches within the attention matrix to capture discriminative spatial features. To the best of our knowledge, this is the first instance of such a pre-processing model being proposed for image inpainting tasks. Furthermore, we show that our methodology can be effectively applied using the pre-trained ViT model with pre-defined patch size. To evaluate the generalization capability of the proposed methodology, we provide experimental results comparing our approach with four standard models across four public datasets, demonstrating the efficacy of our pre-processing technique in enhancing inpainting performance.

Preparing thermal (Gibbs) states is a common task in physics and computer science. Recent algorithms mimic cooling via system-bath coupling, where the cost is determined by mixing time, akin to classical Metropolis-like algorithms. However, few methods exist to demonstrate slow mixing in quantum systems, unlike the well-established classical tools for systems like the Ising model and constraint satisfaction problems. We present a quantum generalization of these tools through a generic bottleneck lemma that implies slow mixing in quantum systems. This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles and quantified either through Bohr spectrum jumps or operator locality. Using our bottleneck lemma, we establish unconditional lower bounds on the mixing times of Gibbs samplers for several families of Hamiltonians at low temperatures. For classical Hamiltonians with mixing time lower bounds $T_\mathrm{mix} = 2^{\Omega(n^\alpha)}$, we prove that quantum Gibbs samplers also have $T_\mathrm{mix} = 2^{\Omega(n^\alpha)}$. This applies to models like random $K$-SAT instances and spin glasses. For stabilizer Hamiltonians, we provide a concise proof of exponential lower bounds $T_\mathrm{mix} = 2^{\Omega(n)}$ on mixing times of good $n$-qubit stabilizer codes at low constant temperature, improving upon previous bounds of $T_\mathrm{mix} = 2^{\Omega(\sqrt n)}$. Finally, for $H = H_0 + h\sum_i X_i$ with $H_0$ diagonal in $Z$ basis, we show that a linear free energy barrier in $H_0$ leads to $T_\mathrm{mix} = 2^{\Omega(n)}$ for local Gibbs samplers at low temperature and small $h$. Even with sublinear barriers, we use Poisson Feynman-Kac techniques to lift classical bottlenecks to quantum ones establishing an asymptotically tight lower bound $T_\mathrm{mix} = 2^{n^{1/2-o(1)}}$ for the 2D transverse field Ising model.

Two-dimensional (2D) kagome lattice metals are interesting because they display flat electronic bands, Dirac points, Van Hove singularities, and can have interplay between charge density wave (CDW), magnetic order, and superconductivity. In kagome lattice antiferromagnet FeGe, a short-range CDW order was found deep within an antiferromagnetically ordered state, interacting with the magnetic order. Surprisingly, post-growth annealing of FeGe at 560$^{\circ}$C can suppress the CDW order while annealing at 320$^{\circ}$C induces a long-range CDW order, with the ability to cycle between the states repeatedly by annealing. Here we perform transport, neutron scattering, scanning transmission electron microscopy (STEM), and muon spin rotation ($\mu$SR) experiments to unveil the microscopic mechanism of the annealing process and its impact on magneto-transport, CDW, and magnetic properties of FeGe. We find that 560$^{\circ}$C annealing creates germanium vacancies uniformly distributed throughout the FeGe kagome lattice, which prevent the formation of Ge-Ge dimers necessary for the CDW order. Upon annealing at 320$^{\circ}$C, the system segregates into stoichiometric FeGe regions with long-range CDW order and regions with stacking faults that act as nucleation sites for the CDW. The presence or absence of CDW order greatly affects the anomalous Hall effect, incommensurate magnetic order, and spin-lattice coupling in FeGe, thus placing FeGe as the only known kagome lattice material with a tunable CDW and magnetic order, potentially useful for sensing and information transmission.

Data with geometric structure is ubiquitous in machine learning often arising from fundamental symmetries in a domain, such as permutation-invariance in graphs and translation-invariance in images. Group-convolutional architectures, which encode symmetries as inductive bias, have shown great success in applications, but can suffer from instabilities as their depth increases and often struggle to learn long range dependencies in data. For instance, graph neural networks experience instability due to the convergence of node representations (over-smoothing), which can occur after only a few iterations of message-passing, reducing their effectiveness in downstream tasks. Here, we propose and study unitary group convolutions, which allow for deeper networks that are more stable during training. The main focus of the paper are graph neural networks, where we show that unitary graph convolutions provably avoid over-smoothing. Our experimental results confirm that unitary graph convolutional networks achieve competitive performance on benchmark datasets compared to state-of-the-art graph neural networks. We complement our analysis of the graph domain with the study of general unitary convolutions and analyze their role in enhancing stability in general group convolutional architectures.

Non-sensory thalamic nuclei interact with the cortex through thalamocortical and cortico-basal ganglia-thalamocortical loops. Reciprocal connections between the mediodorsal thalamus (MD) and the prefrontal cortex are particularly important in cognition, while the reciprocal connections of the ventromedial (VM), ventral anterior (VA), and ventrolateral (VL) thalamus with the prefrontal and motor cortex are necessary for sensorimotor information processing. However, limited and often oversimplified understanding of the connectivity of the MD, VA, and VL nuclei in primates have hampered development of accurate models that explain their contribution to cognitive and sensorimotor functions. The current prevalent view suggests that the MD connects with the prefrontal cortex, while the VA and VL primarily connect with the premotor and motor cortices. However, past studies have also reported diverse connections that enable these nuclei to integrate information across a multitude of brain systems. In this review, we provide a comprehensive overview of the anatomical connectivity of the primate MD, VA, and VL with the cortex. By synthesizing recent findings, we aim to offer a valuable resource for students, newcomers to the field, and experts developing new theories or models of thalamic function. Our review highlights the complexity of these connections and underscores the need for further research to fully understand the diverse roles of these thalamic nuclei in primates., Comment: 31 pages, 8 figures, 1 table

Random spin systems at low temperatures are glassy and feature computational hardness in finding low-energy states. We study the random all-to-all interacting fermionic Sachdev--Ye--Kitaev (SYK) model and prove that, in contrast, (I) the low-energy states have polynomial circuit depth, yet (II) the annealed and quenched free energies agree to inverse-polynomially low temperatures, ruling out a glassy phase transition in this sense. These results are derived by showing that fermionic and spin systems significantly differ in their commutation index, which quantifies the non-commutativity of Hamiltonian terms. Our results suggest that low-temperature strongly interacting fermions, unlike spins, belong in a classically nontrivial yet quantumly easy phase., Comment: New result on commutation index of k-local Paulis for k > log(n)

We respond to arguments against our criticism that claim to show a divergence of Assembly Theory from popular compression. We have proven that any implementation of the concept of `copy number' underlying Assembly Theory (AT) and its assembly index (Ai) is equivalent to Shannon Entropy and not fundamentally or methodologically different from algorithms like ZIP compression. We show that the weak empirical correlation between Ai and LZW, which the authors offered as a defense against the proof that the assembly index calculation method is a compression scheme, is based on an incomplete and misleading experiment. When the experiment is completed, the asymptotic convergence to LZ compression and Shannon Entropy is evident and aligned with the mathematical proof previously offered. Therefore, this completes the theoretical and empirical demonstrations that any variation of the copy-number concept underlying AT, which resorts to counting the number of object repetitions `to arrive at a measure for life,' is equivalent to statistical compression and Shannon Entropy. We demonstrate that the authors' `we-are-better-because-we-are-worse' defense argument against compression does not withstand basic scrutiny and that their empirical results separating organic from inorganic compounds have not only been previously reported -- sans claims to unify physics and biology -- but are also driven solely by molecular length, not a particular feature of life captured by their assembly index. Finally, we show that Ai is a particular case of our BDM introduced almost a decade earlier and that arguments attributing special stochastic properties to Ai are misleading, not unique, and exactly the same as those that Shannon Entropy is already not only equipped with but designed for which we have also proven to be equivalent to Ai making AT redundant even in practice when applied to their own experimental data., Comment: 12 figures, 53 pages (minor tweaks and adding new refs of previous relevant work not cited by the authors of AT)

This paper provides a thorough examination of recent developments in the field of multi-choice Machine Reading Comprehension (MRC). Focused on benchmark datasets, methodologies, challenges, and future trajectories, our goal is to offer researchers a comprehensive overview of the current landscape in multi-choice MRC. The analysis delves into 30 existing cloze-style and multiple-choice MRC benchmark datasets, employing a refined classification method based on attributes such as corpus style, domain, complexity, context style, question style, and answer style. This classification system enhances our understanding of each dataset's diverse attributes and categorizes them based on their complexity. Furthermore, the paper categorizes recent methodologies into Fine-tuned and Prompt-tuned methods. Fine-tuned methods involve adapting pre-trained language models (PLMs) to a specific task through retraining on domain-specific datasets, while prompt-tuned methods use prompts to guide PLM response generation, presenting potential applications in zero-shot or few-shot learning scenarios. By contributing to ongoing discussions, inspiring future research directions, and fostering innovations, this paper aims to propel multi-choice MRC towards new frontiers of achievement.

Exploring nonequilibrium hot carriers from plasmonic metal nanostructures is a dynamic field in optoelectronics, driving photochemical reactions such as solar fuel generation. The hot carrier injection mechanism and the reaction rate are highly impacted by the metal/molecule interaction. However, determining the primary type of the reaction and thus the injection mechanism of the hot carriers has remained elusive. In this work, we reveal an electron injection mechanism deviating from a purely outersphere process for the reduction of ferricyanide redox molecule in a gold/p-type gallium nitride (Au/p- GaN) photocathode system. Combining our experimental approach with ab initio simulations, we discover that the efficient inner-sphere transfer of low-energy electrons leads to a continuous enhancement in the photocathode device performance in the interband regime. These findings provide important mechanistic insights, showing our methodology as a powerful tool for analyzing and engineering hot-carrier-driven processes in plasmonic photocatalytic systems and optoelectronic devices.

This paper studies the usefulness of incorporating path information in predicting chemical properties from molecular graphs, in the domain of QSAR (Quantitative Structure-Activity Relationship). Towards this, we developed a GNN-style model which can be toggled to operate in one of two modes: a non-degenerate mode which incorporates path information, and a degenerate mode which leaves out path information. Thus, by comparing the performance of the non-degenerate mode versus the degenerate mode on relevant QSAR datasets, we were able to directly assess the significance of path information on those datasets. Our results corroborate previous works, by suggesting that the usefulness of path information is datasetdependent. Unlike previous studies however, we took the very first steps towards building a model that could predict upfront whether or not path information would be useful for a given dataset at hand. Moreover, we also found that, albeit its simplicity, the degenerate mode of our model yielded rather surprising results, which outperformed more sophisticated SOTA models in certain cases.

The manifold hypothesis presumes that high-dimensional data lies on or near a low-dimensional manifold. While the utility of encoding geometric structure has been demonstrated empirically, rigorous analysis of its impact on the learnability of neural networks is largely missing. Several recent results have established hardness results for learning feedforward and equivariant neural networks under i.i.d. Gaussian or uniform Boolean data distributions. In this paper, we investigate the hardness of learning under the manifold hypothesis. We ask which minimal assumptions on the curvature and regularity of the manifold, if any, render the learning problem efficiently learnable. We prove that learning is hard under input manifolds of bounded curvature by extending proofs of hardness in the SQ and cryptographic settings for Boolean data inputs to the geometric setting. On the other hand, we show that additional assumptions on the volume of the data manifold alleviate these fundamental limitations and guarantee learnability via a simple interpolation argument. Notable instances of this regime are manifolds which can be reliably reconstructed via manifold learning. Looking forward, we comment on and empirically explore intermediate regimes of manifolds, which have heterogeneous features commonly found in real world data.

Let $G$ be a graph, and let $\lambda(G)$ denote the smallest eigenvalue of $G$. First, we provide an upper bound for $\lambda(G)$ based on induced bipartite subgraphs of $G$. Consequently, we extract two other upper bounds, one relying on the average degrees of induced bipartite subgraphs and a more explicit one in terms of the chromatic number and the independence number of $G$. In particular, motivated by our bounds, we introduce two graph invariants that are of interest on their own. Finally, special attention goes to the investigation of the sharpness of our bounds in various classes of graphs as well as the comparison with an existing well-known upper bound., Comment: 10 pages, to appear in Archiv der Mathematik

We consider the problem of estimating the ground state energy of quantum $p$-local spin glass random Hamiltonians, the quantum analogues of widely studied classical spin glass models. Our main result shows that the maximum energy achievable by product states has a well-defined limit (for even $p$) as $n\to\infty$ and is $E_{\text{product}}^\ast=\sqrt{2 \log p}$ in the limit of large $p$. This value is interpreted as the maximal energy of a much simpler so-called Random Energy Model, widely studied in the setting of classical spin glasses. The proof of the limit existing follows from an extension of Fekete's Lemma after we demonstrate near super-additivity of the (normalized) quenched free energy. The proof of the value follows from a second moment method on the number of states achieving a given energy when restricting to an $\epsilon$-net of product states. Furthermore, we relate the maximal energy achieved over all states to a $p$-dependent constant $\gamma\left(p\right)$, which is defined by the degree of violation of a certain asymptotic independence ansatz over graph matchings. We show that the maximal energy achieved by all states $E^\ast\left(p\right)$ in the limit of large $n$ is at most $\sqrt{\gamma\left(p\right)}E_{\text{product}}^\ast$. We also prove using Lindeberg's interpolation method that the limiting $E^\ast\left(p\right)$ is robust with respect to the choice of the randomness and, for instance, also applies to the case of sparse random Hamiltonians. This robustness in the randomness extends to a wide range of random Hamiltonian models including SYK and random quantum max-cut., Comment: 54 pages, 0 figures. arXiv admin note: substantial text overlap with arXiv:2309.11709

We prove the full equivalence between Assembly Theory (AT) and Shannon Entropy via a method based upon the principles of statistical compression renamed `assembly index' that belongs to the LZ family of popular compression algorithms (ZIP, GZIP, JPEG). Such popular algorithms have been shown to empirically reproduce the results of AT, results that have also been reported before in successful applications to separating organic from non-organic molecules and in the context of the study of selection and evolution. We show that the assembly index value is equivalent to the size of a minimal context-free grammar. The statistical compressibility of such a method is bounded by Shannon Entropy and other equivalent traditional LZ compression schemes, such as LZ77, LZ78, or LZW. In addition, we demonstrate that AT, and the algorithms supporting its pathway complexity, assembly index, and assembly number, define compression schemes and methods that are subsumed into the theory of algorithmic (Kolmogorov-Solomonoff-Chaitin) complexity. Due to AT's current lack of logical consistency in defining causality for non-stochastic processes and the lack of empirical evidence that it outperforms other complexity measures found in the literature capable of explaining the same phenomena, we conclude that the assembly index and the assembly number do not lead to an explanation or quantification of biases in generative (physical or biological) processes, including those brought about by (abiotic or Darwinian) selection and evolution, that could not have been arrived at using Shannon Entropy or that have not been reported before using classical information theory or algorithmic complexity., Comment: 15 pages + appendix, 2 figures

Scattering-type scanning near-field optical microscope (s-SNOM) has become an essential tool to study polaritons - quasiparticles of light coupled to collective charge oscillations - via direct probing of their near field with a spatial resolution far beyond the diffraction limit. However, extraction of the polariton complex propagation constant from the near-field images requires subtle considerations that have not received necessary attention so far. In this study, we discuss important yet overlooked aspects of the near-field analysis. First, we experimentally demonstrate that the sample orientation inside the s-SNOM may significantly affect the near-field interference pattern of mid-infrared polaritons, leading to an error in momentum measurement up to 7.7% even for the modes with effective index of 12.5. Second, we establish a methodology to correctly extract the polariton damping rate from the interference fringes depending on their origin - the s-SNOM nano-tip or the material edge. Overall, our work provides a unified framework for the accurate extraction of the polariton momentum and damping from the near-field interference fringes., Comment: 15 pages, 4 figures

Sign Language Recognition (SLR) has garnered significant attention from researchers in recent years, particularly the intricate domain of Continuous Sign Language Recognition (CSLR), which presents heightened complexity compared to Isolated Sign Language Recognition (ISLR). One of the prominent challenges in CSLR pertains to accurately detecting the boundaries of isolated signs within a continuous video stream. Additionally, the reliance on handcrafted features in existing models poses a challenge to achieving optimal accuracy. To surmount these challenges, we propose a novel approach utilizing a Transformer-based model. Unlike traditional models, our approach focuses on enhancing accuracy while eliminating the need for handcrafted features. The Transformer model is employed for both ISLR and CSLR. The training process involves using isolated sign videos, where hand keypoint features extracted from the input video are enriched using the Transformer model. Subsequently, these enriched features are forwarded to the final classification layer. The trained model, coupled with a post-processing method, is then applied to detect isolated sign boundaries within continuous sign videos. The evaluation of our model is conducted on two distinct datasets, including both continuous signs and their corresponding isolated signs, demonstrates promising results.

We study the problem of learning equivariant neural networks via gradient descent. The incorporation of known symmetries ("equivariance") into neural nets has empirically improved the performance of learning pipelines, in domains ranging from biology to computer vision. However, a rich yet separate line of learning theoretic research has demonstrated that actually learning shallow, fully-connected (i.e. non-symmetric) networks has exponential complexity in the correlational statistical query (CSQ) model, a framework encompassing gradient descent. In this work, we ask: are known problem symmetries sufficient to alleviate the fundamental hardness of learning neural nets with gradient descent? We answer this question in the negative. In particular, we give lower bounds for shallow graph neural networks, convolutional networks, invariant polynomials, and frame-averaged networks for permutation subgroups, which all scale either superpolynomially or exponentially in the relevant input dimension. Therefore, in spite of the significant inductive bias imparted via symmetry, actually learning the complete classes of functions represented by equivariant neural networks via gradient descent remains hard., Comment: 52 pages, 4 figures

Background: Ontologies are fundamental components of informatics infrastructure in domains such as biomedical, environmental, and food sciences, representing consensus knowledge in an accurate and computable form. However, their construction and maintenance demand substantial resources and necessitate substantial collaboration between domain experts, curators, and ontology experts. We present Dynamic Retrieval Augmented Generation of Ontologies using AI (DRAGON-AI), an ontology generation method employing Large Language Models (LLMs) and Retrieval Augmented Generation (RAG). DRAGON-AI can generate textual and logical ontology components, drawing from existing knowledge in multiple ontologies and unstructured text sources. Results: We assessed performance of DRAGON-AI on de novo term construction across ten diverse ontologies, making use of extensive manual evaluation of results. Our method has high precision for relationship generation, but has slightly lower precision than from logic-based reasoning. Our method is also able to generate definitions deemed acceptable by expert evaluators, but these scored worse than human-authored definitions. Notably, evaluators with the highest level of confidence in a domain were better able to discern flaws in AI-generated definitions. We also demonstrated the ability of DRAGON-AI to incorporate natural language instructions in the form of GitHub issues. Conclusions: These findings suggest DRAGON-AI's potential to substantially aid the manual ontology construction process. However, our results also underscore the importance of having expert curators and ontology editors drive the ontology generation process.

This paper outlines a new approach to designing tunable electromagnetic (EM) graphene-based metasurfaces using convolutional neural networks (CNNs). EM metasurfaces have previously been used to manipulate EM waves by adjusting the local phase of subwavelength elements within the wavelength scale, resulting in a variety of intriguing devices. However, the majority of these devices have only been capable of performing a single function, making it difficult to achieve multiple functionalities in a single design. Graphene, as an active material, offers unique properties, such as tunability, making it an excellent candidate for achieving tunable metasurfaces. The proposed procedure involves using two CNNs to design the passive structure of the graphene metasurfaces and predict the chemical potentials required for tunable responses. The CNNs are trained using transfer learning, which significantly reduced the time required to collect the training dataset. The proposed inverse design methodology demonstrates excellent performance in designing reconfigurable EM metasurfaces, which can be tuned to produce multiple functions, making it highly valuable for various applications. The results indicate that the proposed approach is efficient and accurate and provides a promising method for designing reconfigurable intelligent surfaces for future wireless communication systems.