Search

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.

Applications in photodetection, photochemistry, and active metamaterials and metasurfaces require fundamental understanding of ultrafast nonthermal and thermal electron processes in metallic nanosystems. Significant progress has been recently achieved in synthesis and investigation of low-loss monocrystalline gold, opening up opportunities for its use in ultrathin nanophotonic architectures. Here, we reveal fundamental differences in hot-electron thermalisation dynamics between monocrystalline and polycrystalline ultrathin (down to 10 nm thickness) gold films. Comparison of weak and strong excitation regimes showcases a counterintuitive unique interplay between thermalised and non-thermalised electron dynamics in mesoscopic gold with the important influence of the X-point interband transitions on the intraband electron relaxation. We also experimentally demonstrate the effect of hot-electron transfer into a substrate and the substrate thermal properties on electron-electron and electron-phonon scattering in ultrathin films. The hot-electron injection efficiency from monocrystalline gold into TiO2, approaching 9% is measured, close to the theoretical limit. These experimental and modelling results reveal the important role of crystallinity and interfaces on the microscopic electronic processes important in numerous applications., Comment: 9 pages, 4 figures

When in a pristine state, gallium and its alloys have the largest interfacial tensions of any liquid at room temperature. Nonetheless, applying as little as 0.8 V of electric potential across eutectic gallium indium (EGaIn) placed within aqueous NaOH (or other electrolyte) solution will cause the metal to behave as if its interfacial tension is near zero. The mechanism behind this phenomenon has remained poorly understood because NaOH dissolves the oxide species, making it difficult to directly measure the concentration, thickness, or chemical composition of the film that forms at the interface. In addition, the oxide layers formed are atomically-thin. Here, we present a suite of techniques which allow us to simultaneously measure both electrical and interfacial properties as a function of applied electric potential, allowing for new insights into the mechanisms which cause the dramatic decrease in interfacial tension. A key discovery from this work is that the interfacial tension displays hysteresis while lowering the applied potential. We combine these observations with electrochemical impedance spectroscopy to evaluate how these changes in interfacial tension arise from chemical, electrical, and mechanical changes on the interface, and close with ideas for how to build a free energy model to predict these changes from first principles.

This research addresses the challenge of conducting interpretable causal inference between a binary treatment and its resulting outcome when not all confounders are known. Confounders are factors that have an influence on both the treatment and the outcome. We relax the requirement of knowing all confounders under desired treatment, which we refer to as Selective Confounding, to enable causal inference in diverse real-world scenarios. Our proposed scheme is designed to work in situations where multiple decision-makers with different policies are involved and where there is a re-evaluation mechanism after the initial decision to ensure consistency. These assumptions are more practical to fulfill compared to the availability of all confounders under all treatments. To tackle the issue of Selective Confounding, we propose the use of dual-treatment samples. These samples allow us to employ two-step procedures, such as Regression Adjustment or Doubly-Robust, to learn counterfactual predictors. We provide both theoretical error bounds and empirical evidence of the effectiveness of our proposed scheme using synthetic and real-world child placement data. Furthermore, we introduce three evaluation methods specifically tailored to assess the performance in child placement scenarios. By emphasizing transparency and interpretability, our approach aims to provide decision-makers with a valuable tool. The source code repository of this work is located at https://github.com/sohaib730/CausalML.

We introduce a new cross-modal fusion technique designed for generative error correction in automatic speech recognition (ASR). Our methodology leverages both acoustic information and external linguistic representations to generate accurate speech transcription contexts. This marks a step towards a fresh paradigm in generative error correction within the realm of n-best hypotheses. Unlike the existing ranking-based rescoring methods, our approach adeptly uses distinct initialization techniques and parameter-efficient algorithms to boost ASR performance derived from pre-trained speech and text models. Through evaluation across diverse ASR datasets, we evaluate the stability and reproducibility of our fusion technique, demonstrating its improved word error rate relative (WERR) performance in comparison to n-best hypotheses by relatively 37.66%. To encourage future research, we have made our code and pre-trained models open source at https://github.com/Srijith-rkr/Whispering-LLaMA., Comment: Accepted to EMNLP 2023 as main paper. 10 pages. Revised math notations. GitHub: https://github.com/Srijith-rkr/Whispering-LLaMA

Topological materials confined in one-dimension (1D) can transform computing technologies, such as 1D topological semimetals for nanoscale interconnects and 1D topological superconductors for fault-tolerant quantum computing. As such, understanding crystallization of 1D-confined topological materials is critical. Here, we demonstrate 1D-confined crystallization routes during template-assisted nanowire synthesis where we observe diameter-dependent phase selectivity for topological metal tungsten phosphides. A phase bifurcation occurs to produce tungsten monophosphide and tungsten diphosphide at the cross-over nanowire diameter of ~ 35 nm. Four-dimensional scanning transmission electron microscopy was used to identify the two phases and to map crystallographic orientations of grains at a few nm resolution. The 1D-confined phase selectivity is attributed to the minimization of the total surface energy, which depends on the nanowire diameter and chemical potentials of precursors. Theoretical calculations were carried out to construct the diameter-dependent phase diagram, which agrees with experimental observations. Our find-ings suggest a new crystallization route to stabilize topological materials confined in 1D., Comment: 5 figures

We consider the problem of estimating the maximal energy of quantum $p$-local spin glass random Hamiltonians, the quantum analogues of widely studied classical spin glass models. Denoting by $E^*(p)$ the (appropriately normalized) maximal energy in the limit of a large number of qubits $n$, we show that $E^*(p)$ approaches $\sqrt{2\log 6}$ as $p$ increases. 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. Our most notable and (arguably) surprising result proves the existence of near-maximal energy states which are product states, and thus not entangled. Specifically, we prove that with high probability as $n\to\infty$, for any $E

This paper proposes a novel control design for voltage tracking of an islanded AC microgrid in the presence of {nonlinear} loads and parametric uncertainties at the primary level of control. The proposed method is based on the Tube-Based Robust Model Predictive Control (RMPC), an online optimization-based method which can handle the constraints and uncertainties as well. The challenge with this method is the conservativeness imposed by designing the tube based on the worst-case scenario of the uncertainties. This weakness is amended in this paper by employing a combination of a learning-based Gaussian Process (GP) regression and RMPC. The advantage of using GP is that both the mean and variance of the loads are predicted at each iteration based on the real data, and the resulted values of mean and the bound of confidence are utilized to design the tube in RMPC. The theoretical results are also provided to prove the recursive feasibility and stability of the proposed learning based RMPC. Finally, the simulation results are carried out on both single and multiple DG (Distributed Generation) units.

Quantum machine learning has the potential to enable advances in artificial intelligence, such as solving problems intractable on classical computers. Some fundamental ideas behind quantum machine learning are similar to kernel methods in classical machine learning. Both process information by mapping it into high-dimensional vector spaces without explicitly calculating their numerical values. We explore a setup for performing classification on labeled classical datasets, consisting of a classical neural network connected to a quantum annealer. The neural network programs the quantum annealer's controls and thereby maps the annealer's initial states into new states in the Hilbert space. The neural network's parameters are optimized to maximize the distance of states corresponding to inputs from different classes and minimize the distance between quantum states corresponding to the same class. Recent literature showed that at least some of the "learning" is due to the quantum annealer, connecting a small linear network to a quantum annealer and using it to learn small and linearly inseparable datasets. In this study, we consider a similar but not quite the same case, where a classical fully-fledged neural network is connected with a small quantum annealer. In such a setting, the fully-fledged classical neural-network already has built-in nonlinearity and learning power, and can already handle the classification problem alone, we want to see whether an additional quantum layer could boost its performance. We simulate this system to learn several common datasets, including those for image and sound recognition. We conclude that adding a small quantum annealer does not provide a significant benefit over just using a regular (nonlinear) classical neural network., Comment: 15 pages and 9 figures

We find the spatial and dynamic embedding diagrams in some stationary spacetimes. The spatial embeddings include the NUT, pure NUT and Kerr spacetimes. In the case of pure NUT spacetime, the spatial embedding equations are solved in terms of the elliptic integrals. In other cases we obtain the spatial embedding diagrams by numerical integration of the corresponding embedding equations. These embedding diagrams are then compared by calculating their Gaussian and mean curvatures. We also find the dynamic embedding diagrams of NUT and pure NUT spacetimes., Comment: 22 pages, 15 figures

Despite the significant progress made by transformer models in machine reading comprehension tasks, they still fall short in handling complex reasoning tasks due to the absence of explicit knowledge in the input sequence. To address this limitation, many recent works have proposed injecting external knowledge into the model. However, selecting relevant external knowledge, ensuring its availability, and requiring additional processing steps remain challenging. In this paper, we introduce a novel attention pattern that integrates reasoning knowledge derived from a heterogeneous graph into the transformer architecture without relying on external knowledge. The proposed attention pattern comprises three key elements: global-local attention for word tokens, graph attention for entity tokens that exhibit strong attention towards tokens connected in the graph as opposed to those unconnected, and the consideration of the type of relationship between each entity token and word token. This results in optimized attention between the two if a relationship exists. The pattern is coupled with special relative position labels, allowing it to integrate with LUKE's entity-aware self-attention mechanism. The experimental findings corroborate that our model outperforms both the cutting-edge LUKE-Graph and the baseline LUKE model across two distinct datasets: ReCoRD, emphasizing commonsense reasoning, and WikiHop, focusing on multi-hop reasoning challenges., Comment: submitted for Multimedia Tools and Applications Journal

Harnessing non-equilibrium hot carriers from plasmonic metal nanostructures constitutes a vibrant research field. It promises to enable control of activity and selectivity of photochemical reactions, especially for solar fuel generation. However, a comprehensive understanding of the interplay of plasmonic hot carrier-driven processes in metal/semiconducting heterostructures has remained elusive. In this work, we reveal the complex interdependence between plasmon excitation, hot carrier generation, transport and interfacial collection in plasmonic photocatalytic devices, uniquely determining the charge injection efficiencies at the solid/solid and solid/liquid interfaces. Interestingly, by measuring the internal quantum efficiency of ultrathin (14 to 33 nm) single-crystalline plasmonic gold (Au) nanoantenna arrays on titanium dioxide substrates, we find that the performance of the device is governed by hot hole collection at the metal/electrolyte interface. In particular, by combining a solid- and liquid-state experimental approach with ab initio simulations, we show a more efficient collection of high-energy d-band holes traveling in [111] orientation, resulting in a stronger oxidation reaction at the {111} surfaces of the nanoantenna. These results thus establish new guidelines for the design and optimization of plasmonic photocatalytic systems and optoelectronic devices.

Luminescence constitutes a unique source of insight into hot carrier processes in metals, including those in plasmonic nanostructures used for sensing and energy applications. However, being weak in nature, metal luminescence remains poorly understood, its microscopic origin strongly debated, and its potential for unravelling nanoscale carrier dynamics largely unexploited. Here, we reveal quantum-mechanical effects emanating in the luminescence from thin monocrystalline gold flakes. Specifically, we present experimental evidence, supported by first-principles simulations, to demonstrate its photoluminescence origin when exciting in the interband regime. Our model allows us to identify changes to the measured gold luminescence due to quantum-mechanical effects as the gold film thickness is reduced. Excitingly, such effects are observable in the luminescence signal from flakes up to 40 nm in thickness, associated with the out-of-plane discreteness of the electronic band structure near the Fermi level. We qualitatively reproduce the observations with first-principles modelling, thus establishing a unified description of luminescence in gold and enabling its widespread application as a probe of carrier dynamics and light-matter interactions in this material. Our study paves the way for future explorations of hot-carriers and charge-transfer dynamics in a multitude of material systems., Comment: Main text 21 pages and 4 figures. Supplemental Information 33 pages and 17 figures

Machine learning for differential equations paves the way for computationally efficient alternatives to numerical solvers, with potentially broad impacts in science and engineering. Though current algorithms typically require simulated training data tailored to a given setting, one may instead wish to learn useful information from heterogeneous sources, or from real dynamical systems observations that are messy or incomplete. In this work, we learn general-purpose representations of PDEs from heterogeneous data by implementing joint embedding methods for self-supervised learning (SSL), a framework for unsupervised representation learning that has had notable success in computer vision. Our representation outperforms baseline approaches to invariant tasks, such as regressing the coefficients of a PDE, while also improving the time-stepping performance of neural solvers. We hope that our proposed methodology will prove useful in the eventual development of general-purpose foundation models for PDEs. Code: https://github.com/facebookresearch/SSLForPDEs., Comment: NeurIPS 2023

With shrinking dimensions in integrated circuits, sensors, and functional devices, there is a pressing need to develop nanofabrication techniques with simultaneous control of morphology, microstructure, and material composition over wafer length scales. Current techniques are largely unable to meet all these conditions, suffering from poor control of morphology and defect structure or requiring extensive optimization or post-processing to achieve desired nanostructures. Recently, thermomechanical nanomolding (TMNM) has been shown to yield single-crystalline, high aspect ratio nanowires of metals, alloys, and intermetallics over wafer-scale distances. Here, we extend TMNM for wafer-scale fabrication of 2D nanostructures. Using Cu, we successfully nanomold Cu nanoribbons with widths < 50 nm, depths ~ 0.5-1 microns and lengths ~ 7 mm into Si trenches at conditions compatible with back end of line processing. Through SEM cross-section imaging and 4D-STEM grain orientation maps, we show that the grain size of the bulk feedstock is transferred to the nanomolded structures up to and including single crystal Cu. Based on the retained microstructures of molded 2D Cu, we discuss the deformation mechanism during molding for 2D TMNM., Comment: 4 figures

A Chatbot serves as a communication tool between a human user and a machine to achieve an appropriate answer based on the human input. In more recent approaches, a combination of Natural Language Processing and sequential models are used to build a generative Chatbot. The main challenge of these models is their sequential nature, which leads to less accurate results. To tackle this challenge, in this paper, a novel architecture is proposed using conditional Wasserstein Generative Adversarial Networks and a transformer model for answer generation in Chatbots. While the generator of the proposed model consists of a full transformer model to generate an answer, the discriminator includes only the encoder part of a transformer model followed by a classifier. To the best of our knowledge, this is the first time that a generative Chatbot is proposed using the embedded transformer in both generator and discriminator models. Relying on the parallel computing of the transformer model, the results of the proposed model on the Cornell Movie-Dialog corpus and the Chit-Chat datasets confirm the superiority of the proposed model compared to state-of-the-art alternatives using different evaluation metrics.

In this work, we explore Parameter-Efficient-Learning (PEL) techniques to repurpose a General-Purpose-Speech (GSM) model for Arabic dialect identification (ADI). Specifically, we investigate different setups to incorporate trainable features into a multi-layer encoder-decoder GSM formulation under frozen pre-trained settings. Our architecture includes residual adapter and model reprogramming (input-prompting). We design a token-level label mapping to condition the GSM for Arabic Dialect Identification (ADI). This is challenging due to the high variation in vocabulary and pronunciation among the numerous regional dialects. We achieve new state-of-the-art accuracy on the ADI-17 dataset by vanilla fine-tuning. We further reduce the training budgets with the PEL method, which performs within 1.86% accuracy to fine-tuning using only 2.5% of (extra) network trainable parameters. Our study demonstrates how to identify Arabic dialects using a small dataset and limited computation with open source code and pre-trained models., Comment: Accepted to Interspeech 2023, 5 pages. Code is available at: https://github.com/Srijith-rkr/KAUST-Whisper-Adapter under MIT license

Discovering non-linear dynamical models from data is at the core of science. Recent progress hinges upon sparse regression of observables using extensive libraries of candidate functions. However, it remains challenging to model hidden non-observable control variables governing switching between different dynamical regimes. Here we develop a data-efficient derivative-free method, IHCV, for the Identification of Hidden Control Variables. First, the performance and robustness of IHCV against noise are evaluated by benchmarking the IHCV method using well-known bifurcation models (saddle-node, transcritical, pitchfork, Hopf). Next, we demonstrate that IHCV discovers hidden driver variables in the Lorenz, van der Pol, Hodgkin-Huxley, and Fitzhugh-Nagumo models. Finally, IHCV generalizes to the case when only partial observational is given, as demonstrated using the toggle switch model, the genetic repressilator oscillator, and a Waddington landscape model. Our proof-of-principle illustrates that utilizing normal forms could facilitate the data-efficient and scalable discovery of hidden variables controlling transitions between different dynamical regimes and non-linear models., Comment: 12 pages, 2 figures

In an important recent development, Anshu, Breuckmann, and Nirkhe [ABN22] resolved positively the so-called No Low-Energy Trivial State (NLTS) conjecture by Freedman and Hastings. The conjecture postulated the existence of linear-size local Hamiltonians on n qubit systems for which no near-ground state can be prepared by a shallow (sublogarithmic depth) circuit. The construction in [ABN22] is based on recently developed good quantum codes. Earlier results in this direction included the constructions of the so-called Combinatorial NLTS -- a weaker version of NLTS -- where a state is defined to have low energy if it violates at most a vanishing fraction of the Hamiltonian terms [AB22]. These constructions were also based on codes. In this paper we provide a "non-code" construction of a class of Hamiltonians satisfying the Combinatorial NLTS. The construction is inspired by one in [AB22], but our proof uses the complex solution space geometry of random K-SAT instead of properties of codes. Specifically, it is known that above a certain clause-to-variables density the set of satisfying assignments of random K-SAT exhibits an overlap gap property, which implies that it can be partitioned into exponentially many clusters each constituting at most an exponentially small fraction of the total set of satisfying solutions. We establish a certain robust version of this clustering property for the space of near-satisfying assignments and show that for our constructed Hamiltonians every combinatorial near-ground state induces a near-uniform distribution supported by this set. Standard arguments then are used to show that such distributions cannot be prepared by quantum circuits with depth o(log n). Since the clustering property is exhibited by many random structures, including proper coloring and maximum cut, we anticipate that our approach is extendable to these models as well., Comment: 19 pages, 2 figures

Incorporating prior knowledge can improve existing pre-training models in cloze-style machine reading and has become a new trend in recent studies. Notably, most of the existing models have integrated external knowledge graphs (KG) and transformer-based models, such as BERT into a unified data structure. However, selecting the most relevant ambiguous entities in KG and extracting the best subgraph remains a challenge. In this paper, we propose the LUKE-Graph, a model that builds a heterogeneous graph based on the intuitive relationships between entities in a document without using any external KG. We then use a Relational Graph Attention (RGAT) network to fuse the graph's reasoning information and the contextual representation encoded by the pre-trained LUKE model. In this way, we can take advantage of LUKE, to derive an entity-aware representation; and a graph model - to exploit relation-aware representation. Moreover, we propose Gated-RGAT by augmenting RGAT with a gating mechanism that regulates the question information for the graph convolution operation. This is very similar to human reasoning processing because they always choose the best entity candidate based on the question information. Experimental results demonstrate that the LUKE-Graph achieves state-of-the-art performance on the ReCoRD dataset with commonsense reasoning., Comment: submitted for neurocomputing journal

Graph Neural Networks (GNN) are inherently limited in their expressive power. Recent seminal works (Xu et al., 2019; Morris et al., 2019b) introduced the Weisfeiler-Lehman (WL) hierarchy as a measure of expressive power. Although this hierarchy has propelled significant advances in GNN analysis and architecture developments, it suffers from several significant limitations. These include a complex definition that lacks direct guidance for model improvement and a WL hierarchy that is too coarse to study current GNNs. This paper introduces an alternative expressive power hierarchy based on the ability of GNNs to calculate equivariant polynomials of a certain degree. As a first step, we provide a full characterization of all equivariant graph polynomials by introducing a concrete basis, significantly generalizing previous results. Each basis element corresponds to a specific multi-graph, and its computation over some graph data input corresponds to a tensor contraction problem. Second, we propose algorithmic tools for evaluating the expressiveness of GNNs using tensor contraction sequences, and calculate the expressive power of popular GNNs. Finally, we enhance the expressivity of common GNN architectures by adding polynomial features or additional operations / aggregations inspired by our theory. These enhanced GNNs demonstrate state-of-the-art results in experiments across multiple graph learning benchmarks.

Self-supervised learning (SSL) has emerged as a powerful framework to learn representations from raw data without supervision. Yet in practice, engineers face issues such as instability in tuning optimizers and collapse of representations during training. Such challenges motivate the need for a theory to shed light on the complex interplay between the choice of data augmentation, network architecture, and training algorithm. We study such an interplay with a precise analysis of generalization performance on both pretraining and downstream tasks in a theory friendly setup, and highlight several insights for SSL practitioners that arise from our theory.

The Compact Muon Solenoid (CMS) experiment prepares its Phase-2 upgrade for the high-luminosity era of the LHC operation (HL-LHC). Due to the increase of occupancy, trigger latency and rates, the full electronics of the CMS Drift Tube (DT) chambers will need to be replaced. In the new design, the time bin for the digitisation of the chamber signals will be of around 1~ns, and the totality of the signals will be forwarded asynchronously to the service cavern at full resolution. The new backend system will be in charge of building the trigger primitives of each chamber. These trigger primitives contain the information at chamber level about the muon candidates position, direction, and collision time, and are used as input in the L1 CMS trigger. The added functionalities will improve the robustness of the system against ageing. An algorithm based on analytical solutions for reconstructing the DT trigger primitives, called Analytical Method, has been implemented both as a software C++ emulator and in firmware. Its performance has been estimated using the software emulator with simulated and real data samples, and through hardware implementation tests. Measured efficiencies are 96 to 98\% for all qualities and time and spatial resolutions are close to the ultimate performance of the DT chambers. A prototype chain of the HL-LHC electronics using the Analytical Method for trigger primitive generation has been installed during Long Shutdown 2 of the LHC and operated in CMS cosmic data taking campaigns in 2020 and 2021. Results from this validation step, the so-called Slice Test, are presented., Comment: 16 pages, 11 figures

We consider the problem of devising a suitable Quantum Error Correction (QEC) procedures for a generic quantum noise acting on a quantum circuit. In general, there is no analytic universal procedure to obtain the encoding and correction unitary gates, and the problem is even harder if the noise is unknown and has to be reconstructed. The existing procedures rely on Variational Quantum Algorithms (VQAs) and are very difficult to train since the size of the gradient of the cost function decays exponentially with the number of qubits. We address this problem using a cost function based on the Quantum Wasserstein distance of order 1 ($QW_1$). At variance with other quantum distances typically adopted in quantum information processing, $QW_1$ lacks the unitary invariance property which makes it a suitable tool to avoid to get trapped in local minima. Focusing on a simple noise model for which an exact QEC solution is known and can be used as a theoretical benchmark, we run a series of numerical tests that show how, guiding the VQA search through the $QW_1$, can indeed significantly increase both the probability of a successful training and the fidelity of the recovered state, with respect to the results one obtains when using conventional approaches.

In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts given certain classical descriptions of the input. Specifically, we give classical algorithms that calculate ground states and time-evolved expectation values for permutation-invariant Hamiltonians specified in the symmetrized Pauli basis with runtimes polynomial in the system size. We use tensor-network methods to transform symmetry-equivariant operators to the block-diagonal Schur basis that is of polynomial size, and then perform exact matrix multiplication or diagonalization in this basis. These methods are adaptable to a wide range of input and output states including those prescribed in the Schur basis, as matrix product states, or as arbitrary quantum states when given the power to apply low depth circuits and single qubit measurements., Comment: 12 pages, 3 figures

Quantum machine learning has the potential to provide powerful algorithms for artificial intelligence. The pursuit of quantum advantage in quantum machine learning is an active area of research. For current noisy, intermediate-scale quantum (NISQ) computers, various quantum-classical hybrid algorithms have been proposed. One such previously proposed hybrid algorithm is a gate-based variational embedding classifier, which is composed of a classical neural network and a parameterized gate-based quantum circuit. We propose a quantum variational embedding classifier based on an analog quantum computer, where control signals vary continuously in time. In our algorithm, the classical data is transformed into the parameters of the time-varying Hamiltonian of the analog quantum computer by a linear transformation. The nonlinearity needed for a nonlinear classification problem is purely provided by the analog quantum computer through the nonlinear dependence of the final quantum state on the control parameters of the Hamiltonian. We performed numerical simulations that demonstrate the effectiveness of our algorithm for performing binary and multi-class classification on linearly inseparable datasets such as concentric circles and MNIST digits. Our classifier can reach accuracy comparable with the best classical classifiers. We find the performance of our classifier can be increased by increasing the number of qubits until the performance saturates and fluctuates. Moreover, the number of optimization parameters of our classifier scales linearly with the number of qubits. The increase of number of training parameters when the size increases is therefore not as fast as that of neural network. Our algorithm presents the possibility of using current quantum annealers for solving practical machine-learning problems, and it could also be useful to explore quantum advantage in quantum machine learning.

Reduced dimensionality leads to emergent phenomena in quantum materials and there is a need for accelerated materials discovery of nanoscale quantum materials in reduced dimensions. Thermomechanical nanomolding is a rapid synthesis method that produces high quality single-crystalline quantum nanowires with controlled dimensions over wafer-scale sizes. Herein, we apply nanomolding to fabricate nanowires from bulk feedstock of MoP, a triple-point topological metal with extremely high conductivity that is promising for low-resistance interconnects. Surprisingly, we obtained single-crystalline Mo$_{4}$P$_{3}$ nanowires, a metastable phase at room temperature in atmospheric pressure. We thus demonstrate nanomolding can create metastable phases inaccessible by other nanomaterial syntheses and can explore a previously inaccessible synthesis space at high temperatures and pressures. Furthermore, our results suggest that the current understanding of interfacial solid diffusion for nanomolding is incomplete, providing opportunities to explore solid-state diffusion at high-pressure and high-temperature regimes in confined dimensions., Comment: 3 figures

5th Generation Mobile Communication Technology (5G) utilizes the Access Traffic Steering, Switching, and Splitting (ATSSS) rule to enable multi-path data transmission, which is currently being standardized. Recently, the 3rd Generation Partnership Project (3GPP) SA1 and SA2 have been working on the multi-path solution for possible improvement from different perspectives. However, the existing 3GPP multi-path solution has some limitations on ultra-reliable low-latency communication (URLLC) traffic in terms of reliability and latency requirements. In order to capture the potential gains of multi-path architecture in the context of URLLC services, this paper proposes a novel traffic splitting technique that can more efficiently enjoy the benefit of multi-path architecture in reducing user equipment (UE) uplink (UL) end-to-end (E2E) latency. In particular, we formulate an optimization framework that minimizes user's UL E2E latency via the joint optimization on the ratio of traffic assigned to each path and their corresponding transmit power. The performance of the proposed scheme is evaluated via well-designed simulations., Comment: This work has been submitted to the IEEE for possible publication. 5 pages, 6 figures

Explainable Artificial Intelligence (XAI) is a paradigm that delivers transparent models and decisions, which are easy to understand, analyze, and augment by a non-technical audience. Fuzzy Logic Systems (FLS) based XAI can provide an explainable framework, while also modeling uncertainties present in real-world environments, which renders it suitable for applications where explainability is a requirement. However, most real-life processes are not characterized by high levels of uncertainties alone; they are inherently time-dependent as well, i.e., the processes change with time. In this work, we present novel Temporal Type-2 FLS Based Approach for time-dependent XAI (TXAI) systems, which can account for the likelihood of a measurement's occurrence in the time domain using (the measurement's) frequency of occurrence. In Temporal Type-2 Fuzzy Sets (TT2FSs), a four-dimensional (4D) time-dependent membership function is developed where relations are used to construct the inter-relations between the elements of the universe of discourse and its frequency of occurrence. The TXAI system manifested better classification prowess, with 10-fold test datasets, with a mean recall of 95.40\% than a standard XAI system (based on non-temporal general type-2 (GT2) fuzzy sets) that had a mean recall of 87.04\%. TXAI also performed significantly better than most non-explainable AI systems between 3.95\%, to 19.04\% improvement gain in mean recall. In addition, TXAI can also outline the most likely time-dependent trajectories using the frequency of occurrence values embedded in the TXAI model; viz. given a rule at a determined time interval, what will be the next most likely rule at a subsequent time interval. In this regard, the proposed TXAI system can have profound implications for delineating the evolution of real-life time-dependent processes, such as behavioural or biological processes.

Detection of surface defects is one of the most important issues in the field of image processing and machine vision. In this article, a method for detecting surface defects based on energy changes in co-occurrence matrices is presented. The presented method consists of two stages of training and testing. In the training phase, the co-occurrence matrix operator is first applied on healthy images and then the amount of output energy is calculated. In the following, according to the changes in the amount of energy, a suitable feature vector is defined, and with the help of it, a suitable threshold for the health of the images is obtained. Then, in the test phase, with the help of the calculated quorum, the defective parts are distinguished from the healthy ones. In the results section, the mentioned method has been applied on stone and ceramic images and its detection accuracy has been calculated and compared with some previous methods. Among the advantages of the presented method, we can mention high accuracy, low calculations and compatibility with all types of levels due to the use of the training stage. The proposed approach can be used in medical applications to detect abnormalities such as diseases. So, the performance is evaluated on 2d-hela dataset to classify cell phenotypes. The proposed approach provides about 89.56 percent accuracy on 2d-hela.

We demonstrate that the assembly pathway method underlying assembly theory (AT) is an encoding scheme widely used by popular statistical compression algorithms. We show that in all cases (synthetic or natural) AT performs similarly to other simple coding schemes and underperforms compared to system-related indexes based upon algorithmic probability that take into account statistical repetitions but also the likelihood of other computable patterns. Our results imply that the assembly index does not offer substantial improvements over existing methods, including traditional statistical ones, and imply that the separation between living and non-living compounds following these methods has been reported before.

The fundamental goal of self-supervised learning (SSL) is to produce useful representations of data without access to any labels for classifying the data. Modern methods in SSL, which form representations based on known or constructed relationships between samples, have been particularly effective at this task. Here, we aim to extend this framework to incorporate algorithms based on kernel methods where embeddings are constructed by linear maps acting on the feature space of a kernel. In this kernel regime, we derive methods to find the optimal form of the output representations for contrastive and non-contrastive loss functions. This procedure produces a new representation space with an inner product denoted as the induced kernel which generally correlates points which are related by an augmentation in kernel space and de-correlates points otherwise. We analyze our kernel model on small datasets to identify common features of self-supervised learning algorithms and gain theoretical insights into their performance on downstream tasks.