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As data retrieval demands become increasingly complex, traditional search methods often fall short in addressing nuanced and conceptual queries. Vector similarity search has emerged as a promising technique for finding semantically similar information efficiently. However, its effectiveness diminishes when handling intricate queries with contextual nuances. This paper explores a hybrid approach combining vector similarity search with Large Language Models (LLMs) to enhance search accuracy and relevance. The proposed two-step solution first employs vector similarity search to shortlist potential matches, followed by an LLM for context-aware ranking of the results. Experiments on structured datasets demonstrate that while vector similarity search alone performs well for straightforward queries, the LLM-assisted approach excels in processing complex queries involving constraints, negations, or conceptual requirements. By leveraging the natural language understanding capabilities of LLMs, this method improves the accuracy of search results for complex tasks without sacrificing efficiency. We also discuss real-world applications and propose directions for future research to refine and scale this technique for diverse datasets and use cases. Original article: https://engineering.grab.com/llm-assisted-vector-similarity-search

The presence of defects of different kinds, e.g., vacancies, voids, dislocations, grain boundaries, and surfaces, in realistic materials can strongly modify and even dictate the thermodynamics of phase transformations. Our study demonstrates, both theoretically and experimentally, that in the ordering of Fe_xAl_1-x (x>0.6) alloys subjected to high-temperature treatment, the relaxation of the as-prepared chemically disordered alloy into the ordered B2 state is hampered by another process. A manifestation of this is an increase in the alloy's magnetization. A plausible explanation for a non-monotonous behavior of the magnetization we observe is segregation of Al into structural defects, e.g., grain boundaries, and thus purification of the Fe host lattice. Qualitatively, experimental findings reported here are supported by molecular dynamics simulation of the phase transformation kinetics in Fe_xAl_1-x. These studies can be useful for choosing the preparation strategy for functional alloys., Comment: 7 pages, 4 figures, 1 table

A harmonic mapping $f=h+\overline{g}$ in $\mathbb{D}$ is $\varphi$-normal if $f^{\#}(z)=\mathcal{O}(|\varphi(z)|), \text{ as } |z|\to 1^-,$ where $f^{\#}(z)={(|h'(z)|+|g'(z)|)}/{(1+|f(z)|^2)}.$ In this paper, we establish several sufficient conditions for harmonic mappings to be $\varphi$-normal. We also extend the five-point theorem of Lappan for $\varphi$-normal harmonic mappings., Comment: 10 pages

We consider a large class of shallow neural networks with randomly initialized parameters and rectified linear unit activation functions. We prove that these random neural networks are well-defined non-Gaussian processes. As a by-product, we demonstrate that these networks are solutions to stochastic differential equations driven by impulsive white noise (combinations of random Dirac measures). These processes are parameterized by the law of the weights and biases as well as the density of activation thresholds in each bounded region of the input domain. We prove that these processes are isotropic and wide-sense self-similar with Hurst exponent 3/2. We also derive a remarkably simple closed-form expression for their autocovariance function. Our results are fundamentally different from prior work in that we consider a non-asymptotic viewpoint: The number of neurons in each bounded region of the input domain (i.e., the width) is itself a random variable with a Poisson law with mean proportional to the density parameter. Finally, we show that, under suitable hypotheses, as the expected width tends to infinity, these processes can converge in law not only to Gaussian processes, but also to non-Gaussian processes depending on the law of the weights. Our asymptotic results provide a new take on several classical results (wide networks converge to Gaussian processes) as well as some new ones (wide networks can converge to non-Gaussian processes).

In the realm of web agent research, achieving both generalization and accuracy remains a challenging problem. Due to high variance in website structure, existing approaches often fail. Moreover, existing fine-tuning and in-context learning techniques fail to generalize across multiple websites. We introduce Wilbur, an approach that uses a differentiable ranking model and a novel instruction synthesis technique to optimally populate a black-box large language model's prompt with task demonstrations from previous runs. To maximize end-to-end success rates, we also propose an intelligent backtracking mechanism that learns and recovers from its mistakes. Finally, we show that our ranking model can be trained on data from a generative auto-curriculum which samples representative goals from an LLM, runs the agent, and automatically evaluates it, with no manual annotation. Wilbur achieves state-of-the-art results on the WebVoyager benchmark, beating text-only models by 8% overall, and up to 36% on certain websites. On the same benchmark, Wilbur is within 5% of a strong multi-modal model despite only receiving textual inputs, and further analysis reveals a substantial number of failures are due to engineering challenges of operating the web.

Realizations of the holographic correspondence in String/M theory typically involve spacetimes of the form $AdS \times Y$ where $Y$ is some internal space which geometrizes an internal symmetry of the dual field theory, hereafter referred to as an "$R$ symmetry". It has been speculated that areas of Ryu-Takayanagi surfaces anchored on the boundary of a subregion of $Y$, and smeared over the base space of the dual field theory, quantify entanglement of internal degrees of freedom. A natural candidate for the corresponding operators are linear combinations of operators with definite $R$ charge with coefficients given by the "spherical harmonics'' of the internal space: this is natural when the product spaces appear as IR geometries of higher dimensional AdS spaces. We study clustering properties of such operators both for pure $AdS \times Y$ and for flow geometries, where $AdS \times Y$ arises in the IR from a different spacetime in the UV, for example higher dimensional AdS or asymptotically flat spacetime. We show, in complete generality, that the two point functions of such operators separated along the internal space obey clustering properties at scales larger than the $AdS$ scale. For non-compact $Y$, this provides a notion of approximate locality. When $Y$ is compact, clustering happens only when the size of $Y$ is parametrically larger than the $AdS$ scale. This latter situation is realized in flow geometries where the product spaces arise in the IR from an asymptotically AdS geometry at UV, but not typically when they arise near black hole horizons in asymptotically flat spacetimes. We discuss the significance of this result for entanglement and comment on the role of color degrees of freedom., Comment: 24 pages, no figures

In the Randall-Sundrum (RS) II braneworld scenario, general relativity (GR) is modified by adding an extra dimension such that it is indistinguishable from GR in the weak gravity limit. However, such modifications may leave a mark in the strong field regime. We therefore analyze massive scalar perturbations around rotating black holes in the RS II model. Unlike black holes in GR, these braneworld black holes carry a tidal charge that contains information about the extra spatial dimension, and the rotation parameter for such black holes can exceed unity. Through the method of continued fractions, we investigate the quasinormal mode spectra, and the superradiant instabilities associated with the existence of quasibound states, that is, gravitational atoms. In comparison to the four-dimensional Kerr black hole, we report distinctive signatures of the tidal charge and the rotation parameter, which manifest as signals of the extra dimension, on both the fundamental quasinormal mode and the formation of gravitational atoms. These findings offer insights into testing modifications to GR and detecting ultralight bosonic particles around black holes., Comment: v3: 25 pages, 11 figures, 1 table, minor modifications, accepted for publication in Phys. Rev. D

Text classification is a well-studied and versatile building block for many NLP applications. Yet, existing approaches require either large annotated corpora to train a model with or, when using large language models as a base, require carefully crafting the prompt as well as using a long context that can fit many examples. As a result, it is not possible for end-users to build classifiers for themselves. To address this issue, we propose a novel approach to few-shot text classification using an LLM. Rather than few-shot examples, the LLM is prompted with descriptions of the salient features of each class. These descriptions are coauthored by the user and the LLM interactively: while the user annotates each few-shot example, the LLM asks relevant questions that the user answers. Examples, questions, and answers are summarized to form the classification prompt. Our experiments show that our approach yields high accuracy classifiers, within 82% of the performance of models trained with significantly larger datasets while using only 1% of their training sets. Additionally, in a study with 30 participants, we show that end-users are able to build classifiers to suit their specific needs. The personalized classifiers show an average accuracy of 90%, which is 15% higher than the state-of-the-art approach., Comment: Accepted at EMNLP 2023 (Findings)

The ghost-free bi-metric gravity theory is a viable theory of gravity that explores the interaction between a massless and a massive graviton and can be described in terms of two dynamical metrics. In this paper, we present an exact static, spherically symmetric vacuum solution within this theory. The solution is spatially Schwarzschild-de Sitter, with the value of the cosmological constant determined by the graviton mass and the interaction parameters of the theory. Notably, for specific parameter ranges, the solution represents a traversable Lorentzian wormhole that violates the weak energy condition near its throat. Furthermore, we have investigated the evolution of scalar and electromagnetic fields in this wormhole spacetime and observed the presence of arbitrarily long-lived quasi-resonant modes in the quasinormal spectrum., Comment: 15 pages, 7 figures. An appendix and some references are added in the updated version. Matches version to appear in Phys. Rev. D

Creating large, good quality labeled data has become one of the major bottlenecks for developing machine learning applications. Multiple techniques have been developed to either decrease the dependence of labeled data (zero/few-shot learning, weak supervision) or to improve the efficiency of labeling process (active learning). Among those, Weak Supervision has been shown to reduce labeling costs by employing hand crafted labeling functions designed by domain experts. We propose AutoWS -- a novel framework for increasing the efficiency of weak supervision process while decreasing the dependency on domain experts. Our method requires a small set of labeled examples per label class and automatically creates a set of labeling functions to assign noisy labels to numerous unlabeled data. Noisy labels can then be aggregated into probabilistic labels used by a downstream discriminative classifier. Our framework is fully automatic and requires no hyper-parameter specification by users. We compare our approach with different state-of-the-art work on weak supervision and noisy training. Experimental results show that our method outperforms competitive baselines.

The emergence of deep-learning-based methods to solve image-reconstruction problems has enabled a significant increase in reconstruction quality. Unfortunately, these new methods often lack reliability and explainability, and there is a growing interest to address these shortcomings while retaining the boost in performance. In this work, we tackle this issue by revisiting regularizers that are the sum of convex-ridge functions. The gradient of such regularizers is parameterized by a neural network that has a single hidden layer with increasing and learnable activation functions. This neural network is trained within a few minutes as a multistep Gaussian denoiser. The numerical experiments for denoising, CT, and MRI reconstruction show improvements over methods that offer similar reliability guarantees.

Lipschitz-constrained neural networks have several advantages over unconstrained ones and can be applied to a variety of problems, making them a topic of attention in the deep learning community. Unfortunately, it has been shown both theoretically and empirically that they perform poorly when equipped with ReLU activation functions. By contrast, neural networks with learnable 1-Lipschitz linear splines are known to be more expressive. In this paper, we show that such networks correspond to global optima of a constrained functional optimization problem that consists of the training of a neural network composed of 1-Lipschitz linear layers and 1-Lipschitz freeform activation functions with second-order total-variation regularization. Further, we propose an efficient method to train these neural networks. Our numerical experiments show that our trained networks compare favorably with existing 1-Lipschitz neural architectures.

Despite tremendous progress in automatic summarization, state-of-the-art methods are predominantly trained to excel in summarizing short newswire articles, or documents with strong layout biases such as scientific articles or government reports. Efficient techniques to summarize financial documents, including facts and figures, have largely been unexplored, majorly due to the unavailability of suitable datasets. In this work, we present ECTSum, a new dataset with transcripts of earnings calls (ECTs), hosted by publicly traded companies, as documents, and short experts-written telegram-style bullet point summaries derived from corresponding Reuters articles. ECTs are long unstructured documents without any prescribed length limit or format. We benchmark our dataset with state-of-the-art summarizers across various metrics evaluating the content quality and factual consistency of the generated summaries. Finally, we present a simple-yet-effective approach, ECT-BPS, to generate a set of bullet points that precisely capture the important facts discussed in the calls., Comment: 14 pages; Accepted as a Long Paper in EMNLP 2022 (Main Conference); Codes: https://github.com/rajdeep345/ECTSum

The amount of waste heat exergy generated globally is 69.058 EJ which can be divided into, low temperature 373 K, 30.496 EJ, medium temperature 373 K to 573 K, 14.431 EJ and high temperature 573 K, 24.131 EJ. These values of exergy have been used to determine the minimum number of pn junctions required to convert the exergy into electrical power. It is found that the number of junctions required to convert high temperature exergy increases from 8.22x10^11 to 24.66x10^11 when the aspect ratio of the legs increases from 0.5 cm^1 to 1.5 cm^1. To convert the low temperature exergy, 81.76x10^11 to 245.25x10^11 junctions will be required depending on the legs aspect ratio. The quantity of alloys containing elements such as Pb, Bi, Te, Sb, Se and Sn required to synthesize these junctions therefore is of the order of millions of tons which means the elements required is also of similar magnitude. The current world production of these elements however falls far short of this requirement, indicating significant supply chain risk. The production of these elements, even if resources are available, will emit millions of tons of CO2 showing that current alloys are non-sustainable for waste heat recovery., Comment: 32 pages, 5 figures

Lipschitz-constrained neural networks have many applications in machine learning. Since designing and training expressive Lipschitz-constrained networks is very challenging, there is a need for improved methods and a better theoretical understanding. Unfortunately, it turns out that ReLU networks have provable disadvantages in this setting. Hence, we propose to use learnable spline activation functions with at least 3 linear regions instead. We prove that this choice is optimal among all component-wise $1$-Lipschitz activation functions in the sense that no other weight constrained architecture can approximate a larger class of functions. Additionally, this choice is at least as expressive as the recently introduced non component-wise Groupsort activation function for spectral-norm-constrained weights. Previously published numerical results support our theoretical findings.

We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic signals as realizations of sparse stochastic processes, which makes them ideally matched to variational sparsity-promoting techniques. We derive Gibbs sampling schemes to compute the minimum mean-square error estimators for processes with Laplace, Student's t, and Bernoulli-Laplace innovations. These allow our framework to provide quantitative measures of the degree of optimality (in the mean-square-error sense) for any given reconstruction method. We showcase our framework by benchmarking the performance of some well-known variational methods and convolutional neural network architectures that perform direct nonlinear reconstructions in the context of deconvolution and Fourier sampling. Our experimental results support the understanding that, while these neural networks outperform the variational methods and achieve near-optimal results in many settings, their performance deteriorates severely for signals associated with heavy-tailed distributions.

Most modern imaging systems incorporate a computational pipeline to infer the image of interest from acquired measurements. The Bayesian approach to solve such ill-posed inverse problems involves the characterization of the posterior distribution of the image. It depends on the model of the imaging system and on prior knowledge on the image of interest. In this work, we present a Bayesian reconstruction framework for nonlinear imaging models where we specify the prior knowledge on the image through a deep generative model. We develop a tractable posterior-sampling scheme based on the Metropolis-adjusted Langevin algorithm for the class of nonlinear inverse problems where the forward model has a neural-network-like structure. This class includes most practical imaging modalities. We introduce the notion of augmented deep generative priors in order to suitably handle the recovery of quantitative images.We illustrate the advantages of our framework by applying it to two nonlinear imaging modalities-phase retrieval and optical diffraction tomography.

The SARS-CoV2 virus has caused a lot of tribulation to the human population. Predictive modeling that can accurately determine whether a person is infected with COVID-19 is imperative. The study proposes a novel approach that utilizes deep feature extraction technique, pre-trained ResNet50 acting as the backbone of the network, combined with Logistic Regression as the head model. The proposed model has been trained on Kaggle COVID-19 Radiography Dataset. The proposed model achieves a cross-validation accuracy of 100% on the COVID-19 and Normal X-Ray image classes. Similarly, when tested on combined three classes, the proposed model achieves 98.84% accuracy.

Keratoconus is a severe eye disease affecting the cornea (the clear, dome-shaped outer surface of the eye), causing it to become thin and develop a conical bulge. The diagnosis of keratoconus requires sophisticated ophthalmic devices which are non-portable and very expensive. This makes early detection of keratoconus inaccessible to large populations in low- and middle-income countries, making it a leading cause for partial/complete blindness among such populations. We propose SmartKC, a low-cost, smartphone-based keratoconus diagnosis system comprising of a 3D-printed placido's disc attachment, an LED light strip, and an intelligent smartphone app to capture the reflection of the placido rings on the cornea. An image processing pipeline analyzes the corneal image and uses the smartphone's camera parameters, the placido rings' 3D location, the pixel location of the reflected placido rings and the setup's working distance to construct the corneal surface, via the Arc-Step method and Zernike polynomials based surface fitting. In a clinical study with 101 distinct eyes, we found that SmartKC achieves a sensitivity of 94.1% and a specificity of 100.0%. Moreover, the quantitative curvature estimates (sim-K) strongly correlate with a gold-standard medical device (Pearson correlation coefficient =0.78). Our results indicate that SmartKC has the potential to be used as a keratoconus screening tool under real-world medical settings., Comment: Change Log: + Fixed sim-K computation (updated Section 5.5.3); re-ran our pipeline with the updated sim-K values (updated Figure 7); + Conducted the comparative evaluation with doctors again (total 4 doctors), and got improved results (updated Section 7.2 and Table 2); [Note: This is an updated version of the paper that was accepted for publication in IMWUT 2021.]

We explore perturbative corrections to quantum information geometry. In particular, we study a Bures information metric naturally associated with the correlation functions of a conformal field theory. We compute the metric of holographic four-point functions and include corrections generated by tree Witten diagrams in the bulk. In this setting, we translate properties of correlators into the language of information geometry. Cross terms in the information metric encode non-identity operators in the OPE. We find that the information metric is asymptotically AdS. Finally, we discuss an information metric for transition amplitudes., Comment: 18 pages, no figures; v2: typos fixed, transition amplitude discussion refined

We count the number of elements in the set $$G_{3}(n,x) = \{M \in GL_3(\mathbb{Z}_n) \mid perm(M) \equiv x \pmod{n} \}.$$, Comment: 13 pages

In this article we compute the number of invertible $2\times 2$ matrices with integer entries modulo $n$ whose permanents are congruent modulo $n$ to a given integer $x$., Comment: 5 pages

We refine an earlier introduced 5-dimensional gravity solution capable of holographically capturing several qualitative aspects of (lattice) QCD in a strong magnetic background such as the anisotropic behaviour of the string tension, inverse catalysis at the level of the deconfinement transition or sensitivity of the entanglement entropy to the latter. Here, we consistently modify our solution of the considered Einstein-Maxwell-dilaton system to not only overcome an unphysical flattening at large distances in the quark-antiquark potential plaguing earlier work, but also to encapsulate inverse catalysis for the chiral transition in the probe approximation. This brings our dynamical holographic QCD model yet again closer to a stage at which it can be used to predict magnetic QCD quantities not directly computable via lattice techniques., Comment: 15 pages, 23 figures, major revision in the chiral part, appendices added, accepted for publication in PRD