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We propose an $hp$-adaptive discontinuous Galerkin finite element method (DGFEM) to approximate the solution of a static crack boundary value problem. The mathematical model describes the behavior of a geometrically linear strain-limiting elastic body. The compatibility condition for the physical variables, along with a specific algebraically nonlinear constitutive relationship, leads to a second-order quasi-linear elliptic boundary value problem. We demonstrate the existence of a unique discrete solution using Ritz representation theory across the entire range of modeling parameters. Additionally, we derive a priori error estimates for the DGFEM, which are computable and, importantly, expressed in terms of natural energy and $L^2$-norms. Numerical examples showcase the performance of the proposed method in the context of a manufactured solution and a non-convex domain containing an edge crack.

The non-linear regime of the magnetic Rayleigh-Taylor instability (MRTI) plays a crucial role in the transportation and mixing of material in a wide range of laboratory to astrophysical systems. But several fundamental aspects of this regime remain poorly understood. Previous MRTI studies assumed MRTI to have a self-similar, quadratic growth in the non-linear regime, similar to the hydrodynamic (HD) RTI. However, neither the self-similarity nor the relevance of the HD scaling for the MRTI has been proved analytically. Further, the role of magnetic field on the evolution of the instability remain unexplored. Towards this, we perform analytical and numerical study of the MRTI with uniform magnetic field. Our study reveals that the imposed magnetic field deviates the MRTI evolution from self-similarity. However, the HD RTI scaling becomes relevant to the MRTI evolution when the non-linear dynamics dominate the imposed magnetic field. A formula for the $\alpha_{mhd}$, a quantity which represents the non-linear growth of instability in the self-similar regime, was obtained. The formula of $\alpha_{mhd}$ highlight the physical processes that could dictate the growth of instability. Numerical simulations of the MRTI showed the quantitative variation of these physical processes and $\alpha_{mhd}$ across a wide range of magnetic field strengths. Thus, the current study proves, analytically and numerically, the role of magnetic fields on the evolution of MRTI and the factors that influence of non-linear growth constant of the instability., Comment: 31 pages, 18 figures

Since the ground-breaking discovery of the quantum Hall effect, half-quantized quantum Hall plateaus have been some of the most studied and sought-after states. Their importance stems not only from the fact that they transcend the composite fermion framework used to explain fractional quantum Hall states (such as Laughlin states). Crucially, they hold promise for hosting non-Abelian excitations, which are essential for developing topological qubits - key components for fault-tolerant quantum computing. In this work, we show that these coveted half-quantized plateaus can appear in more than one unexpected way. We report the observation of fractional states with conductance quantization at $\nu_H = 5/2$ arising due to charge equilibration in the confined region of a quantum point contact in monolayer graphene., Comment: 30 pages, 18 figures, and 2 tables

The 2023 Big ANN Challenge, held at NeurIPS 2023, focused on advancing the state-of-the-art in indexing data structures and search algorithms for practical variants of Approximate Nearest Neighbor (ANN) search that reflect the growing complexity and diversity of workloads. Unlike prior challenges that emphasized scaling up classical ANN search ~\cite{DBLP:conf/nips/SimhadriWADBBCH21}, this competition addressed filtered search, out-of-distribution data, sparse and streaming variants of ANNS. Participants developed and submitted innovative solutions that were evaluated on new standard datasets with constrained computational resources. The results showcased significant improvements in search accuracy and efficiency over industry-standard baselines, with notable contributions from both academic and industrial teams. This paper summarizes the competition tracks, datasets, evaluation metrics, and the innovative approaches of the top-performing submissions, providing insights into the current advancements and future directions in the field of approximate nearest neighbor search., Comment: Code: https://github.com/harsha-simhadri/big-ann-benchmarks/releases/tag/v0.3.0

This paper explores the pitfalls in evaluating multilingual automatic speech recognition (ASR) models, with a particular focus on Indic language scripts. We investigate the text normalization routine employed by leading ASR models, including OpenAI Whisper, Meta's MMS, Seamless, and Assembly AI's Conformer, and their unintended consequences on performance metrics. Our research reveals that current text normalization practices, while aiming to standardize ASR outputs for fair comparison, by removing inconsistencies such as variations in spelling, punctuation, and special characters, are fundamentally flawed when applied to Indic scripts. Through empirical analysis using text similarity scores and in-depth linguistic examination, we demonstrate that these flaws lead to artificially improved performance metrics for Indic languages. We conclude by proposing a shift towards developing text normalization routines that leverage native linguistic expertise, ensuring more robust and accurate evaluations of multilingual ASR models., Comment: Accepted to EMNLP 2024 Main

The photon parton distribution function (PDF) of the proton is crucial for precise comparisons of LHC cross sections with theoretical predictions. However, it was previously affected by very large uncertainties of around ${\cal O}(100\%)$ or dependent upon phenomenologically inspired models. In the paper~\cite{Manohar:2016nzj}, we demonstrated how the photon PDF could be determined using the proton structure functions $F_2$ and $F_L$ measured in electron--proton scattering experiments. We provided an explicit formula for the PDF, which can be systematically improved order by order in perturbation theory. We obtained a photon PDF with errors $\lesssim 2$\% for $10^{-4} < x < 0.1$. Here, we recall the underlying idea and method used to obtain this result, as well as the progress made since then., Comment: Conference proceedings of the 2nd International Conference of Basics Science, 13 pages , 6 figures

Machine learning (ML), driven by prominent paradigms such as centralized and federated learning, has made significant progress in various critical applications ranging from autonomous driving to face recognition. However, its remarkable success has been accompanied by various attacks. Recently, the model hijacking attack has shown that ML models can be hijacked to execute tasks different from their original tasks, which increases both accountability and parasitic computational risks. Nevertheless, thus far, this attack has only focused on centralized learning. In this work, we broaden the scope of this attack to the federated learning domain, where multiple clients collaboratively train a global model without sharing their data. Specifically, we present HijackFL, the first-of-its-kind hijacking attack against the global model in federated learning. The adversary aims to force the global model to perform a different task (called hijacking task) from its original task without the server or benign client noticing. To accomplish this, unlike existing methods that use data poisoning to modify the target model's parameters, HijackFL searches for pixel-level perturbations based on their local model (without modifications) to align hijacking samples with the original ones in the feature space. When performing the hijacking task, the adversary applies these cloaks to the hijacking samples, compelling the global model to identify them as original samples and predict them accordingly. We conduct extensive experiments on four benchmark datasets and three popular models. Empirical results demonstrate that its attack performance outperforms baselines. We further investigate the factors that affect its performance and discuss possible defenses to mitigate its impact.

Modern artificial intelligence (AI) systems are powered by foundation models. This paper presents a new set of foundation models, called Llama 3. It is a herd of language models that natively support multilinguality, coding, reasoning, and tool usage. Our largest model is a dense Transformer with 405B parameters and a context window of up to 128K tokens. This paper presents an extensive empirical evaluation of Llama 3. We find that Llama 3 delivers comparable quality to leading language models such as GPT-4 on a plethora of tasks. We publicly release Llama 3, including pre-trained and post-trained versions of the 405B parameter language model and our Llama Guard 3 model for input and output safety. The paper also presents the results of experiments in which we integrate image, video, and speech capabilities into Llama 3 via a compositional approach. We observe this approach performs competitively with the state-of-the-art on image, video, and speech recognition tasks. The resulting models are not yet being broadly released as they are still under development.

Despite their powerful chat, coding, and reasoning abilities, Large Language Models (LLMs) frequently hallucinate. Conventional wisdom suggests that hallucinations are a consequence of a balance between creativity and factuality, which can be mitigated, but not eliminated, by grounding the LLM in external knowledge sources. Through extensive systematic experiments, we show that these traditional approaches fail to explain why LLMs hallucinate in practice. Specifically, we show that LLMs augmented with a massive Mixture of Memory Experts (MoME) can easily memorize large datasets of random numbers. We corroborate these experimental findings with a theoretical construction showing that simple neural networks trained to predict the next token hallucinate when the training loss is above a threshold as it usually does in practice when training on internet scale data. We interpret our findings by comparing against traditional retrieval methods for mitigating hallucinations. We use our findings to design a first generation model for removing hallucinations -- Lamini-1 -- that stores facts in a massive mixture of millions of memory experts that are retrieved dynamically.

The N-dimensional radial Schrodinger equation has been solved using the Nikiforov Uvarov (NU) method, in which we used the medium modified form of Cornell potential and quasi-particle Debye mass with strong magnetic field background. The binding energies and the mass spectra of heavy quarkonium have been studied in the N-dimensional space for different values of magnetic field, the binding energy decreases with increasing magnetic field, which shows early dissociation of heavy quarkonium system. The influence of dimensionality number has also been discussed on binding energies of J/{\psi} and {\Upsilon} for fixed value of magnetic field. It is found that with an increase in dimensionality, the binding energy starts decreasing from a higher initial value. The results obtained are quite consistent with recent studies.

Evaluation of multilingual Large Language Models (LLMs) is challenging due to a variety of factors -- the lack of benchmarks with sufficient linguistic diversity, contamination of popular benchmarks into LLM pre-training data and the lack of local, cultural nuances in translated benchmarks. In this work, we study human and LLM-based evaluation in a multilingual, multi-cultural setting. We evaluate 30 models across 10 Indic languages by conducting 90K human evaluations and 30K LLM-based evaluations and find that models such as GPT-4o and Llama-3 70B consistently perform best for most Indic languages. We build leaderboards for two evaluation settings - pairwise comparison and direct assessment and analyze the agreement between humans and LLMs. We find that humans and LLMs agree fairly well in the pairwise setting but the agreement drops for direct assessment evaluation especially for languages such as Bengali and Odia. We also check for various biases in human and LLM-based evaluation and find evidence of self-bias in the GPT-based evaluator. Our work presents a significant step towards scaling up multilingual evaluation of LLMs., Comment: Accepted to EMNLP 2024

Self-supervised learning (SSL) with vision transformers (ViTs) has proven effective for representation learning as demonstrated by the impressive performance on various downstream tasks. Despite these successes, existing ViT-based SSL architectures do not fully exploit the ViT backbone, particularly the patch tokens of the ViT. In this paper, we introduce a novel Semantic Graph Consistency (SGC) module to regularize ViT-based SSL methods and leverage patch tokens effectively. We reconceptualize images as graphs, with image patches as nodes and infuse relational inductive biases by explicit message passing using Graph Neural Networks into the SSL framework. Our SGC loss acts as a regularizer, leveraging the underexploited patch tokens of ViTs to construct a graph and enforcing consistency between graph features across multiple views of an image. Extensive experiments on various datasets including ImageNet, RESISC and Food-101 show that our approach significantly improves the quality of learned representations, resulting in a 5-10\% increase in performance when limited labeled data is used for linear evaluation. These experiments coupled with a comprehensive set of ablations demonstrate the promise of our approach in various settings.

Given unstructured text, Large Language Models (LLMs) are adept at answering simple (single-hop) questions. However, as the complexity of the questions increase, the performance of LLMs degrade. We believe this is due to the overhead associated with understanding the complex question followed by filtering and aggregating unstructured information in the raw text. Recent methods try to reduce this burden by integrating structured knowledge triples into the raw text, aiming to provide a structured overview that simplifies information processing. However, this simplistic approach is query-agnostic and the extracted facts are ambiguous as they lack context. To address these drawbacks and to enable LLMs to answer complex (multi-hop) questions with ease, we propose to use a knowledge graph (KG) that is context-aware and is distilled to contain query-relevant information. The use of our compressed distilled KG as input to the LLM results in our method utilizing up to $67\%$ fewer tokens to represent the query relevant information present in the supporting documents, compared to the state-of-the-art (SoTA) method. Our experiments show consistent improvements over the SoTA across several metrics (EM, F1, BERTScore, and Human Eval) on two popular benchmark datasets (HotpotQA and MuSiQue)., Comment: Accepted at ACL 2024 in the main track

This paper summarizes our acoustic modeling efforts in the Johns Hopkins University speech recognition system for the CHiME-5 challenge to recognize highly-overlapped dinner party speech recorded by multiple microphone arrays. We explore data augmentation approaches, neural network architectures, front-end speech dereverberation, beamforming and robust i-vector extraction with comparisons of our in-house implementations and publicly available tools. We finally achieved a word error rate of 69.4% on the development set, which is a 11.7% absolute improvement over the previous baseline of 81.1%, and release this improved baseline with refined techniques/tools as an advanced CHiME-5 recipe., Comment: Published in: ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

Connectionist temporal classification (CTC) models are known to have peaky output distributions. Such behavior is not a problem for automatic speech recognition (ASR), but it can cause inaccurate forced alignments (FA), especially at finer granularity, e.g., phoneme level. This paper aims at alleviating the peaky behavior for CTC and improve its suitability for forced alignment generation, by leveraging label priors, so that the scores of alignment paths containing fewer blanks are boosted and maximized during training. As a result, our CTC model produces less peaky posteriors and is able to more accurately predict the offset of the tokens besides their onset. It outperforms the standard CTC model and a heuristics-based approach for obtaining CTC's token offset timestamps by 12-40% in phoneme and word boundary errors (PBE and WBE) measured on the Buckeye and TIMIT data. Compared with the most widely used FA toolkit Montreal Forced Aligner (MFA), our method performs similarly on PBE/WBE on Buckeye, yet falls behind MFA on TIMIT. Nevertheless, our method has a much simpler training pipeline and better runtime efficiency. Our training recipe and pretrained model are released in TorchAudio., Comment: Accepted by ICASSP 2024. Github repo: https://github.com/huangruizhe/audio/tree/aligner_label_priors

We give improved lower bounds for binary $3$-query locally correctable codes (3-LCCs) $C \colon \{0,1\}^k \rightarrow \{0,1\}^n$. Specifically, we prove: (1) If $C$ is a linear design 3-LCC, then $n \geq 2^{(1 - o(1))\sqrt{k} }$. A design 3-LCC has the additional property that the correcting sets for every codeword bit form a perfect matching and every pair of codeword bits is queried an equal number of times across all matchings. Our bound is tight up to a factor $\sqrt{8}$ in the exponent of $2$, as the best construction of binary $3$-LCCs (obtained by taking Reed-Muller codes on $\mathbb{F}_4$ and applying a natural projection map) is a design $3$-LCC with $n \leq 2^{\sqrt{8 k}}$. Up to a $\sqrt{8}$ factor, this resolves the Hamada conjecture on the maximum $\mathbb{F}_2$-codimension of a $4$-design. (2) If $C$ is a smooth, non-linear, adaptive $3$-LCC with perfect completeness, then, $n \geq 2^{\Omega(k^{1/5})}$. (3) If $C$ is a smooth, non-linear, adaptive $3$-LCC with completeness $1 - \varepsilon$, then $n \geq \tilde{\Omega}(k^{\frac{1}{2\varepsilon}})$. In particular, when $\varepsilon$ is a small constant, this implies a lower bound for general non-linear LCCs that beats the prior best $n \geq \tilde{\Omega}(k^3)$ lower bound of [AGKM23] by a polynomial factor. Our design LCC lower bound is obtained via a fine-grained analysis of the Kikuchi matrix method applied to a variant of the matrix used in [KM23]. Our lower bounds for non-linear codes are obtained by designing a from-scratch reduction from nonlinear $3$-LCCs to a system of "chain XOR equations": polynomial equations with similar structure to the long chain derivations that arise in the lower bounds for linear $3$-LCCs [KM23].

In this paper, we study the asymptotic behaviour of the v-number of a Noetherian graded filtration $\mathcal{I}= \{I_{[k]}\}_{k\geq 0}$ of a Noetherian $\mathbb{N}$-graded domain $R$. Recently, it is shown that $\mathrm{v}(I_{[k]})$ is periodically linear in $k$ for $k \gg 0$. We show that all these linear functions have the same slope, i.e. $\displaystyle \lim_{k \rightarrow \infty}\frac{\mathrm{v}(I_{[k]})}{k}$ exists, which is equal to $\displaystyle \lim_{k \rightarrow \infty}\frac{\alpha(I_{[k]})}{k}$, where $\alpha(I)$ denotes the minimum degree of a non-zero element in $I$. In particular, for any Noetherian symbolic filtration $\mathcal{I}= \{I^{(k)}\}_{k\geq 0}$ of $R$, it follows that $\displaystyle \lim_{k \rightarrow \infty}\frac{\mathrm{v}(I^{(k)})}{k}=\hat{\alpha}(I)$, the Waldschmidt constant of $I$. Next, for a non-equigenerated square-free monomial ideal $I$, we prove that $\mathrm{v}(I^{(k)}) \leq \mathrm{reg}(R/I^{(k)})$ for $k\gg 0$. Also, for an ideal $I$ having the symbolic strong persistence property, we give a linear upper bound on $\mathrm{v}(I^{(k)})$. As an application, we derive some criteria for a square-free monomial ideal $I$ to satisfy $\mathrm{v}(I^{(k)})\leq \mathrm{reg}(R/I^{(k)})$ for all $k\geq 1$, and provide several examples in support. In addition, for any simple graph $G$, we establish that $\mathrm{v}(J(G)^{(k)}) \leq \mathrm{reg}(R/J(G)^{(k)})$ for all $k \geq 1$, and $\mathrm{v}(J(G)^{(k)}) = \mathrm{reg}(R/J(G)^{(k)})=\alpha(J(G)^{(k)})-1$ for all $k\geq 1$ if and only if $G$ is a Cohen-Macaulay very-well covered graph, where $J(G)$ is the cover ideal of $G$., Comment: Some changes have been made

Four-dimensional (4D) wide coverage computed tomography (CT) is an effective imaging modality for measuring the mechanical function of the myocardium. However, repeated CT measurement across several heartbeats is still a concern. A projection-domain noise emulation method is presented to generate accurate low-dose (mA modulated) 4D cardiac CT scans from high-dose scans, enabling protocol optimization to deliver sufficient image quality for functional cardiac analysis while using a dose level that is as low as reasonably achievable. Given a targeted low-dose mA modulation curve, the proposed noise emulation method injects both quantum and electronic noise of proper magnitude and correlation to the high-dose data in projection domain. A spatially varying detector gain term as well as its calibration method were proposed to further improve the noise emulation accuracy. To determine the low dose threshold, a projection domain image quality (IQ) metric was proposed that is based on the number of projection rays that do not fall under the non-linear region of the detector. Experiments were performed to validate the noise emulation method with both phantom and clinical data. For both phantom and clinical data, the low-dose emulated images exhibited similar noise magnitude, artifacts, and texture to that of the real low-dose images. The proposed channel-dependent detector gain term resulted in additional increase in emulation accuracy. Using the proposed IQ metric, recommended kVp and mA settings were calculated for low dose 4D Cardiac CT acquisitions for patients of different sizes. In conclusion, a detailed method to estimate system-dependent parameters for a raw-data based low dose emulation framework was described. The proposed low-dose emulation method can be used to prospectively select patient-specific minimal-dose protocols for functional cardiac CT., Comment: First two authors contributed equally

Hand-intensive manufacturing processes, such as composite layup and textile draping, require significant human dexterity to accommodate task complexity. These strenuous hand motions often lead to musculoskeletal disorders and rehabilitation surgeries. We develop a data-driven ergonomic risk assessment system with a special focus on hand and finger activity to better identify and address ergonomic issues related to hand-intensive manufacturing processes. The system comprises a multi-modal sensor testbed to collect and synchronize operator upper body pose, hand pose and applied forces; a Biometric Assessment of Complete Hand (BACH) formulation to measure high-fidelity hand and finger risks; and industry-standard risk scores associated with upper body posture, RULA, and hand activity, HAL. Our findings demonstrate that BACH captures injurious activity with a higher granularity in comparison to the existing metrics. Machine learning models are also used to automate RULA and HAL scoring, and generalize well to unseen participants. Our assessment system, therefore, provides ergonomic interpretability of the manufacturing processes studied, and could be used to mitigate risks through minor workplace optimization and posture corrections., Comment: 26 pages, 7 figures

Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanical approach to analyze sparse equation discovery algorithms, which typically balance data fit and parsimony through a trial-and-error selection of hyperparameters. In this framework, statistical mechanics offers tools to analyze the interplay between complexity and fitness, in analogy to that done between entropy and energy. To establish this analogy, we define the optimization procedure as a two-level Bayesian inference problem that separates variable selection from coefficient values and enables the computation of the posterior parameter distribution in closed form. A key advantage of employing statistical mechanical concepts, such as free energy and the partition function, is in the quantification of uncertainty, especially in in the low-data limit; frequently encountered in real-world applications. As the data volume increases, our approach mirrors the thermodynamic limit, leading to distinct sparsity- and noise-induced phase transitions that delineate correct from incorrect identification. This perspective of sparse equation discovery, is versatile and can be adapted to various other equation discovery algorithms., Comment: 21 RevTeX page, 9 figures

Benchmarking is the de-facto standard for evaluating LLMs, due to its speed, replicability and low cost. However, recent work has pointed out that the majority of the open source benchmarks available today have been contaminated or leaked into LLMs, meaning that LLMs have access to test data during pretraining and/or fine-tuning. This raises serious concerns about the validity of benchmarking studies conducted so far and the future of evaluation using benchmarks. To solve this problem, we propose Private Benchmarking, a solution where test datasets are kept private and models are evaluated without revealing the test data to the model. We describe various scenarios (depending on the trust placed on model owners or dataset owners), and present solutions to avoid data contamination using private benchmarking. For scenarios where the model weights need to be kept private, we describe solutions from confidential computing and cryptography that can aid in private benchmarking. We build an end-to-end system, TRUCE, that enables such private benchmarking showing that the overheads introduced to protect models and benchmark are negligible (in the case of confidential computing) and tractable (when cryptographic security is required). Finally, we also discuss solutions to the problem of benchmark dataset auditing, to ensure that private benchmarks are of sufficiently high quality.

The Navier Stokes equations (NSEs) are partial differential equations (PDEs) to describe the nonlinear convective motion of fluids and they are computationally expensive to simulate because of their high nonlinearity and variables being fully coupled. Reduced-order models (ROMs) are simpler models for evolving the flows by capturing only the dominant behaviors of a system and can be used to design controllers for high-dimensional systems. However it is challenging to guarantee the stability of these models either globally or locally. Ensuring the stability of ROMs can improve the interpretability of the behavior of the dynamics and help develop effective system control strategies. For quadratically nonlinear systems that represent many fluid flows, the Schlegel and Noack trapping theorem (JFM, 2015) can be used to check if ROMs are globally stable (long-term bounded). This theorem was subsequently incorporated into system identification techniques that determine models directly from data. In this work, we relax the quadratically energy-preserving constraints in this theorem, and then promote local stability in data-driven models of quadratically nonlinear dynamics. First, we prove a theorem outlining sufficient conditions to ensure local stability in linear-quadratic systems and provide an estimate of the stability radius. Second, we incorporate this theorem into system identification methods and produce a-priori locally stable data-driven models. Several examples are presented to demonstrate the effectiveness and accuracy of the proposed algorithm.