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We propose extending the minimal scotogenic model with a triplet fermion and a singlet scalar. All the fields change non-trivially under an additional $Z_{4}\times Z_{2}$ symmetry. The $Z_{4}\times Z_{2}$ symmetry allows only diagonal Yukawa couplings among different generations of SM leptons and right-handed singlet neutrinos. The one-loop radiative diagrams generate neutrino mass. The Yukawa coupling of the triplet fermion with the inert doublet positively contributes to the muon anomalous magnetic moment. The imposed $Z_{4}\times Z_{2}$ symmetry forbids the conventional leptogenesis from the right-handed neutrino decay. A net lepton asymmetry can be generated in the muonic sector from triplet fermion decay. Involvement of the Yukawa coupling both in leptogenesis and in the anomalous magnetic moment of the muon results in a strong correlation between leptogenesis and the recent Fermi lab result. We show a viable parameter space for TeV scale leptogenesis while explaining the Fermi lab results. The inert scalar is the dark matter candidate in this model. The model also poses the potential to explain the latest results on W boson mass from the CDF-II experiment., Comment: 16 pages, 6 figures, 2 tables

We study the dynamics of the interacting models between the Gauss-Bonnet (GB) coupled scalar field and the dark matter fluid in a homogeneous and isotropic background. A key feature of GB coupling models is the varying speed of gravitational waves (GWs). We utilize recent constraints on the GW speed and conduct our analysis in two primary scenarios: model-dependent and model-independent. In the model-dependent scenario, where determining the GW speed requires a specific GB coupling functional form, we choose an exponential GB coupling. We adopt a dynamical system analysis to obtain the necessary constraints on the model parameters that describe different phases of the universe and produce a stable late-time accelerating solution following the GW constraint, and find that to satisfy all these constraints, fine-tuning of the free parameters involved in the models is often needed. In the model-independent scenario, the GW speed is fixed to one, and we construct the autonomous system to identify the late-time stable accelerating critical points. Furthermore, we adopt a Bayesian inference method using late-time observational data sets, including 31 data points from cosmic chronometer data (Hubble data) and 1701 data points from Pantheon+ and find that all the observational constraints can be satisfied without fine-tuning. In addition, we also utilize simulated binned Roman and LSST data to study the evolution of the universe in the model-independent scenario. We find that the model shows significant deviation at higher redshifts from $\Lambda$CDM and fits the current data much better than $\Lambda$CDM within the error bars., Comment: 31 pages, 21 figures, and 3 tables

Recurrent large language models that compete with Transformers in language modeling perplexity are emerging at a rapid rate (e.g., Mamba, RWKV). Excitingly, these architectures use a constant amount of memory during inference. However, due to the limited memory, recurrent LMs cannot recall and use all the information in long contexts leading to brittle in-context learning (ICL) quality. A key challenge for efficient LMs is selecting what information to store versus discard. In this work, we observe the order in which information is shown to the LM impacts the selection difficulty. To formalize this, we show that the hardness of information recall reduces to the hardness of a problem called set disjointness (SD), a quintessential problem in communication complexity that requires a streaming algorithm (e.g., recurrent model) to decide whether inputted sets are disjoint. We empirically and theoretically show that the recurrent memory required to solve SD changes with set order, i.e., whether the smaller set appears first in-context. Our analysis suggests, to mitigate the reliance on data order, we can put information in the right order in-context or process prompts non-causally. Towards that end, we propose: (1) JRT-Prompt, where context gets repeated multiple times in the prompt, effectively showing the model all data orders. This gives $11.0 \pm 1.3$ points of improvement, averaged across $16$ recurrent LMs and the $6$ ICL tasks, with $11.9\times$ higher throughput than FlashAttention-2 for generation prefill (length $32$k, batch size $16$, NVidia H100). We then propose (2) JRT-RNN, which uses non-causal prefix-linear-attention to process prompts and provides $99\%$ of Transformer quality at $360$M params., $30$B tokens and $96\%$ at $1.3$B params., $50$B tokens on average across the tasks, with $19.2\times$ higher throughput for prefill than FA2.

In the present work, we extend the $f(Q)$ symmetric teleparallel gravity by introducing an arbitrary coupling between the non-metricity $Q$ and matter Lagrangian $L_m$ in the Lagrangian density $f$ of the theory, which thus leads to the $f\left(Q,L_m\right)$ theory. This generalisation encompasses Coincident General Relativity (CGR) and the Symmetric Teleparallel Equivalent to GR (STEGR). Using the metric formalism, we derive the field equation of the theory, which generalizes the field equations of $f(Q)$ gravity. From the study of the covariant divergence of the field equations, it follows that the presence of the geometry-matter coupling leads to the non-conservation of the matter energy-momentum tensor. The cosmological implications of the theory are investigated in the case of a flat, homogeneous, and isotropic Friedmann-Lemaitre-Robertson-Walker geometry. As a first step in this direction, we obtain the modified Friedmann equations for the $f(Q,L_m)$ gravity in a general form. Specific cosmological models are investigated for several choices of $f(Q,L_m)$, including $f(Q,L_m)=-\alpha Q + 2L_m + \beta$, and $f(Q,L_m)=- \alpha Q + (2L_m)^2 + \beta$, respectively. Comparative analyses with the standard $\Lambda$ CDM paradigm are carried out, and the observational implications of the models are investigated in detail., Comment: 21 pages, 11 figures

In this work, we explore the behavior of interacting dark energy and dark matter within a model of $f(Q)$ gravity, employing a standard framework of dynamical system analysis. We consider the power-law $f(Q)$ model incorporating with two different forms of interacting dark energy and dark matter: $3\alpha H\rho_m$ and $\frac{\alpha}{3H}\rho_m \rho_{DE}$. The evolution of $\Omega_m, \Omega_r, \Omega_{DE}, q$, and $\omega$ for different values of the model parameter $n$ and the interaction parameter $\alpha$ has been examined. Our results show that the universe was dominated by matter in the early stages and will be dominated by dark energy in later stages. Using the observational data, the fixed points are found to be stable and can be represented the de Sitter and quintessence acceleration solutions. We discover that the dynamical profiles of the universe in $f(Q)$ dark energy models are influenced by both the interaction term and the relevant model parameters., Comment: v1: 14 pages, many figures

The increasing compute demands of AI systems has led to the emergence of services that train models on behalf of clients lacking necessary resources. However, ensuring correctness of training and guarding against potential training-time attacks, such as data poisoning, poses challenges. Existing works on verifiable training largely fall into two classes: proof-based systems, which struggle to scale due to requiring cryptographic techniques, and "optimistic" methods that consider a trusted third-party auditor who replicates the training process. A key challenge with the latter is that hardware nondeterminism between GPU types during training prevents an auditor from replicating the training process exactly, and such schemes are therefore non-robust. We propose a method that combines training in a higher precision than the target model, rounding after intermediate computation steps, and storing rounding decisions based on an adaptive thresholding procedure, to successfully control for nondeterminism. Across three different NVIDIA GPUs (A40, Titan XP, RTX 2080 Ti), we achieve exact training replication at FP32 precision for both full-training and fine-tuning of ResNet-50 (23M) and GPT-2 (117M) models. Our verifiable training scheme significantly decreases the storage and time costs compared to proof-based systems., Comment: 11 pages, 5 figures, preprint

Recent work has shown that attention-based language models excel at recall, the ability to ground generations in tokens previously seen in context. However, the efficiency of attention-based models is bottle-necked during inference by the KV-cache's aggressive memory consumption. In this work, we explore whether we can improve language model efficiency (e.g. by reducing memory consumption) without compromising on recall. By applying experiments and theory to a broad set of architectures, we identify a key tradeoff between a model's state size and recall ability. We show that efficient alternatives to attention (e.g. H3, Mamba, RWKV) maintain a fixed-size recurrent state, but struggle at recall. We propose BASED a simple architecture combining linear and sliding window attention. By varying BASED window size and linear attention feature dimension, we can dial the state size and traverse the pareto frontier of the recall-memory tradeoff curve, recovering the full quality of attention on one end and the small state size of attention-alternatives on the other. We train language models up to 1.3b parameters and show that BASED matches the strongest sub-quadratic models (e.g. Mamba) in perplexity and outperforms them on real-world recall-intensive tasks by 6.22 accuracy points. Implementations of linear attention are often less efficient than optimized standard attention implementations. To make BASED competitive, we develop IO-aware algorithms that enable 24x higher throughput on language generation than FlashAttention-2, when generating 1024 tokens using 1.3b parameter models. Code for this work is provided at: https://github.com/HazyResearch/based.

We construct the energy conditions for the recently proposed $f(R,L,T)$ gravity theory, for which $f$ is a generic function of the Ricci scalar $R$, matter lagrangian density $L$ and trace of the energy-momentum tensor $T$. We analyse two different forms for the $f(R,L,T)$ function within the framework of the Friedmann-Lem\^aitre-Robertson-Walker universe. We constrain the model parameters from the energy conditions. This approach allows us to assess the feasibility of specific forms of the $f(R,L,T)$ gravity., Comment: EPJ Plus accepted version

Retrieval pipelines-an integral component of many machine learning systems-perform poorly in domains where documents are long (e.g., 10K tokens or more) and where identifying the relevant document requires synthesizing information across the entire text. Developing long-context retrieval encoders suitable for these domains raises three challenges: (1) how to evaluate long-context retrieval performance, (2) how to pretrain a base language model to represent both short contexts (corresponding to queries) and long contexts (corresponding to documents), and (3) how to fine-tune this model for retrieval under the batch size limitations imposed by GPU memory constraints. To address these challenges, we first introduce LoCoV1, a novel 12 task benchmark constructed to measure long-context retrieval where chunking is not possible or not effective. We next present the M2-BERT retrieval encoder, an 80M parameter state-space encoder model built from the Monarch Mixer architecture, capable of scaling to documents up to 32K tokens long. We describe a pretraining data mixture which allows this encoder to process both short and long context sequences, and a finetuning approach that adapts this base model to retrieval with only single-sample batches. Finally, we validate the M2-BERT retrieval encoder on LoCoV1, finding that it outperforms competitive Transformer-based models by at least 23.3 points, despite containing upwards of 90x fewer parameters.

We study the bounce cosmology to construct a singularity-free $f(\mathcal{R})$ model using the reconstruction technique. The formulation of the $f(\mathcal{R})$ model is based on the Raychaudhari equation, a key element employed in reconstructed models to eliminate singularities. We explore the feasibility of obtaining stable gravitational Lagrangians, adhering to the conditions $f_{\mathcal{R}}>0$ and $f_{\mathcal{R}\mathcal{R}}>0$. Consequently, both models demonstrate stability, effectively avoiding the Dolgov-Kawasaki instability. Our assessment extends to testing the reconstructed model using energy conditions and the effective equation-of-state (EoS). Our findings indicate that the reconstructed super-bounce model facilitates the examination of a singularity-free accelerating universe for both phantom and non-phantom phases. However, in the case of the reconstructed oscillatory bounce model, two scenarios are considered with $\omega=-1/3$ and $\omega=-2/3$. While the model proves suitable for studying a singular-free accelerating universe in the $\omega=-1/3$ case, it fails to demonstrate such behavior under energy conditions for the $\omega=-2/3$ scenario. The reconstructed models accommodate early-time bouncing behavior and late-, Comment: EPJC published version

The late time acceleration of the Universe has challenged contemporary cosmology since its discovery. General Relativity explains this phenomenon by introducing the cosmological constant, named the standard cosmological model ($\Lambda$CDM). However, the cosmological constant solution has several drawbacks that have led cosmologists to explore and propose alternative models to explain the late time acceleration of the Universe. These alternatives span from models of a dynamical dark fluid, known as dark energy, to models of large-scale modifications of the gravitational interaction, known as modified gravity. The current dissertation intends to show several ways to investigate late-time cosmology or to look at probable places for future investigations in order to shed more light on the dark sector of the Universe..., Comment: Ph.D. Thesis. Some chapters are published in the following journals: Classical and Quantum Gravity 37, 205022 (2020); Monthly Notices of the Royal Astronomical Society 522, 252-267 (2023); Physics of the Dark Universe 30, 100664 (2020); European Physics Journal C 81, 555 (2021); 133 Pages

We reexamine the kink-like parameterization of the deceleration parameter to derive constraints on the transition redshift from cosmic deceleration to acceleration. This is achieved using observational Hubble data, Type Ia Supernovae Pantheon+ samples and Baryon acoustic oscillations. In this parametrization, the value of the initial $q$ parameter is $q_{i}$, the final value is $q_f$, the present value is denoted by $q_{0}$, and the transition duration is given by $\alpha$. We perform our calculations using the Monte Carlo Markov Chain method, utilizing the emcee package. Under the assumption of a flat geometry, we constrain the range of possible values for three scenarios: when $q_{f}$ is unrestricted, when $q_{f}$ is equal to $-1$, and when $\alpha$ is $1/3$. This is done assuming that $q_{i}=1/2$. Here, we achieve that the $SN$ data fixes the free parameters tightly as in the flat $\Lambda$CDM for unrestricted $q_{f}$. In addition, if we fix $q_{f}=-1$, the model behaves well as the $\Lambda$CDM for the combined dataset. We also acquire the current value of the deceleration parameter, which is consistent with the latest results that assume the $\Lambda$CDM model. Furthermore, we observe a deviation from the standard $\Lambda$CDM model in the current model based on the evolution of $j(z)$, and it is evident that the universe transitions from deceleration to acceleration and will eventually reach the $\Lambda$CDM model in the near future., Comment: Physics of the Dark Universe published version

Attention-free language models that combine gating and convolutions are growing in popularity due to their efficiency and increasingly competitive performance. To better understand these architectures, we pretrain a suite of 17 attention and "gated-convolution" language models, finding that SoTA gated-convolution architectures still underperform attention by up to 2.1 perplexity points on the Pile. In fine-grained analysis, we find 82% of the gap is explained by each model's ability to recall information that is previously mentioned in-context, e.g. "Hakuna Matata means no worries Hakuna Matata it means no" $\rightarrow$ "??". On this task, termed "associative recall", we find that attention outperforms gated-convolutions by a large margin: a 70M parameter attention model outperforms a 1.4 billion parameter gated-convolution model on associative recall. This is surprising because prior work shows gated convolutions can perfectly solve synthetic tests for AR capability. To close the gap between synthetics and real language, we develop a new formalization of the task called multi-query associative recall (MQAR) that better reflects actual language. We perform an empirical and theoretical study of MQAR that elucidates differences in the parameter-efficiency of attention and gated-convolution recall. Informed by our analysis, we evaluate simple convolution-attention hybrids and show that hybrids with input-dependent sparse attention patterns can close 97.4% of the gap to attention, while maintaining sub-quadratic scaling. Our code is accessible at: https://github.com/HazyResearch/zoology.

Large Language Models (LLMs) are notorious for blending fact with fiction and generating non-factual content, known as hallucinations. To address this challenge, we propose an interactive system that helps users gain insight into the reliability of the generated text. Our approach is based on the idea that the self-consistency of multiple samples generated by the same LLM relates to its confidence in individual claims in the generated texts. Using this idea, we design RELIC, an interactive system that enables users to investigate and verify semantic-level variations in multiple long-form responses. This allows users to recognize potentially inaccurate information in the generated text and make necessary corrections. From a user study with ten participants, we demonstrate that our approach helps users better verify the reliability of the generated text. We further summarize the design implications and lessons learned from this research for future studies of reliable human-LLM interactions.

Machine learning models are increasingly being scaled in both sequence length and model dimension to reach longer contexts and better performance. However, existing architectures such as Transformers scale quadratically along both these axes. We ask: are there performant architectures that can scale sub-quadratically along sequence length and model dimension? We introduce Monarch Mixer (M2), a new architecture that uses the same sub-quadratic primitive along both sequence length and model dimension: Monarch matrices, a simple class of expressive structured matrices that captures many linear transforms, achieves high hardware efficiency on GPUs, and scales sub-quadratically. As a proof of concept, we explore the performance of M2 in three domains: non-causal BERT-style language modeling, ViT-style image classification, and causal GPT-style language modeling. For non-causal BERT-style modeling, M2 matches BERT-base and BERT-large in downstream GLUE quality with up to 27% fewer parameters, and achieves up to 9.1$\times$ higher throughput at sequence length 4K. On ImageNet, M2 outperforms ViT-b by 1% in accuracy, with only half the parameters. Causal GPT-style models introduce a technical challenge: enforcing causality via masking introduces a quadratic bottleneck. To alleviate this bottleneck, we develop a novel theoretical view of Monarch matrices based on multivariate polynomial evaluation and interpolation, which lets us parameterize M2 to be causal while remaining sub-quadratic. Using this parameterization, M2 matches GPT-style Transformers at 360M parameters in pretraining perplexity on The PILE--showing for the first time that it may be possible to match Transformer quality without attention or MLPs., Comment: NeurIPS 2023 (Oral)

(111) NiO epitaxial layers embedded with crystallographically oriented Ni-clusters are grown on c-GaN/Sapphire templates using pulsed laser deposition technique. Structural and magnetic properties of the films are examined by a variety of techniques including high resolution x-ray diffraction, precession-electron diffraction and superconducting quantum interference device magnetometry. The study reveals that the inclusion, orientation, shape, size, density and magnetic properties of these clusters depend strongly on the growth temperature (TG). Though, most of the Ni-clusters are found to be crystallographically aligned with the NiO matrix with Ni(111) parallel to NiO(111), clusters with other orientations also exist, especially in samples grown at lower temperatures. Average size and density of the clusters increase with TG . Proportion of the Ni(111) parallel to NiO(111) oriented clusters also improves as TG is increased. All cluster embedded films show ferromagnetic behaviour even at room temperature. Easy-axis is found to be oriented in the layer plane in samples grown at relatively lower temperatures. However, it turns perpendicular to the layer plane for samples grown at sufficiently high temperatures. This reversal of easy-axis has been attributed to the size dependent competition between the shape, magnetoelastic and the surface anisotropies of the clusters. This composite material thus has great potential to serve as spin-injector and spinstorage medium in GaN based spintronics of the future.

We introduce and define the novel problem of multi-distribution information retrieval (IR) where given a query, systems need to retrieve passages from within multiple collections, each drawn from a different distribution. Some of these collections and distributions might not be available at training time. To evaluate methods for multi-distribution retrieval, we design three benchmarks for this task from existing single-distribution datasets, namely, a dataset based on question answering and two based on entity matching. We propose simple methods for this task which allocate the fixed retrieval budget (top-k passages) strategically across domains to prevent the known domains from consuming most of the budget. We show that our methods lead to an average of 3.8+ and up to 8.0 points improvements in Recall@100 across the datasets and that improvements are consistent when fine-tuning different base retrieval models. Our benchmarks are made publicly available., Comment: REML @ SIGIR 2023; 9 pages, 8 figures

Generative Pre-trained Transformer (GPT) models have exhibited exciting progress in their capabilities, capturing the interest of practitioners and the public alike. Yet, while the literature on the trustworthiness of GPT models remains limited, practitioners have proposed employing capable GPT models for sensitive applications such as healthcare and finance -- where mistakes can be costly. To this end, this work proposes a comprehensive trustworthiness evaluation for large language models with a focus on GPT-4 and GPT-3.5, considering diverse perspectives -- including toxicity, stereotype bias, adversarial robustness, out-of-distribution robustness, robustness on adversarial demonstrations, privacy, machine ethics, and fairness. Based on our evaluations, we discover previously unpublished vulnerabilities to trustworthiness threats. For instance, we find that GPT models can be easily misled to generate toxic and biased outputs and leak private information in both training data and conversation history. We also find that although GPT-4 is usually more trustworthy than GPT-3.5 on standard benchmarks, GPT-4 is more vulnerable given jailbreaking system or user prompts, potentially because GPT-4 follows (misleading) instructions more precisely. Our work illustrates a comprehensive trustworthiness evaluation of GPT models and sheds light on the trustworthiness gaps. Our benchmark is publicly available at https://decodingtrust.github.io/ ; our dataset can be previewed at https://huggingface.co/datasets/AI-Secure/DecodingTrust ; a concise version of this work is at https://openreview.net/pdf?id=kaHpo8OZw2 ., Comment: NeurIPS 2023 Outstanding Paper (Datasets and Benchmarks Track)

A long standing goal of the data management community is to develop general, automated systems that ingest semi-structured documents and output queryable tables without human effort or domain specific customization. Given the sheer variety of potential documents, state-of-the art systems make simplifying assumptions and use domain specific training. In this work, we ask whether we can maintain generality by using large language models (LLMs). LLMs, which are pretrained on broad data, can perform diverse downstream tasks simply conditioned on natural language task descriptions. We propose and evaluate EVAPORATE, a simple, prototype system powered by LLMs. We identify two fundamentally different strategies for implementing this system: prompt the LLM to directly extract values from documents or prompt the LLM to synthesize code that performs the extraction. Our evaluations show a cost-quality tradeoff between these two approaches. Code synthesis is cheap, but far less accurate than directly processing each document with the LLM. To improve quality while maintaining low cost, we propose an extended code synthesis implementation, EVAPORATE-CODE+, which achieves better quality than direct extraction. Our key insight is to generate many candidate functions and ensemble their extractions using weak supervision. EVAPORATE-CODE+ not only outperforms the state-of-the art systems, but does so using a sublinear pass over the documents with the LLM. This equates to a 110x reduction in the number of tokens the LLM needs to process, averaged across 16 real-world evaluation settings of 10k documents each.

We investigate the exponential $f(Q)$ symmetric teleparallel gravitation, namely $f(Q)=Q+\alpha Q_0(1-e^{-\beta\sqrt{Q/Q_0}})$ using \texttt{ME-GADGET} code to probe the structure formation with box sizes $L_{\mathrm{box}}=10/100$ Mpc$/h$ and middle resolution $N_p^{1/3}=512$. To reproduce viable cosmology within the aforementioned modified gravity theory, we first perform Markov Chain Monte Carlo (MCMC) sampling on OHD/BAO/Pantheon datasets and constrain a parameter space. Furthermore, we also derive theoretical values for deceleration parameter $q(z)$, statefinder pair $\{r,s\}$ and effective gravitational constant $G_{\mathrm{eff}}$, perform $Om(z)$ diagnostics. While carrying out N-body+SPH simulations, we derive CDM+baryons over density/temperature/mean molecular weight fields, matter power spectrum (both 2/3D, with/without redshift space distortions), bispectrum, two-point correlation function and halo mass function. Results for small and big simulation box sizes are therefore properly compared, halo mass function is related to the Seth-Tormen theoretical prediction and matter power spectrum to the standard \texttt{CAMB} output., Comment: MNRAS accepted version

On the basis of homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) geometry, solutions to the issues of cosmic acceleration and dark energy are being put forth within the context of $f\left( Q\right)$ gravity. We take into account a power law $f(Q)$ model using $f\left( Q\right) =\alpha Q^{n}$, where $\alpha $ and $n$ are free model parameters. In the current scenario, we may establish the energy density and pressure for our $f(Q)$ cosmic model by applying the constant sound speed parameterizations, i.e., $\vartheta_{s}^{2}=\beta$, where a barotropic cosmic fluid is described in terms of $\beta$. The field equations are then derived, and their precise solutions are established. We obtain the constraints on the model parameters using the updated Hubble (Hz) data sets consisting of 31 data points, the recently published Pantheon samples (SNe) with 1048 points, and Baryon acoustic oscillations (BAO) data sets. We also examine the physical behaviour of the deceleration parameter, the equation of state (EoS) parameter, the statefinder diagnostic, and the Om diagnostic. We conclude that our $f\left( Q\right) $\ cosmic model predicts a transition in the universe from deceleration to acceleration. Further, to investigate the feasibility of the model, we discussed some of its thermodynamic aspects., Comment: Nuclear Physics B published version

We use the hybrid model of bulk viscosity and generalized chaplygin gas (GCG), named the viscous generalized chaplygin gas (VGCG) model, which is thought to be an alternate dark fluid of the universe. We explore the dynamics of the VGCG model in the framework of the non-metricity $f(Q)$ gravity using the functional form $f(Q)=\beta Q^n$, where $\beta$ and $n$ are arbitrary constants. For the purpose of constraining model parameters, we use recent observational datasets such as Observational Hubble data, Baryon Acoustic Oscillations, and Type $Ia$ supernovae data. According to our study, the evolution of the deceleration parameter $q$ and the equation of state (EoS) parameter $w$ show a transition from deceleration to an acceleration phase and its deviation from the $\Lambda$CDM model., Comment: Annals of Physics published version

The equation of state parameter is a significant method for characterizing dark energy models. We investigate the evolution of the equation of state parameter with redshift using a Bayesian analysis of recent observational datasets (the Cosmic Chronometer data (CC) and Pantheon samples). The Chevallier-Polarski-Linder parametrization of the effective equation of state parameter, $\omega_{eff}=\omega_0+\omega_a \left( \frac{z}{1+z}\right) $, where $\omega_0$ and $\omega_a$ are free constants, is confined to the Weyl type $f(Q,T)$ gravity, where $Q$ represents the non-metricity and $T$ is the trace of the energy-momentum tensor. We observe the evolution of the deceleration parameter $q$, the density parameter $\rho$, the pressure $p$, and the effective equation of state parameter $\omega$. The cosmic data limit for $\omega$ does not exclude the possibility of $\omega < -1$. It is seen that the parameter $\omega$ shows a transition from deceleration to acceleration, as well as a shift from $\omega>-1$ to $\omega<-1$., Comment: Annals of Physics accepted version

The variety of theories that can account for the dark energy phenomenon encourages current research to concentrate on a more in-depth examination of the potential impacts of modified gravity on both local and cosmic scales. We discuss some cosmological reconstruction in $f(Q,T)$ cosmology (where $Q$ is the non-metricity scalar, and $T$ is the trace of the energy-momentum tensor) corresponding to the evolution background in Friedmann-La\^imatre-Robertson-Walker (FLRW) universe. This helps us to determine how any FLRW cosmology can arise from a specific $f(Q,T)$ theory. We use the reconstruction technique to derive explicit forms of $f(Q,T)$ Lagrangian for the different kinds of matter sources and Einstein's static universe. We also formulate the models using several ansatz forms of the $f(Q,T)$ function for $p=\omega \rho$. We demonstrate that several classes of $f(Q,T)$ theories admit the power-law and de-Sitter solutions in some ranges of $\omega$. Additionally, we reconstruct the cosmological model for the scalar field with a specific form of $f(Q,T)$. These new models with cosmological inspiration may impact gravitational phenomena at other cosmological scales., Comment: PLB published version

Electroluminescence properties of epitaxially grown n-ZnO/p-GaN pn-heterojunctions are investigated as functions of applied bias and temperature. The study reveals the existence of indirect interfacial excitons at sufficiently low temperatures. Electroluminescence feature associated with these excitons redshifts with increasing forward bias. It has been found that the binding energy of these entities can be controlled through applied forward bias and can even be made higher than that of the excitons in ZnO bulk (60 meV). However, formation of these excitons becomes unsustainable when either the applied bias or the temperature crosses a threshold. This has been explained in terms of leakage and thermal escape of electrons (holes) into GaN (ZnO) side. Calculations for the band diagram and the binding energy of these spatially indirect electron-hole coulomb-coupled entities are carried out. Theoretical results are found to explain the experimental findings quite well.

Large language models (LLMs) transfer well to new tasks out-of-the-box simply given a natural language prompt that demonstrates how to perform the task and no additional training. Prompting is a brittle process wherein small modifications to the prompt can cause large variations in the model predictions, and therefore significant effort is dedicated towards designing a painstakingly "perfect prompt" for a task. To mitigate the high degree of effort involved in prompt-design, we instead ask whether producing multiple effective, yet imperfect, prompts and aggregating them can lead to a high quality prompting strategy. Our observations motivate our proposed prompting method, ASK ME ANYTHING (AMA). We first develop an understanding of the effective prompt formats, finding that question-answering (QA) prompts, which encourage open-ended generation ("Who went to the park?") tend to outperform those that restrict the model outputs ("John went to the park. Output True or False."). Our approach recursively uses the LLM itself to transform task inputs to the effective QA format. We apply the collected prompts to obtain several noisy votes for the input's true label. We find that the prompts can have very different accuracies and complex dependencies and thus propose to use weak supervision, a procedure for combining the noisy predictions, to produce the final predictions for the inputs. We evaluate AMA across open-source model families (e.g., EleutherAI, BLOOM, OPT, and T0) and model sizes (125M-175B parameters), demonstrating an average performance lift of 10.2% over the few-shot baseline. This simple strategy enables the open-source GPT-J-6B model to match and exceed the performance of few-shot GPT3-175B on 15 of 20 popular benchmarks. Averaged across these tasks, the GPT-J-6B model outperforms few-shot GPT3-175B. We release our code here: https://github.com/HazyResearch/ama_prompting

We present the coupling of the torsion scalar $T$ and the trace of energy-momentum tensor $\mathcal{T}$, which produces new modified $f(T,\mathcal{T})$ gravity. Moreover, we consider the functional form $f(T,\mathcal{T}) =\alpha \mathcal{T}+\beta T^2$ where $\alpha$ and $\beta$ are free parameters. As an alternative to a cosmological constant, the $f(T,\mathcal{T})$ theory may offer a theoretical explanation of the late-time acceleration. The recent observational data to the considered model especially the bounds on model parameters is applied in detail. Furthermore, we analyze the cosmological behavior of the deceleration, effective equation of state and total equation of state parameters. However, it is seen that the deceleration parameter depicts the transition from deceleration to acceleration and the effective dark sector shows a quintessence-like evolution., Comment: Fortschr. Phys. accepted version

We study an extension of symmetric teleparallel gravity i.e. Weyl-type $f(Q,T)$ gravity and the divergence-free parametrization of the deceleration parameter $q(z) = q_{0}+q_{1}\frac{z(1+z)}{1+z^2}$ ($q_{0}$ and $q_{1}$ are free constants) to explore the evolution of the universe. By considering the above parametric form of $q$, we derive the Hubble solution and further impose it in the Friedmann equations of Weyl-type $f(Q, T)$ gravity. To see whether this model can challenge the $\Lambda$CDM limits, we computed the constraints on the model parameters using the Bayesian analysis for the Observational Hubble data ($OHD$) and the Pantheon sample ($SNe\,Ia$). Furthermore, the deceleration parameter depicts the accelerating behavior of the universe with the present value $q_0$ and the transition redshift $z_t$ (at which the expansion transits from deceleration to acceleration) with $1-\sigma$ and $2-\sigma$ confidence level. We also examine the evolution of the energy density, pressure, and effective equation of state parameters. Finally, we demonstrate that the divergence-free parametric form of the deceleration parameter is consistent with the Weyl-type $f(Q,T)$ gravity., Comment: Chinese Journal of Physics published version

Theories of gravity are fundamentally a relation between matter and the geometric structure of the underlying spacetime. So once we put some additional restrictions on the spacetime geometry, the theory of gravity is bound to get the impact, irrespective of whether it is general relativity or the modified theories of gravity. In the present article, we consider two curvature-based constraints, namely the almost pseudo-Ricci symmetric and weakly Ricci symmetric condition. As a novel result, such spacetimes with non-null associated vectors are entirely classified, and then applying the obtained results, we investigate these spacetimes as solutions of the $F(R)$-gravity theory. The modified Friedmann equations are derived and analysed in a model-independent way first. Finally, two $F(R)$ gravity models are examined for recent observational constrained values of the deceleration, jerk, and Hubble parameters. We further discuss the behavior of energy conditions., Comment: EPJC accepted version

The latest results of CDF-II collaboration show a discrepancy of $7\sigma$ with standard model expectations. There is, also, a $4.2\sigma$ discrepancy in the measurement of muon magnetic moment reported by Fermilab. We study the connection between neutrino masses, dark matter, muon ($g-2$) and W-boson mass anomaly within a single coherent framework based on $Z_{4}$ extension of the scotogenic model with vector like lepton (VLL). Neutrino masses are generated at one loop level. The inert doublet, also, provide a solution to W-boson mass anomaly through correction in oblique parameters $S$, $T$ and $U$. The coupling of VLL triplet $\psi_T$ to inert doublet $\eta$ provides positive contribution to muon anomalous magnetic moment. In the model, the VLL triplet provides a lepton portal to dark matter ($\eta_R^0$). The model predicts a lower bound $m_{ee}>0.025$ eV at 3$\sigma$, which is well within the sensitivity reach of the $0\nu\beta\beta$ decay experiments. The model explains muon anomalous magnetic moment $\Delta a_\mu$ for $1.3

We address the important issue of isotropisation of a pre-bounce contracting phase in $f(R)$ gravity, which would be relevant to construct any viable nonsingular bouncing scenario in $f(R)$ gravity. The main motivation behind this work is to investigate whether the $f(R)$ gravity, by itself, can isotropise a contracting universe starting initially with small anisotropy without incorporating a super-stiff or non-ideal fluid, that is impossible in general relativity. Considering Bianchi I cosmology and employing a dynamical system analysis, we see that this is not possible for $R^n$ ($n>1$) and $R+\alpha R^2$ ($\alpha>0$) theory, but possible for $\frac{1}{\alpha}e^{\alpha R}$ ($\alpha>0$) theory. On the other hand, if one does not specify an $f(R)$ theory a priori but demands a cosmology smoothly connecting an ekpyrotic contraction phase to a nonsingular bounce, the ekpyrotic phase \emph{may} not fulfil the condition for isotropisation and physically viability simultaneously., Comment: 35 pages, 4 figures

The latest results of anomalous muon magnetic moment at Fermilab show a discrepancy of 4.2 $\sigma$ between the Standard Model (SM) prediction and experimental value. In this work, we revisit $U(1)_{L_{\mu}-L_{\tau}}$ symmetry with in the paradigm of scotogenic model which explains muon ($g-2$) and neutrino mass generation, simultaneously. The mass of new gauge boson $M_{Z_{\mu\tau}}$ generated after the spontaneous symmetry breaking of $U(1)_{L_{\mu}-L_{\tau}}$ is constrained, solely, in light of the current neutrino oscillation data to explain muon ($g-2$). In particular, we have obtained two regions I and II, around 150 MeV and 500 MeV, respectively, in $M_{Z_{\mu\tau}}-g_{\mu\tau}$ plane which explain the neutrino phenomenology. Region I is found to be consistent with muon neutrino trident (MNT) bound ($g_{\mu\tau}$ $\leq$ $10^{-3}$) to explain muon ($g-2$), however, region II violates it for mass range $M_{Z_{\mu\tau}}>300$ MeV. We, then, extend the minimal gauged scotogenic model by a vector like lepton (VLL) triplet $\psi_T$. The mixing of $\psi_T$ with inert scalar doublet $\eta$ leads to chirally enhanced positive contribution to muon anomalous magnetic moment independent of $Z_{\mu\tau}$ mass. Furthermore, we have, also, investigated the implication of the model for $0\nu\beta\beta$ decay and $CP$ violation. The non-observation of $0\nu\beta\beta$ decay down to the sensitivity of 0.01 eV shall refute the model. The model, in general,is found to be consistent with both $CP$ conserving and $CP$ violating solutions., Comment: 19 pages, 8 figures

The generalized Chaplygin gas (GCG), which has an unusual perfect fluid equation of state, is another promising candidate for dark energy. We investigate the GCG scenario coupled with a baryonic matter in a newly suggested $f(Q,T)$ gravity, an arbitrary function of non-metricity $Q$ and the trace of energy-momentum tensor $T$. We consider the functional form of $f(Q, T)$ as a linear combination of $Q$ and an arbitrary function of $T$, denoted by $h(T)$. Furthermore, we obtain two different functional forms of the $f(Q,T)$ model under high pressure and high-density scenarios of GCG. We also test each model with the recent Pantheon supernovae data set of 1048 data points, Hubble data set of 31 points, and baryon acoustic oscillations. The deceleration parameter is constructed using $OHD+SNeIa+BAO$, predicting a transition from decelerated to accelerated phases of the universe expansion. Also, the equation of state parameter acquires a negative behavior depicting acceleration. Finally, we analyze the statefinder diagnostic to discriminate between the GCG and other dark energy models., Comment: Physics of the Dark Universe published version

We investigate the possibility of crossing a phantom divide line in the extension of symmetric teleparallel gravity or the $f(Q)$ gravity, where $Q$ is the non-metricity. We study the cosmic evolution of the effective equation of state parameter for dark energy considering exponential, logarithmic, and combined $f(Q)$ theories. Moreover, the exponential model behaves like the $\Lambda$CDM at high redshifts before deviating to $\omega_{eff}<-1$ or $\omega_{eff}>-1$, respectively, depending on the value of model parameter. It also approaches a de-sitter phase asymptotically. However, the crossing of the phantom divide line, i.e., $\omega= -1$, is realized in the combined $f(Q)$ theory. Furthermore, statefinder diagnostics are studied in order to differentiate between several dark energy models. To ensure the three model's stability, we employ the stability analysis using linear perturbations. We demonstrate how to reassemble $f(Q)$ via a numerical inversion approach based on existing observational constraints on cosmographic parameters and the potential of bridging the phantom divide in the resulting model. It explicitly demonstrates that future crossings of the phantom dividing line are a generic feature of feasible $f(Q)$ gravity models., Comment: Annalen der Physik accepted version

A key promise of machine learning is the ability to assist users with personal tasks. Because the personal context required to make accurate predictions is often sensitive, we require systems that protect privacy. A gold standard privacy-preserving system will satisfy perfect secrecy, meaning that interactions with the system provably reveal no private information. However, privacy and quality appear to be in tension in existing systems for personal tasks. Neural models typically require copious amounts of training to perform well, while individual users typically hold a limited scale of data, so federated learning (FL) systems propose to learn from the aggregate data of multiple users. FL does not provide perfect secrecy, but rather practitioners apply statistical notions of privacy -- i.e., the probability of learning private information about a user should be reasonably low. The strength of the privacy guarantee is governed by privacy parameters. Numerous privacy attacks have been demonstrated on FL systems and it can be challenging to reason about the appropriate privacy parameters for a privacy-sensitive use case. Therefore our work proposes a simple baseline for FL, which both provides the stronger perfect secrecy guarantee and does not require setting any privacy parameters. We initiate the study of when and where an emerging tool in ML -- the in-context learning abilities of recent pretrained models -- can be an effective baseline alongside FL. We find in-context learning is competitive with strong FL baselines on 6 of 7 popular benchmarks from the privacy literature and a real-world case study, which is disjoint from the pretraining data. We release our code here: https://github.com/simran-arora/focus, Comment: Keywords: privacy-preserving, personalized machine learning, in-context learning

Foundation Models (FMs) are models trained on large corpora of data that, at very large scale, can generalize to new tasks without any task-specific finetuning. As these models continue to grow in size, innovations continue to push the boundaries of what these models can do on language and image tasks. This paper aims to understand an underexplored area of FMs: classical data tasks like cleaning and integration. As a proof-of-concept, we cast five data cleaning and integration tasks as prompting tasks and evaluate the performance of FMs on these tasks. We find that large FMs generalize and achieve SoTA performance on data cleaning and integration tasks, even though they are not trained for these data tasks. We identify specific research challenges and opportunities that these models present, including challenges with private and domain specific data, and opportunities to make data management systems more accessible to non-experts. We make our code and experiments publicly available at: https://github.com/HazyResearch/fm_data_tasks., Comment: 12 pages, 5 figures; additional experiments, typo corrections, modifications to Section 5 (Research Agenda)

The standard formulation of General Relativity Theory, in the absence of a cosmological constant, is unable to explain the responsible mechanism for the observed late-time cosmic acceleration. On the other hand, by inserting the cosmological constant in Einstein's field equations it is possible to describe the cosmic acceleration, but the cosmological constant suffers from an unprecedented fine-tunning problem. This motivates one to modify Einstein's space-time geometry of General Relativity. The $f(Q)$ modified theory of gravity is an alternative theory to General Relativity, where the non-metricity scalar $Q$ is the responsible candidate for gravitational interactions. In the present work we consider a Friedmann-Lem\^aitre-Robertson-Walker cosmological model dominated by bulk viscous cosmic fluid in $f(Q)$ gravity with the functional form $f(Q)=\alpha Q^n$, where $\alpha$ and $n$ are free parameters of the model. We constrain our model with the recent Pantheon supernovae data set of 1048 data points, Hubble data set of 31 data points and baryon acoustic oscillations data set consisting of six points. For higher values of redshift, it is clear that the $f(Q)$ cosmology better fits data than standard cosmology. We present the evolution of our deceleration parameter with redshift and it properly predicts a transition from decelerated to accelerated phases of the universe expansion. Also, we present the evolution of density, bulk viscous pressure and the effective equation of state parameter with redshift. Those show that bulk viscosity in a cosmic fluid is a valid candidate to acquire the negative pressure to drive the cosmic expansion efficiently.We also examine the behavior of different energy conditions to test the viability of our cosmological $f(Q)$ model. Furthermore, the statefinder diagnostics are also investigated in order to distinguish among different dark energy models., Comment: Comments are welcome

Users and organizations are generating ever-increasing amounts of private data from a wide range of sources. Incorporating private data is important to personalize open-domain applications such as question-answering, fact-checking, and personal assistants. State-of-the-art systems for these tasks explicitly retrieve relevant information to a user question from a background corpus before producing an answer. While today's retrieval systems assume the corpus is fully accessible, users are often unable or unwilling to expose their private data to entities hosting public data. We first define the PUBLIC-PRIVATE AUTOREGRESSIVE INFORMATION RETRIEVAL (PAIR) privacy framework for the novel retrieval setting over multiple privacy scopes. We then argue that an adequate benchmark is missing to study PAIR since existing textual benchmarks require retrieving from a single data distribution. However, public and private data intuitively reflect different distributions, motivating us to create ConcurrentQA, the first textual QA benchmark to require concurrent retrieval over multiple data-distributions. Finally, we show that existing systems face large privacy vs. performance tradeoffs when applied to our proposed retrieval setting and investigate how to mitigate these tradeoffs.

In today's scenario, going beyond Einstein's theory of gravity leads us to some more complete and modified gravity theories. One of them is the $f(R,T)$ gravity in which $ R $ is the Ricci scalar, and $ T $ is the trace of the energy-momentum tensor. Using a well-motivated linear $f(R,T)$ gravity model with a single parameter, we studied the strong energy condition (SEC), the weak energy condition (WEC), the null energy condition (NEC), and the dominant energy condition (DEC) under the simplest non-minimal matter geometry coupling with a perfect fluid distribution. The model parameter is constrained by energy conditions and a single parameter proposed equation of state (EoS), resulting in the compatibility of the $f(R,T)$ models with the accelerated expansion of the universe. It is seen that the EoS parameter illustrate the quintessence phase in a dominated accelerated phase, pinpoint to the cosmological constant yields as a prediction the phantom era. Also, the present values of the cosmological constant and the acceleration of the universe are used to check the viability of our linear $f(R,T)$ model of gravity. It is observed that the positive behavior of DEC and WEC indicates the validation of the model. In contrast, SEC is violating the condition resulting in the accelerated expansion of the universe., Comment: Astronomische Nachrichten published version

Language models (LMs) have made remarkable progress, but still struggle to generalize beyond the training data to rare linguistic patterns. Since rare entities and facts are prevalent in the queries users submit to popular applications such as search and personal assistant systems, improving the ability of LMs to reliably capture knowledge over rare entities is a pressing challenge studied in significant prior work. Noticing that existing approaches primarily modify the LM architecture or introduce auxiliary objectives to inject useful entity knowledge, we ask to what extent we could match the quality of these architectures using a base LM architecture, and only changing the data? We propose metadata shaping, a method in which readily available metadata, such as entity descriptions and categorical tags, are appended to examples based on information theoretic metrics. Intuitively, if metadata corresponding to popular entities overlap with metadata for rare entities, the LM may be able to better reason about the rare entities using patterns learned from similar popular entities. On standard entity-rich tasks (TACRED, FewRel, OpenEntity), with no changes to the LM whatsoever, metadata shaping exceeds the BERT-baseline by up to 5.3 F1 points, and achieves or competes with state-of-the-art results. We further show the improvements are up to 10x larger on examples containing tail versus popular entities.