arXiv subjects

Zhen Guo

Publications and source records attributed to Zhen Guo.

At least 73 records · Page 4Linked to original sources

arXiv2024

Scaling Law Hypothesis for Multimodal Model

We propose a scaling law hypothesis for multimodal models processing text, audio, images, and video within a shared token and embedding space. Our framework predicts model performance based on modality-specific compression and tokenization efficiency, extending established scaling laws from text-based decoder models to mixed-modality systems. We explore whether leveraging more training data in multiple modalities can reduce the size of the multimodal model, enabling efficient deployment on resource-constrained devices.

cs.LG↗

arXiv2024

On moments of the error term of the multivariable k-th divisor functions

Suppose $k\geqslant3$ is an integer. Let $τ_k(n)$ be the number of ways $n$ can be written as a product of $k$ fixed factors. For any fixed integer $r\geqslant2$, we have the asymptotic formula \begin{equation*} \sum_{n_1,\cdots,n_r\leqslant x}τ_k(n_1 \cdots n_r)=x^r\sum_{\ell=0}^{r(k-1)}d_{r,k,\ell}(\log x)^{\ell}+O(x^{r-1+α_k+\varepsilon}), \end{equation*} where $d_{r,k,\ell}$ and $0<α_k<1$ are computable constants. In this paper we study the mean square of $Δ_{r,k}(x)$ and give upper bounds for $k\geqslant4$ and an asymptotic formula for the mean square of $Δ_{r,3}(x)$. We also get an upper bound for the third power moment of $Δ_{r,3}(x)$. Moreover, we study the first power moment of $Δ_{r,3}(x)$ and then give a result for the sign changes of it.

math.NT↗

arXiv2024

The Role of Thermal Instability in Accretion Outbursts in High-Mass Stars

High-mass young stellar objects (HMYSOs) can exhibit episodic bursts of accretion, accompanied by intense outflows and luminosity variations. Thermal Instability (TI) due to Hydrogen ionisation is among the most promising mechanisms of episodic accretion in low mass ($M_*\lesssim 1M_{\odot}$) protostars. Its role in HMYSOs has not yet been elucidated. Here, we investigate the properties of TI outbursts in young, massive ($M_*\gtrsim 5M_{\odot}$) stars, and compare them to those observed so far. Our simulations show that modelled TI bursts can replicate the durations and peak accretion rates of long (a few years to decades) outbursts observed in HMYSOs with similar mass characteristics. However, they struggle with short-duration (less than a year) bursts with short (a few weeks or months) rise times, suggesting the need for alternative mechanisms. Moreover, while our models match the durations of longer bursts, they fail to reproduce the multiple outbursts seen in some HMYSOs, regardless of model parameters. We also emphasise the significance of not just evaluating model accretion rates and durations, but also performing photometric analysis to thoroughly evaluate the consistency between model predictions and observational data. Our findings suggest that some other plausible mechanisms, such as gravitational instabilities and disc fragmentation can be responsible for generating the observed outburst phenomena in HMYSOs and underscore the need for further investigation into alternative mechanisms driving short outbursts. However, the physics of TI is crucial in sculpting the inner disc physics in the early bright epoch of massive star formation, and comprehensive parameter space exploration and the use of 2D modeling are essential for obtaining a more detailed understanding of the underlying physical processes.

astro-ph.SR↗

arXiv2024

On a sum of the error term of the Dirichlet divisor function over primes

Let $d(n)$ be the Dirichlet divisor function and $Δ(x)$ denote the error term of the sum $\sum_{n\leqslant x}d(n)$ for a large real variable $x$. In this paper we focus on the sum $\sum_{p\leqslant x}Δ^2(p)$, where $p$ runs over primes. We prove that there exists an asymptotic formula.

math.NT↗

arXiv2024

On high power moments of the error term of the Dirichlet divisor function over primes

Let $3\leqslant k\leqslant9$ be a fixed integer, $p$ be a prime and $d(n)$ denote the Dirichlet divisor function. We use $Δ(x)$ to denote the error term in the asymptotic formula of the summatory function of $d(n)$. The aim of this paper is to study the $k$-th power moments of $Δ(p)$, namely $\sum_{p\leqslant x}Δ^k(p)$, and we give an asymptotic formula.

math.NT↗

arXiv2024

A Multi-wavelength, Multi-epoch Monitoring Campaign of Accretion Variability in T Tauri Stars from the ODYSSEUS Survey. III. Optical Spectra

Classical T Tauri Stars (CTTSs) are highly variable stars that possess gas- and dust-rich disks from which planets form. Much of their variability is driven by mass accretion from the surrounding disk, a process that is still not entirely understood. A multi-epoch optical spectral monitoring campaign of four CTTSs (TW Hya, RU Lup, BP Tau, and GM Aur) was conducted along with contemporaneous HST UV spectra and ground-based photometry in an effort to determine accretion characteristics and gauge variability in this sample. Using an accretion flow model, we find that the magnetospheric truncation radius varies between 2.5-5 R* across all of our observations. There is also significant variability in all emission lines studied, particularly Halpha, Hbeta, and Hgamma. Using previously established relationships between line luminosity and accretion, we find that, on average, most lines reproduce accretion rates consistent with accretion shock modeling of HST spectra to within 0.5 dex. Looking at individual contemporaneous observations, however, these relationships are less accurate, suggesting that variability trends differ from the trends of the population and that these empirical relationships should be used with caution in studies of variability.

astro-ph.SR↗

arXiv2024

Solving Sharp Bounded-error Quantum Polynomial Time Problem by Evolution methods

Counting ground state degeneracy of a $k$-local Hamiltonian is important in many fields of physics. Its complexity belongs to the problem of sharp bounded-error quantum polynomial time (#BQP) class and few methods are known for its solution. Finding ground states of a $k$-local Hamiltonian, on the other hand, is an easier problem of Quantum Merlin Arthur (QMA) class, for which many efficient methods exist. In this work, we propose an algorithm of mapping a #BQP problem into one of finding a special ground state of a $k$-local Hamiltonian. We prove that all traditional methods, which solve the QMA problem by evolution under a function of a Hamiltonian, can be used to find the special ground state from a well-designed initial state, thus can solve the #BQP problem. We combine our algorithm with power method, Lanczos method, and quantum imaginary time evolution method for different systems to illustrate the detection of phase boundaries, competition between frustration and quantum fluctuation, and potential implementations with quantum circuits.

quant-ph↗

arXiv2024

Probing the Shock Breakout Signal of SN 2024ggi from the Transformation of Early Flash Spectroscopy

We present early-time, hour-to-day cadence spectroscopy of the nearby type II supernova (SN II) 2024ggi, which was discovered at a phase when the SN shock just emerged from the red-supergiant (RSG) progenitor star. Over the first few days after the first light, SN 2024ggi exhibited prominent narrow emission lines formed through intense and persistent photoionization of the nearby circumstellar material (CSM). In the first 63 hours, spectral lines of He, C, N, and O revealed a rapid rise in ionization, as a result of the progressive sweeping-up of the CSM by the shock. The duration of the IIn-like spectra indicates a dense and relatively confined CSM distribution extending up to $\sim 4 \times 10^{14}$ cm. Spectral modeling reveals a CSM mass loss rate at this region exceeding $5 \times 10^{-3}{\rm M}_{\odot}$ yr$^{-1}$ is required to reproduce low-ionization emissions, which dramatically exceeds that of an RSG. Analyzing H$α$ emission shift implies the velocity of the unshocked outer CSM to be between 20 and 40 km s$^{-1}$, matching the typical wind velocity of an RSG. The differences between the inner and outer layers of the CSM and an RSG progenitor highlight a complex mass loss history before the explosion of SN 2024ggi.

astro-ph.HE↗

arXiv2024

Unveiling the Unseen: Exploring Whitebox Membership Inference through the Lens of Explainability

The increasing prominence of deep learning applications and reliance on personalized data underscore the urgent need to address privacy vulnerabilities, particularly Membership Inference Attacks (MIAs). Despite numerous MIA studies, significant knowledge gaps persist, particularly regarding the impact of hidden features (in isolation) on attack efficacy and insufficient justification for the root causes of attacks based on raw data features. In this paper, we aim to address these knowledge gaps by first exploring statistical approaches to identify the most informative neurons and quantifying the significance of the hidden activations from the selected neurons on attack accuracy, in isolation and combination. Additionally, we propose an attack-driven explainable framework by integrating the target and attack models to identify the most influential features of raw data that lead to successful membership inference attacks. Our proposed MIA shows an improvement of up to 26% on state-of-the-art MIA.

cs.LG↗

arXiv2024

GPU-accelerated Auxiliary-field quantum Monte Carlo with multi-Slater determinant trial states

The accuracy of phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) can be systematically improved with better trial states. Using multi-Slater determinant trial states, ph-AFQMC has the potential to faithfully treat strongly correlated systems, while balancing the static and dynamical correlations on an equal footing. This preprint presents an implementation and application of graphics processing unit-accelerated ph-AFQMC, for multi-Slater determinant trial wavefunctions (GPU-accelerated MSD-AFQMC), to enable efficient simulation of large-scale, strongly correlated systems. This approach allows for nearly-exact computation of ground state energies in multi-reference systems. Our GPU-accelerated MSD-AFQMC is implemented in the open-source code \texttt{ipie}, a Python-based AFQMC package [\textit{J. Chem. Theory Comput.}, 2022, 19(1): 109-121]. We benchmark the performance of the GPU code on transition-metal clusters like [Cu$_2$O$_2$]$^{2+}$ and [Fe$_2$S$_2$(SCH$_3$)]$^{2-}$. The GPU code achieves at least sixfold speedup in both cases, comparing the timings of a single A100 GPU to that of a 32-CPU node. For [Fe$_2$S$_2$(SCH$_3$)]$^{2-}$, we demonstrate that our GPU MSD-AFQMC can recover the dynamical correlation necessary for chemical accuracy with an MSD trial, despite the large number of determinants required ($>10^5$). Our work significantly enhances the efficiency of MSD-AFQMC calculations for large, strongly correlated molecules by utilizing GPUs, offering a promising path for exploring the electronic structure of transition metal complexes.

physics.chem-ph↗

arXiv2024

The verification of periodicity with the use of recurrent neural networks

The ability to automatically and robustly self-verify periodicity present in time-series astronomical data is becoming more important as data sets rapidly increase in size. The age of large astronomical surveys has rendered manual inspection of time-series data less practical. Previous efforts in generating a false alarm probability to verify the periodicity of stars have been aimed towards the analysis of a constructed periodogram. However, these methods feature correlations with features that do not pertain to periodicity, such as light curve shape, slow trends and stochastic variability. The common assumption that photometric errors are Gaussian and well determined is also a limitation of analytic methods. We present a novel machine learning based technique which directly analyses the phase folded light curve for its false alarm probability. We show that the results of this method are largely insensitive to the shape of the light curve, and we establish minimum values for the number of data points and the amplitude to noise ratio.

astro-ph.IM↗

arXiv2024

Curvature bounds for the spectrum of closed Einstein spaces and Simon conjecture

Let $(M^{n}, g)$ be a closed connected Einstein space, $n=dim M ,$ and $κ_{0} $ be the lower bound of the sectional curvature. In this paper, we prove Udo Simon's conjecture: on closed Einstein spaces, $n\geq 3,$ there is no eigenvalue $λ$ such that $$nκ_{0} < λ< 2(n + 1)κ_{0},$$ and both bounds are the best possible. Furthermore, we develop Simon's conjecture to the next gap of eigenvalue $λ:$ on closed Einstein spaces, there is no $λ$ such that $$ 2(n + 1)κ_{0}< λ< 2(n+2)κ_{0}, $$ and both bounds are the best possible.

math.DG↗

arXiv2024

A Multi-wavelength, Multi-epoch Monitoring Campaign of Accretion Variability in T Tauri Stars from the ODYSSEUS Survey. I. HST FUV and NUV Spectra

The Classical T Tauri Star (CTTS) stage is a critical phase of the star and planet formation process. In an effort to better understand the mass accretion process, which can dictate further stellar evolution and planet formation, a multi-epoch, multi-wavelength photometric and spectroscopic monitoring campaign of four CTTSs (TW Hya, RU Lup, BP Tau, and GM Aur) was carried out in 2021 and 2022/2023 as part of the Outflows and Disks Around Young Stars: Synergies for the Exploration of ULYSSES Spectra (ODYSSEUS) program. Here we focus on the HST UV spectra obtained by the HST Director's Discretionary Time UV Legacy Library of Young Stars as Essential Standards (ULLYSES) program. Using accretion shock modeling, we find that all targets exhibit accretion variability, varying from short increases in accretion rate by up to a factor of 3 within 48 hours, to longer decreases in accretion rate by a factor of 2.5 over the course of 1 year. This is despite the generally consistent accretion morphology within each target. Additionally, we test empirical relationships between accretion rate and UV luminosity and find stark differences, showing that these relationships should not be used to estimate the accretion rate for individual target. Our work reinforces that future multi-epoch and simultaneous multi-wavelength studies are critical in our understanding of the accretion process in low-mass star formation.

astro-ph.SR↗

arXiv2024

A Multi-wavelength, Multi-epoch Monitoring Campaign of Accretion Variability in T Tauri Stars from the ODYSSEUS Survey. II. Photometric Light Curves

Classical T Tauri Stars (CTTSs) are young, low-mass stars which accrete material from their surrounding protoplanetary disk. To better understand accretion variability, we conducted a multi-epoch, multi-wavelength photometric monitoring campaign of four CTTSs: TW Hya, RU Lup, BP Tau, and GM Aur, in 2021 and 2022, contemporaneous with HST UV and optical spectra. We find that all four targets display significant variability in their light curves, generally on days-long timescales (but in some cases year-to-year) often due to periodicity associated with stellar rotation and to stochastic accretion variability. Their is a strong connection between mass accretion and photometric variability in all bands, but the relationship varies per target and epoch. Thus, photometry should be used with caution as a direct measure of accretion in CTTSs.

astro-ph.SR↗

arXiv2024

Can near-to-mid infrared spectral energy distribution quantitatively trace protoplanetary disk evolution?

Infrared (IR) spectral energy distribution (SED) is the major tracer of protoplanetary disks. It was recently proposed to use the near-to-mid IR (or K-24) SED slope $α$ defined between 2-24$μ$m as a potential quantitative tracer of disk age. We critically examine the viability of this idea and confront it with additional statistics of IR luminosities and SED shapes. We point out that, because the statistical properties of most of the complicated physical factors involved in disk evolution are still poorly understood in a quantitative sense, the only viable way is to assume them to be random so that an idealized `average disk' can be defined, which allows the $α$ histogram to trace its age. We confirm that the statistics of the zeroth order (luminosity), first order (slope $α$) and second order characteristics (concavity) of the observed K-24 SEDs indeed carry useful information upon the evolutionary processes of the `average disk'. We also stress that intrinsic diversities in K-24 SED shapes and luminosities are always large at the level of individual stars so that the application of the evolutionary path of the `average disk' to individual stars must be done with care. The data of most curves in plots are provided on GitHub.

astro-ph.SR↗

arXiv2024

More Compute Is What You Need

Large language model pre-training has become increasingly expensive, with most practitioners relying on scaling laws to allocate compute budgets for model size and training tokens, commonly referred to as Compute-Optimal or Chinchilla Optimal. In this paper, we hypothesize a new scaling law that suggests model performance depends mostly on the amount of compute spent for transformer-based models, independent of the specific allocation to model size and dataset size. Using this unified scaling law, we predict that (a) for inference efficiency, training should prioritize smaller model sizes and larger training datasets, and (b) assuming the exhaustion of available web datasets, scaling the model size might be the only way to further improve model performance.

cs.LG↗

arXiv2024

JetMoE: Reaching Llama2 Performance with 0.1M Dollars

Large Language Models (LLMs) have achieved remarkable results, but their increasing resource demand has become a major obstacle to the development of powerful and accessible super-human intelligence. This report introduces JetMoE-8B, a new LLM trained with less than $0.1 million, using 1.25T tokens from carefully mixed open-source corpora and 30,000 H100 GPU hours. Despite its low cost, the JetMoE-8B demonstrates impressive performance, with JetMoE-8B outperforming the Llama2-7B model and JetMoE-8B-Chat surpassing the Llama2-13B-Chat model. These results suggest that LLM training can be much more cost-effective than generally thought. JetMoE-8B is based on an efficient Sparsely-gated Mixture-of-Experts (SMoE) architecture, composed of attention and feedforward experts. Both layers are sparsely activated, allowing JetMoE-8B to have 8B parameters while only activating 2B for each input token, reducing inference computation by about 70% compared to Llama2-7B. Moreover, JetMoE-8B is highly open and academia-friendly, using only public datasets and training code. All training parameters and data mixtures have been detailed in this report to facilitate future efforts in the development of open foundation models. This transparency aims to encourage collaboration and further advancements in the field of accessible and efficient LLMs. The model weights are publicly available at https://github.com/myshell-ai/JetMoE.

cs.CL↗

arXiv2024

Automated HER2 Scoring in Breast Cancer Images Using Deep Learning and Pyramid Sampling

Human epidermal growth factor receptor 2 (HER2) is a critical protein in cancer cell growth that signifies the aggressiveness of breast cancer (BC) and helps predict its prognosis. Accurate assessment of immunohistochemically (IHC) stained tissue slides for HER2 expression levels is essential for both treatment guidance and understanding of cancer mechanisms. Nevertheless, the traditional workflow of manual examination by board-certified pathologists encounters challenges, including inter- and intra-observer inconsistency and extended turnaround times. Here, we introduce a deep learning-based approach utilizing pyramid sampling for the automated classification of HER2 status in IHC-stained BC tissue images. Our approach analyzes morphological features at various spatial scales, efficiently managing the computational load and facilitating a detailed examination of cellular and larger-scale tissue-level details. This method addresses the tissue heterogeneity of HER2 expression by providing a comprehensive view, leading to a blind testing classification accuracy of 84.70%, on a dataset of 523 core images from tissue microarrays. Our automated system, proving reliable as an adjunct pathology tool, has the potential to enhance diagnostic precision and evaluation speed, and might significantly impact cancer treatment planning.

eess.IV↗