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Yiming Dong

Publications and source records attributed to Yiming Dong.

25 records · Page 2Linked to original sources

From Macro to Micro: Probing Dataset Diversity in Language Model Fine-Tuning

Dataset diversity plays a pivotal role for the successful training of many machine learning models, particularly in the supervised fine-tuning (SFT) stage of large language model (LLM) development. Despite increasing recognition of its importance, systematic analyses of dataset diversity still remain underexplored. To address this gap, this work presents a systematic taxonomy of existing diversity-control strategies, which primarily focus on the instruction component, operating at either macroscopic (entire instruction semantics) or mesoscopic levels (instruction units), and furthermore introduces a novel analysis of microscopic diversity within the response component, specifically analyzing the statistical distribution of tokens in SFT training samples. In the experimental evaluation, we construct fixed-size datasets (e.g., 10,000 samples each) from a corpus of 117,000 open-source SFT samples, incorporating six distinct diversity-control strategies spanning macro-, meso-, and microscopic levels applied to both instructions and responses. We then fine-tune LLMs on these datasets to assess the six diversity-control strategies. Results reveal that while macroscopic and mesoscopic strategies lead to higher performance with increasing diversity, the microscopic strategy in responses exhibits both a stronger correlation between model performance and the degree of diversity and superior performance with maximum diversity across all strategies. These findings offer actionable insights for constructing high-performance SFT datasets.

cs.CL↗

On the $O(\frac{\sqrt{d}}{T^{1/4}})$ Convergence Rate of RMSProp and Its Momentum Extension Measured by $\ell_1$ Norm

Although adaptive gradient methods have been extensively used in deep learning, their convergence rates proved in the literature are all slower than that of SGD, particularly with respect to their dependence on the dimension. This paper considers the classical RMSProp and its momentum extension and establishes the convergence rate of $\frac{1}{T}\sum_{k=1}^T E\left[\|\nabla f(x^k)\|_1\right]\leq O(\frac{\sqrt{d}C}{T^{1/4}})$ measured by $\ell_1$ norm without the bounded gradient assumption, where $d$ is the dimension of the optimization variable, $T$ is the iteration number, and $C$ is a constant identical to that appeared in the optimal convergence rate of SGD. Our convergence rate matches the lower bound with respect to all the coefficients except the dimension $d$. Since $\|x\|_2\ll\|x\|_1\leq\sqrt{d}\|x\|_2$ for problems with extremely large $d$, our convergence rate can be considered to be analogous to the $\frac{1}{T}\sum_{k=1}^T E\left[\|\nabla f(x^k)\|_2\right]\leq O(\frac{C}{T^{1/4}})$ rate of SGD in the ideal case of $\|\nabla f(x)\|_1=\varTheta(\sqrt{d}\|\nabla f(x)\|_2)$.

math.OC↗

Reanalyzing the ringdown signal of GW150914 using the F-statistic method

The ringdown phase of a gravitational wave (GW) signal from a binary black hole merger provides valuable insights into the properties of the final black hole and serves as a critical test of general relativity in the strong-field regime. A key aspect of this investigation is to determine whether the first overtone mode exists in real GW data, as its presence would offer significant implications for our understanding of general relativity under extreme conditions. To address this, we conducted a reanalysis of the ringdown signal from GW150914, using the newly proposed F-statistic method to search for the first overtone mode. Our results are consistent with those obtained through classical time-domain Bayesian inference, indicating that there is no evidence of the first overtone mode in the ringdown signal of GW150914. However, our results show the potentiality of utilizing the F-statistic methodology to unearth nuanced features within GW signals, thereby contributing novel insights into black hole properties.

gr-qc↗

A practical Bayesian method for gravitational-wave ringdown analysis with multiple modes

Gravitational-wave (GW) ringdown signals from black holes (BHs) encode crucial information about the gravitational dynamics in the strong-field regime, which offers unique insights into BH properties. In the future, the improving sensitivity of GW detectors is to enable the extraction of multiple quasi-normal modes (QNMs) from ringdown signals. However, incorporating multiple modes drastically enlarges the parameter space, posing computational challenges to data analysis. Inspired by the $F$-statistic method in the continuous GW searches, we develope an algorithm, dubbed as FIREFLY, for accelerating the ringdown signal analysis. FIREFLY analytically marginalizes the amplitude and phase parameters of QNMs to reduce the computational cost and speed up the full-parameter inference from hours to minutes, while achieving consistent posterior and evidence. The acceleration becomes more significant when more QNMs are considered. Rigorously based on the principle of Bayesian inference and importance sampling, our method is statistically interpretable, flexible in prior choice, and compatible with various advanced sampling techniques, providing a new perspective for accelerating future GW data analysis.

gr-qc↗

New limits on the local Lorentz invariance violation of gravity in the Standard-Model Extension with pulsars

Lorentz Violation (LV) is posited as a possible relic effect of quantum gravity at low energy scales. The Standard-Model Extension provides an effective field-theoretic framework for examining possible deviations attributed to LV. With their high observational accuracy, pulsars serve as ideal laboratories for probing LV. In the presence of LV, both the spin precession of solitary pulsars and orbital dynamics of binary pulsars would undergo modifications. Observations of pulse profiles and times of arrival (TOAs) of pulses allow for an in-depth investigation of these effects, leading to the establishment of strict limits on LV coefficients. We revisit the project of limiting local LV with updated pulsar observations. We employ a new parameter estimation method and utilize state-of-the-art pulsar timing observation data and get new limits on 8 linear combinations of LV coefficients based on 25 tests from 12 different systems. Compared to previous limits from pulsars, precision has improved by a factor of two to three. Additionally, we explore prospects for further improvements from pulsars. Simulation results indicate that more observations of spin precession in solitary millisecond pulsars could significantly enhance the accuracy of spatial LV coefficients, potentially by three to four orders of magnitude. As observational data accumulate, pulsars are anticipated to increasingly contribute to the tests of LV.

astro-ph.HE↗

Moment of Inertia for Axisymmetric Neutron Stars in the Standard-Model Extension

We develop a consistent approach to calculate the moment of inertia (MOI) for axisymmetric neutron stars (NSs) in the Lorentz-violating Standard-Model Extension (SME) framework. To our knowledge, this is the first relativistic MOI calculation for axisymmetric NSs in a Lorentz-violating gravity theory other than deformed, rotating NSs in the General Relativity. Under Lorentz violation, there is a specific direction in the spacetime and NSs get stretched or compressed along that direction. When a NS is spinning stationarily along this direction, a conserved angular momentum and the concept of MOI are well defined. In the SME framework, we calculate the partial differential equation governing the rotation and solve it numerically with the finite element method to get the MOI for axisymmetric NSs caused by Lorentz violation. Besides, we study an approximate case where the correction to the MOI is regarded solely from the deformation of the NS and compare it with its counterpart in the Newtonian gravity. Our formalism and the numerical method can be extended to other theories of gravity for static axisymmetric NSs.

gr-qc↗

Prospects for Constraining the Yukawa Gravity with Pulsars around Sagittarius A*

The discovery of radio pulsars (PSRs) around the supermassive black hole (SMBH) in our Galactic Center (GC), Sagittarius A* (Sgr A*), will have significant implications for tests of gravity. In this paper, we predict restrictions on the parameters of the Yukawa gravity by timing a pulsar around Sgr A* with a variety of orbital parameters. Based on a realistic timing accuracy of the times of arrival (TOAs), $σ_{\rm TOA}=100\,μ{\rm s}$, and using a number of 960 TOAs in a 20-yr observation, our numerical simulations show that the PSR-SMBH system will improve current tests of the Yukawa gravity when the range of the Yukawa interaction varies between $10^{1}$-$10^{4}\,{\rm AU}$, and it can limit the graviton mass to be $m_g \lesssim 10^{-24}\,{\rm eV}/c^2$.

astro-ph.HE↗