arXiv subjects

Jinshu Huang

Publications and source records attributed to Jinshu Huang.

At least 19 recordsLinked to original sources

arXiv2026

From Score Learning to Discretized Sampling: An End-to-End Generalization Analysis of Diffusion Models

Despite the empirical success of score-based diffusion models, a complete theoretical understanding of how finite-sample learning, network parameterization, and numerical discretization jointly dictate generative quality remains underdeveloped. Existing sampling analyses often evaluate the generative performance conditional on an oracle score or a pre-specified error threshold. In this work, we establish a unified convergence and generalization framework for score-based diffusion models parameterized by practical ResNet-type architectures. We analyze the generalization and convergence properties from the practical finite-sample, discrete-time learning problem of the score function to the ideal continuous-time, population-level objective. Based on the generalization result of the learning problem of score function, we analyze the sampling process induced by the learned score function and provide an end-to-end total variation distance estimate for the generated terminal distribution. This estimate explicitly decomposes the overall generative error into four interpretable components: the truncation error of the forward process, the reverse-time discretization error, the generalization error incorporating both finite data and forward-time discretization, and the training optimization gap. Our results quantitatively characterize how the training sample size, temporal discretization grids, and optimization accuracy jointly control the final fidelity of samples generated by diffusion models.

cs.LG↗

arXiv2026

On the Generalization Behavior of Deep Residual Networks From a Dynamical System Perspective

Deep neural networks (DNNs) have significantly advanced machine learning, with model depth playing a central role in their successes. The dynamical system modeling approach has recently emerged as a powerful framework, offering new mathematical insights into the structure and learning behavior of DNNs. In this work, we establish generalization error bounds for both discrete- and continuous-time residual networks (ResNets) by combining Rademacher complexity, flow maps of dynamical systems, and the convergence behavior of ResNets in the deep-layer limit. The resulting bounds are of order $O(1/\sqrt{S})$ with respect to the number of training samples $S$, and include a structure-dependent negative term, yielding depth-uniform and asymptotic generalization bounds under milder assumptions. These findings provide a unified understanding of generalization across both discrete- and continuous-time ResNets, helping to close the gap in both the order of sample complexity and assumptions between the discrete- and continuous-time settings.

cs.LG↗

arXiv2025

Mathematical Modeling and Convergence Analysis of Deep Neural Networks with Dense Layer Connectivities in Deep Learning

In deep learning, dense layer connectivity has become a key design principle in deep neural networks (DNNs), enabling efficient information flow and strong performance across a range of applications. In this work, we model densely connected DNNs mathematically and analyze their learning problems in the deep-layer limit. For a broad applicability, we present our analysis in a framework setting of DNNs with densely connected layers and general non-local feature transformations (with local feature transformations as special cases) within layers, which is called dense non-local (DNL) framework and includes standard DenseNets and variants as special examples. In this formulation, the densely connected networks are modeled as nonlinear integral equations, in contrast to the ordinary differential equation viewpoint commonly adopted in prior works. We study the associated training problems from an optimal control perspective and prove convergence results from the network learning problem to its continuous-time counterpart. In particular, we show the convergence of optimal values and the subsequence convergence of minimizers, using a piecewise linear extension and $Γ$-convergence analysis. Our results provide a mathematical foundation for understanding densely connected DNNs and further suggest that such architectures can offer stability of training deep models.

cs.LG↗

arXiv2022

Possibility of experimental study on nonleptonic $B_{c}^{\ast}$ weak decays

The ground vector $B_{c}^{\ast}$ meson has not yet been experimentally discovered until now. Besides the dominant electromagnetic decays, nonleptonic weak decays provide another choice to search for the mysterious $B_{c}^{\ast}$ mesons. Inspired by the potential prospects of $B_{c}^{\ast}$ mesons in future high-luminosity colliders, nonleptonic $B_{c}^{\ast}$ weak decays induced by bottom and charm quark decays are studied within the SM by using a naive factorization approach. It is found that for $B_{c}^{\ast}$ ${\to}$ $B_{s,d}π$, $B_{s,d}^{\ast}π$, $B_{s,d}ρ$, $B_{s}K$, $B_{s}^{\ast}K$, $B_{s}K^{\ast}$, $η_{c}(1S,2S)π$, $η_{c}(1S,2S)ρ$ and $ψ(1S,2S)π$ decays, a few hundred and even thousand of events might be observable in CEPC, FCC-ee and LHCb@HL-LHC experiments.

hep-ph↗

arXiv2022

Feasibility of searching for the Cabibbo-favored $D^{\ast}$ ${\to}$ $\bar{K}π^{+}$, $\bar{K}^{\ast}π^{+}$, $\bar{K}ρ^{+}$ decays

The current knowledge on the $D^{\ast}$ mesons are still inadequate. Encouraged by the positive development prospects of high-luminosity and high-precision experiments, the Cabibbo-favored nonleptonic $D^{\ast}$ ${\to}$ $\bar{K}π^{+}$, $\bar{K}^{\ast}π^{+}$, $\bar{K}ρ^{+}$ weak decays are studied with the naive factorization approach. It is found that branching ratios of these processes can reach up to ${\cal O}(10^{-10})$ or more, and can be accessible at STCF, CEPC, FCC-ee and LHCb@HL-LHC experiments in the future. It might even be possible to search for the $D^{{\ast}0}$ ${\to}$ $K^{{\ast}-}π^{+}$ and $K^{-}ρ^{+}$ decays at the running SuperKEKB experiments.

hep-ph↗

arXiv2022

Reinvestigating the $B$ ${\to}$ $PV$ decays by including the contributions from $ϕ_{B2}$ with the perturbative QCD approach

Considering the $B$ mesonic wave function $ϕ_{B2}$, the $B$ ${\to}$ $PV$ decays are restudied at the leading order for three scenarios using the perturbative QCD approach within the standard model, where $P$ $=$ $π$ and $K$, and $V$ denotes the ground $SU(3)$ vector mesons. It is found that contributions from $ϕ_{B2}$ can enhance most branching ratios, and are helpful for improving the overall consistency of branching ratios between the updated calculations and available data, although there are still several discrepancies between the experimental and theoretical results.

hep-ph↗

arXiv2022

Feasibility of the experimental study of $D_{s}^{\ast}$ ${\to}$ $ϕπ$ decay

The current knowledge on the $D_{s}^{\ast}$ meson are very limited. Besides the dominant electromagnetic decays, the $D_{s}^{\ast}$ weak decays are legal and offer the valuable opportunities to explore the wanted $D_{s}^{\ast}$ meson. In this paper, the $D_{s}^{\ast}$ ${\to}$ $ϕπ$ decay was studied with the factorization approach. It is found that the branching ratio ${\cal B}(D_{s}^{\ast}{\to}ϕπ)$ ${\sim}$ ${\cal O}(10^{-7})$, which corresponds to several thousands of events at the $e^{+}e^{-}$ collider experiments including STCF, SuperKEKB, CEPC and FCC-ee, and several millions of events at the hadron collider experiments, such as LHCb@HL-LHC. It is feasible to experimentally study the $D_{s}^{\ast}$ ${\to}$ $ϕπ$ weak decay in the future, even considering the identification efficiency.

hep-ph↗

arXiv2021

Purely leptonic decays of the ground charged vector mesons

The study of the purely leptonic decays of the ground charged vector mesons is very interesting and significant in determining the CKM matrix elements, obtaining the decay constant of vector mesons, examining the lepton flavor universality, and searching for new physics beyond the standard model. These purely leptonic decays of the ground charged vector mesons are induced by the weak interactions within the standard model, and usually have very small branching ratios, ${\cal B}(ρ^{-}{\to}{\ell}^{-}ν_{\ell})$ ${\sim}$ ${\cal O}(10^{-13})$, ${\cal B}(K^{{\ast}-}{\to}{\ell}^{-}ν_{\ell})$ ${\sim}$ ${\cal O}(10^{-13})$, ${\cal B}(D_{d}^{{\ast}-}{\to}{\ell}^{-}ν_{\ell})$ ${\sim}$ ${\cal O}(10^{-10})$, ${\cal B}(B_{u}^{{\ast}-}{\to}{\ell}^{-}ν_{\ell})$ ${\sim}$ ${\cal O}(10^{-10})$, ${\cal B}(D_{s}^{{\ast}-}{\to}{\ell}^{-}ν_{\ell})$ ${\sim}$ ${\cal O}(10^{-6})$ and ${\cal B}(B_{c}^{{\ast}-}{\to}{\ell}^{-}ν_{\ell})$ ${\sim}$ ${\cal O}(10^{-6})$. Inspired by the potential prospects of LHCb, Belle-II, STCF, CEPC and FCC-ee experiments, we discussed the probabilities of experimental investigation on these purely leptonic decays. It is found that the measurements of these decays might be possible and feasible with the improvement of data statistics, analytical technique, and measurement precision in the future. (1) With the hadron-hadron collisions, the purely leptonic decays of $ρ^{-}$, $K^{{\ast}-}$, $D_{d,s}^{{\ast}-}$ and $B_{u,c}^{{\ast}-}$ mesons might be accessible at LHC experiments. (2) With the $e^{+}e^{-}$ collisions, the purely leptonic decays of $D_{d,s}^{{\ast}-}$ and $B_{u,c}^{{\ast}-}$ mesons might be measurable with over $10^{12}$ $Z^{0}$ bosons available at CEPC and FCC-ee experiments. In addition, the $D_{d,s}^{{\ast}-}$ ${\to}$ ${\ell}^{-}ν_{\ell}$ decays could also be studied at Belle-II and SCTF experiments.

hep-ph↗

arXiv2021

Study of $C$ parity violating and strangeness changing $J/ψ$ ${\to}$ $PP$ weak decays

The $J/ψ$ weak decays are rare but possible within the standard model of elementary particles. Inspired by the potential prospects at the future intensity frontier, the $C$ parity violating $J/ψ$ ${\to}$ $πη^{({\prime})}$, $ηη^{\prime}$ decays and the strangeness changing $J/ψ$ ${\to}$ $πK$, $Kη^{({\prime})}$ decays are studied with the perturbative QCD approach. It is found that the $J/ψ$ ${\to}$ $ηη^{\prime}$ decays have relatively large branching ratios, about the order of $10^{-11}$, which might be within the measurement capability and sensitivity of the future STCF experiment.

hep-ph↗

arXiv2021

Reinvestigating the $B$ ${\to}$ $PP$ decays by including the contributions from $ϕ_{B2}$

Considering the $B$ mesonic distribution amplitude $ϕ_{B2}$, we reinvestigated the $B$ ${\to}$ $PP$ (where $P$ $=$ $π$ and $K$) decays with the perturbative QCD (pQCD) approach based on the $k_{T}$ factorization for three scenarios. It is found that the contributions of $ϕ_{B2}$ to formfactors $F_{0}^{B{\to}P}(0)$ and branching ratios are comparable with those from the NLO corrections. The $B$ ${\to}$ $Kπ$ decays could be well explained by considering the $ϕ_{B2}$. Hence, when the nonleptonic $B$ decays are studied withe the pQCD approach, the $ϕ_{B2}$ should be taken into account seriously.

hep-ph↗

arXiv2021

Study of the $Υ(1S)$ ${\to}$ $DP$ decays

Inspired by the potential prospects of high-luminosity dedicated colliders and the high enthusiasms in searching for new physics in the flavor sector at the intensity frontier, the $Υ(1S)$ ${\to}$ $D^{-}π^{+}$, $\overline{D}^{0}π^{0}$ and $D_{s}^{-}K^{+}$ weak decays are studied with the perturbative QCD approach. It is found within the standard model that the branching ratios for the concerned processes are tiny, about ${\cal O}(10^{-18})$, and far beyond the detective ability of current experiments unless there exists some significant enhancements from a noval interaction.

hep-ph↗

arXiv2021

The study of $η_{c}(1S)$ ${\to}$ $PP^{\prime}$ decays

The $η_{c}(1S)$ ${\to}$ $PP^{\prime}$ decays are the parity violation modes. These decays can be induced by the weak interactions within the standard model, and have been searched for based on the available experimental data. To meet the needs of experimental investigation, the $η_{c}(1S)$ ${\to}$ $PP^{\prime}$ decays are studied with the perturbative QCD approach. It is found that branching ratios are the order of $10^{-15}$ and less, which offers a ready reference for future analyses.

hep-ph↗

arXiv2017

$Υ(nS)$ ${\to}$ $B_{c}ρ$, $B_{c}K^{\ast}$ decays with perturbative QCD approach

Inspired by the potential prospects of $Υ(nS)$ data samples ($n$ $=$ $1$, $2$, $3$) at LHC and SuperKEKB, $Υ(nS)$ ${\to}$ $B_{c}ρ$, $B_{c}K^{\ast}$ decays are studied phenomenologically with pQCD approach. Branching ratios for $Υ(nS)$ ${\to}$ $B_{c}ρ$ and $B_{c}K^{\ast}$ decays are estimated to reach up to ${\cal O}(10^{-11})$ and ${\cal O}(10^{-12})$, respectively. Given the identification and detection efficiency of final states, searching for these weak decay modes should be fairly challenging experimentally in the future.

hep-ph↗

arXiv2017

Study of $J/ψ$ ${\to}$ $D_{s,d}V$ decays with perturbative QCD approach

Inspired by the recent measurements on two-body nonleptonic $J/ψ$ weak decay at BESIII, the charm-changing $J/ψ$ ${\to}$ $D_{s,d}V$ weak decays are studied with perturbative QCD approach, where $V$ denotes $ρ$ and $K^{\ast}$ vector mesons. It is found that branching ratio for $J/ψ$ ${\to}$ $D_{s}ρ$ decay can reach up to ${\cal O}(10^{-9})$, which is within the potential measurement capability of the future high-luminosity experiments.

hep-ph↗

arXiv2017

$J/ψ$ ${\to}$ $D_{s,d}π$, $D_{s,d}K$ decays with perturbative QCD approach

Besides the conventional strong and electromagnetic decay modes, the $J/ψ$ particle can also decay via the weak interaction in the standard model. In this paper, nonleptonic $J/ψ$ ${\to}$ $D_{s,d}π$, $D_{s,d}K$ weak decays, corresponding to the externally emitted virtual $W$ boson process, are investigated with the perturbative QCD approach. It is found that branching ratio for the Cabibbo-favored $J/ψ$ ${\to}$ $D_{s}π$ decay can reach up to ${\cal O}(10^{-10})$, which might be potentially measurable at the future high-luminosity experiments.

hep-ph↗

arXiv2017

$Υ(nS)$ ${\to}$ $B_{c}^{\ast}D$ decays with perturbative QCD approach

The $Υ(nS)$ ${\to}$ $B_{c}^{\ast}D$ weak decays ($n$ $=$ $1$, $2$, $3$) are investigated with perturbative QCD approach. It is found that the CKM-favored $Υ(nS)$ ${\to}$ $B_{c}^{\ast}D_{s}$ decays have branching ratio of ${\cal O}(10^{-10})$, which might be potentially accessible to the future LHC and SuperKEKB experiments.

hep-ph↗

arXiv2017

Study of the $\bar{B}_{q}^{\ast}$ ${\to}$ $DM$ decays with perturbative QCD approach

The $\bar{B}_{q}^{\ast}$ ${\to}$ $DP$, $DV$ weak decays are studied with the perturbative QCD approach, where $q$ $=$ $u$, $d$ and $s$; $P$ and $V$ denote the ground $SU(3)$ pseudoscalar and vector meson nonet. It is found that the branching ratios for the color-allowed $\bar{B}_{q}^{\ast}$ ${\to}$ $D_{q}ρ^{-}$ decays can reach up to $10^{-9}$ or more, and should be promisingly measurable at the running LHC and forthcoming SuperKEKB experiments in the near future.

hep-ph↗

arXiv2017

Study on the $Υ(1S)$ ${\to}$ $B_{c}D_{s}$ decay

The branching ratio and direct $CP$ asymmetry of the $Υ(1S)$ ${\to}$ $B_{c}D_{s}$ weak decay are estimated with the perturbative QCD approach. It is found that (1) The direct $CP$-violating asymmetry is close to zero. (2) the branching ratio ${\cal B}r(Υ(1S){\to}B_{c}D_{s})$ ${\gtrsim}$ $10^{-10}$ might be measurable at the future experiments.

hep-ph↗