arXiv subjects

Jaeho Hwang

Publications and source records attributed to Jaeho Hwang.

4 recordsLinked to original sources

arXiv2026

Quantum Tunneling-Aware Machine Learning: Physics-Derived Noise Models for Robust Deployment

Transistor scaling is approaching a quantum-mechanical limit, as thin gate oxides induce electron leakage through quantum tunneling. Unlike conventional digital systems, AI inference can tolerate such errors provided their structure is modeled correctly. In this paper, we introduce quantum tunneling-aware machine learning (QTAML). We derive the deployment-time weight-error distribution from first principles using the Wentzel-Kramers-Brillouin (WKB) approximation and show that it has structure that generic Gaussian noise models miss: an exact affine mean drift, a per-bit variance hierarchy dominated by the most-significant bit, and a per-layer dependence on $\|W_\ell\|_\infty$ and the trained-network Jacobian. We package these three structural properties into a single deployment-time algorithm, Tunneling-Aware Compensation (TAC), that combines closed-form mean correction with an optimal layer-adaptive bit-budget allocation derived from the WKB variance decomposition. Across four convolutional architectures at $p_\mathrm{flip}$=0.10 and a transformer encoder at $p_\mathrm{flip}$=0.05, TAC reaches $95\%$ of clean accuracy with 3.4$\times$ to 33.6$\times$ less ECC overhead than Uniform-MSP, the natural baseline derived from the same physics. The closed-form saturation ratio $\rho^*$ predicts these gains in advance, and on heterogeneous architectures WKB-derived scoring outperforms magnitude-based allocation by up to 24 percentage points at small budgets. The algorithm requires no retraining, no labels, and no inference-time overhead. We also verify the WKB-derived distributional theorems to Monte Carlo precision. These results connect WKB tunneling physics with noise-aware deep learning and suggest a principled path toward hardware--software co-design beyond conventional scaling limits.

cs.LG↗

arXiv2022

A New Necessary and Sufficient Condition for the Existence of Global Solutions to Semilinear Parabolic Equations on Bounded Domains

The purpose of this paper is to give a necessary and sufficient condition for the existence and non-existence of global solutions of the following semilinear parabolic equations \[ u_{t}=\Delta u+\psi(t)f(u),\,\,\mbox{ in }\Omega\times (0,t^{*}), \] under the Dirichlet boundary condition on a bounded domain. In fact, this has remained as an open problem for a few decades, even for the case $f(u)=u^{p}$. As a matter of fact, we prove: \[ \begin{aligned} &\mbox{there is no global solution for any initial data if and only if } &\mbox{the function } f \mbox{ satisfies} &\hspace{20mm}\int_{0}^{\infty}\psi(t)\frac{f\left(\lVert S(t)u_{0}\rVert_{\infty}\right)}{\lVert S(t)u_{0}\rVert_{\infty}}dt=\infty &\mbox{for every }\,\epsilon>0\,\mbox{ and nonnegative nontrivial initial data }\,u_{0}\in C_{0}(\Omega). \end{aligned} \] Here, $(S(t))_{t\geq 0}$ is the heat semigroup with the Dirichlet boundary condition.

math.AP↗

arXiv2019

A complete characterization of the blow-up solutions to discrete $p$-Laplacian parabolic equations with $q$-reaction under the mixed boundary conditions

In this paper, we consider discrete $p$-Laplacian parabolic equations with $q$-reaction term under the mixed boundary condition and the initial condition as follows: \begin{equation*} \begin{cases} u_{t}\left(x,t\right) = Δ_{p,ω} u\left(x,t\right) +λ\left\vert u\left(x,t\right) \right\vert^{q-1} u\left(x,t\right), &\left(x,t\right) \in S \times \left(0,\infty\right), \\ μ(z)\frac{\partial u}{\partial_{p} n}(z)+σ(z)\vert u(z)\vert^{p-2}u(z)=0, &\left(x,t\right) \in \partial S \times \left[0,\infty\right), \\ u\left(x,0\right) = u_{0}(x) \geq 0, &x \in \overline{S}. \end{cases} \end{equation*} where $p>1$, $q>0$, $λ>0$ and $μ,σ$ are nonnegative functions on the boundary $\partial S$ of a network $S$, with $μ(z)+σ(z)>0$, $z\in\partial S$. Here, $Δ_{p,ω}$ and $\frac{\partial ϕ}{\partial_{p} n}$ denote the discrete $p$-Laplace operator and the $p$-normal derivative, respectively. The parameters $p>1$ and $q>0$ are completely characterized to see when the solution blows up, vanishes, or exists globally. Indeed, the blow-up rates when blow-up does occur are derived. Also, we give some numerical illustrations which explain the main results.

math.AP↗

arXiv2019

A Condition for Blow-up solutions to Discrete $p$-Laplacian Parabolic Equations under the mixed boundary conditions on Networks

The purpose of this paper is to investigate a condition \begin{equation*} (C_{p}) \hspace{1cm} α\int_{0}^{u}f(s)ds \leq uf(u)+βu^{p}+γ,\,\,u>0 \end{equation*} for some $α>2$, $γ>0$, and $0\leqβ\leq\frac{\left(α-p\right)λ_{p,0}}{p}$, where $p>1$ and $λ_{p,0}$ is the first eigenvalue of the discrete $p$-Laplacian $Δ_{p,ω}$. Using the above condition, we obtain blow-up solutions to discrete $p$-Laplacian parabolic equations \begin{equation*} \begin{cases} u_{t}\left(x,t\right)=Δ_{p,ω}u\left(x,t\right)+f(u(x,t)), & \left(x,t\right)\in S\times\left(0,+\infty\right), μ(z)\frac{\partial u}{\partial_{p} n}(x,t)+σ(z)|u(x,t)|^{p-2}u(x,t)=0, & \left(x,t\right)\in\partial S\times\left[0,+\infty\right), u\left(x,0\right)=u_{0}\geq0(nontrivial), & x\in S, \end{cases} \end{equation*} on a discrete network $S$, where $\frac{\partial u}{\partial_{p}n}$ denotes the discrete $p$-normal derivative. Here, $μ$ and $σ$ are nonnegative functions on the boundary $\partial S$ of $S$, with $μ(z)+σ(z)>0$, $z\in \partial S$. In fact, it will be seen that the condition $(C_{p})$, the generalized version of the condition $(C)$, improves the conditions known so far.

math.AP↗