arXiv subjects

Jaeho Hwang

Publications and source records attributed to Jaeho Hwang.

7 recordsLinked to original sources

arXiv2026

When Does Exploration Prevent Collapse? Three Regimes and the Path of the Reward in Self-Consistency Training

Test-time reinforcement learning (TTRL) adapts a model without labels by rewarding answers that agree with the majority, but it collapses the policy onto its majority answer and can remove the correct answer from the samples. Exploration can prevent this collapse, yet its strength is chosen by trial and error, and how the training algorithm changes the required strength is unclear. We model training on a single problem as a continuous flow of the logits of a softmax policy and analyze which policies are stable as the exploration coefficient varies. Only collapsed policies are stable below a lower boundary and only policies spread over many answers above an upper boundary, and we derive these boundaries in closed form for an agreement reward with smoothing toward the uniform policy, compute them for the majority reward of TTRL on policies with one leading answer and bound them with interval arithmetic for actions on ordered bins. We prove that under exact gradients, the learning rate and, in a mean-field model, the normalization of GRPO leave these boundaries unchanged when exploration passes through them together with the reward but shift them when exploration bypasses them. Exact sums on these policies then show that a bonus for rare answers needs a coefficient above $1/\log(G-1)$ for groups of $G$ samples before the normalization and about two to three times that after it. In free-form TTRL on MATH-500, a bonus placed before the normalization prevented collapse and kept more correct answers among the samples, although it lowered pass@1.

cs.LG↗

arXiv2026

The Batch Size Can Be One: Test-Time Adaptation from Classifier Geometry

Test-time adaptation updates a deployed model on an unlabeled test stream. In practice this stream often arrives one sample at a time, with the classes in no particular order. A single sample then provides limited information for estimating distribution-level statistics, and selecting samples by confidence can admit predictions that are wrong yet confident. A corruption, however, shifts the features while leaving the decision regions of the frozen classifier unchanged. We therefore propose Origin-recentered Test-Time Adaptation (OriTTA), which constructs fixed geometric targets from the source model and adapts selected features toward them. Seen from the origin of the feature space, the classes lean toward a common direction. We choose a new origin to bring class scores closer together while keeping it near the mean feature of one synthetic prototype per class. From this origin, prototype directions spread more evenly, and each class obtains an axis and an ideal point before any test data arrives. During adaptation, OriTTA aligns selected features with their predicted class axis and penalizes excessive radius, keeps one input per predicted class in memory to limit feature changes for classes absent from the stream, and resets the model when re-classifying this memory reveals collapse. Without tuning for each setting, OriTTA achieves the highest mean accuracy at batch size 1 on CIFAR-10-C, CIFAR-100-C and ImageNet-C in all sixteen combinations of four backbones, two protocols and two stream orders. On ImageNet-C fog, recent methods collapse in up to two thirds of one hundred runs, while OriTTA never does.

cs.LG↗

arXiv2026

Certified Adaptive List Decoding for Error-Correcting Codes

Maximum-likelihood (ML) decoding of linear block codes is NP-hard, so neural decoders are evaluated by how closely they approach it. We observe that proving a candidate optimal can be far easier than finding it, and build a decoder that does both. We cast decoding as a search over an absorbing-state discrete diffusion model, whose sequential commitment of coordinates turns generation into a tree, and run a probability beam search over it. A dual bound from a linear-programming relaxation and a distance-based test, both derived from the code, then certify per frame that the current candidate is the global ML solution; because both are theorems, certified frames incur no accuracy-computation trade-off. Across $15$ codes and five operating points we certify up to $99.9\%$ of frames, the two tests dividing the space as their derivations predict, one strong for sparse parity-check matrices and the other for codes with a large minimum distance. Certification also behaves as a per-frame reliability signal, with $96.7$-$100\%$ of all frame errors falling on uncertified frames. Against an exact ML reference at $5$ dB the decoder is within one standard deviation on three of the four codes where the reference is uncensored, and against four neural baselines it attains the best bit-error rate in $71$ of $75$ cells.

cs.IT↗

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 $ρ^*$ 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 \[ u_{t}=Δu+ψ(t)f(u),\,\,\mbox{ in }Ω\times (0,t^{*}), \] 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: \[ \begin{aligned} &\mbox{there is no global solution for any initial data if and only if } &\mbox{the function } f \mbox{ satisfies} &\hspace{20mm}\int_{0}^{\infty}ψ(t)\frac{f\left(\lVert S(t)u_{0}\rVert_{\infty}\right)}{\lVert S(t)u_{0}\rVert_{\infty}}dt=\infty &\mbox{for every }\,ε>0\,\mbox{ and nonnegative nontrivial initial data }\,u_{0}\in C_{0}(Ω). \end{aligned} \] 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↗