stat.ML · 2026-07-08 · No. 47
Machine Learning, 2026-07-08.
7 new papers in stat.ML. Titles, authors,
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01 — The papers
7 entries-
01
A Function-Space Dichotomy for Compositional Learning: Exponential Sub-Optimality of the Neural Tangent Kernel
Arkaprabha Ganguli, Emil Constantinescu
stat.ML · cs.LG
A persistent empirical observation is that trained neural networks outperform their neural tangent kernel (NTK) limit on tasks with compositional structure, yet a quantitative account of $\textbf{when}$ and $\textbf{by how much}$ has been lacking. Working on the unit circle, we give such an account through a dichotomy between two complexity measures of the target: its $\textbf{Fourier complexity}$, which controls NTK kernel regression, and...
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02
A Convex Approximation Framework for Neural Likelihood-Based Bayesian Inverse Problems
Fabian Schneider, Tapio Helin, Leila Taghizadeh
stat.ML · cs.LG · math.PR · stat.ME
Many problems in science and engineering are difficult to model accurately, either due to unknown physical mechanisms, poorly quantified measurement uncertainty, or prohibitive computational costs of high-fidelity simulations. These challenges limit the applicability of classical probabilistic inference methods such as Markov chain Monte Carlo, especially in high-dimensional Bayesian inverse problems. As data from scientific experiments...
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03
Separation Capacity of Scattering Networks on Low-Dimensional Datasets
Konstantin Häberle, Helmut Bölcskei
stat.ML · cs.IT · cs.LG · math.CA
We aim to identify scattering network architectures that maximize the separation capacity on data with low intrinsic dimension. The networks we consider employ a fixed monomial nonlinearity and no pooling, so that the only design variable is the frame generated by the network filters. For data modeled as rectifiable sets, we first characterize and bound the separation capacity of general feature extractors in terms of the geometry of the...
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04
On the convergence of graph Laplacians with a symmetric divergence
Liane Xu
stat.ML · cs.LG
When analyzing a manifold learning algorithm for data lying on a smooth, compact, connected Riemannian submanifold $(\mathcal{M}, g)$ of $\mathbb{R}^d$, a key estimate for the geodesic distance $d_g$ is that there exists $K > 0$ such that $0 \leq d_g(p, q)^2 - \|p-q\|^2 \leq K d_g(p, q)^4$ for all $p, q \in \mathcal{M}$. We observe that more generally, when $\mathcal{M}$ is equipped with a smooth symmetric divergence $D$ satisfying a...
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05
Boosting with List-Decodable Codes
Addison Prairie, Li-Yang Tan
stat.ML · cs.CC · cs.DS · cs.LG
Boosting is a fundamental technique for generically improving the accuracy of learning algorithms (Schapire 1989). Existing boosting algorithms construct a strong learner using $O(\log(\frac{1}ε)/γ^2)$ calls to a $γ$-advantage weak learner, and this round complexity is known to be optimal for generic boosters that succeed on all concept classes (Freund 1995). We show that this lower bound can be circumvented for concept classes that satisfy a...
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06
Width-Robust Learnability in Mean-Field Bayesian Neural Networks
Dmitry Vaintrob, Kaarel Hänni
stat.ML · cs.LG
Infinite-width limits are a standard way to reason about neural networks, but it is not automatic that the limiting learner has the same complexity-theoretic inductive bias as large finite networks. We study this question for Bayesian neural networks at the mean-field, or critical feature-learning, scaling. The central quantity is the \emph{reduced entropy} \[ s_\infty(y,\varepsilon)=\limsup_N -\frac{1}{N}\log π_N^0(L\le \varepsilon), \] the...
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07
Beyond Heuristic Tuning: Power-Calibrated LLM Watermarking
Xiaopu Wang, Zelin He, Chengyuan Liu, Runze Li
stat.ML · cs.LG
Logit-based watermarking is a widely used mechanism for identifying LLM generated content, yet its effectiveness is governed by a fundamental trade-off between detectability and semantic distortion. Existing analyses provide limited guidance for principled hyperparameter selection, leaving practical deployments reliant on heuristic tuning. In this work, we develop a power-calibrated statistical framework that establishes explicit quantitative...
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