#01Nov 6, 2026
cs.LG
On the (non-)closedness of the set of ReLU networks
Eloi Martinet, Leon Bungert
We prove that the set $\mathcal{N}_N$ of ReLU networks with one hidden layer and at most $N\in\mathbb N$ neurons is weakly closed in $W^{1,p}(Ω)$, for a bounded connected open set $Ω\subset\mathbb R^d$. Consequently, every coercive, weakly lower semicontinuous energy on this space attains its minimum over $\mathcal{N}_N$. This covers the Deep Ritz method with convex integrands, Sobolev training and Lipschitz learning. Moreover, as the weight decay parameter tends to zero, minimizers of the regularized problem converge, up to subsequences, to minimizers with minimal parameter norm. We also prove that the set of ReLU networks with two hidden layers of bounded widths is not closed in $W^{1,p}(Ω)$ or in $C(\overlineΩ)$. This disproves a conjecture of Petersen, Raslan and Voigtlaender.
#02Nov 6, 2026
eess.IV
Super-resolved digital terrain models for GEDI geolocation correction: agreement with airborne LiDAR DTM-based corrections at the beam level, not the footprint level
Natsuki Yuda, Shinichiro Shirota
The Global Ecosystem Dynamics Investigation (GEDI) mission measures three-dimensional forest structure with a LiDAR aboard the International Space Station. GEDI observations have geolocation errors of about 10 m, which cause misalignment with other remote sensing data and reduce the accuracy of downstream tasks. Matching GEDI ground elevations against high-resolution digital terrain models (DTMs) from airborne LiDAR is one way to correct these errors, but such DTMs exist in few regions. To widen this method's applicability, we super-resolved a more widely available low-resolution DTM and used it for the matching. Our question is whether a super-resolved DTM yields the same correction as a 1 m-resolution airborne LiDAR DTM and, if not, why. In steep forests of western Japan, we super-resolved an existing 10 m-resolution DTM to 1 m. Improving its accuracy required fusion with a global 30 m-resolution DTM from a different source. Using the resulting DTM, we corrected GEDI observation positions first by a single shift per ground track, then per observation. For most tracks, the shifts nearly matched those from the airborne LiDAR DTM, likely because DTM errors canceled out across many observations. Per-observation corrections, however, did not match. At a single observation, the error does not cancel out and is too large for the correction. This error likely originates mainly from the input DTM. Therefore, even without a 1 m-resolution DTM, a roughly 10 m-resolution DTM, fused with a global DTM and super-resolved to 1 m, should yield track-wise corrections nearly matching those from a 1 m-resolution DTM.
#03Nov 6, 2026
cs.LG
Fifty-Two Shades of Pig: What the UCR Archive Really Asks Classifiers to Do
Omar Swelam, Jaris Küken, Shi Bin Hoo and 2 more
The pigs were bleeding. That was the point of the experiment: could airway pressure reveal hemorrhage before it became critical? In the UCR Time Series Classification Archive, the de facto benchmark for Time Series Classification (TSC), the same recordings ask a different question: "which of 52 pigs produced this trace?". The dataset PigAirwayPressure is not an outlier. Although the archive is the standard benchmark, whether its tasks resemble the problems TSC is meant to solve has rarely been examined. We find that several datasets are repurposed from their original task, built from toy setups, or have flawed test splits. We further question how representative the archive's ordered non-temporal sequences (e.g. spectra, shape outlines) are of real TSC, and the potential downsides from the decomposition of multivariate problems. Our findings call for more careful interpretation of archive-wide scores and greater attention to deployment-relevant evaluation. The audit is at https://github.com/automl/ucr-provenance-audit.
#04Nov 6, 2026
eess.IV
AdaptivePnP: Fast Auto-Tuned Plug-and-Play for Deconvolution
Haley Duba-Sullivan, Emma J. Reid, Charles A. Bouman and 1 more
Plug-and-play (PnP) methods reconstruct images by alternating a data-fitting step with an image denoiser. Their performance depends on two parameters: the step size $γ$ and the measurement noise level $σ$. In practice, $γ$ is often tuned by grid search over validation images and must be retuned whenever the problem setting changes, and $σ$ is assumed known or estimated separately. We propose AdaptivePnP, a PnP framework that jointly estimates $σ$ and $γ$ at every iteration from the data-fitting residual. To do so, we apply the PnP virtual model to the data-fitting proximal map and show that the residual is zero-mean Gaussian with covariance parameterized by $γ$ and $σ$. However, when one parameter is much larger than the other, the residual carries little information about the smaller one and using the maximum likelihood (ML) estimator can degrade the PnP iterations. We therefore introduce the identifiable maximum likelihood (IML) estimator, which restricts the ML estimator to an identifiable window in which the normalized Cramér--Rao bound of every parameter is bounded by a user-specified tolerance. For the virtual model, this window is an interval of ratios $ρ= γ/σ$, so computing the IML estimate reduces to a one-dimensional search over $ρ$. We apply AdaptivePnP to two standard PnP methods, yielding algorithms that require neither a tuned $γ$ nor a known $σ$. On image deblurring and super-resolution, AdaptivePnP matches or outperforms PnP baselines tuned with the true $σ$. Code is available at https://github.com/hdubasullivan/AdaptivePnP.
#05Nov 6, 2026
hep-lat
Machine learning for lattice QCD
Gurtej Kanwar, Scott Lawrence, Alessandro Nada and 1 more
Machine learning (ML) methods have been explored as a means of optimizing lattice field theory calculations, with increasing interest in recent years. This chapter gives an introduction and summary to the use of ML methods to optimize lattice field theory without introducing any uncontrolled approximations. We focus on those directions which are clearly established as of late 2025, marking the 50th anniversary of the beginning of the study of lattice gauge theory. This chapter is a contribution to the online book ``Lattice QCD at 50 years,'' (LQCD@50), edited by Tanmoy Bhattacharya, Maarten Golterman, Rajan Gupta, Laurent Lellouch, and Steve Sharpe.