#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
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.
#03Nov 6, 2026
cs.LG
The Cost of Coverage: Conformalising Native Forecast Uncertainty for GB Wind Power
Carl Somers
Uncertainty bands on wind forecasts help inform reserve sizing and commitments, but often fail to deliver their stated coverage. We apply conformal prediction to native bands to see what it adds and what it costs, comparing six forecasters, from ARIMA to a tabular foundation model, at two wind farms in Great Britain (GB) under operational conditions. We show that calibration repairs empirical marginal coverage with little or no Winkler Score penalty, but this apparent success conceals under-coverage in high winds. Calibrating by forecast wind regime turns marginal coverage into regime-level coverage, cutting day-ahead out-of-band volume in high winds by over 40% relative to pooled calibration while narrowing bands overall.
#04Nov 6, 2026
cs.AI
Assessing the Impact of Retrieval-Augmented Generation on Algorithmic Problem-Solving
Gabriel Souza Baggio, Gabriel Machado Lunardi, Guilherme Medeiros Machado and 3 more
Competitive programming problems pose distinctive challenges for Large Language Models, as they demand not only proficient code generation but also advanced algorithmic reasoning. This study presents a Retrieval-Augmented Generation approach specifically designed to enhance the capacity of Large Language Models to address such problems. Our approach integrates an embedding-based retrieval mechanism and a similarity search algorithm to identify analogous problems within a knowledge database, employing a dynamically adjusted threshold to mitigate retrieval noise. We conducted an evaluation using the CodeContests dataset, focusing on the test split problems that exhibit similarity to instances from the training split. The experimental framework considered three conditions: (i) problems provided solely with their original descriptions, (ii) problems supplemented with randomly selected examples from the training split, and (iii) problems augmented with similar examples retrieved through the proposed method. In addition, we incorporated a Min-K membership inference analysis to examine whether the generated code solutions were influenced by potential memorization of training data within the evaluated Large Language Models. This complementary perspective enables a deeper understanding of model behavior by distinguishing genuine generalization through retrieval from implicit recall of pretraining samples. Performance was assessed using both pass rates and the CodeForces Elo rating of the problems. The results provide empirical evidence that similarity-based retrieval substantially enhances Large Language Models performance in competitive programming scenarios, offering an scalable framework for improving code generation in algorithmic problem-solving contexts.
#05Nov 6, 2026
cs.CV
Graded convolutional networks: scale invariance without the scale and robustness to unknown blur
Tanush Shaska
The Gaussian jet of an image is a graded vector space: a dilation by $λ$ multiplies derivatives of order $k$ by $λ^{-k}$. Local graded convolutions are exactly homogeneous differential operators, and a local feature is dilation-invariant if and only if it factors through the scale-normalized jet or, without the scale, through the retraction onto the weighted sphere of the grading. Under unknown Gaussian blur the retraction changes only by a change of scale, whereas the scale-normalized jet acquires a grading factor that no radial normalization removes. At the zero jet the retraction separates image families that radial normalizations and continuous classifiers cannot. Networks built on the retraction are universal for invariant features. On MNIST such a network keeps 88.4% accuracy under a two-pixel blur, against 66.2% for the same network on scale-normalized derivatives; in Lindeberg's Gaussian derivative network the retraction raises accuracy at that blur from 91.5% to 95.1%.