#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.AI
Can Agentic Systems Close the Gap in Radiology with Production AI Tools?
Aubin Charley, Julien Khlaut, Charles Corbière and 3 more
Radiology AI has developed along two paths: specialized models that perform well on narrow tasks but cover few clinical findings, and generalist models that address a broader range of tasks but remain prone to hallucination and inaccurate measurements. Combining the two through agentic systems offers a route towards comprehensive radiology reporting, but published systems are tied to one modality or body part. We describe a radiology agentic framework that standardizes how an orchestrator calls modular tools to produce a structured report, and use it to measure what such a system can do with the tools from FDA-cleared radiology AI devices. Report generation is simulated on a large multi-modality report corpus, with the orchestrator given either a catalog of finding classes consolidated from the cleared devices, each available on the modalities it is cleared for, or an unlimited catalog in which any class can be requested, and planning either from the clinical indication or from the target report. Tool outputs are simulated from the reference report, so the comparison isolates tool availability and orchestration from tool error. With the cleared catalog and the indication alone, the orchestrator recovers under a third of the clinically actionable findings; recovery improves substantially with the unlimited catalog, and further when the plan is written from the target report. Attributing every missed finding to a cause shows that most are classes no cleared device offers for the study's modality, and that a third are classes or tools that were offered and not called. Adding the most frequently missing tools closes most of the gap to the unlimited catalog on held-out reports, whereas a smaller orchestrator with the unlimited catalog gives up the whole gain. Tool availability and effective orchestration are thus complementary constraints on comprehensive AI-assisted radiology reporting.
#03Nov 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%.
#04Nov 6, 2026
cs.CL
Compaction, decay and reinforcement in a two-tier conversational memory: a paired evaluation against retrieval-augmented generation
Osamudiamen Edogun, Joshua Obigwe, Irfan Mehmood
A conversational agent that remembers has to decide what to keep. Retrieval-augmented generation keeps the transcript and searches it; the alternative is to compact each turn into atomic facts and search those. We compare the two on LoCoMo, with both arms answering all 1,985 questions in one window, against the same stores, with the same generator and judge, and both predictions on one row, which licenses McNemar's exact test on the 512 questions where they disagree. On the four categories comparable work reports, compaction scores 71.4 per cent against 64.6, a lead of 6.8 points (p = 5.5e-08) at 34 per cent fewer prompt tokens. On all five, including the adversarial set comparable work drops, the lead falls to 2.0 and stops being significant, because the baseline leads adversarial by 14.6. That loss has a structure. Our lead falls as the reference answer demands more source wording, 9.6 points ahead at one or two reference words and 3.1 behind past eight, with token overlap moving the same way, so the judge is not the cause. Compaction keeps what a fact asserts and discards how it was said, so it wins where the answer is a value and loses where it is a phrasing. We also report four negative results with their power calculations.
#05Nov 6, 2026
cs.LG
Scaling Graph Similarity Learning with Graph Neural Networks
Ahmet Tüzen, Helge Langseth, Kjetil Nørvåg
Graph similarity computation is an important task in graph mining with many real-world applications, such as chemical compound analysis, program dependence comparison, and social network analysis. The problem is computationally challenging: Graph Edit Distance (GED) and Maximum Common Subgraph (MCS), which quantify the distance between graphs and identify their largest shared subgraph, respectively, are NP-hard to compute exactly. To address these computational challenges, Graph Neural Networks (GNNs) have been applied to this problem. However, existing GNN-based approaches have primarily focused on small-scale graph datasets, while scalability to larger scales remains underexplored. In this work, we propose FiLSim, a scalable GNN-based framework, and investigate whether a simplified GNN pipeline can maintain competitive performance on standard benchmarks while scaling to large graphs. We additionally propose a sequential graph-editing strategy to construct large-scale graph datasets with reliable GED labels to evaluate scalability. The proposed framework is evaluated on four benchmark datasets and four newly created large-scale datasets, demonstrating its effectiveness and scalability. FiLSim remains accurate on graphs with more than 150{,}000 nodes, where the baseline methods run out of memory or fail to learn, and scores all test pairs within seconds on a single GPU.