#01Nov 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%.
#02Nov 6, 2026
quant-ph
Discovering formally verified quantum programs with AI
Sergey Shirobokov, Ben Jaderberg, Katerina Hristova and 22 more
The timeline by which quantum computers can solve breakthrough problems in science depends on improved quantum algorithms as much as on better hardware. Such algorithmic advances are typically achieved through many years of expert human collaboration. In mathematics and computer science, large language models have accelerated progress through automated discovery loops. However, quantum algorithms can only be evaluated by classical computers on restricted or small instances. Here we demonstrate automated discovery of quantum programs beyond these regimes including order-of-magnitude improvements on scientific applications. To achieve this, we build a quantum program library in the Lean theorem prover in which large language model agents synthesize novel programs against formal problem specifications and verify their correctness and cost. Agent teams collaborate, sharing results and knowledge through wikis and discussing ideas at organized conferences. Our results improve on prior baselines for parallel search (up to 1.4x), quantum arithmetic (290x), and simulations relevant to fusion, photochemistry and drug-metabolism by 11x, 8x and 2.5x respectively. Combining human and artificial intelligence at scale, under the rigor of mathematical proof, lets researchers design algorithms that today's classical and quantum computers cannot test, shortening the path to practical quantum computation.
#03Nov 6, 2026
cs.CL
ROSE: Risk-Aware Orthogonal Subspace Navigation for Lifelong Knowledge Editing in Multimodal Large Language Models
Lingyun Song, Ziyao Chen, Kang Pan and 5 more
Multimodal Large Language Models (MLLMs) require continuous factual updates to stay current, yet lifelong knowledge editing remains a daunting challenge. The primary obstacle is the severe Locality Erosion and Catastrophic Forgetting, where sequential edits inevitably interfere with pre-trained capabilities and prior updates. In this paper, we propose \textbf{ROSE}, a \textbf{R}isk-aware \textbf{O}rthogonal \textbf{S}ubspace navigation framework for lifelong knowledge \textbf{E}diting. ROSE addresses forgetting by aiming to restrict parameter updates to the orthogonal complement of previously edited subspaces. Crucially, it introduces a risk-guided mechanism that utilizes a dynamically computed risk mask to safeguard specific factual parameter subspaces essential for model stability. During inference, ROSE employs a multi-granularity knowledge integration strategy, featuring prototype-anchored semantic gating and perturbation-driven subspace fusion to precisely activate edited knowledge for relevant queries while limiting interference on unrelated inputs. Comprehensive experiments on two prominent multimodal benchmarks show that ROSE is competitive with state-of-the-art approaches across five key metrics, while maintaining outstanding stability over $1,000$ sequential updates. Our code is available at https://github.com/sunlitsong/ROSE.
#04Nov 6, 2026
cs.AI
Ensemble Methodology for Reference-Free Confidence Estimation in LLM-based Code Summarization
Marco Colombo, Balaji A Jayaram, Sowmyakumari Selvaraj and 5 more
This paper describes an approach and use case to estimate the correctness of LLM-generated COBOL summaries without access to human-authored references. The core intuition is that inter-model agreement on semantics is informative about truth, and that an LLM-as-judge can provide higher-fidelity pairwise assessments than traditional string- or embedding-based metrics. We operationalise this intuition with (i) controlled summary generation from diverse models; (ii) a LLM evaluator that compares pairs of summaries and emits structured judgments; and (iii) a calibrated aggregation rule that combines supportive evidence while penalising only corroborated contradictions.
#05Nov 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.