We consider the problem of discretization of neural operators between Hilbert spaces in a general framework including skip connections. We focus on bijec-tive neural operators through the lens of diffeomorphisms in infinite dimensions.

We consider the problem of discretization of neural operators between Hilbert spaces in a general framework including skip connections. We focus on bijec-tive neural operators through the lens of diffeomorphisms in infinite dimensions.

More'Frankenstein' rabbits are appearing across the US, sparking fears of a wider outbreak. Originally spotted in Colorado, these bizarre rabbits, with tentacle-like growths sprouting from their faces, have now been reported in Minnesota, Nebraska, and South Dakota. The animals are infected with cottontail rabbit papilloma virus (CRPV), also known as Shope papilloma virus, which can be spread through mosquito and tick bites. While humans are unlikely to contract CRPV, Dr Omer Awan of the University of Maryland School of Medicine cautioned that people could still face risks from other diseases carried by ticks or mosquitoes that have fed on infected rabbits. 'You're not going to get CRPV, and you likely won't show symptoms of it,' Dr Awan told the Daily Mail.

Remote sensing (RS) techniques, by enabling non-contact acquisition of extensive ground observations, have become a valuable tool for corn yield prediction. Traditional process-based (PB) models are limited by fixed input features and struggle to incorporate large volumes of RS data. In contrast, machine learning (ML) models are often criticized for being ``black boxes'' with limited interpretability. To address these limitations, we used Knowledge-Guided Machine Learning (KGML), which combined the strengths of both approaches and fully used RS data. However, previous KGML methods overlooked the crucial role of soil moisture in plant growth. To bridge this gap, we proposed the Knowledge-Guided Machine Learning with Soil Moisture (KGML-SM) framework, using soil moisture as an intermediate variable to emphasize its key role in plant development. Additionally, based on the prior knowledge that the model may overestimate under drought conditions, we designed a drought-aware loss function that penalizes predicted yield in drought-affected areas. Our experiments showed that the KGML-SM model outperformed other ML models. Finally, we explored the relationships between drought, soil moisture, and corn yield prediction, assessing the importance of various features and analyzing how soil moisture impacts corn yield predictions across different regions and time periods.

Efficient and socially equitable restoration of transportation networks post disasters is crucial for community resilience and access to essential services. The ability to rapidly recover critical infrastructure can significantly mitigate the impacts of disasters, particularly in underserved communities where prolonged isolation exacerbates vulnerabilities. Traditional restoration methods prioritize functionality over computational efficiency and equity, leaving low-income communities at a disadvantage during recovery. To address this gap, this research introduces a novel framework that combines quantum computing technology with an equity-focused approach to network restoration. Optimization of road link recovery within budget constraints is achieved by leveraging D Wave's hybrid quantum solver, which targets the connectivity needs of low, average, and high income communities. This framework combines computational speed with equity, ensuring priority support for underserved populations. Findings demonstrate that this hybrid quantum solver achieves near instantaneous computation times of approximately 8.7 seconds across various budget scenarios, significantly outperforming the widely used genetic algorithm. It offers targeted restoration by first aiding low-income communities and expanding aid as budgets increase, aligning with equity goals. This work showcases quantum computing's potential in disaster recovery planning, providing a rapid and equitable solution that elevates urban resilience and social sustainability by aiding vulnerable populations in disasters.

We consider the problem of discretization of neural operators between Hilbert spaces in a general framework including skip connections. We focus on bijective neural operators through the lens of diffeomorphisms in infinite dimensions. Framed using category theory, we give a no-go theorem that shows that diffeomorphisms between Hilbert spaces or Hilbert manifolds may not admit any continuous approximations by diffeomorphisms on finite-dimensional spaces, even if the approximations are nonlinear. The natural way out is the introduction of strongly monotone diffeomorphisms and layerwise strongly monotone neural operators which have continuous approximations by strongly monotone diffeomorphisms on finite-dimensional spaces. For these, one can guarantee discretization invariance, while ensuring that finite-dimensional approximations converge not only as sequences of functions, but that their representations converge in a suitable sense as well. Finally, we show that bilipschitz neural operators may always be written in the form of an alternating composition of strongly monotone neural operators, plus a simple isometry. Thus we realize a rigorous platform for discretization of a generalization of a neural operator. We also show that neural operators of this type may be approximated through the composition of finite-rank residual neural operators, where each block is strongly monotone, and may be inverted locally via iteration. We conclude by providing a quantitative approximation result for the discretization of general bilipschitz neural operators.

We present a novel approach for enhancing diversity and control in data annotation tasks by personalizing large language models (LLMs). We investigate the impact of injecting diverse persona descriptions into LLM prompts across two studies, exploring whether personas increase annotation diversity and whether the impacts of individual personas on the resulting annotations are consistent and controllable. Our results show that persona-prompted LLMs produce more diverse annotations than LLMs prompted without personas and that these effects are both controllable and repeatable, making our approach a suitable tool for improving data annotation in subjective NLP tasks like toxicity detection.

The widespread use of Large Language Models (LLMs) in society creates new information security challenges for developers, organizations, and end-users alike. LLMs are trained on large volumes of data, and their susceptibility to reveal the exact contents of the source training datasets poses security and safety risks. Although current alignment procedures restrict common risky behaviors, they do not completely prevent LLMs from leaking data. Prior work demonstrated that LLMs may be tricked into divulging training data by using out-of-distribution queries or adversarial techniques. In this paper, we demonstrate a simple, query-based decompositional method to extract news articles from two frontier LLMs. We use instruction decomposition techniques to incrementally extract fragments of training data. Out of 3723 New York Times articles, we extract at least one verbatim sentence from 73 articles, and over 20% of verbatim sentences from 6 articles. Our analysis demonstrates that this method successfully induces the LLM to generate texts that are reliable reproductions of news articles, meaning that they likely originate from the source training dataset. This method is simple, generalizable, and does not fine-tune or change the production model. If replicable at scale, this training data extraction methodology could expose new LLM security and safety vulnerabilities, including privacy risks and unauthorized data leaks. These implications require careful consideration from model development to its end-use.