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1. Skeletons and Fans of Logarithmic Structures

   https://doi.org/10.1007/978-3-319-30945-3  

   Abramovich, Dan; Chen, Qile; Marcus, Steffen; Ulirsch, Martin; Wise, Jonathan (January 2016, Nonarchimedean and Tropical Geometry)

   We survey a collection of closely related methods for generalizing fans of toric varieties, include skeletons, Kato fans, Artin fans, and polyhedral cone complexes, all of which apply in the wider context of logarithmic geometry. Under appropriate assumptions these structures are equivalent, but their different realizations have provided for surprisingly disparate uses. We highlight several current applications and suggest some future possibilities. 

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2. Stability and Generalization of Adversarial Training for Shallow Neural Networks with Smooth Activation

   Zhang, Kaibo; Wang, Yunjuan; Arora, Raman (December 2024, 38th Conference on Neural Information Processing Systems (NeurIPS 2024))

   Adversarial training has emerged as a popular approach for training models that are robust to inference-time adversarial attacks. However, our theoretical understanding of why and when it works remains limited. Prior work has offered generalization analysis of adversarial training, but they are either restricted to the Neural Tangent Kernel (NTK) regime or they make restrictive assumptions about data such as (noisy) linear separability or robust realizability. In this work, we study the stability and generalization of adversarial training for two-layer networks without any data distribution assumptions and beyond the NTK regime. Our findings suggest that for networks with any given initialization and sufficiently large width, the generalization bound can be effectively controlled via early stopping. We further improve the generalization bound by leveraging smoothing using Moreau’s envelope. 

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3. The impact of contamination and correlated design on the Lasso: An average case analysis

   https://doi.org/10.1016/j.spl.2025.110417  

   Minsker, Stanislav; Shen, Yiqiu (August 2025, Statistics & Probability Letters)

   We study the prediction problem in the context of the high-dimensional linear regression model. We focus on the practically relevant framework where a fraction of the linear measurements is corrupted while the columns of the design matrix can be moderately correlated. Our findings suggest that for most sparse signals, the Lasso estimator admits strong performance guarantees under more easily verifiable and less stringent assumptions on the design matrix compared to much of the existing literature. 

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4. Heavy and wet: The consequences of violating assumptions of measuring soil microbial growth efficiency using the 18O water method

   https://doi.org/10.1525/elementa.069  

   Pold, Grace; Domeignoz-Horta, Luiz A.; DeAngelis, Kristen M. (January 2020, Elementa: Science of the Anthropocene)

   null (Ed.)

   Soils store more carbon than the biosphere and atmosphere combined, and the efficiency to which soil microorganisms allocate carbon to growth rather than respiration is increasingly considered a proxy for the soil capacity to store carbon. This carbon use efficiency (CUE) is measured via different methods, and more recently, the 18O-H2O method has been embraced as a significant improvement for measuring CUE of soil microbial communities. Based on extrapolating 18O incorporation into DNA to new biomass, this measurement makes various implicit assumptions about the microbial community at hand. Here we conducted a literature review to evaluate how viable these assumptions are and then developed a mathematical model to test how violating them affects estimates of the growth component of CUE in soil. We applied this model to previously collected data from two kinds of soil microbial communities. By changing one parameter at a time, we confirmed our previous observation that CUE was reduced by fungal removal. Our results also show that depending on the microbial community composition, there can be substantial discrepancies between estimated and true microbial growth. Of the numerous implicit assumptions that might be violated, not accounting for the contribution of sources of oxygen other than extracellular water to DNA leads to a consistent underestimation of CUE. We present a framework that allows researchers to evaluate how their experimental conditions may influence their 18O-H2O-based CUE measurements and suggest the parameters that need further constraining to more accurately quantify growth and CUE. 

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5. From Prescription to Description: Mapping the GDPR to a Privacy Policy Corpus Annotation Scheme

   Poplavska, E. (January 2020, Frontiers in artificial intelligence and applications)

   Villata, S. (Ed.)

   The European Union’s General Data Protection Regulation (GDPR) has compelled businesses and other organizations to update their privacy policies to state specific information about their data practices. Simultaneously, researchers in natural language processing (NLP) have developed corpora and annotation schemes for extracting salient information from privacy policies, often independently of specific laws. To connect existing NLP research on privacy policies with the GDPR, we introduce a mapping from GDPR provisions to the OPP-115 annotation scheme, which serves as the basis for a growing number of projects to automatically classify privacy policy text. We show that assumptions made in the annotation scheme about the essential topics for a privacy policy reflect many of the same topics that the GDPR requires in these documents. This suggests that OPP-115 continues to be representative of the anatomy of a legally compliant privacy policy, and that the legal assumptions behind it represent the elements of data processing that ought to be disclosed within a policy for transparency. The correspondences we show between OPP-115 and the GDPR suggest the feasibility of bridging existing computational and legal research on privacy policies, benefiting both areas. 

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