In this paper, the solution to the empirical risk minimization problem with $f$-divergence regularization (ERM-$f$DR) is presented and conditions under which the solution also serves as the solution to the minimization of the expected empirical risk subject to an $f$-divergence constraint are established. The proposed approach extends applicability to a broader class of $f$-divergences than previously reported and yields theoretical results that recover previously known results. Additionally, the difference between the expected empirical risk of the ERM-$f$DR solution and that of its reference measure is characterized, providing insights into previously studied cases of $f$-divergences. A central contribution is the introduction of the normalization function, a mathematical object that is critical in both the dual formulation and practical computation of the ERM-$f$DR solution. This work presents an implicit characterization of the normalization function as a nonlinear ordinary differential equation (ODE), establishes its key properties, and subsequently leverages them to construct a numerical algorithm for approximating the normalization factor under mild assumptions. Further analysis demonstrates structural equivalences between ERM-$f$DR problems with different $f$-divergences via transformations of the empirical risk. Finally, the proposed algorithm is used to compute the training and test risks of ERM-$f$DR solutions under different $f$-divergence regularizers. This numerical example highlights the practical implications of choosing different functions $f$ in ERM-$f$DR problems.

Coral reefs are rapidly declining due to anthropogenic pressures such as climate change, underscoring the urgent need for scalable, automated monitoring. We introduce ReefNet, a large public coral reef image dataset with point-label annotations mapped to the World Register of Marine Species (WoRMS). ReefNet aggregates imagery from 76 curated CoralNet sources and an additional site from Al Wajh in the Red Sea, totaling approximately 925000 genus-level hard coral annotations with expert-verified labels. Unlike prior datasets, which are often limited by size, geography, or coarse labels and are not ML-ready, ReefNet offers fine-grained, taxonomically mapped labels at a global scale to WoRMS. We propose two evaluation settings: (i) a within-source benchmark that partitions each source's images for localized evaluation, and (ii) a cross-source benchmark that withholds entire sources to test domain generalization. We analyze both supervised and zero-shot classification performance on ReefNet and find that while supervised within-source performance is promising, supervised performance drops sharply across domains, and performance is low across the board for zero-shot models, especially for rare and visually similar genera. This provides a challenging benchmark intended to catalyze advances in domain generalization and fine-grained coral classification. We will release our dataset, benchmarking code, and pretrained models to advance robust, domain-adaptive, global coral reef monitoring and conservation.

Large Language Models (LLMs) are rapidly being adopted in conservation to address the biodiversity crisis, yet their reliability for species evaluation is uncertain. This study systematically validates five leading models on 21,955 species across four core IUCN Red List assessment components: taxonomy, conservation status, distribution, and threats. A critical paradox was revealed: models excelled at taxonomic classification (94.9%) but consistently failed at conservation reasoning (27.2% for status assessment). This knowledge-reasoning gap, evident across all models, suggests inherent architectural constraints, not just data limitations. Furthermore, models exhibited systematic biases favoring charismatic vertebrates, potentially amplifying existing conservation inequities. These findings delineate clear boundaries for responsible LLM deployment: they are powerful tools for information retrieval but require human oversight for judgment-based decisions. A hybrid approach is recommended, where LLMs augment expert capacity while human experts retain sole authority over risk assessment and policy.

Marine ecosystems face increasing pressure due to climate change, driving the need for scalable, AI-powered monitoring solutions. This paper examines the rapid emergence of underwater AI as a major research frontier and analyzes the factors that have transformed marine perception from a niche application into a catalyst for AI innovation. We identify three convergent drivers: environmental necessity for ecosystem-scale monitoring, democratization of underwater datasets through citizen science platforms, and researcher migration from saturated terrestrial computer vision domains. Our analysis reveals how unique underwater challenges - turbidity, cryptic species detection, expert annotation bottlenecks, and cross-ecosystem generalization - are driving fundamental advances in weakly supervised learning, open-set recognition, and robust perception under degraded conditions. We survey emerging trends in datasets, scene understanding and 3D reconstruction, highlighting the paradigm shift from passive observation toward AI-driven, targeted intervention capabilities. The paper demonstrates how underwater constraints are pushing the boundaries of foundation models, self-supervised learning, and perception, with methodological innovations that extend far beyond marine applications to benefit general computer vision, robotics, and environmental monitoring.

--The dual formulation of empirical risk minimization with f -divergence regularization (ERM-f DR) is introduced. The solution of the dual optimization problem to the ERM-f DR is connected to the notion of normalization function introduced as an implicit function. This dual approach leverages the Legendre-Fenchel transform and the implicit function theorem to provide a nonlinear ODE expression to the normalization function. Furthermore, the nonlinear ODE expression and its properties provide a computationally efficient method to calculate the normalization function of the ERM-f DR solution under a mild condition. Empirical risk minimization (ERM) [1]-[6] is often posed as an optimization problem regularized by a statistical distance between the probability measure to be optimized and a given reference measure [7]-[13].

Can a language model trained largely on Anglo-American texts generate stories that are culturally relevant to other nationalities? To find out, we generated 11,800 stories - 50 for each of 236 countries - by sending the prompt "Write a 1500 word potential {demonym} story" to OpenAI's model gpt-4o-mini. Although the stories do include surface-level national symbols and themes, they overwhelmingly conform to a single narrative plot structure across countries: a protagonist lives in or returns home to a small town and resolves a minor conflict by reconnecting with tradition and organising community events. Real-world conflicts are sanitised, romance is almost absent, and narrative tension is downplayed in favour of nostalgia and reconciliation. The result is a narrative homogenisation: an AI-generated synthetic imaginary that prioritises stability above change and tradition above growth. We argue that the structural homogeneity of AI-generated narratives constitutes a distinct form of AI bias, a narrative standardisation that should be acknowledged alongside the more familiar representational bias. These findings are relevant to literary studies, narratology, critical AI studies, NLP research, and efforts to improve the cultural alignment of generative AI.

This study examines the role of human judges in legal decision-making by using machine learning to predict child physical custody outcomes in French appellate courts. Building on the legal realism-formalism debate, we test whether individual judges' decision-making patterns significantly influence case outcomes, challenging the assumption that judges are neutral variables that apply the law uniformly. To ensure compliance with French privacy laws, we implement a strict pseudonymization process. Our analysis uses 18,937 living arrangements rulings extracted from 10,306 cases. We compare models trained on individual judges' past rulings (specialist models) with a judge-agnostic model trained on aggregated data (generalist models). The prediction pipeline is a hybrid approach combining large language models (LLMs) for structured feature extraction and ML models for outcome prediction (RF, XGB and SVC). Our results show that specialist models consistently achieve higher predictive accuracy than the general model, with top-performing models reaching F1 scores as high as 92.85%, compared to the generalist model's 82.63% trained on 20x to 100x more samples. Specialist models capture stable individual patterns that are not transferable to other judges. In-Domain and Cross-Domain validity tests provide empirical support for legal realism, demonstrating that judicial identity plays a measurable role in legal outcomes. All data and code used will be made available.

Inference-Time Scaling has been critical to the success of recent models such as OpenAI o1 and DeepSeek R1. However, many techniques used to train models for inference-time scaling require tasks to have answers that can be verified, limiting their application to domains such as math, coding and logical reasoning. We take inspiration from how humans make first attempts, ask for detailed feedback from others and make improvements based on such feedback across a wide spectrum of open-ended endeavors. To this end, we collect data for and train dedicated Feedback and Edit Models that are capable of performing inference-time scaling for open-ended general-domain tasks. In our setup, one model generates an initial response, which are given feedback by a second model, that are then used by a third model to edit the response. We show that performance on Arena Hard, a benchmark strongly predictive of Chatbot Arena Elo can be boosted by scaling the number of initial response drafts, effective feedback and edited responses. When scaled optimally, our setup based on 70B models from the Llama 3 family can reach SoTA performance on Arena Hard at 92.7 as of 5 Mar 2025, surpassing OpenAI o1-preview-2024-09-12 with 90.4 and DeepSeek R1 with 92.3.

Closed-form expressions are presented for the variation of the expectation of a given function due to changes in the probability measure used for the expectation. They unveil interesting connections with Gibbs probability measures, the mutual information, and the lautum information.

Rigorous statements and formal proofs are presented for both foundational and advanced folklore theorems on the Radon-Nikodym derivative. The cases of product and marginal measures are carefully considered; and the hypothesis under which the statements hold are rigorously enumerated.