Sustainability via LLM Right-sizing

Large language models (LLMs) have become increasingly embedded in organizational workflows. This has raised concerns over their energy consumption, financial costs, and data sovereignty. While performance benchmarks often celebrate cutting-edge models, real-world deployment decisions require a broader perspective: when is a smaller, locally deployable model "good enough"? This study offers an empirical answer by evaluating eleven proprietary and open-weight LLMs across ten everyday occupational tasks, including summarizing texts, generating schedules, and drafting emails and proposals. Using a dual-LLM-based evaluation framework, we automated task execution and standardized evaluation across ten criteria related to output quality, factual accuracy, and ethical responsibility. Results show that GPT-4o delivers consistently superior performance but at a significantly higher cost and environmental footprint. Notably, smaller models like Gemma-3 and Phi-4 achieved strong and reliable results on most tasks, suggesting their viability in contexts requiring cost-efficiency, local deployment, or privacy. A cluster analysis revealed three model groups -- premium all-rounders, competent generalists, and limited but safe performers -- highlighting trade-offs between quality, control, and sustainability. Significantly, task type influenced model effectiveness: conceptual tasks challenged most models, while aggregation and transformation tasks yielded better performances. We argue for a shift from performance-maximizing benchmarks to task- and context-aware sufficiency assessments that better reflect organizational priorities. Our approach contributes a scalable method to evaluate AI models through a sustainability lens and offers actionable guidance for responsible LLM deployment in practice.

Approximating Latent Manifolds in Neural Networks via Vanishing Ideals

Deep neural networks have reshaped modern machine learning by learning powerful latent representations that often align with the manifold hypothesis: high-dimensional data lie on lower-dimensional manifolds. In this paper, we establish a connection between manifold learning and computational algebra by demonstrating how vanishing ideals can characterize the latent manifolds of deep networks. To that end, we propose a new neural architecture that (i) truncates a pretrained network at an intermediate layer, (ii) approximates each class manifold via polynomial generators of the vanishing ideal, and (iii) transforms the resulting latent space into linearly separable features through a single polynomial layer. The resulting models have significantly fewer layers than their pretrained baselines, while maintaining comparable accuracy, achieving higher throughput, and utilizing fewer parameters. Furthermore, drawing on spectral complexity analysis, we derive sharper theoretical guarantees for generalization, showing that our approach can in principle offer tighter bounds than standard deep networks. Numerical experiments confirm the effectiveness and efficiency of the proposed approach.

Capturing Temporal Dynamics in Large-Scale Canopy Tree Height Estimation

With the rise in global greenhouse gas emissions, accurate large-scale tree canopy height maps are essential for understanding forest structure, estimating above-ground biomass, and monitoring ecological disruptions. To this end, we present a novel approach to generate large-scale, high-resolution canopy height maps over time. Our model accurately predicts canopy height over multiple years given Sentinel-2 time series satellite data. Using GEDI LiDAR data as the ground truth for training the model, we present the first 10m resolution temporal canopy height map of the European continent for the period 2019-2022. As part of this product, we also offer a detailed canopy height map for 2020, providing more precise estimates than previous studies. Our pipeline and the resulting temporal height map are publicly available, enabling comprehensive large-scale monitoring of forests and, hence, facilitating future research and ecological analyses. For an interactive viewer, see https://europetreemap.projects.earthengine.app/view/temporalcanopyheight.

Implicit Riemannian Optimism with Applications to Min-Max Problems

We introduce a Riemannian optimistic online learning algorithm for Hadamard manifolds based on inexact implicit updates. Unlike prior work, our method can handle in-manifold constraints, and matches the best known regret bounds in the Euclidean setting with no dependence on geometric constants, like the minimum curvature. Building on this, we develop algorithms for g-convex, g-concave smooth min-max problems on Hadamard manifolds. Notably, one method nearly matches the gradient oracle complexity of the lower bound for Euclidean problems, for the first time.

Beyond Short Steps in Frank-Wolfe Algorithms

We introduce novel techniques to enhance Frank-Wolfe algorithms by leveraging function smoothness beyond traditional short steps. Our study focuses on Frank-Wolfe algorithms with step sizes that incorporate primal-dual guarantees, offering practical stopping criteria. We present a new Frank-Wolfe algorithm utilizing an optimistic framework and provide a primal-dual convergence proof. Additionally, we propose a generalized short-step strategy aimed at optimizing a computable primal-dual gap. Interestingly, this new generalized short-step strategy is also applicable to gradient descent algorithms beyond Frank-Wolfe methods. As a byproduct, our work revisits and refines primal-dual techniques for analyzing Frank-Wolfe algorithms, achieving tighter primal-dual convergence rates. Empirical results demonstrate that our optimistic algorithm outperforms existing methods, highlighting its practical advantages.

Neural Discovery in Mathematics: Do Machines Dream of Colored Planes?

We demonstrate how neural networks can drive mathematical discovery through a case study of the Hadwiger-Nelson problem, a long-standing open problem from discrete geometry and combinatorics about coloring the plane avoiding monochromatic unit-distance pairs. Using neural networks as approximators, we reformulate this mixed discrete-continuous geometric coloring problem as an optimization task with a probabilistic, differentiable loss function. This enables gradient-based exploration of admissible configurations that most significantly led to the discovery of two novel six-colorings, providing the first improvements in thirty years to the off-diagonal variant of the original problem (Mundinger et al., 2024a). Here, we establish the underlying machine learning approach used to obtain these results and demonstrate its broader applicability through additional results and numerical insights.

S-CFE: Simple Counterfactual Explanations

We study the problem of finding optimal sparse, manifold-aligned counterfactual explanations for classifiers. Canonically, this can be formulated as an optimization problem with multiple non-convex components, including classifier loss functions and manifold alignment (or \emph{plausibility}) metrics. The added complexity of enforcing \emph{sparsity}, or shorter explanations, complicates the problem further. Existing methods often focus on specific models and plausibility measures, relying on convex $\ell_1$ regularizers to enforce sparsity. In this paper, we tackle the canonical formulation using the accelerated proximal gradient (APG) method, a simple yet efficient first-order procedure capable of handling smooth non-convex objectives and non-smooth $\ell_p$ (where $0 \leq p < 1$) regularizers. This enables our approach to seamlessly incorporate various classifiers and plausibility measures while producing sparser solutions. Our algorithm only requires differentiable data-manifold regularizers and supports box constraints for bounded feature ranges, ensuring the generated counterfactuals remain \emph{actionable}. Finally, experiments on real-world datasets demonstrate that our approach effectively produces sparse, manifold-aligned counterfactual explanations while maintaining proximity to the factual data and computational efficiency.

The Good, the Bad and the Ugly: Watermarks, Transferable Attacks and Adversarial Defenses

We formalize and extend existing definitions of backdoor-based watermarks and adversarial defenses as interactive protocols between two players. The existence of these schemes is inherently tied to the learning tasks for which they are designed. Our main result shows that for almost every discriminative learning task, at least one of the two -- a watermark or an adversarial defense -- exists. The term "almost every" indicates that we also identify a third, counterintuitive but necessary option, i.e., a scheme we call a transferable attack. By transferable attack, we refer to an efficient algorithm computing queries that look indistinguishable from the data distribution and fool all efficient defenders. To this end, we prove the necessity of a transferable attack via a construction that uses a cryptographic tool called homomorphic encryption. Furthermore, we show that any task that satisfies our notion of a transferable attack implies a cryptographic primitive, thus requiring the underlying task to be computationally complex. These two facts imply an "equivalence" between the existence of transferable attacks and cryptography. Finally, we show that the class of tasks of bounded VC-dimension has an adversarial defense, and a subclass of them has a watermark.

Estimating Canopy Height at Scale

We propose a framework for global-scale canopy height estimation based on satellite data. Our model leverages advanced data preprocessing techniques, resorts to a novel loss function designed to counter geolocation inaccuracies inherent in the ground-truth height measurements, and employs data from the Shuttle Radar Topography Mission to effectively filter out erroneous labels in mountainous regions, enhancing the reliability of our predictions in those areas. A comparison between predictions and ground-truth labels yields an MAE / RMSE of 2.43 / 4.73 (meters) overall and 4.45 / 6.72 (meters) for trees taller than five meters, which depicts a substantial improvement compared to existing global-scale maps. The resulting height map as well as the underlying framework will facilitate and enhance ecological analyses at a global scale, including, but not limited to, large-scale forest and biomass monitoring.

Neural Parameter Regression for Explicit Representations of PDE Solution Operators

We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets (Lu et al., 2021) by employing Physics-Informed Neural Network (PINN, Raissi et al., 2019) techniques to regress Neural Network (NN) parameters. By parametrizing each solution based on specific initial conditions, it effectively approximates a mapping between function spaces. Our method enhances parameter efficiency by incorporating low-rank matrices, thereby boosting computational efficiency and scalability. The framework shows remarkable adaptability to new initial and boundary conditions, allowing for rapid fine-tuning and inference, even in cases of out-of-distribution examples.