The impossibility theorem of fairness is a foundational result in the algorithmic fairness literature. It states that outside of special cases, one cannot exactly and simultaneously satisfy all three common and intuitive definitions of fairness demographic parity, equalized odds, and predictive rate parity. This result has driven most works to focus on solutions for one or two of the metrics.

Neural-guided equation discovery systems use a data set as prompt and predict an equation that describes the data set without extensive search. However, if the equation does not meet the user's expectations, there are few options for getting other equation suggestions without intensive work with the system. To fill this gap, we propose Residuals for Equation Discovery (RED), a post-processing method that improves a given equation in a targeted manner, based on its residuals. By parsing the initial equation to a syntax tree, we can use node-based calculation rules to compute the residual for each subequation of the initial equation. It is then possible to use this residual as new target variable in the original data set and generate a new prompt. If, with the new prompt, the equation discovery system suggests a subequation better than the old subequation on a validation set, we replace the latter by the former. RED is usable with any equation discovery system, is fast to calculate, and is easy to extend for new mathematical operations. In experiments on 53 equations from the Feynman benchmark, we show that it not only helps to improve all tested neural-guided systems, but also all tested classical genetic programming systems.

Magnetic Resonance Imaging (MRI) is the primary imaging modality used in the diagnosis, assessment, and treatment planning for brain pathologies. However, most automated MRI analysis tools, such as segmentation and registration pipelines, are optimized for healthy anatomies and often fail when confronted with large lesions such as tumors. To overcome this, image inpainting techniques aim to locally synthesize healthy brain tissues in tumor regions, enabling the reliable application of general-purpose tools. In this work, we systematically evaluate state-of-the-art inpainting models and observe a saturation in their standalone performance. In response, we introduce a methodology combining model ensembling with efficient post-processing strategies such as median filtering, histogram matching, and pixel averaging. Further anatomical refinement is achieved via a lightweight U-Net enhancement stage. Comprehensive evaluation demonstrates that our proposed pipeline improves the anatomical plausibility and visual fidelity of inpainted regions, yielding higher accuracy and more robust outcomes than individual baseline models. By combining established models with targeted post-processing, we achieve improved and more accessible in-painting outcomes, supporting broader clinical deployment and sustainable, resource-conscious research.

However, in computer vision or natural language applications, it is common to start with a large generic model and then fine-tune to a specific use-case.

Self-supervised learning (SSL) models offer powerful representations for sound event detection (SED), yet their synergistic potential remains underexplored. This study systematically evaluates state-of-the-art SSL models to guide optimal model selection and integration for SED. We propose a framework that combines heterogeneous SSL representations (e.g., BEATs, HuBERT, WavLM) through three fusion strategies: individual SSL embedding integration, dual-modal fusion, and full aggregation. Experiments on the DCASE 2023 Task 4 Challenge reveal that dual-modal fusion (e.g., CRNN+BEATs+WavLM) achieves complementary performance gains, while CRNN+BEATs alone delivers the best results among individual SSL models. We further introduce normalized sound event bounding boxes (nSEBBs), an adaptive post-processing method that dynamically adjusts event boundary predictions, improving PSDS1 by up to 4% for standalone SSL models. These findings highlight the compatibility and complementarity of SSL architectures, providing guidance for task-specific fusion and robust SED system design.

In many applications, decision-makers must choose between multiple predictive models that may all be miscalibrated. Which model (i.e., predictor) is more "useful" in downstream decision tasks? To answer this, our first contribution introduces the notion of the informativeness gap between any two predictors, defined as the maximum normalized payoff advantage one predictor offers over the other across all decision-making tasks. Our framework strictly generalizes several existing notions: it subsumes U-Calibration [KLST-23] and Calibration Decision Loss [HW-24], which compare a miscalibrated predictor to its calibrated counterpart, and it recovers Blackwell informativeness [Bla-51, Bla-53] as a special case when both predictors are perfectly calibrated. Our second contribution is a dual characterization of the informativeness gap, which gives rise to a natural informativeness measure that can be viewed as a relaxed variant of the earth mover's distance (EMD) between two prediction distributions. We show that this measure satisfies natural desiderata: it is complete and sound, and it can be estimated sample-efficiently in the prediction-only access setting. Along the way, we also obtain novel combinatorial structural results when applying this measure to perfectly calibrated predictors.