Symbolic regression provides an analytical method to derive explicit mathematical relationships from empirical data that elucidate underlying processes. The model produced aims to be interpretable and as reliable as a physical law. In this context, a neural network architecture named Equation Learner (EQL) has been crafted to formulate equations via a fully differentiable system. Traditionally, the clarity and precision of EQL predictions are maintained through a hybrid strategy that initially sets to 0 the model parameters' L1 regularization to maximize accuracy, then activates the L1 regularization later in training to drive the model towards structural simplicity. This paper identifies weaknesses in this regularization approach and introduces a continuous adaptive L1 regularization technique, we have named L1adapt. This new approach progressively adjusts the level of constraints on the model weights, finely tuning the penalty intensity in relation to the model’s accuracy as training advances.

Language models are often evaluated with scalar metrics like accuracy, but such measures fail to capture how models internally represent ambiguity, especially when human annotators disagree.We propose a topological perspective to analyze how fine-tuned models encode ambiguity and more generally instances.Applied to RoBERTa-Large on the MD-Offense dataset, Mapper, a tool from topological data analysis, reveals that fine-tuning restructures embedding space into modular, non-convex regions aligned with model predictions, even for highly ambiguous cases.Over 98% of connected components exhibit ≥ 90% prediction purity, yet alignment with ground-truth labels drops in ambiguous data, surfacing a hidden tension between structural confidence and label uncertainty.Unlike traditional tools such as PCA or UMAP, Mapper captures this geometry directly uncovering decision regions, boundary collapses, and overconfident clusters.Our findings position Mapper as a powerful diagnostic tool for understanding how models resolve ambiguity.Beyond visualization, it also enables topological metrics that may inform proactive modeling strategies in subjective NLP tasks.For reproducibility, all code and experiment configurations are released 1 .

The detection and control of diseases constitute a primary objective of French viticultural research.In this paper, we present a bottom-up hierarchical approach for selecting spectral bands suitable for class discrimination of spectra acquired by Infrared spectroscopy.Our method entails evaluating neighboring bands using various similarity metrics, applying aggregation criteria, and ultimately identifying a limited number of the most relevant bands for the separation of classes.The bandwidths are limited within a range as is typically required for choosing existing optical filters or specifying colored filter arrays.Our approach facilitates the discovery of distinctive spectral bands associated with a disease of interest, enabling the customization of multispectral cameras to meet specific requirements.It was applied to spectra collected on vine leaves spanning a three-year period with the goal to identify the most discriminant bands for the detection of grapevine yellows.The results show that a limited number of bands are sufficient to identify this class of interest through a classifier based on Linear Discriminant Analysis.

The detection and control of diseases is a primary objective of French viticultural research. In this context, we have collected Near Infra-Red (NIR) spectra on vine leaves over different acquisition times, three years from 2021 to 2023, with the aim of selecting the discriminating spectral bands of yellowing of the vine compared to healthy plants, confounding symptoms, and other diseases of vines: rolling of leaves and esca. We also want these bands to be insensitive with respect to the acquisition time. To achieve this, we adapt the Correlation Explanation (CorEx) algorithm so that it can select suitable bands from NIR spectra under the constraint of insensitivity versus the acquisition times (CorEx-BS). Our two-steps method consists firstly in searching for a set of bands that best explain the correlations between the wavelengths, as measured by the multivariate mutual information, and secondly to bind these bands with the labels and the acquisition time to get the bands relevant to the labels. This approach facilitates the discovery of distinctive spectral bands associated with a class of interest, yellowing of the vine in our application, which are robust regarding the different acquisition times of spectra, the years in our case. The results in terms of Davies-Bouldin index (DB) and Calinski-Harabasz Index (CH) show that our method outperforms other classical bands clustering selection techniques. Index Terms-Correlation Explanation, Band clustering, Band selection, Classification, Grapevine Flavescence Dorée

Time series with large dispersion can be challenging for learning algorithms to predict intrinsic value, such as trend. To deal with this types of time series, we propose a novel method, namely the Recurrent Variational Information Bottleneck (RVIB). We first derive the objective function inspired by the Information Bottleneck principle. Then, the objective is integrated into a Gated Recurrent Unit architecture. Experiments on simulated time series with large and varied dispersion show that RVIB properly approximates their trends.

The rapid evolution of image processing equipment and techniques ensures the development of novel picture analysis methodologies. One of the most powerful yet computationally possible algebraic techniques for measuring the topological characteristics of functions is persistent homology. It's an algebraic invariant that can capture topological details at different spatial resolutions. Persistent homology investigates the topological features of a space using a set of sampled points, such as pixels. It can track the appearance and disappearance of topological features caused by changes in the nested space created by an operation known as filtration, in which a parameter scale, in our case the intensity of pixels, is increased to detect changes in the studied space over a range of varying scales. In addition, at the level of machine learning there were many studies and articles witnessing recently the combination between homological persistence and machine learning algorithms. On another level, prostate cancer is diagnosed referring to a scoring criterion describing the severity of the cancer called Gleason score. The classical Gleason system defines five histological growth patterns (grades). In our study we propose to study the Gleason score on some glands issued from a new optical microscopy technique called SLIM. This new optical microscopy technique that combines two classic ideas in light imaging: Zernike's phase contrast microscopy and Gabor's holography. Persistent homology features are computed on these images. We suggested machine learning methods to classify these images into the corresponding Gleason score. Machine learning techniques applied on homological persistence features was very effective in the detection of the right Gleason score of the prostate cancer in these kinds of images and showed an accuracy of above 95%.

Mid-IR spectral imaging is an efficient method to analyze biological samples. Several research studies showed its potential to diagnose cancerous tissues. However, some limitations appear when formalin-fixed paraffin-embedded tissues are studied due to the intense IR contribution of paraffin, unless to perform a time-consuming and aggressive chemical dewaxing. We propose in this paper to analyze the efficiency of two digital dewaxing methods developed to remove the paraffin influence on IR images acquired on a cancerous skin sample. The first method is the extended multiplicative signal correction (EMSC), which is a preprocessing step applied to neutralize the IR contribution of paraffin. The second one, previously developed for Raman spectroscopy of paraffined tissues, is based on the independent component analysis (ICA) and the nonnegatively constrained least squares (NCLS). ICA+NCLS permits to remove the IR spectral signature from tissue spectra. Both preprocessing methods are compared on the basis of K-means-clusterized IR images in respect to a conventional histopathological staining. In conclusion, these preliminary results show the efficiency of the preprocessing methods; however ICA+NCLS has to be improved to get more relevant outcomes.

Rank-order based filters are usually implemented using reduced ordering, since there is no natural way to order vector data, such as color pixel values. This paper proposes a new statistics for multivariate data which is a mean rank obtained by aggregating partial ordering ranks. This statistics is then used for the reduced ordering of vector data; the median statistic is characterized by the best mean rank vector (BMRV). We devise two filtering structures based on the BMRV statistics: one that uses a classical square neighborhood, and one which is based on adaptive neighborhoods. We show that the proposed filters are highly effective for filtering color images heavily corrupted by impulsive noise, and compare favorably to state-of-the-art filtering structures.