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.

Impulsive noise, where large amplitudes arise with a relatively high probability, arises in many communication systems including interference in Low Power Wide Area Networks. A challenge in coping with impulsive noise, particularly alpha-stable models, is that tractable expressions for the log-likelihood ratio (LLR) are not available, which has a large impact on soft-input decoding schemes, e.g., low-density parity-check (LDPC) packets. On the other hand, constraints on packet length also mean that pilot signals are not available resulting in non-trivial approximation and parameter estimation problems for the LLR. In this paper, a new unsupervised parameter estimation algorithm is proposed for LLR approximation. In terms of the frame error rate (FER), this algorithm is shown to significantly outperform existing unsupervised estimation methods for short LDPC packets (on the order of 500 symbols), with nearly the same performance as when the parameters are perfectly known. The performance is also compared with an upper bound on the information-theoretic limit for the FER, which suggests that in impulsive noise further improvements require the use of an alternative code structure other than LDPC.

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%.

In impulsive noise, the inputs of the belief propagation decoder can be complex to compute or even impossible when the noise distribution is not known. We propose a simple approximation of the log-likelihood ratio that maps the channel output to the input of the error correcting decoder, for instance, LDPC decoders. This approximation is designed for additive impulsive noise channels, nevertheless, it is not computationally demanding and easy to be implemented. It requires the estimation of three parameters and we propose an efficient way to do it. Moreover, in terms of performance, our solution is barely discernible from the optimal receiver which is computationally prohibitive.

Robust communication is necessary for many wireless applications. Making a decision at the receiver requires an evaluation of the likelihood. However, in impulsive noise, the traditional Gaussian-based receiver exhibits a very significant performance loss. This paper proposes to approximate the likelihood ratio in a binary transmission with a function adapted to impulsive noise conditions but also efficient when noise is purely Gaussian. We introduce a blind estimation of the two parameters defining the approximation and evaluate its performance when used as the inputs of the belief propagation decoder. Our proposal allows us not only to achieve performance close to the optimal decoding but also to have a simple implementation and to adapt to different environment, impulsive or not, independently of the underlying statistical noise model, without the need of a training sequence.

Spectral graph analysis based on Laplace operators has been ubiquitously applied in graph signal processing. Extending these tools to a generalization of graphs is helpful for several applications, such as network analysis, a sensor network coverage problem, and other fields, where the relationships between two or more vertices should be modeled. Such mathematical theories already exist, but the associated algorithms are still in their infancy. In this letter, we propose a new algorithm to compute harmonic forms, i.e., solutions of the Laplace equation, whose implementation is simple enough to be distributed among networks without central control center.

Impulsive noise features in many modern communication systems-ranging from wireless to molecular-and is often modeled by the α-stable distribution. At present, the capacity of α-stable noise channels is not well understood, with the exception of Cauchy noise (α = 1) with a logarithmic constraint and Gaussian noise (α = 2) with a power constraint. In this paper, we consider additive symmetric α-stable noise channels with α ∈ (1, 2]. We derive bounds for the capacity with an absolute moment constraint. We then compare our bounds with a numerical approximation via the Blahut-Arimoto algorithm, which provides insight into the effect of noise parameters on the bounds. In particular, we find that our lower bound is in good agreement with the numerical approximation for α near 2.

Impulsive noise arises in many communication systems - ranging from wireless to molecular - and is often modeled via the α-stable distribution. In this paper, we investigate properties of the capacity of complex isotropic α-stable noise channels, which can arise in the context of wireless cellular communications and are not well understood at present. In particular, we derive a tractable lower bound, as well as prove existence and uniqueness of the optimal input distribution. We then apply our lower bound to study the case of parallel α-stable noise channels and derive a bound that provides insight into the effect of the tail index α on the achievable rate.

This paper deals with the robustness of soft iterative decoders in impulsive interference modeled by Middleton class A distribution, epsilon-contaminated Gaussian noise or a sum of a Gaussian thermal noise and an impulsive alpha-stable noise. The inputs of belief propagation decoder should be the log-likelihood ratios of the received symbols. But in case of impulsive interference, their computation are highly non-linear and relies on the knowledge of the noise probability distribution. Besides, two of the most often used models - Middleton and alpha-stable noises - give complex analytical expression, for instance through infinite series. In a previous work, we proposed an easily computable approximation of the log likelihood ratio in an impulsive environment. Even with this simplification, performance stays close to the one obtained using the true probability density function. In this paper, we investigate the robustness of our approximation against different interference models and its parameters' estimation method.

Models for noncoherent error control in random linear network coding (RLNC) and store and forward (SAF) have been recently proposed. In this paper, we model different types of random network communications as the transmission of flats of matroids. This novel framework encompasses RLNC and SAF and allows us to introduce a novel protocol, referred to as random affine network coding (RANC), based on affine combinations of packets. Although the models previously proposed for RLNC and SAF only consider error control, using our framework, we first evaluate and compare the performance of different network protocols in the error-free case. We define and determine the rate, average delay, and throughput of such protocols, and we also investigate the possibilities of partial decoding before the entire message is received. We thus show that RANC outperforms RLNC in terms of data rate and throughput thanks to a more efficient encoding of messages into packets. Second, we model the possible alterations of a message by the network as an operator channel, which generalizes the channels proposed for RLNC and SAF. Error control is thus reduced to a coding-theoretic problem on flats of a matroid, where two distinct metrics can be used for error correction. We study the maximum cardinality of codes on flats in general, and codes for error correction in RANC in particular. We finally design a class of nearly optimal codes for RANC based on rank metric codes for which we propose a low-complexity decoding algorithm. The gain of RANC over RLNC is thus preserved with no additional cost in terms of complexity.

In this paper, we address the problem of providing unequal error protection (UEP) with LDPC codes built on finite sets of order strictly greater than 2 (nonbinary codes). The main interest of providing UEP with nonbinary LDPC codes is that future standards are likely to prefer nonbinary coding schemes because of their better robustness to the codeword length and the modulation size. However, the problem of giving UEP properties with nonbinary LDPC codes is much more difficult than with binary LDPC codes. We present a first attempt to solve this difficult problem, based on LDPC codes built on finite groups. The framework and the basis about group LDPC codes are first presented in details, and the framework is used to give examples of UEP nonbinary LDPC codes that actually achieve different UEP properties at the bit level while the symbol error properties are kept equally protected.

We introduce a wide class of low-density parity-check (LDPC) codes, large enough to include LDPC codes over finite fields, rings, or groups, as well as some nonlinear codes. A belief-propagation decoding procedure with the same complexity as for the decoding of LDPC codes over finite fields is also presented. Moreover, an encoding procedure is developed

A new scheme of detection for multiple access channel is investigated, which consists in the combining of PIC-like detection and joint decoding of LDPC codes. The joint decoding is first studied through the use of LDPC codes over Galois extensions of binary field for the AWGN multiple access channel. Then, a hierarchical MC-CDMA system which uses both parallel interference canceler and joint detection is implemented and simulations show that it can provide a substantial improvement without any complexity growth of the emitter in a MC-CDMA like up-link framework

In a paper entitled "Variation on Euclid's Algorithm for Plynomials", Calvez et al. has shown that the extended Euclid's algorithm can be partially obtained by the nonextended one; in fact, it can obtain only two of the three unknowns of the Bezout's theorem. This letter goes further and shows that all polynomials given by the extended Euclid's algorithm and all the intermediate values can be obtained directly by the nonextended Euclid's algorithm. Consequently, only remainder computations are used. Avoiding multiplications and divisions of polynomials decreases the computational complexity. This variation of Calvez et al. justifies the title of the present letter.

A Markovian model of the error probability density for decision feedback equalizer is proposed and its application to the error propagation probability computation is derived. The model is a generalization of the Lutkemeyer and Noll (see ICC, Porto Carras, Greece, June 1998). It is obtained by the analysis of the Gaussian mixture distribution of the errors which follows a Markov process. The analysis of this process shows that the error propagation probability of the weighted DFE is less than the one of the classical DFE.