We introduce a new adaptive step-size strategy for convex optimization with stochastic gradient that exploits the local geometry of the objective function only by means of a first-order stochastic oracle and without any hyper-parameter tuning. The method comes from a theoretically-grounded adaptation of the Adaptive Gradient Descent Without Descent method to the stochastic setting. We prove the convergence of stochastic gradient descent with our step-size under various assumptions, and we show that it empirically competes against tuned baselines.

We consider the problem of sampling distributions stemming from non-convex potentials with Unadjusted Langevin Algorithm (ULA). We prove the stability of the discrete-time ULA to drift approximations under the assumption that the potential is strongly convex at infinity. In many context, e.g. imaging inverse problems, potentials are non-convex and non-smooth. Proximal Stochastic Gradient Langevin Algorithm (PSGLA) is a popular algorithm to handle such potentials. It combines the forward-backward optimization algorithm with a ULA step. Our main stability result combined with properties of the Moreau envelope allows us to derive the first proof of convergence of the PSGLA for non-convex potentials. We empirically validate our methodology on synthetic data and in the context of imaging inverse problems. In particular, we observe that PSGLA exhibits faster convergence rates than Stochastic Gradient Langevin Algorithm for posterior sampling while preserving its restoration properties.

In this document, we present the main properties satisfied by the Moreau envelope of weakly convex functions. The Moreau envelope has been introduced in convex optimization to regularize convex functionals while preserving their global minimizers. However, the Moreau envelope is also defined for the more general class of weakly convex function and can be a useful tool for optimization in this context. The main properties of the Moreau envelope have been demonstrated for convex functions and are generalized to weakly convex function in various works. This document summarizes the vast literature on the properties of the Moreau envelope and provides the associated proofs.

Explainable AI (XAI) has become increasingly important with the rise of large transformer models, yet many explanation methods designed for CNNs transfer poorly to Vision Transformers (ViTs). Existing ViT explanations often rely on attention weights, which tend to yield noisy maps as they capture token-to-token interactions within each this http URL attribution methods incorporating MLP blocks have been proposed, we argue that attention remains a valuable and interpretable signal when properly filtered. We propose a method that combines attention maps with a statistical filtering, initially proposed for CNNs, to remove noisy or uninformative patterns and produce more faithful explanations. We further extend our approach with a class-specific variant that yields discriminative explanations. Evaluation against popular state-of-the-art methods demonstrates that our approach produces sharper and more interpretable maps. In addition to perturbation-based faithfulness metrics, we incorporate human gaze data to assess alignment with human perception, arguing that human interpretability remains essential for XAI. Across multiple datasets, our approach consistently outperforms or is comparable to the SOTA methods while remaining efficient and human plausible.

Fast convergence and high-quality image recovery are two essential features of algorithms for solving ill-posed imaging inverse problems. Existing methods, such as regularization by denoising (RED), often focus on designing sophisticated image priors to improve reconstruction quality, while leaving convergence acceleration to heuristics. To bridge the gap, we propose Restarted Inertia with Score-based Priors (RISP) as a principled extension of RED. RISP incorporates a restarting inertia for fast convergence, while still allowing score-based image priors for high-quality reconstruction. We prove that RISP attains a faster stationary-point convergence rate than RED, without requiring the convexity of the image prior. We further derive and analyze the associated continuous-time dynamical system, offering insight into the connection between RISP and the heavy-ball ordinary differential equation (ODE). Experiments across a range of imaging inverse problems demonstrate that RISP enables fast convergence while achieving high-quality reconstructions.

Superpixels are widely used in computer vision to simplify image representation and reduce computational complexity. While traditional methods rely on low-level features, deep learning-based approaches leverage high-level features but also tend to sacrifice regularity of superpixels to capture complex objects, leading to accurate but less interpretable segmentations. In this work, we introduce SPAM (SuperPixel Anything Model), a versatile framework for segmenting images into accurate yet regular superpixels. We train a model to extract image features for superpixel generation, and at inference, we leverage a large-scale pretrained model for semantic-agnostic segmentation to ensure that superpixels align with object masks. SPAM can handle any prior high-level segmentation, resolving uncertainty regions, and is able to interactively focus on specific objects. Comprehensive experiments demonstrate that SPAM qualitatively and quantitatively outperforms state-of-the-art methods on segmentation tasks, making it a valuable and robust tool for various applications. Code and pre-trained models are available here: this https URL.

Plug-and-Play methods constitute a class of iterative algorithms for imaging problems where regularization is performed by an off-the-shelf denoiser. Although Plug-and-Play methods can lead to tremendous visual performance for various image problems, the few existing convergence guarantees are based on unrealistic (or suboptimal) hypotheses on the denoiser, or limited to strongly convex data terms. In this work, we propose a new type of Plug-and-Play methods, based on half-quadratic splitting, for which the denoiser is realized as a gradient descent step on a functional parameterized by a deep neural network. Exploiting convergence results for proximal gradient descent algorithms in the non-convex setting, we show that the proposed Plug-and-Play algorithm is a convergent iterative scheme that targets stationary points of an explicit global functional. Besides, experiments show that it is possible to learn such a deep denoiser while not compromising the performance in comparison to other state-of-the-art deep denoisers used in Plug-and-Play schemes. We apply our proximal gradient algorithm to various ill-posed inverse problems, e.g. deblurring, super-resolution and inpainting. For all these applications, numerical results empirically confirm the convergence results. Experiments also show that this new algorithm reaches state-of-the-art performance, both quantitatively and qualitatively.

Machine learning and deep learning models have become essential in the recent fast development of artificial intelligence in many sectors of the society. It is now widely acknowledge that the development of these models has an environmental cost that has been analyzed in many studies. Several online and software tools have been developed to track energy consumption while training machine learning models. In this paper, we propose a comprehensive introduction and comparison of these tools for AI practitioners wishing to start estimating the environmental impact of their work. We review the specific vocabulary, the technical requirements for each tool. We compare the energy consumption estimated by each tool on two deep neural networks for image processing and on different types of servers. From these experiments, we provide some advice for better choosing the right tool and infrastructure.

The design of complex self-organising systems producing life-like phenomena, such as the open-ended evolution of virtual creatures, is one of the main goals of artificial life. Lenia, a family of cellular automata (CA) generalizing Conway's Game of Life to continuous space, time and states, has attracted a lot of attention because of the wide diversity of self-organizing patterns it can generate. Among those, some spatially localized patterns (SLPs) resemble life-like artificial creatures and display complex behaviors. However, those creatures are found in only a small subspace of the Lenia parameter space and are not trivial to discover, necessitating advanced search algorithms. Furthermore, each of these creatures exist only in worlds governed by specific update rules and thus cannot interact in the same one. This paper proposes as mass-conservative extension of Lenia, called Flow Lenia, that solve both of these issues. We present experiments demonstrating its effectiveness in generating SLPs with complex behaviors and show that the update rule parameters can be optimized to generate SLPs showing behaviors of interest. Finally, we show that Flow Lenia enables the integration of the parameters of the CA update rules within the CA dynamics, making them dynamic and localized, allowing for multi-species simulations, with locally coherent update rules that define properties of the emerging creatures, and that can be mixed with neighbouring rules. We argue that this paves the way for the intrinsic evolution of self-organized artificial life forms within continuous CAs.

Dynamic networks are a complex subject. Not only do they inherit the complexity of static networks (as a particular case); they are also sensitive to definitional subtleties that are a frequent source of confusion and incomparability of results in the literature. In this paper, we take a step back and examine three such aspects in more details, exploring their impact in a systematic way; namely, whether the temporal paths are required to be \emph{strict} (i.e., the times along a path must increasing, not just be non-decreasing), whether the time labeling is \emph{proper} (two adjacent edges cannot be present at the same time) and whether the time labeling is \emph{simple} (an edge can have only one presence time). In particular, we investigate how different combinations of these features impact the expressivity of the graph in terms of reachability. Our results imply a hierarchy of expressivity for the resulting settings, shedding light on the loss of generality that one is making when considering either combination. Some settings are more general than expected; in particular, proper temporal graphs turn out to be as expressive as general temporal graphs where non-strict paths are allowed. Also, we show that the simplest setting, that of \emph{happy} temporal graphs (i.e., both proper and simple) remains expressive enough to emulate the reachability of general temporal graphs in a certain (restricted but useful) sense. Furthermore, this setting is advocated as a target of choice for proving negative results. We illustrates this by strengthening two known results to happy graphs (namely, the inexistence of sparse spanners, and the hardness of computing temporal components). Overall, we hope that this article can be seen as a guide for choosing between different settings of temporal graphs, while being aware of the way these choices affect generality.

Complex organic molecules (COMs) are observed to be abundant in various astrophysical environments, in particular toward star forming regions they are observed both toward protostellar envelopes as well as shocked regions. Emission spectrum especially of heavier COMs may consists of up to hundreds of lines, where line blending hinders the analysis. However, identifying the molecular composition of the gas leading to the observed millimeter spectra is the first step toward a quantitative analysis. We develop a new method based on supervised machine learning to recognize spectroscopic features of the rotational spectrum of molecules in the 3mm atmospheric transmission band for a list of species including COMs with the aim to obtain a detection probability. We used local thermodynamic equilibrium (LTE) modeling to build a large set of synthetic spectra of 20 molecular species including COMs with a range of physical conditions typical for star forming regions. We successfully designed and trained a Convolutional Neural Network (CNN) that provides detection probabilities of individual species in the spectra. We demonstrate that the produced CNN-model has a robust performance to detect spectroscopic signatures from these species in synthetic spectra. We evaluate its ability to detect molecules according to the noise level, frequency coverage, and line-richness, and also test its performance for incomplete frequency coverage with high detection probabilities for the tested parameter space, and no false predictions. Ultimately, we apply the CNN-model to obtain predictions on observational data from the literature toward line-rich hot-core like sources, where detection probabilities remain reasonable with no false detection. We prove the use of CNNs facilitating the analysis of complex millimeter spectra both on synthetic spectra as well as first tests on observational data.

The science of Human-Computer Interaction (HCI) is populated by isolated empirical findings, often tied to specific technologies, designs, and tasks. This situation probably lies in observing the wrong object of study, that is to say, observing interfaces rather than interaction. This paper proposes an experimental methodology, powered by a research methodology, that enables tackling the ambition of observing interaction (rather than interfaces). These observations are done during the treatment of applicative cases, allowing to generate and replicate results covering various experimental conditions, expressed from the need of end users and the evolution of technologies. Performing these observations when developing applicative prototypes illustrating novel technologies' utility allows, in the same time, to benefit from an optimization of these prototypes to better accomplish end users tasks. This paper depicts a long term research direction, from generating the initial observations of interaction properties and their replication, to their integration, that would then lead to exploring the possible relations existing between those properties, to end toward the description of human-computer interaction's physics.

Recent JWST observations of the temperate sub-Neptune K2-18 b with NIRISS SOSS/NIRSpec G395H and MIRI LRS have yielded apparently inconsistent results: the MIRI spectra exhibit spectral features nearly twice as large as those seen at shorter wavelengths, challenging the high-metallicity, CH4-rich non-equilibrium model that fits the NIRISS/NIRSpec data. We perform a suite of atmospheric retrievals on both datasets, including free-chemistry, non-equilibrium, and aerosol models, using laboratory-derived complex refractive indices for a variety of photochemical haze analogues. Free retrievals systematically return lower metallicities than inferred by self-consistent chemical disequilibrium models, and the inclusion of absorbing aerosols, especially CH4-dominated, nitrogen-poor tholins, can further reduce the inferred metallicity by over an order of magnitude. These hazes reproduce the observed NIRISS slope through scattering and match MIRI features via C-H bending absorption near 7 um, while yielding particle properties consistent with photochemical production in H2-rich atmospheres. Although their inclusion improves the joint fit and reduces tension between datasets, it also significantly lowers the retrieved CH4 abundance, highlighting degeneracies between metallicity, composition, and aerosol properties. Our results underscore the importance of aerosol absorption in interpreting temperate sub-Neptune spectra, and motivate future JWST observations and laboratory work to break these degeneracies.

Seven rocky planets orbit the nearby dwarf star TRAPPIST-1, providing a unique opportunity to search for atmospheres on small planets outside the Solar System (Gillon et al., 2017). Thanks to the recent launch of JWST, possible atmospheric constituents such as carbon dioxide (CO2) are now detectable (Morley et al., 2017, Lincowski et al., 2018}. Recent JWST observations of the innermost planet TRAPPIST-1 b showed that it is most probably a bare rock without any CO2 in its atmosphere (Greene et al., 2023). Here we report the detection of thermal emission from the dayside of TRAPPIST-1 c with the Mid-Infrared Instrument (MIRI) on JWST at 15 micron. We measure a planet-to-star flux ratio of fp/fs = 421 +/- 94 parts per million (ppm) which corresponds to an inferred dayside brightness temperature of 380 +/- 31 K. This high dayside temperature disfavours a thick, CO2-rich atmosphere on the planet. The data rule out cloud-free O2/CO2 mixtures with surface pressures ranging from 10 bar (with 10 ppm CO2) to 0.1 bar (pure CO2). A Venus-analogue atmosphere with sulfuric acid clouds is also disfavoured at 2.6 sigma confidence. Thinner atmospheres or bare-rock surfaces are consistent with our measured planet-to-star flux ratio. The absence of a thick, CO2-rich atmosphere on TRAPPIST-1 c suggests a relatively volatile-poor formation history, with less than 9.5 +7.5 -2.3 Earth oceans of water. If all planets in the system formed in the same way, this would indicate a limited reservoir of volatiles for the potentially habitable planets in the system.

Hydrodynamic interactions can give rise to a collective motion of rotating particles. This, in turn, can lead to coherent fluid flows. Using large scale hydrodynamic simulations, we study the coupling between these two in spinner monolayers at weakly inertial regime. We observe an instability, where the initially uniform particle layer separates into particle void and particle rich areas. The particle void region corresponds to a fluid vortex, and it is driven by a surrounding spinner edge current. We show that the instability originates from a hydrodynamic lift force between the particle and fluid flows. The cavitation can be tuned by the strength of the collective flows. It is suppressed when the spinners are confined by a no-slip surface, and multiple cavity and oscillating cavity states are observed when the particle concentration is reduced.

Most superpixel algorithms compute a trade-off between spatial and color features at the pixel level. Hence, they may need fine parameter tuning to balance the two measures, and highly fail to group pixels with similar local texture properties. In this paper, we address these issues with a new Texture-Aware SuperPixel (TASP) method. To accurately segment textured and smooth areas, TASP automatically adjusts its spatial constraint according to the local feature variance. Then, to ensure texture homogeneity within superpixels, a new pixel to superpixel patch-based distance is proposed. TASP outperforms the segmentation accuracy of the state-of-the-art methods on texture and also natural color image datasets.

Analysing biological spiking neural network models with synaptic plasticity has proven to be challenging both theoretically and numerically. In a network with N all-to-all connected neurons, the number of synaptic connections is on the order of $N^2$, making these models computationally demanding. Furthermore, the intricate coupling between neuron and synapse dynamics, along with the heterogeneity generated by plasticity, hinder the use of classic theoretical tools such as mean-field or slow-fast analyses. To address these challenges, we introduce a new variable which we term a typical neuron X. Viewed as a post-synaptic neuron, X is composed of the activity state V , the time since its last spike S, and the empirical distribution $\xi$ of the triplet V , S and W (incoming weight) associated to the pre-synaptic neurons. In particular, we study a stochastic spike-timing-dependent plasticity (STDP) model of connection in a probabilistic Wilson-Cowan spiking neural network model, which features binary neural activity. Taking the large N limit, we obtain from the empirical distribution of the typical neuron a simplified yet accurate representation of the original spiking network. This mean-field limit is a piecewise deterministic Markov process (PDMP) of McKean-Vlasov type, where the typical neuron dynamics depends on its own distribution. We term this analysis McKean-Vlasov mean-field (MKV-MF). Our approach not only reduces computational complexity but also provides insights into the dynamics of this spiking neural network with plasticity. The model obtained is mathematically exact and capable of tracking transient changes. This analysis marks the first exploration of MKV-MF dynamics in a network of spiking neurons interacting with STDP.

The different spatial distributions of N-bearing and O-bearing species, as is well known towards Orion~KL, is one of the long-lasting mysteries. We conducted a survey observation and chemical modeling study to investigate if the different distributions of O- and N-bearing species are widely recognized in general star-forming regions. First, we report our observational results of complex organic molecules (COMs) with the 45~m radio telescope at the Nobeyama Radio Observatory towards eight star-forming regions. Through our spectral survey ranging from 80 to 108~GHz, we detected CH$_3$OH, HCOOCH$_3$, CH$_3$OCH$_3$, (CH$_3$)$_2$CO, CH$_3$CHO, CH$_3$CH$_2$CN, CH$_2$CHCN, and NH$_2$CHO. Their molecular abundances were derived via the rotation diagram and the least squares methods. We found that N-bearing molecules, tend to show stronger correlations with other N-bearing molecules rather than O-bearing molecules. While G10.47+0.03 showed high fractional abundances of N-bearing species, those in NGC6334F were not so rich, being less than 0.01 compared to CH$_3$OH. Then, the molecular abundances towards these sources were evaluated by chemical modeling with NAUTILUS three-phase gas-grain chemical code. Through the simulations of time evolutions for the abundances of COMs, we suggest that observed correlations of fractional abundances between COMs can be explained by the combination of the different temperature structures inside the hot cores and the different evolutionary phase. Since our modeling could not fully explain the observed excitation temperatures, it is important to investigate the efficiency of grain surface reactions and their activation barriers, and the binding energy of COMs to further promote our understanding.

We propose a physics-informed machine learning framework called P-DivGNN to reconstruct local stress fields at the micro-scale, in the context of multi-scale simulation given a periodic micro-structure mesh and mean, macro-scale, stress values. This method is based in representing a periodic micro-structure as a graph, combined with a message passing graph neural network. We are able to retrieve local stress field distributions, providing average stress values produced by a mean field reduced order model (ROM) or Finite Element (FE) simulation at the macro-scale. The prediction of local stress fields are of utmost importance considering fracture analysis or the definition of local fatigue criteria. Our model incorporates physical constraints during training to constraint local stress field equilibrium state and employs a periodic graph representation to enforce periodic boundary conditions. The benefits of the proposed physics-informed GNN are evaluated considering linear and non linear hyperelastic responses applied to varying geometries. In the non-linear hyperelastic case, the proposed method achieves significant computational speed-ups compared to FE simulation, making it particularly attractive for large-scale applications.

Over the years, the use of superpixel segmentation has become very popular in various applications, serving as a preprocessing step to reduce data size by adapting to the content of the image, regardless of its semantic content. While the superpixel segmentation of standard planar images, captured with a 90° field of view, has been extensively studied, there has been limited focus on dedicated methods to omnidirectional or spherical images, captured with a 360° field of view. In this study, we introduce the first deep learning-based superpixel segmentation approach tailored for omnidirectional images called DSS (for Deep Spherical Superpixels). Our methodology leverages on spherical CNN architectures and the differentiable K-means clustering paradigm for superpixels, to generate superpixels that follow the spherical geometry. Additionally, we propose to use data augmentation techniques specifically designed for 360° images, enabling our model to efficiently learn from a limited set of annotated omnidirectional data. Our extensive validation across two datasets demonstrates that taking into account the inherent circular geometry of such images into our framework improves the segmentation performance over traditional and deep learning-based superpixel methods. Our code is available online.