Miracle-dz/UniFAR-FTUs huggingface dataset:
Adaptive local minimax Galerkin methods for variational problems

In many applications of practical interest, solutions of partial differential equation models arise as critical points of an underlying (energy) functional. If such solutions are saddle points, rather than being maxima or minima, then the theoretical framework is non-standard, and the development of suitable numerical approximation procedures turns out to be highly challenging. In this paper, our aim is to present an iterative discretization methodology for the numerical solution of nonlinear variational problems with multiple (saddle point) solutions. In contrast to traditional numerical approximation schemes, which typically fail in such situations, the key idea of the current work is to employ a simultaneous interplay of a previously developed local minimax approach and adaptive Galerkin discretizations. We thereby derive an adaptive local minimax Galerkin (LMMG) method, which combines the search for saddle point solutions and their approximation in finite-dimensional spaces in a highly effective way. Under certain assumptions, we will prove that the generated sequence of approximate solutions converges to the solution set of the variational problem. This general framework will be applied to the specific context of finite element discretizations of (singularly perturbed) semilinear elliptic boundary value problems, and a series of numerical experiments will be presented.
Fuzzy Tiling Activations: A Simple Approach to Learning Sparse Representations Online

Recent work has shown that sparse representations—where only a small percentage of units are active—can signiﬁcantly reduce interference. Those works, however, relied on relatively complex regularization or meta-learning approaches, that have only been used ofﬂine in a pre-training phase. In this work, we pursue a direction that achieves sparsity by design, rather than by learning. Speciﬁcally, we design an activation function that produces sparse representations deterministically by construction, and so is more amenable to online training. The idea relies on the simple approach of binning, but overcomes the two key limitations of binning: zero gradients for the ﬂat regions almost everywhere, and lost precision—reduced discrimination—due to coarse aggregation. We introduce a Fuzzy Tiling Activation (FTA) that provides non-negligible gradients and produces overlap between bins that improves discrimination. We ﬁrst show that FTA is robust under covariate shift in a synthetic online supervised learning problem, where we can vary the level of correlation and drift. Then we move to the deep reinforcement learning setting and investigate both value-based and policy gradient algorithms that use neural networks with FTAs, in classic discrete control and Mujoco continuous control environments. We show that algorithms equipped with FTAs are able to learn a stable policy faster without needing target networks on most domains. 1
R-process enrichment in ultrafaint dwarf galaxies

We study the enrichment and mixing of r-process elements in ultrafaint dwarf galaxies (UFDs). We assume that r-process elements are produced by neutron-star mergers (NSMs), and examine multiple models with different natal kick velocities and explosion energies. To this end, we perform cosmological simulations of galaxy formation to follow mixing of the dispersed r-process elements driven by star formation and the associated stellar feedback in progenitors of UFDs. We show that the observed europium abundance in Reticulum II is reproduced by our inner explosion model where an NSM is triggered at the centre of the galaxy, whereas the relatively low abundance in Tucana III is reproduced if an NSM occurs near the virial radius of the progenitor galaxy. The latter case is realized only if the neutron-star binary has a large natal kick velocity and travels over a long distance of a kiloparsec before merger. In both the inner and outer explosion cases, it is necessary for the progenitor galaxy to sustain prolonged star formation over a few hundred million years after the NSM, so that the dispersed r-process elements are well mixed within the interstellar medium. Short-duration star formation results in inefficient mixing, and then a large variation is imprinted in the stellar europium abundances, which is inconsistent with the observations of Reticulum II and Tucana III.
BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learning

Ensembles, where multiple neural networks are trained individually and their predictions are averaged, have been shown to be widely successful for improving both the accuracy and predictive uncertainty of single neural networks. However, an ensemble's cost for both training and testing increases linearly with the number of networks, which quickly becomes untenable. In this paper, we propose BatchEnsemble, an ensemble method whose computational and memory costs are significantly lower than typical ensembles. BatchEnsemble achieves this by defining each weight matrix to be the Hadamard product of a shared weight among all ensemble members and a rank-one matrix per member. Unlike ensembles, BatchEnsemble is not only parallelizable across devices, where one device trains one member, but also parallelizable within a device, where multiple ensemble members are updated simultaneously for a given mini-batch. Across CIFAR-10, CIFAR-100, WMT14 EN-DE/EN-FR translation, and out-of-distribution tasks, BatchEnsemble yields competitive accuracy and uncertainties as typical ensembles; the speedup at test time is 3X and memory reduction is 3X at an ensemble of size 4. We also apply BatchEnsemble to lifelong learning, where on Split-CIFAR-100, BatchEnsemble yields comparable performance to progressive neural networks while having a much lower computational and memory costs. We further show that BatchEnsemble can easily scale up to lifelong learning on Split-ImageNet which involves 100 sequential learning tasks.
What is Trending on Wikipedia? Capturing Trends and Language Biases Across Wikipedia Editions

In this work, we propose an automatic evaluation and comparison of the browsing behavior of Wikipedia readers that can be applied to any language editions of Wikipedia. As an example, we focus on English, French, and Russian languages during the last four months of 2018. The proposed method has three steps. Firstly, it extracts the most trending articles over a chosen period of time. Secondly, it performs a semi-supervised topic extraction and thirdly, it compares topics across languages. The automated processing works with the data that combines Wikipedia’s graph of hyperlinks, pageview statistics and summaries of the pages. The results show that people share a common interest and curiosity for entertainment, e.g. movies, music, sports independently of their language. Differences appear in topics related to local events or about cultural particularities. Interactive visualizations showing clusters of trending pages in each language edition are available online https://wiki-insights.epfl. ch/wikitrendshttps://wiki-insights.epfl. ch/wikitrends
Linear System Identification Under Multiplicative Noise from Multiple Trajectory Data

The study of multiplicative noise models has a long history in control theory but is re-emerging in the context of complex networked systems and systems with learning-based control. We consider linear system identification with multiplicative noise from multiple state-input trajectory data. We propose exploratory input signals along with a least-squares algorithm to simultaneously estimate nominal system parameters and multiplicative noise covariance matrices. The asymptotic consistency of the least-squares estimator is demonstrated by analyzing first and second moment dynamics of the system. The results are illustrated by numerical simulations.
Learning Group Structure and Disentangled Representations of Dynamical Environments

Discovering the underlying structure of a dynamical environment involves learning representations that are interpretable and disentangled, which is a challenging task. In physics, interpretable representations of our universe and its underlying dynamics are formulated in terms of representations of groups of symmetry transformations. We propose a physics-inspired method, built upon the theory of group representation, that learns a representation of an environment structured around the transformations that generate its evolution. Experimentally, we learn the structure of explicitly symmetric environments without supervision while ensuring the interpretability of the representations. We show that the learned representations allow for accurate long-horizon predictions and further demonstrate a correlation between the quality of predictions and disentanglement in the latent space.
Performative Prediction

When predictions support decisions they may influence the outcome they aim to predict. We call such predictions performative; the prediction influences the target. Performativity is a well-studied phenomenon in policy-making that has so far been neglected in supervised learning. When ignored, performativity surfaces as undesirable distribution shift, routinely addressed with retraining. We develop a risk minimization framework for performative prediction bringing together concepts from statistics, game theory, and causality. A conceptual novelty is an equilibrium notion we call performative stability. Performative stability implies that the predictions are calibrated not against past outcomes, but against the future outcomes that manifest from acting on the prediction. Our main results are necessary and sufficient conditions for the convergence of retraining to a performatively stable point of nearly minimal loss. In full generality, performative prediction strictly subsumes the setting known as strategic classification. We thus also give the first sufficient conditions for retraining to overcome strategic feedback effects.
Symplectic Coarse-Grained Classical and Semi-Classical Evolution of Subsystems: New Theoretical Aspects

We study the classical and semiclassical time evolutions of subsystems of a Hamiltonian system; this is done using a generalization of Heller's thawed Gaussian approximation introduced by Littlejohn. The key tool in our study is an extension of Gromov's "principle of the symplectic camel" obtained in collaboration with N. Dias and J. Prata. This extension says that the orthogonal projection of a symplectic phase space ball on a phase space with a smaller dimension also contains a symplectic ball with the same radius. In the quantum case, the radii of these symplectic balls are taken equal to sqrt(h_bar) and represent ellipsoids of minimum uncertainty, which we have called "quantum blobs" in previous work.
Reducing the H0 tension with generalized Proca theory

We investigate the cosmological viability of the generalized proca theory. We first implement the background and linear perturbation equations of motion in the Boltzmann code and then study the constraints on the parameters of the generalized proca theory after running MCMC against the cosmological data set. With Planck + HST data, we obtain the constraint h=0.7334−0.0269+0.0246, which indicates that the tension between early universe and late time universe within this theory is removed. By adding other late-time data sets (BAO, RSD, etc.) we show that the tension is reduced, as the 2σ allowed region for h in Proca, h=0.7041−0.0087+0.0094, overlaps with the 2σ region of the HST data.
The life cycle of the Central Molecular Zone - II. Distribution of atomic and molecular gas tracers.

We use the hydrodynamical simulation of our inner Galaxy presented in Armillotta et al. to study the gas distribution and kinematics within the Central Molecular Zone (CMZ). We use a resolution high enough to capture the gas emitting in dense molecular tracers such as NH3 and HCN, and simulate a time window of 50 Myr, long enough to capture phases during which the CMZ experiences both quiescent and intense star formation. We then post-process the simulated CMZ to calculate its spatially dependent chemical and thermal state, producing synthetic emission data cubes and maps of both H i and the molecular gas tracers CO, NH3, and HCN. We show that, as viewed from Earth, gas in the CMZ is distributed mainly in two parallel and elongated features extending from positive longitudes and velocities to negative longitudes and velocities. The molecular gas emission within these two streams is not uniform, and it is mostly associated with the region where gas flowing towards the Galactic Centre through the dust lanes collides with gas orbiting within the ring. Our simulated data cubes reproduce a number of features found in the observed CMZ. However, some discrepancies emerge when we use our results to interpret the position of individual molecular clouds. Finally, we show that, when the CMZ is near a period of intense star formation, the ring is mostly fragmented as a consequence of supernova feedback, and the bulk of the emission comes from star-forming molecular clouds. This correlation between morphology and star formation rate should be detectable in observations of extragalactic CMZs.
Velocity Gradient in the Presence of Self-gravity: Identifying Gravity-induced Inflow and Determining Collapsing Stage

Understanding how star formation is regulated requires studying the energy balance between turbulence, magnetic fields, stellar feedback, and gravity within molecular clouds. However, identifying the transition region where the gravity takes over remains elusive. Recent studies of the Velocity Gradient Technique (VGT), which is an advanced tool for magnetic field studies, reveal that the gradients of spectroscopic observables change their directions by 90° with respect to the magnetic fields in the regions of gravitational collapse. In this study, we perform 3D MHD numerical simulations. We observe that star formation successfully proceeds in strongly magnetized and fully ionized media. We confirm that the self-gravity induces the change of gradients’ orientation and gradients’ high amplitude. We explore two ways of identifying collapsing self-gravitating regions through the double-peak feature in the histogram of gradients’ orientation and the curvature of gradients. We show that velocity gradients’ morphology and amplitude can be synthetically used to trace the convergent inflows. By comparing with the column density Probability Density Functions method, we show that VGT is a powerful new tool for studying the gas dynamics and tracing magnetic field in star-forming regions. By analogy with VGT, we extend the Intensity Gradient Technique (IGT) to locate the gravitational collapsing region and shocks. We demonstrate that the synergy of VGT and IGT can determine the collapsing stages in a star-forming region.
A mean-field analysis of two-player zero-sum games

Finding Nash equilibria in two-player zero-sum continuous games is a central problem in machine learning, e.g. for training both GANs and robust models. The existence of pure Nash equilibria requires strong conditions which are not typically met in practice. Mixed Nash equilibria exist in greater generality and may be found using mirror descent. Yet this approach does not scale to high dimensions. To address this limitation, we parametrize mixed strategies as mixtures of particles, whose positions and weights are updated using gradient descent-ascent. We study this dynamics as an interacting gradient flow over measure spaces endowed with the Wasserstein-Fisher-Rao metric. We establish global convergence to an approximate equilibrium for the related Langevin gradient-ascent dynamic. We prove a law of large numbers that relates particle dynamics to mean-field dynamics. Our method identifies mixed equilibria in high dimensions and is demonstrably effective for training mixtures of GANs.
Extension of $\delta_{-}ziti$ method in the unit ball: Numerical integration, resolution of Poisson's problem and Heat transfer

Inspired by the Galerkin and particular method, a new approximation approach is recalled in the Cartesian case. In this paper, we are interested specially by constructing this method, when the domain of consideration is a two dimensional ball, to extend this work to the several dimension. We reduce the number of iterations to calculate integrals and numerical solution of Poisson and the Heat problems (elliptic nd parabolic PDEs), in a very fast way.
Query-Efficient Physical Hard-Label Attacks on Deep Learning Visual Classification

We present Survival-OPT, a physical adversarial example algorithm in the black-box hard-label setting where the attacker only has access to the model prediction class label. Assuming such limited access to the model is more relevant for settings such as proprietary cyber-physical and cloud systems than the whitebox setting assumed by prior work. By leveraging the properties of physical attacks, we create a novel approach based on the survivability of perturbations corresponding to physical transformations. Through simply querying the model for hard-label predictions, we optimize perturbations to survive in many different physical conditions and show that adversarial examples remain a security risk to cyber-physical systems (CPSs) even in the hard-label threat model. We show that Survival-OPT is query-efficient and robust: using fewer than 200K queries, we successfully attack a stop sign to be misclassified as a speed limit 30 km/hr sign in 98.5% of video frames in a drive-by setting. Survival-OPT also outperforms our baseline combination of existing hard-label and physical approaches, which required over 10x more queries for less robust results.
Spectrum Translation for Cross-Spectral Ocular Matching

Cross-spectral verification remains a big issue in biometrics, especially for the ocular area due to differences in the reflected features in the images depending on the region and spectrum used. In this paper, we investigate the use of Conditional Adversarial Networks for spectrum translation between near infra-red and visual light images for ocular biometrics. We analyze the transformation based on the overall visual quality of the transformed images and the accuracy drop of the identification system when trained with opposing data. We use the PolyU database and propose two different systems for biometric verification, the first one based on Siamese Networks trained with Softmax and Cross-Entropy loss, and the second one a Triplet Loss network. We achieved an EER of 1\% when using a Triplet Loss network trained for NIR and finding the Euclidean distance between the real NIR images and the fake ones translated from the visible spectrum. We also outperform previous results using baseline algorithms.
On the Feasibility of Sybil Attacks in Shard-Based Permissionless Blockchains

Bitcoin's single leader consensus protocol (Nakamoto consensus) suffers from significant transaction throughput and network scalability issues due to the computational requirements of it Proof-of-Work (PoW) based leader selection strategy. To overcome this, committee-based approaches (e.g., Elastico) that partition the outstanding transaction set into shards and (randomly) select multiple committees to process these transactions in parallel have been proposed and have become very popular. However, by design these committee or shard-based blockchain solutions are easily vulnerable to the Sybil attacks, where an adversary can easily compromise/manipulate the consensus protocol if it has enough computational power to generate multiple Sybil committee members (by generating multiple valid node identifiers). Despite the straightforward nature of these attacks, they have not been systematically analyzed. In this paper, we fill this research gap by modelling and analyzing Sybil attacks in a representative and popular shard-based protocol called Elastico. We show that the PoW technique used for identifier or ID generation in the initial phase of the protocol is vulnerable to Sybil attacks, and a node with high hash-power can generate enough Sybil IDs to successfully compromise Elastico. We analytically derive conditions for two different categories of Sybil attacks and perform numerical simulations to validate our theoretical results under different network and protocol parameters.
Helly groups.

Helly graphs are graphs in which every family of pairwise intersecting balls has a non-empty intersection. This is a classical and widely studied class of graphs. In this article we focus on groups acting geometrically on Helly graphs -- Helly groups. We provide numerous examples of such groups: all (Gromov) hyperbolic, CAT(0) cubical, finitely presented graphical C(4)$-$T(4) small cancellation groups, and type-preserving uniform lattices in Euclidean buildings of type $C_n$ are Helly; free products of Helly groups with amalgamation over finite subgroups, graph products of Helly groups, some diagram products of Helly groups, some right-angled graphs of Helly groups, and quotients of Helly groups by finite normal subgroups are Helly. We show many properties of Helly groups: biautomaticity, existence of finite dimensional models for classifying spaces for proper actions, contractibility of asymptotic cones, existence of EZ-boundaries, satisfiability of the Farrell-Jones conjecture and of the coarse Baum-Connes conjecture. This leads to new results for some classical families of groups (e.g. for FC-type Artin groups) and to a unified approach to results obtained earlier.
On the order of magnitude of Sudler products

abstract:Given an irrational number $\alpha\in(0,1)$, the Sudler product is defined by $P_N(\alpha) = \prod_{r=1}^{N}2|\sin\pi r\alpha|$. Answering a question of Grepstad, Kaltenb\"ock and Neum\"uller we prove an asymptotic formula for distorted Sudler products when $\alpha$ is the golden ratio $(\sqrt{5}+1)/2$ and establish that in this case $\limsup_{N \to \infty} P_N(\alpha)/N < \infty$. We obtain similar results for quadratic irrationals $\alpha$ with continued fraction expansion $\alpha = [a,a,a,\ldots]$ for some integer $a \geq 1$, and give a full characterisation of the values of $a$ for which $\liminf_{N \to \infty} P_N(\alpha)>0$ and $\limsup_{N \to \infty} P_N(\alpha) / N < \infty$ hold, respectively. We establish that there is a (sharp) transition point at $a=6$, and resolve as a by-product a problem of the first author, Larcher, Pillichshammer, Saad Eddin, and Tichy.
Rapid prediction of earthquake ground shaking intensity using raw waveform data and a Convolutional Neural Network

This study describes a deep convolutional neural network (CNN) based technique to predict intensity measurements (IMs) of earthquake ground shaking. The input data to the CNN model consists of multistation, 3C acceleration waveforms recorded during the 2016 Central Italy earthquake sequence for M ≥ 3.0 events. Using a 10 s window starting at the earthquake origin time, we find that the CNN is capable of accurately predicting IMs at stations far from the epicentre which have not yet recorded the maximum ground shaking. The CNN IM predictions do not require previous knowledge of the earthquake source (location and magnitude). Comparison between the CNN model predictions and those obtained with the Bindi et al. GMPE (which requires location and magnitude) shows that the CNN model features similar error variance but smaller bias. Although the technique is not strictly designed for earthquake early warning, we find that it can provide useful estimates of ground motions within 15–20 s after earthquake origin time depending on various setup elements (e.g. times for data transmission, computation, latencies). The technique has been tested on raw data without any initial data pre-selection in order to closely replicate real-time data streaming. When noise examples were included with the earthquake data the CNN was found to be stable, accurately predicting the ground shaking intensity corresponding to the noise amplitude.