Miracle-dz/UniFAR-FTUs huggingface dataset:
Optimal Feedback Law Recovery by Gradient-Augmented Sparse Polynomial Regression

A sparse regression approach for the computation of high-dimensional optimal feedback laws arising in deterministic nonlinear control is proposed. The approach exploits the control-theoretical link between Hamilton-Jacobi-Bellman PDEs characterizing the value function of the optimal control problems, and ﬁrst-order optimality conditions via Pontryagin’s Maximum Principle. The latter is used as a representation formula to recover the value function and its gradient at arbitrary points in the space-time domain through the solution of a two-point boundary value problem. After generating a dataset consisting of diﬀerent state-value pairs, a hyperbolic cross polynomial model for the value function is ﬁtted using a LASSO regression. An extended set of low and high-dimensional numerical tests in nonlinear optimal control reveal that enriching the dataset with gradient information reduces the number of training samples, and that the sparse polynomial regression consistently yields a feedback law of lower complexity
Informer: Transformer Likes Informed Attention

Transformer is the backbone of modern NLP models. In this paper, we propose Informer , a simple architecture that signiﬁcantly outperforms canonical Transformers on a spectrum of tasks including Masked Language Modeling, GLUE, and SQuAD. Qualitatively, In-former is easy to implement and requires minimal hyper-parameter tuning. It also stabilizes training and leads to models with sparser at-tentions. Code will be open-sourced upon paper acceptance.
Influencers and the Giant Component: the Fundamental Hardness in Privacy Protection for Socially Contagious Attributes

The presence of correlation is known to make privacy protection more difficult. We investigate the privacy of socially contagious attributes on a network of individuals, where each individual possessing that attribute may influence a number of others into adopting it. We show that for contagions following the Independent Cascade model there exists a giant connected component of infected nodes, containing a constant fraction of all the nodes who all receive the contagion from the same set of sources. We further show that it is extremely hard to hide the existence of this giant connected component if we want to obtain an estimate of the activated users at an acceptable level. Moreover, an adversary possessing this knowledge can predict the real status ("active"or"inactive") with decent probability for many of the individuals regardless of the privacy (perturbation) mechanism used. As a case study, we show that the Wasserstein mechanism, a state-of-the-art privacy mechanism designed specifically for correlated data, introduces a noise with magnitude of order $\Omega(n)$ in the count estimation in our setting. We provide theoretical guarantees for two classes of random networks: Erdos Renyi graphs and Chung-Lu power-law graphs under the Independent Cascade model. Experiments demonstrate that a giant connected component of infected nodes can and does appear in real-world networks and that a simple inference attack can reveal the status of a good fraction of nodes.
The Effect of Nudging Personal and Injunctive Norms on the Trade-Off Between Objective Equality and Efficiency

We report three pre-registered studies (total N=1,799) exploring the effect of nudging personal and injunctive norms in decisions that involve a trade-off between objective equality and efficiency. The first two studies provide evidence that: (i) nudging the personal norm has a similar effect to nudging the injunctive norm; (ii) when both norms are nudged towards the same direction, there is no additive effect; (iii) when the personal norm and the injunctive norm are nudged towards opposite directions, some people tend to follow the personal norm, while others tend to follow the injunctive norm. Study 3 tests whether these two classes of people, those who tend to follow the injunctive norm and those who tend to follow the personal norm, map onto the two sub-dimensions of Aquino and Reed’s moral identity scale. We find partial evidence of this hypothesis: people higher in the symbolisation dimension are weakly more likely to follow the injunctive norm; however, we do not find any evidence that people higher in the internalisation dimension are more likely to follow the personal norm.
A Distributional Approach to Controlled Text Generation

We propose a Distributional Approach for addressing Controlled Text Generation from pre-trained Language Models (LMs). This approach permits to specify, in a single formal framework, both “pointwise” and “distributional” constraints over the target LM — to our knowledge, the first model with such generality — while minimizing KL divergence from the initial LM distribution. The optimal target distribution is then uniquely determined as an explicit EBM (Energy-Based Model) representation. From that optimal representation we then train a target controlled Autoregressive LM through an adaptive distributional variant of Policy Gradient. We conduct a first set of experiments over pointwise constraints showing the advantages of our approach over a set of baselines, in terms of obtaining a controlled LM balancing constraint satisfaction with divergence from the initial LM. We then perform experiments over distributional constraints, a unique feature of our approach, demonstrating its potential as a remedy to the problem of Bias in Language Models. Through an ablation study, we show the effectiveness of our adaptive technique for obtaining faster convergence.1
Image Captioning as an Assistive Technology: Lessons Learned from VizWiz 2020 Challenge

Image captioning has recently demonstrated impressive progress largely owing to the introduction of neural network algorithms trained on curated dataset like MS-COCO. Often work in this field is motivated by the promise of deployment of captioning systems in practical applications. However, the scarcity of data and contexts in many competition datasets renders the utility of systems trained on these datasets limited as an assistive technology in real-world settings, such as helping visually impaired people navigate and accomplish everyday tasks. This gap motivated the introduction of the novel VizWiz dataset, which consists of images taken by the visually impaired and captions that have useful, task-oriented information. In an attempt to help the machine learning computer vision field realize its promise of producing technologies that have positive social impact, the curators of the VizWiz dataset host several competitions, including one for image captioning. This work details the theory and engineering from our winning submission to the 2020 captioning competition. Our work provides a step towards improved assistive image captioning systems. This article appears in the special track on AI & Society.
Non simple blow ups for the Nirenberg problem on half spheres

<p style='text-indent:20px;'>In this paper we study a Nirenberg type problem on standard half spheres <inline-formula><tex-math id="M1">\begin{document}$ (\mathbb{S}^n_+,g_0) $\end{document}</tex-math></inline-formula> consisting of finding conformal metrics of prescribed scalar curvature and zero boundary mean curvature. This problem amounts to solve the following boundary value problem involving the critical Sobolev exponent:</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} (\mathcal{P}) \quad \begin{cases} - \Delta_{g_0} u \, + \, \frac{n(n-2)}{4} u \, = K \, u^{\frac{n+2}{n-2}},\, u > 0 \quad \mbox{in } \mathbb{S}^n_+, \\ \frac{\partial u}{\partial \nu }\, = \, 0 \quad \mbox{on } \partial \mathbb{S}^n_+, \end{cases} \end{equation*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M2">\begin{document}$ K \in C^3(\mathbb{S}^n_+) $\end{document}</tex-math></inline-formula> is a positive function. We construct, under generic conditions on the function <inline-formula><tex-math id="M3">\begin{document}$ K $\end{document}</tex-math></inline-formula>, finite energy solutions of a subcritical approximation of <inline-formula><tex-math id="M4">\begin{document}$ (\mathcal{P}) $\end{document}</tex-math></inline-formula> on half spheres of dimension <inline-formula><tex-math id="M5">\begin{document}$ n \geq 5 $\end{document}</tex-math></inline-formula>, which exhibit multiple blow up of <i>cluster-type</i> at the same boundary point. These solutions may have zero or non zero weak limit and may develop clusters at different boundary points. Such a blow up phenomena on half spheres drastically contrast with the case of the Nirenberg problem on spheres, where non simple blow up for finite energy solutions cannot occur and unveils an unexpected connection with vortex type problems arising in Euler equations in fluid dynamic and mean fields type equations in mathematical physics. We construct also, under suitable conditions on the restriction of <inline-formula><tex-math id="M6">\begin{document}$ K $\end{document}</tex-math></inline-formula> on <inline-formula><tex-math id="M7">\begin{document}$ \partial \mathbb{S}^n_+ $\end{document}</tex-math></inline-formula>, approximate solutions of arbitrarily large energy and Morse index. </p>
Velocity-dependent interacting dark energy and dark matter with a Lagrangian description of perfect fluids

We consider a cosmological scenario where the dark sector is described by two perfect fluids that interact through a velocity-dependent coupling. This coupling gives rise to an interaction in the dark sector driven by the relative velocity of the components, thus making the background evolution oblivious to the interaction and only the perturbed Euler equations are affected at first order. We obtain the equations governing this system with the Schutz-Sorkin Lagrangian formulation for perfect fluids and derive the corresponding stability conditions to avoid ghosts and Laplacian instabilities. As a particular example, we study a model where dark energy behaves as a radiation fluid at high redshift while it effectively becomes a cosmological constant in the late Universe. Within this scenario, we show that the interaction of both dark components leads to a suppression of the dark matter clustering at late times. We also argue the possibility that this suppression of clustering together with the additional dark radiation at early times can simultaneously alleviate the σ8 and H0 tensions.
Nonparametric Bayesian inference for reversible multi-dimensional diffusions

We study nonparametric Bayesian models for reversible multidimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem for the drift gradient vector field under approximation-theoretic conditions on the induced prior for the invariant measure. The general theorem is applied to Gaussian priors and p -exponential priors, which are shown to converge to the truth at the optimal nonparametric rate over Sobolev smoothness classes in any dimension.
Non-autoregressive electron flow generation for reaction prediction

Reaction prediction is a fundamental problem in computational chemistry. Existing approaches typically generate a chemical reaction by sampling tokens or graph edits sequentially, conditioning on previously generated outputs. These autoregressive generating methods impose an arbitrary ordering of outputs and prevent parallel decoding during inference. We devise a novel decoder that avoids such sequential generating and predicts the reaction in a Non-Autoregressive manner. Inspired by physical-chemistry insights, we represent edge edits in a molecule graph as electron flows, which can then be predicted in parallel. To capture the uncertainty of reactions, we introduce latent variables to generate multi-modal outputs. Following previous works, we evaluate our model on USPTO MIT dataset. Our model achieves both an order of magnitude lower inference latency, with state-of-the-art top-1 accuracy and comparable performance on Top-K sampling.
On the scaling relations of bulges and early-type galaxies

Following from our recent work, we present here a detailed structural analysis of a representative sample of nearby spiral and early-type galaxies (ETGs) taken from the Key Insights on Nearby Galaxies: a Far-Infrared Survey with Herschel/ (KINGFISH) / Spitzer Infrared Nearby Galaxies Survey (SINGS) surveys. The photometric parameters of bulges are obtained from bulge-disc decompositions using Galfi data analysis algorithm. The method and corrections for projection and dust effects previously obtained are used to derive intrinsic photometric and structural bulge parameters. We show the main bulge scaling relations and the black hole relations, both observed and intrinsic ones, in B band. We find dust and inclination effects to produce more important changes in the parameters of the Kormendy relation for spiral galaxies, with the respective bulges of late-type galaxies (LTGs) residing on a steeper slope relation than the early-type galaxies (ETGs). We observe that the Kormendy relation in combination with a bulge Sérsic index (nb) threshold does not produce a conclusive morphological separation of bulges. The nb- bulge-to-total flux ratio (B/T) and B/T-stellar mass could be used to discriminate between LTGs and ETGs, while a further use of these parameters to divide bulges with different morphologies is problematic due to overlaps in the two distributions or large spread in values. We confirm the existence of two distinct intrinsic relations between the bulge luminosity (or absolute magnitude) and Sérsic index for LTGs and ETGs, while the relations between the black hole mass (MBH) and bulge luminosity are not found to be statistically different at p<0.05. Within errors, we find statistically similar intrinsic MBH − nb relations for all bulges.
Effect of Acceleration and Escape of Energetic Particles on Spectral Steepening at Shocks

Energetic particles spectra at interplanetary shocks often exhibit a power law within a narrow momentum range softening at higher energy. We introduce a transport equation accounting for particle acceleration and escape with diffusion contributed by self-generated turbulence close to the shock and by preexisting turbulence far upstream. The upstream particle intensity steepens within one diffusion length from the shock as compared with diffusive shock acceleration rollover. The momentum spectrum, controlled by macroscopic parameters such as shock compression, speed, far-upstream diffusion coefficient, and escape time at the shock, can be reduced to a log-parabola and also to a broken power law. In the case of upstream uniform diffusion coefficient, the largely used power-law/exponential cutoff solution is retrieved.
(3+1)-Field Equation for Gravity with Torsion and Non-Metricity

We derive the generalized Gauss-Codazzi-Mainardi (GCM) equation for a general affine connection with torsion and non-metricity. Moreover, we show that the metric compatibility and torsionless condition of a connection on a manifold are inherited to the connection of its hypersurface. As a physical application to these results, we derive the (3+1)-Einstein Field Equation (EFE) for a special case of Metric-Affine f (R)-gravity when f (R) = R, the Metric-Affine Gravity (MAG). Motivated by the concept of geometrodynamics, we introduce additional variables on the hypersurface as a consequence of non-vanishing torsion and non-metricity. With these additional variables, we show that for MAG, the energy, momentum, and the stress-energy part of the EFE are dynamical, i.e., all of them contain the derivative of a quantity with respect to the time coordinate. For the Levi-Civita connection, one could recover the Hamiltonian and the momentum (diffeomorphism) constraint, and obtain the standard dynamics of GR.
Smoothed Gaussian Mixture Models for Video Classification and Recommendation

Cluster-and-aggregate techniques such as Vector of Locally Aggregated Descriptors (VLAD), and their end-to-end discriminatively trained equivalents like NetVLAD have recently been popular for video classification and action recognition tasks. These techniques operate by assigning video frames to clusters and then representing the video by aggregating residuals of frames with respect to the mean of each cluster. Since some clusters may see very little video-specific data, these features can be noisy. In this paper, we propose a new cluster-and-aggregate method which we call smoothed Gaussian mixture model (SGMM), and its end-to-end discriminatively trained equivalent, which we call deep smoothed Gaussian mixture model (DSGMM). SGMM represents each video by the parameters of a Gaussian mixture model (GMM) trained for that video. Low-count clusters are addressed by smoothing the video-specific estimates with a universal background model (UBM) trained on a large number of videos. The primary benefit of SGMM over VLAD is smoothing which makes it less sensitive to small number of training samples. We show, through extensive experiments on the YouTube-8M classification task, that SGMM/DSGMM is consistently better than VLAD/NetVLAD by a small but statistically significant margin. We also show results using a dataset created at LinkedIn to predict if a member will watch an uploaded video.
Social NCE: Contrastive Learning of Socially-aware Motion Representations

Learning socially-aware motion representations is at the core of recent advances in multi-agent problems, such as human motion forecasting and robot navigation in crowds. Despite promising progress, existing representations learned with neural networks still struggle to generalize in closed-loop predictions (e.g., output colliding trajectories). This issue largely arises from the non-i.i. d. nature of sequential prediction in conjunction with ill-distributed training data. Intuitively, if the training data only comes from human behaviors in safe spaces, i.e., from "positive" examples, it is difficult for learning algorithms to capture the notion of "negative" examples like collisions. In this work, we aim to address this issue by explicitly modeling negative examples through self-supervision: (i) we intro-duce a social contrastive loss that regularizes the extracted motion representation by discerning the ground-truth positive events from synthetic negative ones; (ii) we construct informative negative samples based on our prior knowledge of rare but dangerous circumstances. Our method substantially reduces the collision rates of recent trajectory forecasting, behavioral cloning and reinforcement learning algorithms, outperforming state-of-the-art methods on several benchmarks. Our code is available at https://github.com/vita-epfl/social-nce.
Search for Low-energy Electron Antineutrinos in KamLAND Associated with Gravitational Wave Events

We present the results of a search for MeV-scale electron antineutrino events in KamLAND coincident with the 60 gravitational wave events/candidates reported by the LIGO/Virgo collaboration during their second and third observing runs. We find no significant coincident signals within a ±500 s timing window from each gravitational wave and present 90% C.L. upper limits on the electron antineutrino fluence between 108 and 1013 cm−2 for neutrino energies in the energy range of 1.8–111 MeV.
Do We Really Need Scene-specific Pose Encoders?

Visual pose regression models estimate the camera pose from a query image with a single forward pass. Current models learn pose encoding from an image using deep convolutional networks which are trained per scene. The resulting encoding is typically passed to a multi-layer perceptron in order to regress the pose. In this work, we propose that scene-specific pose encoders are not required for pose regression and that encodings trained for visual similarity can be used instead. In order to test our hypothesis, we take a shallow architecture of several fully connected layers and train it with pre-computed encodings from a generic image retrieval model. We find that these encodings are not only sufficient to regress the camera pose, but that, when provided to a branching fully connected architecture, a trained model can achieve competitive results and even surpass current state-of-the-art pose regressors in some cases. Moreover, we show that for outdoor localization, the proposed architecture is the only pose regressor, to date, consistently localizing in under 2 meters and 5 degrees.
Processing of Body-Induced Thermal Signatures for Physical Distancing and Temperature Screening

Massive and unobtrusive screening of people in public environments is a critical task to guarantee safety in congested shared spaces, as well as to support early non-invasive diagnosis and response to disease outbreaks. Among various sensors and Internet of Things (IoT) technologies, thermal vision systems, based on low-cost infrared (IR) array sensors, allow to track thermal signatures induced by moving people. Unlike contact tracing applications, based short-range communications, IR-based sensing systems are passive, as they do not need the cooperation of the subject(s) and do not pose a threat to user privacy. The paper develops a signal processing framework that enables the joint analysis of subject mobility while automating the temperature screening process. The system consists of IR-based sensors that monitor both subject motions and health status through temperature measurements. Sensors are networked via wireless IoT devices that are deployed according to different layouts. The system targets the joint passive localization of subjects by tracking their mutual distance and direction of arrival, in addition to the detection of anomalous body temperatures for subjects close to the IR sensors. Focusing on Bayesian methods, the paper also addresses best practices and relevant implementation challenges using on field measurements. Being privacy-neutral, the proposed framework can be employed in public and private services for healthcare, smart living and shared spaces scenarios without any privacy concerns. Wall- and ceiling-mounted setups are considered targeting both industrial, smart space and living environments.
Iteratively Reweighted Least Squares for 𝓁1-minimization with Global Linear Convergence Rate

Iteratively Reweighted Least Squares (IRLS), whose history goes back more than 80 years, represents an important family of algorithms for non-smooth optimization as it is able to optimize these problems by solving a sequence of linear systems. In 2010, Daubechies, DeVore, Fornasier, and Güntürkproved that IRLS for ℓ 1 -minimization, an optimization program ubiquitous in the ﬁeld of compressed sensing, globally converges to a sparse solution. While this algorithm has been popular in applications in engineering and statistics, fundamental algorithmic questions have remained unanswered. As a matter of fact, existing convergence guarantees only provide global convergence without any rate , except for the case that the support of the underlying signal has already been identiﬁed. In this paper, we prove that IRLS for ℓ 1 -minimization converges to a sparse solution with a global linear rate . We support our theory by numerical experiments indicating that our linear rate essentially captures the correct dimension dependence.