Miracle-dz/UniFAR-FTUs huggingface dataset:
Stability Via Adversarial Training of Neural Network Stochastic Control of Mean-Field Type

In this paper, we present an approach to neural network mean-field-type control and its stochastic stability analysis by means of adversarial inputs (aka adversarial attacks). This is a class of data-driven mean-field-type control where the distribution of the variables such as the system states and control inputs are incorporated into the problem. Besides, we present a methodology to validate the feasibility of the approximations of the solutions via neural networks and evaluate their stability. Moreover, we enhance the stability by enlarging the training set with adversarial inputs to obtain a more robust neural network. Finally, a worked-out example based on the linear-quadratic mean-field type control problem (LQ-MTC) is presented to illustrate our methodology.
Dissipative Imitation Learning for Robust Dynamic Output Feedback

Robust imitation learning seeks to mimic expert controller behavior while ensuring stability, but current methods require accurate plant models. Here, robust imitation learning is addressed for stabilizing poorly modeled plants with linear dynamic output feedback. Open-loop input-output properties are used to characterize an uncertain plant, and the feedback matrix of the dynamic controller is learned while enforcing stability through the controller’s open-loop QSR-dissipativity properties. The imitation learning method is applied to two systems with parametric uncertainty.
VIP: Towards Universal Visual Reward and Representation via Value-Implicit Pre-Training

Reward and representation learning are two long-standing challenges for learning an expanding set of robot manipulation skills from sensory observations. Given the inherent cost and scarcity of in-domain, task-specific robot data, learning from large, diverse, offline human videos has emerged as a promising path towards acquiring a generally useful visual representation for control; however, how these human videos can be used for general-purpose reward learning remains an open question. We introduce $\textbf{V}$alue-$\textbf{I}$mplicit $\textbf{P}$re-training (VIP), a self-supervised pre-trained visual representation capable of generating dense and smooth reward functions for unseen robotic tasks. VIP casts representation learning from human videos as an offline goal-conditioned reinforcement learning problem and derives a self-supervised dual goal-conditioned value-function objective that does not depend on actions, enabling pre-training on unlabeled human videos. Theoretically, VIP can be understood as a novel implicit time contrastive objective that generates a temporally smooth embedding, enabling the value function to be implicitly defined via the embedding distance, which can then be used to construct the reward for any goal-image specified downstream task. Trained on large-scale Ego4D human videos and without any fine-tuning on in-domain, task-specific data, VIP's frozen representation can provide dense visual reward for an extensive set of simulated and $\textbf{real-robot}$ tasks, enabling diverse reward-based visual control methods and significantly outperforming all prior pre-trained representations. Notably, VIP can enable simple, $\textbf{few-shot}$ offline RL on a suite of real-world robot tasks with as few as 20 trajectories.
Stability Analysis and Generalization Bounds of Adversarial Training

In adversarial machine learning, deep neural networks can fit the adversarial examples on the training dataset but have poor generalization ability on the test set. This phenomenon is called robust overfitting, and it can be observed when adversarially training neural nets on common datasets, including SVHN, CIFAR-10, CIFAR-100, and ImageNet. In this paper, we study the robust overfitting issue of adversarial training by using tools from uniform stability. One major challenge is that the outer function (as a maximization of the inner function) is nonsmooth, so the standard technique (e.g., hardt et al., 2016) cannot be applied. Our approach is to consider $\eta$-approximate smoothness: we show that the outer function satisfies this modified smoothness assumption with $\eta$ being a constant related to the adversarial perturbation $\epsilon$. Based on this, we derive stability-based generalization bounds for stochastic gradient descent (SGD) on the general class of $\eta$-approximate smooth functions, which covers the adversarial loss. Our results suggest that robust test accuracy decreases in $\epsilon$ when $T$ is large, with a speed between $\Omega(\epsilon\sqrt{T})$ and $\mathcal{O}(\epsilon T)$. This phenomenon is also observed in practice. Additionally, we show that a few popular techniques for adversarial training (e.g., early stopping, cyclic learning rate, and stochastic weight averaging) are stability-promoting in theory.
Effective Boundary Conditions Arising from the Heat Equation with Three-dimensional Interior Inclusion

We study the initial boundary value problem for a heat equation in a domain containing a thin layer. The thermal conductivity of the layer is drastically different from that of the bulk of the domain; moreover, the layer is anisotropic and ``optimally aligned"in the sense that the normal direction in the layer is always an eigenvector of the thermal tensor. To reveal the effects of the layer, we regard it as a thickless surface on which ``effective boundary conditions"(EBCs) are satisfied by the limit of solutions of the initial boundary value problem as the thickness of the layer shrinks to zero. These EBCs are rich in variety and type, including some nonstandard ones such as the Dirichlet-to-Neumann mapping and the fractional Laplacian.
User Customizable and Robust Geo-Indistinguishability for Location Privacy

Location obfuscation functions generated by existing systems for ensuring location privacy are monolithic and do not allow users to customize their obfuscation range. This can lead to the user being mapped in undesirable locations (e.g., shady neighborhoods) to the location-requesting services. Modifying the obfuscation function generated by a centralized server on the user side can result in poor privacy as the original function is not robust against such updates. Users themselves might find it challenging to understand the parameters involved in obfuscation mechanisms (e.g., obfuscation range and granularity of location representation) and therefore struggle to set realistic trade-offs between privacy, utility, and customization. In this paper, we propose a new framework called, CORGI, i.e., CustOmizable Robust Geo-Indistinguishability, which generates location obfuscation functions that are robust against user customization while providing strong privacy guarantees based on the Geo-Indistinguishability paradigm. CORGI utilizes a tree representation of a given region to assist users in specifying their privacy and customization requirements. The server side of CORGI takes these requirements as inputs and generates an obfuscation function that satisfies Geo-Indistinguishability requirements and is robust against customization on the user side. The obfuscation function is returned to the user who can then choose to update the obfuscation function (e.g., obfuscation range, granularity of location representation). The experimental results on a real dataset demonstrate that CORGI can efficiently generate obfuscation matrices that are more robust to the customization by users.
Mesh-free Eulerian Physics-Informed Neural Networks

Physics-informed Neural Networks (PINNs) have recently emerged as a principled way to include prior physical knowledge in form of partial differential equations (PDEs) into neural networks. Although PINNs are generally viewed as mesh-free, current approaches still rely on collocation points within a bounded region, even in settings with spatially sparse signals. Furthermore, if the boundaries are not known, the selection of such a region is difﬁcult and often results in a large proportion of collocation points being selected in areas of low relevance. To resolve this severe drawback of current methods, we present a mesh-free and adaptive approach termed particle-density PINN (pdPINN), which is inspired by the microscopic viewpoint of ﬂuid dynamics. The method is based on the Eulerian formulation and, different from classical mesh-free method, does not require the introduction of Lagrangian updates. We propose to sample directly from the distribution over the particle positions, eliminating the need to introduce boundaries while adaptively focusing on the most relevant regions. This is achieved by interpreting a non-negative physical quantity (such as the density or temperature) as an unnormalized probability distribution from which we sample with dynamic Monte Carlo methods. The proposed method leads to higher sample efﬁciency and improved performance of PINNs. These advantages are demonstrated on various experiments based on the continuity equations, Fokker-Planck equations, and the heat equation.
Multiwavelength study of the galactic PeVatron candidate LHAASO J2108+5157

LHAASO J2108+5157 is one of the few known unidentified Ultra-High-Energy (UHE) gamma-ray sources with no Very-High-Energy (VHE) counterpart, recently discovered by the LHAASO collaboration. We observed LHAASO J2108+5157 in the X-ray band with XMM-Newton in 2021 for a total of 3.8 hours and at TeV energies with the Large-Sized Telescope prototype (LST-1), yielding 49 hours of good quality data. In addition, we analyzed 12 years of Fermi-LAT data, to better constrain emission of its High-Energy (HE) counterpart 4FGL J2108.0+5155. We found an excess (3.7 sigma) in the LST-1 data at energies E>3 TeV. Further analysis in the whole LST-1 energy range assuming a point-like source, resulted in a hint (2.2 sigma) of hard emission which can be described with a single power law with photon index Gamma = 1.6 +- 0.2 between 0.3 - 100 TeV. We did not find any significant extended emission which could be related to a Supernova Remnant (SNR) or Pulsar Wind Nebula (PWN) in the XMM-Newton data, which puts strong constraints on possible synchrotron emission of relativistic electrons. The LST-1 and LHAASO observations can be explained as inverse Compton-dominated leptonic emission of relativistic electrons with a cutoff energy of $100^{+70}_{-30}$ TeV. The low magnetic field in the source imposed by the X-ray upper limits on synchrotron emission is compatible with a hypothesis of a PWN or a TeV halo. The lack of a pulsar in the neighborhood of the UHE source is a challenge to the PWN/TeV-halo scenario. The UHE gamma rays can also be explained as $\pi^0$ decay-dominated hadronic emission due to interaction of relativistic protons with one of the two known molecular clouds in the direction of the source. The hard spectrum in the LST-1 band is compatible with protons escaping a shock around a middle-aged SNR because of their high low-energy cut-off.
Robust Empirical Risk Minimization with Tolerance

Developing simple, sample-efficient learning algorithms for robust classification is a pressing issue in today's tech-dominated world, and current theoretical techniques requiring exponential sample complexity and complicated improper learning rules fall far from answering the need. In this work we study the fundamental paradigm of (robust) $\textit{empirical risk minimization}$ (RERM), a simple process in which the learner outputs any hypothesis minimizing its training error. RERM famously fails to robustly learn VC classes (Montasser et al., 2019a), a bound we show extends even to `nice' settings such as (bounded) halfspaces. As such, we study a recent relaxation of the robust model called $\textit{tolerant}$ robust learning (Ashtiani et al., 2022) where the output classifier is compared to the best achievable error over slightly larger perturbation sets. We show that under geometric niceness conditions, a natural tolerant variant of RERM is indeed sufficient for $\gamma$-tolerant robust learning VC classes over $\mathbb{R}^d$, and requires only $\tilde{O}\left( \frac{VC(H)d\log \frac{D}{\gamma\delta}}{\epsilon^2}\right)$ samples for robustness regions of (maximum) diameter $D$.
Identifying Selections Operating on HIV-1 Reverse Transcriptase via Uniform Manifold Approximation and Projection: Code available at github.com/shefaliqamar/HIV-Epistatic

We analyze 14,651 HIV1 reverse transcriptase (HIV RT) sequences from the Stanford HIV Drug Resistance Database labeled with treatment regimen in order to study the evolution this enzyme under drug selection in the clinic. Our goal is to identify distinct sectors of HIV RT's sequence space that are undergoing evolution as a way to identify individual selections and/or evolutionary solutions. We utilize Uniform Manifold Approximation and Projection (UMAP), a graph-based dimensionality reduction technique uniquely suited for the detection of non-linear dependencies and visualize the results using an unsupervised clustering algorithm based on density analysis. Our analysis produced 21 distinct clusters of sequences. Supporting the biological significance of these clusters, they tend to represent phylogenetically related sequences with strong correspondence to distinct treatment regimens. Thus, this method for visualization of areas of HIV RT undergoing evolution can help infer information about selective pressures, although it is correlative. The mutation signatures associated with each cluster may represent the higher-order epistatic context facilitating these evolutionary pathways, information that is generally not accessible by other types of mutational co-dependence analyses.
Evolutionary Behavior in a Two-Locus System

In this short note we study a dynamical system generated by a two-parametric quadratic operator mapping a 3-dimensional simplex to itself. This is an evolution operator of the frequencies of gametes in a two-locus system. We find the set of all (a continuum set of) fixed points and show that each fixed point is nonhyperbolic. We completely describe the set of all limit points of the dynamical system. Namely, for any initial point (taken from the 3-dimensional simplex) we find an invariant set containing the initial point and a unique fixed point of the operator, such that the trajectory of the initial point converges to this fixed point.
Wavefit: an Iterative and Non-Autoregressive Neural Vocoder Based on Fixed-Point Iteration

Denoising diffusion probabilistic models (DDPMs) and generative adversarial networks (GANs) are popular generative models for neural vocoders. The DDPMs and GANs can be characterized by the iterative denoising framework and adversarial training, respectively. This study proposes a fast and high-quality neural vocoder called WaveFit, which integrates the essence of GANs into a DDPM-like iterative framework based on fixed-point iteration. WaveFit iteratively denoises an input signal, and trains a deep neural network (DNN) for minimizing an adversarial loss calculated from intermediate outputs at all iterations. Subjective (side-by-side) listening tests showed no statistically significant differences in naturalness between human natural speech and those synthesized by WaveFit with five iterations. Furthermore, the inference speed of WaveFit was more than 240 times faster than WaveRNN. Audio demos are available at google.github. io/df-conformer/wavefit/.
Task Space Tracking of Soft Manipulators: Inner-Outer Loop Control Based on Cosserat-Rod Models

The control problem of soft robots has been considered a challenging subject because they are of infinite degrees of freedom and highly under-actuated. Existing studies have mainly relied on approximated finite-dimensional models. In this work, we exploit infinite-dimensional feedback control for soft robots. We adopt the Cosserat-rod theory and employ nonlinear partial differential equations (PDEs) to model the kinematics and dynamics of soft manipulators, including their translational motions (for shear and elongation) and rotational motions (for bending and torsion). The objective is to achieve position tracking of the entire manipulator in a planar task space by controlling the moments (generated by actuators). The design is inspired by the energy decay property of damped wave equations and has an inner-outer loop structure. In the outer loop, we design desired rotational motions that rotate the translational component into a direction that asymptotically dissipates the energy associated with position tracking errors. In the inner loop, we design inputs for the rotational components to track their desired motions, again by dissipating the rotational energy. We prove that the closed-loop system is exponentially stable and evaluate its performance through simulations.
Normalized solutions for a biharmonic Choquard equation with exponential critical growth in $\mathbb{R}^4$

In this paper, we study the following biharmonic Choquard type equation \begin{align*} \begin{split} \left\{ \begin{array}{ll} \gamma\Delta^2u-\beta\Delta u=\lambda u+(I_\mu*F(u))f(u), \quad\mbox{in}\ \ \mathbb{R}^4, \displaystyle\int_{\mathbb{R}^4}|u|^2dx=c^2>0,\quad u\in H^2(\mathbb{R}^4), \end{array} \right. \end{split} \end{align*} where $\gamma>0$, $\beta\geq0$, $\lambda\in \mathbb{R}$, $I_\mu=\frac{1}{|x|^\mu}$ with $\mu\in (0,4)$, $F(u)$ is the primitive function of $f(u)$, and $f$ is a continuous function with exponential critical growth. We can prove the existence of ground state normalized solutions for the above problem when the nonlinearity $f$ satisfies some conditions.
Emitter-Optomechanical Interaction in high-Q hBN Nanocavities

We investigate the interaction between charged boron vacancies V − B in hBN and optomechanical modes in a nanobeam cavity using spatially resolved photoluminescence (PL) and Raman spectroscopy. V − B is a point defect emitter and the emission is dominated by phonon-assisted processes. As such, the V − B emission is intrinsically sensitive to, and interacts with local deformations such as lattice phonons and cavity optomechanical vibrations. We observe a pronounced spectral asymmetry of the high-Q ( ∼ 10 5 ) nanocavity photonic mode that is only presented for cavities containing V − B emitters, revealing the emitter-induced active cavity optomechanics. Meanwhile, we reveal the cavity-induced control of phonon-assisted V − B emission by exploring the luminescence with position-dependent vibrations in freely suspended structures and the resonant excitation of cavity photons with cooling and heating detunings. Our results show how V − B defect related phonons mediate the coupling between defect emission, cavity photonic and vibronic modes as an emitter-optomechanical system. Such an interplay bewteen diﬀerent vibronic (defect phonon, nanomechanical vibration) and photonic (cavity modes) extends the cavity QED system and provide new paradigms for interfacing spin, photons and phonons in condensed matters.
A chaotic discrete-time continuous-state Hopfield network with piecewise-affine activation functions

We construct a chaotic discrete-time continuous-state Hopfield network with piecewise-affine nonnegative activation functions and weight matrix with small positive entries. More precisely, there exists a Cantor set $C$ in the state space such that the network has sensitive dependence on initial conditions at initial states in $C$ and the network orbit of each initial state in $C$ has $C$ as its $\omega$-limit set. The approach we use is based on tools developed and employed recently in the study of the topological dynamics of piecewise-contractions. The parameters of the chaotic network are explicitly given.
Explaining Website Reliability by Visualizing Hyperlink Connectivity

As the information on the Internet continues growing exponentially, understanding and assessing the reliability of a website is becoming increasingly important. Misinformation has far-ranging repercussions, from sowing mistrust in media to undermining democratic elections. While some research investigates how to alert people to misinformation on the web, much less research has been conducted on explaining how websites engage in spreading false information. To fill the research gap, we present MisVis, a web-based interactive visualization tool that helps users assess a website's reliability by understanding how it engages in spreading false information on the World Wide Web. MisVis visualizes the hyperlink connectivity of the website and summarizes key characteristics of the Twitter accounts that mention the site. A large-scale user study with 139 participants demonstrates that MisVis facilitates users to assess and understand false information on the web and node-link diagrams can be used to communicate with non-experts. MisVis is available at the public demo link: https://poloclub.github. io/MisVis.
On the tightness of linear relaxation based robustness certification methods

There has been a rapid development and interest in adversarial training and defenses in the machine learning community in the recent years. One line of research focuses on improving the performance and efficiency of adversarial robustness certificates for neural networks \cite{gowal:19, wong_zico:18, raghunathan:18, WengTowardsFC:18, wong:scalable:18, singh:convex_barrier:19, Huang_etal:19, single-neuron-relax:20, Zhang2020TowardsSA}. While each providing a certification to lower (or upper) bound the true distortion under adversarial attacks via relaxation, less studied was the tightness of relaxation. In this paper, we analyze a family of linear outer approximation based certificate methods via a meta algorithm, IBP-Lin. The aforementioned works often lack quantitative analysis to answer questions such as how does the performance of the certificate method depend on the network configuration and the choice of approximation parameters. Under our framework, we make a first attempt at answering these questions, which reveals that the tightness of linear approximation based certification can depend heavily on the configuration of the trained networks.
Entanglement witnessing and quantum cryptography with nonideal ferromagnetic detectors

We investigate theoretically the use of nonideal ferromagnetic contacts as a means to detect quantum entanglement of electron spins in transport experiments. We use a designated entanglement witness and find a minimal spin polarization of eta < 1/root 3 approximate to 58% required to demonstrate spin entanglement. This is significantly less stringent than the ubiquitous tests of Bell`s inequality with eta < 1/(4)root 2 approximate to 84%. In addition, we discuss the impact of decoherence and noise on entanglement detection and apply the presented framework to a simple quantum cryptography protocol. Our results are directly applicable to a large variety of experiments.