Miracle-dz/UniFAR-FTUs huggingface dataset:
Computing fusion products of MV cycles using the Mirkovi\'c--Vybornov isomorphism

The fusion of two Mirkovic-Vilonen cycles is a degeneration of their product, defined using the Beilinson-Drinfeld Grassmannian. In this paper, we put in place a conceptually elementary approach to computing this product in type $A$. We do so by transferring the problem to a fusion of generalized orbital varieties using the Mirkovic-Vybornov isomorphism. As an application, we explicitly compute all cluster exchange relations in the coordinate ring of the upper-triangular subgroup of $GL_4$, confirming that all the cluster variables are contained in the Mirkovic-Vilonen basis.
CRASH: Raw Audio Score-based Generative Modeling for Controllable High-resolution Drum Sound Synthesis

In this paper, we propose a novel score-base generative model for unconditional raw audio synthesis. Our proposal builds upon the latest developments on diffusion process modeling with stochastic differential equations, which already demonstrated promising results on image generation. We motivate novel heuristics for the choice of the diffusion processes better suited for audio generation, and consider the use of a conditional U-Net to approximate the score function. While previous approaches on diffusion models on audio were mainly designed as speech vocoders in medium resolution, our method termed CRASH (Controllable Raw Audio Synthesis with High-resolution) allows us to generate short percussive sounds in 44.1kHz in a controllable way. Through extensive experiments, we showcase on a drum sound generation task the numerous sampling schemes offered by our method (unconditional generation, deterministic generation, inpainting, interpolation, variations, class-conditional sampling) and propose the class-mixing sampling, a novel way to generate"hybrid"sounds. Our proposed method closes the gap with GAN-based methods on raw audio, while offering more flexible generation capabilities with lighter and easier-to-train models.
Joint Client Scheduling and Resource Allocation Under Channel Uncertainty in Federated Learning

The performance of federated learning (FL) over wireless networks depend on the reliability of the client-server connectivity and clients’ local computation capabilities. In this article we investigate the problem of client scheduling and resource block (RB) allocation to enhance the performance of model training using FL, over a pre-defined training duration under imperfect channel state information (CSI) and limited local computing resources. First, we analytically derive the gap between the training losses of FL with clients scheduling and a centralized training method for a given training duration. Then, we formulate the gap of the training loss minimization over client scheduling and RB allocation as a stochastic optimization problem and solve it using Lyapunov optimization. A Gaussian process regression-based channel prediction method is leveraged to learn and track the wireless channel, in which, the clients’ CSI predictions and computing power are incorporated into the scheduling decision. Using an extensive set of simulations, we validate the robustness of the proposed method under both perfect and imperfect CSI over an array of diverse data distributions. Results show that the proposed method reduces the gap of the training accuracy loss by up to 40.7% compared to state-of-the-art client scheduling and RB allocation methods.
Mitigating Biases in Toxic Language Detection through Invariant Rationalization

Automatic detection of toxic language plays an essential role in protecting social media users, especially minority groups, from verbal abuse. However, biases toward some attributes, including gender, race, and dialect, exist in most training datasets for toxicity detection. The biases make the learned models unfair and can even exacerbate the marginalization of people. Considering that current debiasing methods for general natural language understanding tasks cannot effectively mitigate the biases in the toxicity detectors, we propose to use invariant rationalization (InvRat), a game-theoretic framework consisting of a rationale generator and a predictor, to rule out the spurious correlation of certain syntactic patterns (e.g., identity mentions, dialect) to toxicity labels. We empirically show that our method yields lower false positive rate in both lexical and dialectal attributes than previous debiasing methods.
Gate-Controlled Supercurrent in Epitaxial Al/InAs Nanowires

Gate-controlled supercurrent (GCS) in superconducting nanobridges has recently attracted attention as a means to create superconducting switches. Despite the clear advantages for applications, the microscopic mechanism of this effect is still under debate. In this work, we realize GCS for the first time in a highly crystalline superconductor epitaxially grown on an InAs nanowire. We show that the supercurrent in the epitaxial Al layer can be switched to the normal state by applying ≃±23 V on a bottom gate insulated from the nanowire by a crystalline hBN layer. Our extensive study of the temperature and magnetic field dependencies suggests that the electric field is unlikely to be the origin of GCS in our device. Though hot electron injection alone cannot explain our experimental findings, a very recent non-equilibrium phonons based picture is compatible with most of our results.
Pharmacokinetics of Cefpirome Following Intravenous and Intramuscular Administration in Cow Calves

Background: Cefpirome is a broad-spectrum semi synthetic β-lactamase resistant fourth generation cephalosporin. Looking to potential for clinical use, pharmacokinetics of cefpirome following intravenous and intramuscular administration (10 mg kg ) in cow calves was determined. Methods: Cefpirome concentration in plasma samples was 1 determined by reverse-phase high performance liquid chromatography with mobile phase. The mobile phase was a mixture of 0.2 M sodium acetate (3.5%), acetronitrile (17.5%) and HPLC water (79%) with a pH of 5.1. Mobile phase was filtered by 0.45 µ filters and pumped into column at a flow rate of 1.0 mL min at ambient temperature. The 1 effluent was monitored at 258 nm wavelength. Results: Following intravenous administration of the cefpirome in goats, volume of distribution at steady-state (Vd ), elimination half-life (t ) and total body clearance (Cl ) wer e ss 1/2β B reported 0.33±0.01 L kg , 2.41±0.23 h and 2.36±0.18 mL min kg , respectively. Following intramuscular 1 1 1
Adversarial Robustness via Fisher-Rao Regularization

Adversarial robustness has become a topic of growing interest in machine learning since it was observed that neural networks tend to be brittle. We propose an information-geometric formulation of adversarial defense and introduce Fire, a new Fisher-Rao regularization for the categorical cross-entropy loss, which is based on the geodesic distance between the softmax outputs corresponding to natural and perturbed input features. Based on the information-geometric properties of the class of softmax distributions, we derive an explicit characterization of the Fisher-Rao Distance (FRD) for the binary and multiclass cases, and draw some interesting properties as well as connections with standard regularization metrics. Furthermore, we verify on a simple linear and Gaussian model, that all Pareto-optimal points in the accuracy-robustness region can be reached by Fire while other state-of-the-art methods fail. Empirically, we evaluate the performance of various classifiers trained with the proposed loss on standard datasets, showing up to a simultaneous 1% of improvement in terms of clean and robust performances while reducing the training time by 20% over the best-performing methods.
Spherical CR uniformization of the magic 3-manifold

We show the 3-manifold at infinity of the complex hyperbolic triangle group $\Delta_{3,\infty,\infty;\infty}$ is the three-cusped"magic"3-manifold $6_1^3$. We also show the 3-manifold at infinity of the complex hyperbolic triangle group $\Delta_{3,4,\infty;\infty}$ is the two-cusped 3-manifold $m295$ in the Snappy Census, which is a 3-manifold obtained by Dehn filling on one cusp of $6_1^3$. In particular, hyperbolic 3-manifolds $6_1^3$ and $m295$ admit spherical CR uniformizations. These results support our conjecture that the 3-manifold at infinity of the complex hyperbolic triangle group $\Delta_{3,n,m;\infty}$ is the one-cusped hyperbolic 3-manifold from the"magic"$6_1^3$ via Dehn fillings with filling slopes $(n-2)$ and $(m-2)$ on the first two cusps of it.
MathBERT: A Pre-trained Language Model for General NLP Tasks in Mathematics Education

Since the introduction of the original BERT (i.e., BASE BERT), researchers have developed various customized BERT models with improved performance for specific domains and tasks by exploiting the benefits of transfer learning. Due to the nature of mathematical texts, which often use domain specific vocabulary along with equations and math symbols, we posit that the development of a new BERT model for mathematics would be useful for many mathematical downstream tasks. In this resource paper, we introduce our multi-institutional effort (i.e., two learning platforms and three academic institutions in the US) toward this need: MathBERT, a model created by pre-training the BASE BERT model on a large mathematical corpus ranging from pre-kindergarten (pre-k), to high-school, to college graduate level mathematical content. In addition, we select three general NLP tasks that are often used in mathematics education: prediction of knowledge component, auto-grading open-ended Q&A, and knowledge tracing, to demonstrate the superiority of MathBERT over BASE BERT. Our experiments show that MathBERT outperforms prior best methods by 1.2-22% and BASE BERT by 2-8% on these tasks. In addition, we build a mathematics specific vocabulary 'mathVocab' to train with MathBERT. We discover that MathBERT pre-trained with 'mathVocab' outperforms MathBERT trained with the BASE BERT vocabulary (i.e., 'origVocab'). MathBERT is currently being adopted at the participated leaning platforms: Stride, Inc, a commercial educational resource provider, and ASSISTments.org, a free online educational platform. We release MathBERT for public usage at: https://github.com/tbs17/MathBERT.
Zero-Cost Proxies Meet Differentiable Architecture Search

Differentiable neural architecture search (NAS) has attracted signiﬁcant attention in recent years due to its ability to quickly discover promising architectures of deep neural networks even in very large search spaces. Despite its success, DARTS lacks robustness in certain cases, e.g. it may degenerate to trivial architectures with excessive parametric-free operations such as skip connection or random noise, leading to inferior performance. In particular, operation selection based on the magnitude of architectural parameters was recently proven to be fundamentally wrong showcasing the need to rethink this aspect. On the other hand, zero-cost proxies have been recently studied in the context of sample-based NAS showing promising results – speeding up the search process drastically in some cases but also failing on some of the large search spaces typical for differentiable NAS. In this work we propose a novel operation selection paradigm in the context of differentiable NAS which utilises zero-cost proxies. Our “perturbation-based zero-cost operation selection” (Zero-Cost-PT) improves searching time and, in many cases, accuracy compared to the best available differentiable architecture search, regardless of the search space size. Speciﬁcally, we are able to ﬁnd comparable architectures to DARTS-PT on the DARTS CNN search space while being over 40 × faster (total searching time 25 minutes on a single GPU). Our code will be available at: https://github.com/avail-upon-acceptance .
Age of Information for Multiple-Source Multiple-Server Networks

Having timely and fresh knowledge about the current state of information sources is critical in a variety of applications. In particular, a status update may arrive at the destination later than its generation time due to processing and communication delays. The freshness of the status update at the destination is captured by the notion of age of information. In this study, we analyze a multiple sensing network with multiple sources, multiple servers, and a monitor (destination). Each source corresponds to an independent piece of information and its age is measured individually. Given a particular source, the servers independently sense the source of information and send the status update to the monitor. We assume that updates arrive at the servers according to Poisson random processes. Each server sends its updates to the monitor through a direct link, which is modeled as a queue. The service time to transmit an update is considered to be an exponential random variable. We examine both homogeneous and heterogeneous service and arrival rates for the single-source case, and only homogeneous arrival and service rates for the multiple-source case. We derive a closed-form expression for the average age of information under a last-come-first-serve (LCFS) queue for a single source and arbitrary number of homogeneous servers. Using a recursive method, we derive the explicit average age of information for any number of sources and homogeneous servers. We also investigate heterogeneous servers and a single source, and present algorithms for finding the average age of information.
Feasibility of Bell inequality violation at the ATLAS experiment with flavor entanglement of 
B0B¯0
 pairs from 
pp
 collisions

On the Feasibility of Bell Inequality Violation at ATLAS Experiment with Flavor Entanglement of BB̄ Pairs from pp Collisions Yosuke Takubo, 2, ∗ Tsubasa Ichikawa, † Satoshi Higashino, ‡ Yuichiro Mori, § Kunihiro Nagano, 2, ¶ and Izumi Tsutsui 5, ∗∗ Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), Ibaraki 305-0801, Japan. The Graduate University for Advanced Studies (SOKENDAI), Hayama 240-0193, Japan. Center for Quantum Information and Quantum Biology, Osaka University, Osaka 560-0043, Japan Department of Physics, Kobe University, Hyogo 657-8501, Japan. Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan. (Dated: June 15, 2021)
Video Super-Resolution Transformer

Video super-resolution (VSR), with the aim to restore a high-resolution video from its corresponding low-resolution version, is a spatial-temporal sequence prediction problem. Recently, Transformer has been gaining popularity due to its parallel computing ability for sequence-to-sequence modeling. Thus, it seems to be straightforward to apply the vision Transformer to solve VSR. However, the typical block design of Transformer with a fully connected self-attention layer and a token-wise feed-forward layer does not fit well for VSR due to the following two reasons. First, the fully connected self-attention layer neglects to exploit the data locality because this layer relies on linear layers to compute attention maps. Second, the token-wise feed-forward layer lacks the feature alignment which is important for VSR since this layer independently processes each of the input token embeddings without any interaction among them. In this paper, we make the first attempt to adapt Transformer for VSR. Specifically, to tackle the first issue, we present a spatial-temporal convolutional self-attention layer with a theoretical understanding to exploit the locality information. For the second issue, we design a bidirectional optical flow-based feed-forward layer to discover the correlations across different video frames and also align features. Extensive experiments on several benchmark datasets demonstrate the effectiveness of our proposed method. The code will be available at https://github.com/caojiezhang/VSR-Transformer.
Grammar equations

Diagrammatically speaking, grammatical calculi such as pregroups provide wires between words in order to elucidate their interactions, and this enables one to verify grammatical correctness of phrases and sentences. In this paper we also provide wirings within words. This will enable us to identify grammatical constructs that we expect to be either equal or closely related. Hence, our work paves the way for a new theory of grammar, that provides novel ‘grammatical truths’. We give a nogo-theorem for the fact that our wirings for words make no sense for preordered monoids, the form which grammatical calculi usually take. Instead, they require diagrams – or equivalently, (free) monoidal categories.
Atlas Based Representation and Metric Learning on Manifolds

We explore the use of a topological manifold, represented as a collection of charts, as the target space of neural network based representation learning tasks. This is achieved by a simple adjustment to the output of an encoder's network architecture plus the addition of a maximal mean discrepancy (MMD) based loss function for regularization. Most algorithms in representation and metric learning are easily adaptable to our framework and we demonstrate its effectiveness by adjusting SimCLR (for representation learning) and standard triplet loss training (for metric learning) to have manifold encoding spaces. Our experiments show that we obtain a substantial performance boost over the baseline for low dimensional encodings. In the case of triplet training, we also find, independent of the manifold setup, that the MMD loss alone (i.e. keeping a flat, euclidean target space but using an MMD loss to regularize it) increases performance over the baseline in the typical, high-dimensional Euclidean target spaces. Code for reproducing experiments is provided at https://github.com/ekorman/neurve .
Heterogeneous Edge-Enhanced Graph Attention Network For Multi-Agent Trajectory Prediction

Simultaneous trajectory prediction for multiple heterogeneous traffic participants is essential for the safe and efficient operation of connected automated vehicles under complex driving situations in the real world. The multi-agent prediction task is challenging, as the motions of traffic participants are affected by many factors, including their individual dynamics, their interactions with surrounding agents, the traffic infrastructures, and the number and modalities of the target agents. To further advance the trajectory prediction techniques, in this work we propose a three-channel framework together with a novel Heterogeneous Edge-enhanced graph ATtention network (HEAT), which is able to deal with the heterogeneity of the target agents and traffic participants involved. Specifically, the agent's dynamics are extracted from their historical states using type-specific encoders. The inter-agent interactions are represented with a directed edge-featured heterogeneous graph, and then interaction features are extracted using the proposed HEAT network. Besides, the map features are shared across all agents by introducing a selective gate mechanism. And finally, the trajectories of multi-agent are executed simultaneously. Validations using both urban and highway driving datasets show that the proposed model can realize simultaneous trajectory predictions for multiple agents under complex traffic situations, and achieve state-of-the-art performance with respect to prediction accuracy, demonstrating its feasibility and effectiveness.
Advanced DFT–NEGF Transport Techniques for Novel 2-D Material and Device Exploration Including HfS2/WSe2 van der Waals Heterojunction TFET and WTe2/WS2 Metal/Semiconductor Contact

We present, here, advanced density functional theory and nonequilibrium Green’s function (DFT–NEGF) techniques that we have implemented in our ATOmistic MOdeling Solver (ATOMOS) to explore transport in novel materials and devices, particularly in van der Waals (vdW) heterojunction transistors. We describe our methodologies using plane-wave DFT, followed by a Wannierization step, and a linear combination of atomic orbital DFT that lead to orthogonal and nonorthogonal NEGF models, respectively. We then describe in detail our nonorthogonal NEGF implementation including the Sancho–Rubio method and electron–phonon (e–ph) scattering within a nonorthogonal framework. We also present our methodology to extract e–ph coupling from first principles and include them in our transport simulations. Finally, we apply our methods to the exploration of novel 2-D materials and devices. This includes 2-D material selection and the dynamically doped FET for ultimately scaled MOSFETS, the exploration of vdW tunneling field-effect transistors (TFETs), in particular the HfS2/WSe2 TFET that could achieve high ON-current levels, and the study of Schottky barrier height and transport through a metal-semiconducting WTe2/WS2 vdW junction transistor.
Recomposing the Reinforcement Learning Building Blocks with Hypernetworks

The Reinforcement Learning (RL) building blocks, i.e. Q-functions and policy networks, usually take elements from the cartesian product of two domains as input. In particular, the input of the Q-function is both the state and the action, and in multi-task problems (Meta-RL) the policy can take a state and a context. Standard architectures tend to ignore these variables' underlying interpretations and simply concatenate their features into a single vector. In this work, we argue that this choice may lead to poor gradient estimation in actor-critic algorithms and high variance learning steps in Meta-RL algorithms. To consider the interaction between the input variables, we suggest using a Hypernetwork architecture where a primary network determines the weights of a conditional dynamic network. We show that this approach improves the gradient approximation and reduces the learning step variance, which both accelerates learning and improves the final performance. We demonstrate a consistent improvement across different locomotion tasks and different algorithms both in RL (TD3 and SAC) and in Meta-RL (MAML and PEARL).
Do Not Escape From the Manifold: Discovering the Local Coordinates on the Latent Space of GANs

The discovery of the disentanglement properties of the latent space in GANs motivated a lot of research to find the semantically meaningful directions on it. In this paper, we suggest that the disentanglement property is closely related to the geometry of the latent space. In this regard, we propose an unsupervised method for finding the semantic-factorizing directions on the intermediate latent space of GANs based on the local geometry. Intuitively, our proposed method, called Local Basis, finds the principal variation of the latent space in the neighborhood of the base latent variable. Experimental results show that the local principal variation corresponds to the semantic factorization and traversing along it provides strong robustness to image traversal. Moreover, we suggest an explanation for the limited success in finding the global traversal directions in the latent space, especially W-space of StyleGAN2. We show that W-space is warped globally by comparing the local geometry, discovered from Local Basis, through the metric on Grassmannian Manifold. The global warpage implies that the latent space is not well-aligned globally and therefore the global traversal directions are bound to show limited success on it.