Miracle-dz/UniFAR-FTUs huggingface dataset:
The semi-infinite cohomology of Weyl modules with two singular points

In their study of spherical representations of an affine Lie algebra at the critical level and of unramified opers, Frenkel and Gaitsgory introduced what they called the Weyl module $\mathbb{V}^{\lambda}$ corresponding to a dominant weight $\lambda$. This object plays an important role in the theory. In arXiv:2012.01858, we introduced a possible analogue $\mathbb{V}^{{\lambda},{\mu}}$ of the Weyl module in the setting of opers with two singular points, and in the case of sl(2) we proved that it has the"correct"endomorphism ring. In this paper, we compute the semi-infinite cohomology of $\mathbb{V}^{{\lambda},{\mu}}$ and we show that it does not share some of the properties of the semi-infinite cohomology of the Weyl module of Frenkel and Gaitsgory. For this reason, we introduce a new module $\tilde{\mathbb{V}}^{{\lambda},{\mu}}$ which, in the case of sl(2), enjoys all the expected properties of a Weyl module.
Towards Semantic-Aware Transport Layer Protocols: A Control Performance Perspective

Networked control systems (NCSs) are an example of task-oriented communication systems, where the purpose of communication is real-time control of processes over a network. In the context of NCSs, with the processes sending their state measurements to the remote controllers, the deterioration of control performance due to the network congestion can be partly mitigated by shaping the traffic injected into the network at the transport layer (TL). In this work, we conduct an extensive performance evaluation of selected TL protocols and show that existing approaches from communication and control theories fail to deliver sufficient control performance in realistic network scenarios. Moreover, we propose a new semantic-aware TL policy, which uses the process state information to filter the most relevant updates and the network state information to prevent delays due to network congestion. The proposed mechanism is shown to outperform all the considered TL protocols with respect to control performance.
NP-Match: Towards a New Probabilistic Model for Semi-Supervised Learning

Semi-supervised learning (SSL) has been widely explored in recent years, and it is an effective way of leveraging unlabeled data to reduce the reliance on labeled data. In this work, we adjust neural processes (NPs) to the semi-supervised image classification task, resulting in a new method named NP-Match. NP-Match is suited to this task for two reasons. Firstly, NP-Match implicitly compares data points when making predictions, and as a result, the prediction of each unlabeled data point is affected by the labeled data points that are similar to it, which improves the quality of pseudo-labels. Secondly, NP-Match is able to estimate uncertainty that can be used as a tool for selecting unlabeled samples with reliable pseudo-labels. Compared with uncertainty-based SSL methods implemented with Monte-Carlo (MC) dropout, NP-Match estimates uncertainty with much less computational overhead, which can save time at both the training and the testing phases. We conducted extensive experiments on five public datasets under three semi-supervised image classification settings, namely, the standard semi-supervised image classification, the imbalanced semi-supervised image classification, and the multi-label semi-supervised image classification, and NP-Match outperforms state-of-the-art (SOTA) approaches or achieves competitive results on them, which shows the effectiveness of NP-Match and its potential for SSL. The codes are at https://github.com/Jianf-Wang/NP-Match
Affinity Uncertainty-based Hard Negative Mining in Graph Contrastive Learning

Hard negative mining has shown effective in enhancing self-supervised contrastive learning (CL) on diverse data types, including graph CL (GCL). The existing hardness-aware CL methods typically treat negative instances that are most similar to the anchor instance as hard negatives, which helps improve the CL performance, especially on image data. However, this approach often fails to identify the hard negatives but leads to many false negatives on graph data. This is mainly due to that the learned graph representations are not sufficiently discriminative due to oversmooth representations and/or non-independent and identically distributed (non-i.i.d.) issues in graph data. To tackle this problem, this article proposes a novel approach that builds a discriminative model on collective affinity information (i.e., two sets of pairwise affinities between the negative instances and the anchor instance) to mine hard negatives in GCL. In particular, the proposed approach evaluates how confident/uncertain the discriminative model is about the affinity of each negative instance to an anchor instance to determine its hardness weight relative to the anchor instance. This uncertainty information is then incorporated into the existing GCL loss functions via a weighting term to enhance their performance. The enhanced GCL is theoretically grounded that the resulting GCL loss is equivalent to a triplet loss with an adaptive margin being exponentially proportional to the learned uncertainty of each negative instance. Extensive experiments on ten graph datasets show that our approach does the following: 1) consistently enhances different state-of-the-art (SOTA) GCL methods in both graph and node classification tasks and 2) significantly improves their robustness against adversarial attacks. Code is available at https://github.com/mala-lab/AUGCL.
A Framework for Adapting Offline Algorithms to Solve Combinatorial Multi-Armed Bandit Problems with Bandit Feedback

We investigate the problem of stochastic, combinatorial multi-armed bandits where the learner only has access to bandit feedback and the reward function can be non-linear. We provide a general framework for adapting discrete offline approximation algorithms into sublinear $\alpha$-regret methods that only require bandit feedback, achieving $\mathcal{O}\left(T^\frac{2}{3}\log(T)^\frac{1}{3}\right)$ expected cumulative $\alpha$-regret dependence on the horizon $T$. The framework only requires the offline algorithms to be robust to small errors in function evaluation. The adaptation procedure does not even require explicit knowledge of the offline approximation algorithm -- the offline algorithm can be used as a black box subroutine. To demonstrate the utility of the proposed framework, the proposed framework is applied to diverse applications in submodular maximization. The new CMAB algorithms for submodular maximization with knapsack constraints outperform a full-bandit method developed for the adversarial setting in experiments with real-world data.
MILO: Model-Agnostic Subset Selection Framework for Efficient Model Training and Tuning

Training deep networks and tuning hyperparameters on large datasets is computationally intensive. One of the primary research directions for efficient training is to reduce training costs by selecting well-generalizable subsets of training data. Compared to simple adaptive random subset selection baselines, existing intelligent subset selection approaches are not competitive due to the time-consuming subset selection step, which involves computing model-dependent gradients and feature embeddings and applies greedy maximization of submodular objectives. Our key insight is that removing the reliance on downstream model parameters enables subset selection as a pre-processing step and enables one to train multiple models at no additional cost. In this work, we propose MILO, a model-agnostic subset selection framework that decouples the subset selection from model training while enabling superior model convergence and performance by using an easy-to-hard curriculum. Our empirical results indicate that MILO can train models $3\times - 10 \times$ faster and tune hyperparameters $20\times - 75 \times$ faster than full-dataset training or tuning without compromising performance.
Review of methods for automatic cerebral microbleeds detection

Cerebral microbleeds detection is an important and challenging task. With the gaining popularity of the MRI, the ability to detect cerebral microbleeds also raises. Unfortunately, for radiologists, it is a time-consuming and laborious procedure. For this reason, various solutions to automate this process have been proposed for several years, but none of them is currently used in medical practice. In this context, the need to systematize the existing knowledge and best practices has been recognized as a factor facilitating the imminent synthesis of a real CMBs detection system practically applicable in medicine. To the best of our knowledge, all available publications regarding automatic cerebral microbleeds detection have been gathered, described, and assessed in this paper in order to distinguish the current research state and provide a starting point for future studies.
Iterative configuration of programmable unitary converter based on few layer redundant multi-plane light conversion

Programmable unitary photonic devices are emerging as promising tools to implement unitary transformation for quantum information processing, machine learning, and optical communication. These devices typically use a rectangular mesh of Mach-Zehnder interferometers (MZIs), which has a clear mathematical structure and can be configured deterministically. However, this mesh architecture is sensitive to fabrication errors, and the correction techniques are still under investigation. In contrast, the multi-plane light conversion (MPLC) architecture is more robust against fabrication errors, but a deterministic method for configuring the converter has not yet been developed due to its complex mathematical structure. In this work, we propose a fast iterative configuration method for MPLC, following the mathematical review of the matrix distance and proposal of a new norm. We show through numerical simulations that adding a few redundant layers significantly improves the convergence of the MPLC architecture, making it a practical and attractive option. We also consider the effects of finite resolution and crosstalk in phase shifters in our simulations. In addition, we propose a phase-insensitive distance suited for applications using only intensity detections. Our method demonstrates orders of magnitude better accuracy and a 20-fold speed-up compared to previous approaches.
An Analysis of Classification Approaches for Hit Song Prediction using Engineered Metadata Features with Lyrics and Audio Features

Hit song prediction, one of the emerging fields in music information retrieval (MIR), remains a considerable challenge. Being able to understand what makes a given song a hit is clearly beneficial to the whole music industry. Previous approaches to hit song prediction have focused on using audio features of a record. This study aims to improve the prediction result of the top 10 hits among Billboard Hot 100 songs using more alternative metadata, including song audio features provided by Spotify, song lyrics, and novel metadata-based features (title topic, popularity continuity and genre class). Five machine learning approaches are applied, including: k-nearest neighbours, Naive Bayes, Random Forest, Logistic Regression and Multilayer Perceptron. Our results show that Random Forest (RF) and Logistic Regression (LR) with all features (including novel features, song audio features and lyrics features) outperforms other models, achieving 89.1% and 87.2% accuracy, and 0.91 and 0.93 AUC, respectively. Our findings also demonstrate the utility of our novel music metadata features, which contributed most to the models' discriminative performance.
Green's functions for a source in a mixing layer: direct waves, refracted arrival waves and instability waves

Green's functions for a source embedded in an isothermal transversely sheared mixing layer are compared with direct numerical simulation (DNS) at various frequencies. Based on the third-order convective wave equation (Lilley 1974), three types of wave responses are analysed. For direct waves, a vortex sheet is used in the low-frequency limit, while in the high-frequency limit the procedure derived by Goldstein (1982) is re-visited. For refracted arrival waves propagating in the zone of silence, the vortex sheet model derived by Friedland & Pierce (1969) is re-visited in the low-frequency limit, while in the high-frequency limit the finite thickness model derived by Suzuki & Lele (2002) is applied. Instability waves excited by a very low-frequency source are formulated in the linear regime using the normal mode decomposition: eigen-functions are normalized using the adjoint convective wave equation, and the receptivity of instability waves is predicted. These theoretical predictions are compared with numerical simulations in two dimensions: DNS are performed based on the full Navier–Stokes equations (the free-stream Mach number is $M_1=0.8$, and the ratios of the acoustic wavelength to the vorticity thickness $\lambda/\delta_V$ are 4.0, 1.0 and 0.25). The DNS results agree fairly well with the high-frequency limit in all three cases for direct waves, although the lowest-frequency case ($\lambda/\delta_V = 4.0$) indicates some features predicted in the low-frequency limit. For refracted arrival waves, the DNS data follow the low- and high-frequency limits to a reasonable degree of accuracy in all cases. Moreover, by setting $\lambda/\delta_V = 16.0$, instability waves are simulated, and a comparison with the theoretical prediction shows that the instability wave response is predicted well when a mixing-layer Reynolds number is high ($Re = 10^5$). They also reveal that the receptivity is fairly sensitive to the Reynolds number and the source position within the mixing layer.
Reverse engineering adversarial attacks with fingerprints from adversarial examples

In spite of intense research efforts, deep neural networks remain vulnerable to adversarial examples: an input that forces the network to confidently produce incorrect outputs. Adversarial examples are typically generated by an attack algorithm that optimizes a perturbation added to a benign input. Many such algorithms have been developed. If it were possible to reverse engineer attack algorithms from adversarial examples, this could deter bad actors because of the possibility of attribution. Here we formulate reverse engineering as a supervised learning problem where the goal is to assign an adversarial example to a class that represents the algorithm and parameters used. To our knowledge it has not been previously shown whether this is even possible. We first test whether we can classify the perturbations added to images by attacks on undefended single-label image classification models. Taking a"fight fire with fire"approach, we leverage the sensitivity of deep neural networks to adversarial examples, training them to classify these perturbations. On a 17-class dataset (5 attacks, 4 bounded with 4 epsilon values each), we achieve an accuracy of 99.4% with a ResNet50 model trained on the perturbations. We then ask whether we can perform this task without access to the perturbations, obtaining an estimate of them with signal processing algorithms, an approach we call"fingerprinting". We find the JPEG algorithm serves as a simple yet effective fingerprinter (85.05% accuracy), providing a strong baseline for future work. We discuss how our approach can be extended to attack agnostic, learnable fingerprints, and to open-world scenarios with unknown attacks.
Quasiextremal primordial black holes are a viable dark matter candidate

Black hole evaporation is generally considered inevitable for low-mass black holes, yet there is no confirmation of this remarkable hypothesis. Here, we propose a phenomenological model that appeals to the possible survival of light quasi-extremal primordial black holes as a significant dark matter component and show that the related cosmological and astrophysical constraints disappear for reasonable degrees of quasi-extremality. The results obtained are general, conservative and should be taken as a proof of principle for future, model-specific analyses.
Neural Target Speech Extraction: An overview

Humans can listen to a target speaker even in challenging acoustic conditions that have noise, reverberation, and interfering speakers. This phenomenon is known as the cocktail party effect. For decades, researchers have focused on approaching the listening ability of humans. One critical issue is handling interfering speakers because the target and nontarget speech signals share similar characteristics, complicating their discrimination. Target speech/speaker extraction (TSE) isolates the speech signal of a target speaker from a mixture of several speakers, with or without noises and reverberations, using clues that identify the speaker in the mixture. Such clues might be a spatial clue indicating the direction of the target speaker, a video of the speaker’s lips, and a prerecorded enrollment utterance from which the speaker’s voice characteristics can be derived. TSE is an emerging field of research that has received increased attention in recent years because it offers a practical approach to the cocktail party problem and involves such aspects of signal processing as audio, visual, and array processing as well as deep learning. This article focuses on recent neural-based approaches and presents an in-depth overview of TSE. We guide readers through the different major approaches, emphasizing the similarities among frameworks and discussing potential future directions.
On Using The Two-Way Cluster-Robust Standard Errors

Thousands of papers have reported two-way cluster-robust (TWCR) standard errors. However, the recent econometrics literature points out the potential non-gaussianity of two-way cluster sample means, and thus invalidity of the inference based on the TWCR standard errors. Fortunately, simulation studies nonetheless show that the gaussianity is rather common than exceptional. This paper provides theoretical support for this encouraging observation. Specifically, we derive a novel central limit theorem for two-way clustered triangular arrays that justifies the use of the TWCR under very mild and interpretable conditions. We, therefore, hope that this paper will provide a theoretical justification for the legitimacy of most, if not all, of the thousands of those empirical papers that have used the TWCR standard errors. We provide a guide in practice as to when a researcher can employ the TWCR standard errors.
Quantum Boltzmann Machines: Applications in Quantitative Finance

In this thesis we explore using the D-Wave Advantage 4.1 quantum annealer to sample from quantum Boltzmann distributions and train quantum Boltzmann machines (QBMs). We focus on the real-world problem of using QBMs as generative models to produce synthetic foreign exchange market data and analyze how the results stack up against classical models based on restricted Boltzmann machines (RBMs). Additionally, we study a small 12-qubit problem which we use to compare samples obtained from the Advantage 4.1 with theory, and in the process gain vital insights into how well the Advantage 4.1 can sample quantum Boltzmann random variables and be used to train QBMs. Through this, we are able to show that the Advantage 4.1 can sample classical Boltzmann random variables to some extent, but is limited in its ability to sample from quantum Boltzmann distributions. Our findings indicate that QBMs trained using the Advantage 4.1 are much noisier than those trained using simulations and struggle to perform at the same level as classical RBMs. However, there is the potential for QBMs to outperform classical RBMs if future generation annealers can generate samples closer to the desired theoretical distributions.
The Fair Value of Data Under Heterogeneous Privacy Constraints

Modern data aggregation often involves a platform collecting data from a network of users with various privacy options. Platforms must solve the problem of how to allocate incentives to users to convince them to share their data. This paper puts forth an idea for a \textit{fair} amount to compensate users for their data at a given privacy level based on an axiomatic definition of fairness, along the lines of the celebrated Shapley value. To the best of our knowledge, these are the first fairness concepts for data that explicitly consider privacy constraints. We also formulate a heterogeneous federated learning problem for the platform with privacy level options for users. By studying this problem, we investigate the amount of compensation users receive under fair allocations with different privacy levels, amounts of data, and degrees of heterogeneity. We also discuss what happens when the platform is forced to design fair incentives. Under certain conditions we find that when privacy sensitivity is low, the platform will set incentives to ensure that it collects all the data with the lowest privacy options. When the privacy sensitivity is above a given threshold, the platform will provide no incentives to users. Between these two extremes, the platform will set the incentives so some fraction of the users chooses the higher privacy option and the others chooses the lower privacy option.
Free boundary problem with a nonlocal kernel

In this paper, we propose a new nonlocal model for two-phase Stefan problem, where the nonlocal version of the one-phase Stefan problem arises naturally as a special case. Among other things, we obtain the optimal condition for the pointwise convergence between local and nonlocal one-phase Stefan problem and an equivalent characterization of this optimal condition. Moreover, we provide some suﬃcient criteria for the continuous expansion of free boundaries, and when the suﬃcient conditions are violated, we construct examples to demonstrate that the jumping phenomena could happen on the free boundaries. The jumping phenomena is essentially induced by the nonlocal diﬀusion and thus it does not appear in the classical Stefan problem.
Active nematic multipoles: Flow responses and the dynamics of defects and colloids

We introduce a general description of localised distortions in active nematics using the framework of active nematic multipoles. We give the Stokesian flows for arbitrary multipoles in terms of differentiation of a fundamental flow response and describe them explicitly up to quadrupole order. We also present the response in terms of the net active force and torque associated to the multipole. This allows the identification of the dipolar and quadrupolar distortions that generate self-propulsion and self-rotation respectively and serves as a guide for the design of arbitrary flow responses. Our results can be applied to both defect loops in three-dimensional active nematics and to systems with colloidal inclusions. They reveal the geometry-dependence of the self-dynamics of defect loops and provide insights into how colloids might be designed to achieve propulsive or rotational dynamics, and more generally for the extraction of work from active nematics. Finally, we extend our analysis also to two dimensions and to systems with chiral active stresses.