Miracle-dz/UniFAR-FTUs huggingface dataset:
An odd feature of the “most classical” states of SU(2) invariant quantum mechanical systems

Complex and spinorial techniques of general relativity are used to determine all the states of SU(2) invariant quantum mechanical systems in which the equality holds in uncertainty relations for the components of the angular momentum vector operator in two given directions. The expectation values depend on a discrete quantum number and two parameters, one of them is the angle between two angular momentum components and the other is the quotient of two standard deviations. Allowing the angle between two angular momentum components to be arbitrary, a new genuine quantum mechanical phenomenon emerges: it is shown that although standard deviations change continuously, one of the expectation values changes discontinuously on this parameter space. Since physically neither of the angular momentum components is distinguished over the other, this discontinuity suggests that the genuine parameter space must be a double cover of this classical one: it must be diffeomorphic to a Riemann surface known in connection with the complex function [Formula: see text]. Moreover, the angle between angular momentum components plays the role of the parameter of an interpolation between the continuous range of expectation values in the special case of orthogonal angular momentum components and the discrete point spectrum of one angular momentum component. The consequences in the simultaneous measurements of these angular momentum components are also discussed briefly.
Optimal Water-Filling Algorithm in Downlink Multi-Cluster NOMA Systems

The key idea of power-domain non-orthogonal multiple access (NOMA) is to exploit the superposition coding (SC) combined with successive interference cancellation (SIC) technique (called SC-SIC) while reducing the receivers’ complexity as well as error propagation. Actually, NOMA suggests a low-complexity scheme, where users are grouped into multiple clusters operating in isolated resource blocks, and SC-SIC is performed among users within each cluster. In this paper, we propose a globally optimal joint intra- and inter-cluster power allocation for any arbitrary user grouping to maximize users’ sum-rate. In this algorithm, we exploit the closed-form of optimal intra-cluster power allocation obtained in our previous work. Then, by transforming network-NOMA to an equivalent virtual network-OMA, we show that the optimal power allocation can be obtained based on the very fast water-filling algorithm. Interestingly, we observe that each NOMA cluster acts as a virtual OMA user whose effective channel gain is obtained in closed form. Also, each virtual OMA user requires a minimum power to satisfy the minimum rate demand of its real multiplexed user. In simulation results, we evaluate the performance gap between fully SC-SIC, NOMA, and OMA, in terms of users sum-rate, and outage probability.
Personalized News Recommendation: A Survey

Personalized news recommendation is an important technique to help users find their interested news information and alleviate their information overload. It has been extensively studied over decades and has achieved notable success in improving users’ news reading experience. However, there are still many unsolved problems and challenges that need to be further studied. To help researchers master the advances in personalized news recommendation over the past years, in this paper we present a comprehensive overview of personalized news recommendation. Instead of following the conventional taxonomy of news recommendation methods, in this paper we propose a novel perspective to understand personalized news recommendation based on its core problems and the associated techniques and challenges. We first review the techniques for tackling each core problem in a personalized news recommender system and the challenges they face. Next, we introduce the public datasets and evaluation metrics used for personalized news recommendation. We then discuss the key points on improving the responsibility of personalized news recommender systems. Finally, we raise several research directions that are worth investigating in future. This paper can provide up-to-date and comprehensive views to help readers understand the personalized news recommendation field. We hope this paper can facilitate research on personalized news recommendation and as well as related fields in natural language processing and data mining.
Degeneracy and hidden symmetry for the asymmetric quantum Rabi model with integral bias

The hidden symmetry of the asymmetric quantum Rabi model (AQRM) with a half-integral bias (ibQRM (cid:96) ) was uncovered in recent studies by the explicit construction of operators J (cid:96) commuting with the Hamiltonian. The existence of such symmetry has been widely believed to cause the degeneration of the spectrum, that is, the crossings on the energy curves. In this paper we propose a conjectural relation between the symmetry and degeneracy for the ibQRM (cid:96) given explicitly in terms of two polynomials appearing independently in the respective investigations. Concretely, one of the polynomials appears as the quotient of the constraint polynomials that assure the existence of degenerate solutions while the other determines a quadratic relation (in general, it deﬁnes a curve of hyperelliptic type) between the ibQRM (cid:96) Hamiltonian and its basic commuting operator J (cid:96) . Following this conjecture, we derive several interesting structural insights of the whole spectrum. For instance, the energy curves are naturally shown to lie on a surface determined by the family of hyperelliptic curves by considering the coupling constant as a variable. This geometric picture contains the generalization of the parity decomposition of the symmetric quantum Rabi model. Moreover, it allows us to describe a remarkable approximation of the ﬁrst (cid:96) energy curves by the zero-section of the corresponding hyperelliptic curve. These investigations naturally lead to a geometric picture of the (hyper-)elliptic surfaces given by the Kodaira-N´eron type model for a family of curves over the projective line in connection with the energy curves, which may be expected to provide a complex analytic proof of the conjecture.
Thermodynamical and spectral phase transition for local diffeomorphisms in the circle

It is known that all uniformly expanding dynamics have no phase transition with respect to Hölder continuous potentials. In this paper we show that given a local diffeomorphism f on the circle, that is neither a uniformly expanding dynamics nor invertible, the topological pressure function ℝ∋t↦Ptop(f,−tlog|Df |) is not analytical. In other words, f has a thermodynamic phase transition with respect to geometric potential. Assuming that f is transitive and that Df is Hölder continuous, we show that there exists t0∈(0,1] such that the transfer operator Lf,−tlog|Df| , acting on the space of Hölder continuous functions, has the spectral gap property for all t<t0 and has not the spectral gap property for all t⩾t0 . Similar results are also obtained when the transfer operator acts on the space of bounded variations functions and smooth functions. In particular, we show that in the transitive case f has a unique thermodynamic phase transition and it occurs in t 0. In addition, if the loss of expansion of the dynamics occurs because of an indifferent fixed point or the dynamics admits an absolutely continuous invariant probability with positive Lyapunov exponent then t0=1.
Knowledge-Adaptation Priors

Humans and animals have a natural ability to quickly adapt to their surroundings, but machine-learning models, when subjected to changes, often require a complete retraining from scratch. We present Knowledge-adaptation priors (K-priors) to reduce the cost of retraining by enabling quick and accurate adaptation for a wide-variety of tasks and models. This is made possible by a combination of weight and function-space priors to reconstruct the gradients of the past, which recovers and generalizes many existing, but seemingly-unrelated, adaptation strategies. Training with simple first-order gradient methods can often recover the exact retrained model to an arbitrary accuracy by choosing a sufficiently large memory of the past data. Empirical results show that adaptation with K-priors achieves performance similar to full retraining, but only requires training on a handful of past examples.
Non-PSD Matrix Sketching with Applications to Regression and Optimization

A variety of dimensionality reduction techniques have been applied for computations involving large matrices. The underlying matrix is randomly compressed into a smaller one, while approximately retaining many of its original properties. As a result, much of the expensive computation can be performed on the small matrix. The sketching of positive semidefinite (PSD) matrices is well understood, but there are many applications where the related matrices are not PSD, including Hessian matrices in non-convex optimization and covariance matrices in regression applications involving complex numbers. In this paper, we present novel dimensionality reduction methods for non-PSD matrices, as well as their ``square-roots", which involve matrices with complex entries. We show how these techniques can be used for multiple downstream tasks. In particular, we show how to use the proposed matrix sketching techniques for both convex and non-convex optimization, $\ell_p$-regression for every $1 \leq p \leq \infty$, and vector-matrix-vector queries.
Amplitude-Phase Modulated CVQKD Protocol

—Here we report the performance of a discrete mod- ulated Continuous Variable Quantum Key Distribution protocol based on eight and sixteen state optimal Amplitude Phase Keying constellations with pure loss quantum channel transmission. Our constellations use the same amplitudes and state probability as in an optimal four-state unidimensional constellation model and apply amplitude/phase modulation to the quadratures of coherent states. We compare the obtained results with the performance of conventional m -PSK and m -APK constellations. The results presented show that protocols that use the proposed constellations outperform the ones based on conventional constellations in both secret key rate and link distance. In special, our protocol is able to accomplish viable SKR’s in low transmittance regime, τ < 0 . 2 .
A Survey on Fault-tolerance in Distributed Optimization and Machine Learning

The robustness of distributed optimization is an emerging field of study, motivated by various applications of distributed optimization including distributed machine learning, distributed sensing, and swarm robotics. With the rapid expansion of the scale of distributed systems, resilient distributed algorithms for optimization are needed, in order to mitigate system failures, communication issues, or even malicious attacks. This survey investigates the current state of fault-tolerance research in distributed optimization, and aims to provide an overview of the existing studies on both fault-tolerant distributed optimization theories and applicable algorithms.
KALE Flow: A Relaxed KL Gradient Flow for Probabilities with Disjoint Support

We study the gradient flow for a relaxed approximation to the Kullback-Leibler (KL) divergence between a moving source and a fixed target distribution. This approximation, termed the KALE (KL approximate lower-bound estimator), solves a regularized version of the Fenchel dual problem defining the KL over a restricted class of functions. When using a Reproducing Kernel Hilbert Space (RKHS) to define the function class, we show that the KALE continuously interpolates between the KL and the Maximum Mean Discrepancy (MMD). Like the MMD and other Integral Probability Metrics, the KALE remains well defined for mutually singular distributions. Nonetheless, the KALE inherits from the limiting KL a greater sensitivity to mismatch in the support of the distributions, compared with the MMD. These two properties make the KALE gradient flow particularly well suited when the target distribution is supported on a low-dimensional manifold. Under an assumption of sufficient smoothness of the trajectories, we show the global convergence of the KALE flow. We propose a particle implementation of the flow given initial samples from the source and the target distribution, which we use to empirically confirm the KALE's properties.
Source Separation-based Data Augmentation for Improved Joint Beat and Downbeat Tracking

Due to advances in deep learning, the performance of automatic beat and downbeat tracking in musical audio signals has seen great improvement in recent years. In training such deep learning based models, data augmentation has been found an important technique. However, existing data augmentation methods for this task mainly target at balancing the distribution of the training data with respect to their tempo. In this paper, we investigate another approach for data augmentation, to account for the composition of the training data in terms of the percussive and non-percussive sound sources. Specifically, we propose to employ a blind drum separation model to segregate the drum and non-drum sounds from each training audio signal, filtering out training signals that are drumless, and then use the obtained drum and non-drum stems to augment the training data. We report experiments on four completely unseen test sets, validating the effectiveness of the proposed method, and accordingly the importance of drum sound composition in the training data for beat and downbeat tracking.
MPC-based Reinforcement Learning for a Simplified Freight Mission of Autonomous Surface Vehicles

In this work, we propose a Model Predictive Control (MPC)-based Reinforcement Learning (RL) method for Autonomous Surface Vehicles (ASVs). The objective is to find an optimal policy that minimizes the closed-loop performance of a simplified freight mission, including collision-free path following, autonomous docking, and a skillful transition between them. We use a parametrized MPC-scheme to approximate the optimal policy, which considers path-following/docking costs and states (position, velocity)/inputs (thruster force, angle) constraints. The Least Squares Temporal Difference (LSTD)-based Deterministic Policy Gradient (DPG) method is then applied to update the policy parameters. Our simulation results demonstrate that the proposed MPC-LSTD-based DPG method could improve the closed-loop performance during learning for the freight mission problem of ASV.
Collision Avoidance with Stochastic Model Predictive Control for Systems with a Twofold Uncertainty Structure

Model Predictive Control (MPC) has shown to be a successful method for many applications that require control. Especially in the presence of prediction uncertainty, various types of MPC offer robust or efficient control system behavior. For modeling, uncertainty is most often approximated in such a way that established MPC approaches are applicable for specific uncertainty types. However, for a number of applications, especially automated vehicles, uncertainty in predicting the future behavior of other agents is more suitably modeled by a twofold description: a high-level task uncertainty and a low-level execution uncertainty of individual tasks. In this work, we present an MPC framework that is capable of dealing with this twofold uncertainty. A scenario MPC approach considers the possibility of other agents performing one of multiple tasks, with an arbitrary probability distribution, while an analytic stochastic MPC method handles execution uncertainty within a specific task, based on a Gaussian distribution. Combining both approaches allows to efficiently handle the twofold uncertainty structure of many applications. Application of the proposed MPC method is demonstrated in an automated vehicle simulation study, resulting in less collisions than applying stochastic MPC or scenario MPC individually.
Locality defeats the curse of dimensionality in convolutional teacher–student scenarios

Convolutional neural networks perform a local and translationally-invariant treatment of the data: quantifying which of these two aspects is central to their success remains a challenge. We study this problem within a teacher–student framework for kernel regression, using ‘convolutional’ kernels inspired by the neural tangent kernel of simple convolutional architectures of given filter size. Using heuristic methods from physics, we find in the ridgeless case that locality is key in determining the learning curve exponent β (that relates the test error ϵ t ∼ P −β to the size of the training set P), whereas translational invariance is not. In particular, if the filter size of the teacher t is smaller than that of the student s, β is a function of s only and does not depend on the input dimension. We confirm our predictions on β empirically. We conclude by proving, under a natural universality assumption, that performing kernel regression with a ridge that decreases with the size of the training set leads to similar learning curve exponents to those we obtain in the ridgeless case.
Topological charge conservation for continuous insulators

This paper proposes a classification of elliptic (pseudo-)differential Hamiltonians describing topological insulators and superconductors in Euclidean space by means of domain walls. Augmenting a given Hamiltonian by one or several domain walls results in confinement that naturally yields a Fredholm operator, whose index is taken as the topological charge of the system. The index is computed explicitly in terms of the symbol of the Hamiltonian by a Fedosov–Hörmander formula, which implements in Euclidean spaces an Atiyah–Singer index theorem. For Hamiltonians admitting an appropriate decomposition in a Clifford algebra, the index is given by the easily computable topological degree of a naturally associated map. A practically important property of topological insulators is the asymmetric transport observed along one-dimensional lines generated by the domain walls. This asymmetry is captured by the edge conductivity, a physical observable of the system. We prove that the edge conductivity is quantized and given by the index of a second Fredholm operator of the Toeplitz type. We also prove topological charge conservation by stating that the two aforementioned indices agree. This result generalizes to higher dimensions and higher-order topological insulators, the bulk-edge correspondence of two-dimensional materials. We apply this procedure to evaluate the topological charge of several classical examples of (standard and higher-order) topological insulators and superconductors in one, two, and three spatial dimensions.
Sleeper Agent: Scalable Hidden Trigger Backdoors for Neural Networks Trained from Scratch

As the curation of data for machine learning becomes increasingly automated, dataset tampering is a mounting threat. Backdoor attackers tamper with training data to embed a vulnerability in models that are trained on that data. This vulnerability is then activated at inference time by placing a"trigger"into the model's input. Typical backdoor attacks insert the trigger directly into the training data, although the presence of such an attack may be visible upon inspection. In contrast, the Hidden Trigger Backdoor Attack achieves poisoning without placing a trigger into the training data at all. However, this hidden trigger attack is ineffective at poisoning neural networks trained from scratch. We develop a new hidden trigger attack, Sleeper Agent, which employs gradient matching, data selection, and target model re-training during the crafting process. Sleeper Agent is the first hidden trigger backdoor attack to be effective against neural networks trained from scratch. We demonstrate its effectiveness on ImageNet and in black-box settings. Our implementation code can be found at https://github.com/hsouri/Sleeper-Agent.
Distributed Optimization Over Time-Varying Graphs With Imperfect Sharing of Information

We study strongly convex distributed optimization problems where a set of agents are interested in solving a separable optimization problem collaboratively. In this article, we propose and study a two-time-scale decentralized gradient descent algorithm for a broad class of lossy sharing of information over time-varying graphs. One time-scale fades out the (lossy) incoming information from neighboring agents, and one time-scale regulates the local loss functions' gradients. We show that assuming a proper choice of step-size sequences, certain connectivity conditions, and bounded gradients along the trajectory of the dynamics, the agents' estimates converge to the optimal solution with the rate of $\mathcal {O}(T^{-1/2})$. We also provide novel tools to study distributed optimization with diminishing averaging weights over time-varying graphs.
Attention-Based Keyword Localisation in Speech using Visual Grounding

Visually grounded speech models learn from images paired with spoken captions. By tagging images with soft text labels using a trained visual classifier with a fixed vocabulary, previous work has shown that it is possible to train a model that can detect whether a particular text keyword occurs in speech utterances or not. Here we investigate whether visually grounded speech models can also do keyword localisation: predicting where, within an utterance, a given textual keyword occurs without any explicit text-based or alignment supervision. We specifically consider whether incorporating attention into a convolutional model is beneficial for localisation. Although absolute localisation performance with visually supervised models is still modest (compared to using unordered bag-of-word text labels for supervision), we show that attention provides a large gain in performance over previous visually grounded models. As in many other speech-image studies, we find that many of the incorrect localisations are due to semantic confusions, e.g. locating the word 'backstroke' for the query keyword 'swimming'.
A polynomial Time Algorithm to Solve The Max-atom Problem

In this paper we consider $m$ ($m \geq 1$)conjunctions of Max-atoms that is atoms of the form $\max(z,y) + r \geq x$, where the offset $r$ is a real constant and $x,y,z$ are variables. We show that the Max-atom problem (MAP) belongs to $\textsf{P}$. Indeed, we provide an algorithm which solves the MAP in $O(n^{6} m^{2} + n^{4} m^{3} + n^{2} m^{4})$ operations, where $n$ is the number of variables which compose the max-atoms. As a by-product other problems also known to be in $\textsf{NP} \cap \textsf{co-NP}$ are in $\textsf{P}$. P1: the problem to know if a tropical cone is trivial or not. P2: problem of tropical rank of a tropical matrix. P3: parity game problem. P4: scheduling problem with AND/OR precedence constraints. P5: problem on hypergraph (shortest path). P6: problem in model checking and $\mu$-calculus.