Miracle-dz/UniFAR-FTUs huggingface dataset:
Differentiating and Integrating ZX Diagrams

ZX-calculus has proved to be a useful tool for quantum technology with a wide range of successful applications. Most of these applications are of an algebraic nature. However, other tasks that involve differentiation and integration remain unreachable with current ZX techniques. Here we elevate ZX to an analytical perspective by realising differentiation and integration entirely within the framework of ZX-calculus. We explicitly illustrate the new analytic framework of ZX-calculus by applying it in context of quantum machine learning for the analysis of barren plateaus.
Frequency-Dependent Constraints on Cosmic Birefringence from the LFI and HFI Planck Data Release 4

We present new constraints on the frequency dependence of the cosmic birefringence angle from the Planck Data Release 4 polariza- tion maps. An axion ﬁeld coupled to electromagnetism predicts a nearly frequency-independent birefringence angle, β ν = β , while Faraday rotation from local magnetic ﬁelds and Lorentz violating theories predict a cosmic birefringence angle that is proportional to the frequency, ν , to the power of some integer n , β ν ∝ ν n . In this work, we ﬁrst sampled β ν individually for each polarized HFI frequency band in addition to the 70GHz channel from the LFI. We also constrained a power law formula for the birefringence angle, β ν = β 0 ( ν/ν 0 ) n , with ν 0 = 150GHz. For a nearly full-sky measurement, f sky = 0 . 93, we ﬁnd β 0 = 0 . 26 ◦ ± 0 . 11 ◦ (68% C.L.) and n = − 0 . 45 + 0 . 61 − 0 . 82 when we ignore the intrinsic EB correlations of the polarized foreground emission, and β 0 = 0 . 33 ◦ ± 0 . 12 ◦ and n = − 0 . 37 + 0 . 49 − 0 . 64 when we use a ﬁlamentary dust model for the foreground EB . Next, we used all the polarized Planck maps, including the 30 and 44GHz frequency bands. These bands have a negligible foreground contribution from polarized dust emission and we thus treated them separately. Without any modeling of the intrinsic EB of the foreground, we generally ﬁnd that the inclusion of the 30 and 44GHz frequency bands raises the measured values of β ν and tightens n . At nearly full-sky, we measure β 0 = 0 . 29 ◦ + 0 . 10 ◦ − 0 . 11 ◦ and n = − 0 . 35 + 0 . 48 − 0 . 47 . Assuming no frequency dependence, we measure β = 0 . 33 ◦ ± 0 . 10 ◦ . If our measurements have e ﬀ ectively mitigated the EB of the foreground, our constraints are consistent with a mostly frequency-independent signal of cosmic birefringence.
Counterfactual Plans under Distributional Ambiguity

Counterfactual explanations are attracting significant attention due to the flourishing applications of machine learning models in consequential domains. A counterfactual plan consists of multiple possibilities to modify a given instance so that the model's prediction will be altered. As the predictive model can be updated subject to the future arrival of new data, a counterfactual plan may become ineffective or infeasible with respect to the future values of the model parameters. In this work, we study the counterfactual plans under model uncertainty, in which the distribution of the model parameters is partially prescribed using only the first- and second-moment information. First, we propose an uncertainty quantification tool to compute the lower and upper bounds of the probability of validity for any given counterfactual plan. We then provide corrective methods to adjust the counterfactual plan to improve the validity measure. The numerical experiments validate our bounds and demonstrate that our correction increases the robustness of the counterfactual plans in different real-world datasets.
Self-similarity in quantum states and long-range entanglement in fractional dimension

Quantum matter with fractal geometry has been recently observed and studied in experiments. The fractal self-similarity and the fractional nature of the spatial dimension in such systems suggest exotic quantum order lying beyond paradigms developed in integer dimension. However, the existence of such uncomprehended novelty is still to be established in terms of quantum states with nontrivial many-body entanglement. To lay a foundation for exploring such states and to provide example that demonstrates such novelty, we study many-body entanglement patterns in entanglement-renormalization fixed points of qudit systems with Sierpiński lattice geometry, and introduce corresponding toy models. We show that the interplay between entanglement and selfsimilarity can be realized in fixed-point states with well-defined self-similar entanglement patterns. These fixed-point states exhibit distinct orders and are all given by single tensors as solutions to a scale invariance equation. In particular, we prove that an example of fixed-point state possesses long-range entanglement, i.e., it is short-range correlated but cannot be completely disentangled through constant-depth local quantum circuit. While the existence of long-range entanglement implies topological order in 2D and is disproved in 1D, our example proves the coexistence between long-range entanglement and fractality, a paradigm in fractional dimension. We show that such long-range entanglement pattern cannot be read as an extension of topological order, but rather exhibits novel quantum ordering inherent in fractional dimension, an evidence of new paradigm describing long-range entanglement.
Tunneling effect induced by a curved magnetic edge

Experimentally observed magnetic fields with nanoscale variations are theoretically modeled by a piece-wise constant function with jump discontinuity along a smooth curve, the magnetic edge. Assuming the edge is a closed curve with an axis of symmetry and the field is sign changing and with exactly two distinct values, we prove that semi-classical tunneling occurs and calculate the magnitude of this tunneling effect. This paper is dedicated to Elliott H. Lieb on the occasion of his 90th birthday.
Sparse Centroid-Encoder: A Nonlinear Model for Feature Selection

Autoencoders have been widely used as a nonlinear tool for data dimensionality reduction. While autoencoders don't utilize the label information, Centroid-Encoders (CE)\cite{ghosh2022supervised} use the class label in their learning process. In this study, we propose a sparse optimization using the Centroid-Encoder architecture to determine a minimal set of features that discriminate between two or more classes. The resulting algorithm, Sparse Centroid-Encoder (SCE), extracts discriminatory features in groups using a sparsity inducing $\ell_1$-norm while mapping a point to its class centroid. One key attribute of SCE is that it can extract informative features from a multi-modal data set, i.e., data sets whose classes appear to have multiple clusters. The algorithm is applied to a wide variety of real world data sets, including single-cell data, high dimensional biological data, image data, speech data, and accelerometer sensor data. We compared our method to various state-of-the-art feature selection techniques, including supervised Concrete Autoencoders (SCAE), Feature Selection Network (FsNet), deep feature selection (DFS), Stochastic Gate (STG), and LassoNet. We empirically showed that SCE features often produced better classification accuracy than other methods on sequester test set.
Aggregating Global Features into Local Vision Transformer

Local Transformer-based classification models have recently achieved promising results with relatively low computational costs. However, the effect of aggregating spatial global information of local Transformer-based architecture is not clear. This work investigates the outcome of applying a global attention-based module named multi-resolution overlapped attention (MOA) in the local window-based transformer after each stage. The proposed MOA employs slightly larger and overlapped patches in the key to enable neighborhood pixel information transmission, which leads to significant performance gain. In addition, we thoroughly investigate the effect of the dimension of essential architecture components through extensive experiments and discover an optimum architecture design. Extensive experimental results CIFAR-10, CIFAR-100, and ImageNet-1K datasets demonstrate that the proposed approach outperforms previous vision Transformers with a comparatively fewer number of parameters. The source code and models are publicly available at: https://github.com/krushi1992/MOA-transformer
Deletion Robust Submodular Maximization over Matroids

Maximizing a monotone submodular function is a fundamental task in machine learning. In this paper, we study the deletion robust version of the problem under the classic matroids constraint. Here the goal is to extract a small size summary of the dataset that contains a high value independent set even after an adversary deleted some elements. We present constant-factor approximation algorithms, whose space complexity depends on the rank $k$ of the matroid and the number $d$ of deleted elements. In the centralized setting we present a $(3.582+O(\varepsilon))$-approximation algorithm with summary size $O(k + \frac{d \log k}{\varepsilon^2})$. In the streaming setting we provide a $(5.582+O(\varepsilon))$-approximation algorithm with summary size and memory $O(k + \frac{d \log k}{\varepsilon^2})$. We complement our theoretical results with an in-depth experimental analysis showing the effectiveness of our algorithms on real-world datasets.
The Geography of Facebook Groups in the United States

We present a de-identified and aggregated dataset based on geographical patterns of Facebook Groups usage and demonstrate its association with measures of social capital. The dataset is aggregated at United States county level. Established spatial measures of social capital are known to vary across US counties. Their availability and recency depends on running costly surveys. We examine to what extent a dataset based on usage patterns of Facebook Groups, which can be generated at regular intervals, could be used as a partial proxy by capturing local online associations. We identify four main latent factors that distinguish Facebook group engagement by county, obtained by exploratory factor analysis. The first captures small and private groups, dense with friendship connections. The second captures very local and small groups. The third captures non-local, large, public groups, with more age mixing. The fourth captures partially local groups of medium to large size. Only two of these factors, the first and third, correlate with offline community level social capital measures, while the second and fourth do not. Together and individually, the factors are predictive of offline social capital measures, even controlling for various demographic attributes of the counties. To our knowledge this is the first systematic test of the association between offline regional social capital and patterns of online community engagement in the same regions. By making the dataset available to the research community, we hope to contribute to the ongoing studies in social capital.
Achieving Efficient Distributed Machine Learning Using a Novel Non-Linear Class of Aggregation Functions

Distributed machine learning (DML) over time-varying networks can be an enabler for emerging decentralized ML applications such as autonomous driving and drone fleeting. However, the commonly used weighted arithmetic mean model aggregation function in existing DML systems can result in high model loss, low model accuracy, and slow convergence speed over time-varying networks. To address this issue, in this paper, we propose a novel non-linear class of model aggregation functions to achieve efficient DML over time-varying networks. Instead of taking a linear aggregation of neighboring models as most existing studies do, our mechanism uses a nonlinear aggregation, a weighted power-p mean (WPM), as the aggregation function of local models from neighbors. The subsequent optimizing steps are taken using mirror descent defined by a Bregman divergence that maintains convergence to optimality. In this paper, we analyze properties of the WPM and rigorously prove convergence properties of our aggregation mechanism. Additionally, through extensive experiments, we show that when p>1, our design significantly improves the convergence speed of the model and the scalability of DML under time-varying networks compared with arithmetic mean aggregation functions, with little additional computation overhead.
Comparative Assessment of GaN as a Microwave Source with Si and SiC for Mixed Mode Operation at Submillimetre Wave Band of Frequency

The potentials of GaN, SiC, and Si for application as microwave sources in mixed tunnelling avalanche transit time mode operation at submillimetre wave (sub-mm wave) frequency around 0.35 terahertz (THz) are investigated using some computer simulation methods. Design criteria to choose width, doping concentration, and area are highlighted. From the results of our simulation we observed that the Si diode produces the least power output of 41 mW followed by the GaN diode with 760 mW and the SiC diode with 2.89 W. In addition, the GaN diode has more noise than the SiC diode (by 5 dB) as well as the Si diode (by 10 dB). The drastically different performance between the GaN and the SiC diode is attributed to the incorporation of disparate carrier velocity in GaN which were not being used by other authors. In spite of the low power and high noise of the GaN compared to the SiC diode, the presence of several peaks in the mean square noise voltage curves and the existence of several minima in the noise measure curves would open a new direction in the design of GaN low-noise ATT diodes capable of multifrequency tuning like a DAR diode.
Deep Learning Approaches on Image Captioning: A Review

Image captioning is a research area of immense importance, aiming to generate natural language descriptions for visual content in the form of still images. The advent of deep learning and more recently vision-language pre-training techniques has revolutionized the field, leading to more sophisticated methods and improved performance. In this survey article, we provide a structured review of deep learning methods in image captioning by presenting a comprehensive taxonomy and discussing each method category in detail. Additionally, we examine the datasets commonly employed in image captioning research, as well as the evaluation metrics used to assess the performance of different captioning models. We address the challenges faced in this field by emphasizing issues such as object hallucination, missing context, illumination conditions, contextual understanding, and referring expressions. We rank different deep learning methods’ performance according to widely used evaluation metrics, giving insight into the current state-of-the-art. Furthermore, we identify several potential future directions for research in this area, which include tackling the information misalignment problem between image and text modalities, mitigating dataset bias, incorporating vision-language pre-training methods to enhance caption generation, and developing improved evaluation tools to accurately measure the quality of image captions.
Asymptotic behaviour of penalized robust estimators in logistic regression when dimension increases

Penalized $M-$estimators for logistic regression models have been previously study for fixed dimension in order to obtain sparse statistical models and automatic variable selection. In this paper, we derive asymptotic results for penalized $M-$estimators when the dimension $p$ grows to infinity with the sample size $n$. Specifically, we obtain consistency and rates of convergence results, for some choices of the penalty function. Moreover, we prove that these estimators consistently select variables with probability tending to 1 and derive their asymptotic distribution.
Soliton resolution for the energy critical wave equation with inverse-square potential in the radial case

In this paper, we establish the soliton resolution for the energy critical wave equation with inverse square potential in the radial case and in all dimensions $N\geq3$. The structure of the radial linear operator $\mathcal{L}_a :=-\Delta +\frac{a}{|x|^2}=A^*A$, is essential for the channel of energy, where $A$ is a first order differential operator and $A^*$ is its adjoint operator. Modulation and analysis of the multi-solitons are performed in the function spaces $\dot{H}^1_a(\Bbb R^N)\times L^2(\Bbb R^N)$ associated with $\mathcal{L}_a$.
Poynting vector controversy in axion modified electrodynamics

The most sensitive haloscopes that search for axion dark matter through the two photon electromagnetic anomaly, convert axions into photons through the mixing of axions with a large DC magnetic field. In this work we apply Poynting theorem to the resulting axion modified electrodynamics and identify two possible Poynting vectors, one similar to the Abraham Poynting vector and the other to the Minkowski Poynting vector in electrodynamics. The latter picks up the extra non-conservative terms while the former does not. To understand the source of energy conversion and power flow in the detection systems, we apply the two Poynting theorems to axion modified electrodynamics, for both the resonant cavity and broadband low-mass axion detectors. We show that both Poynting theorems give the same sensitivity for a resonant cavity axion haloscope, but predict markedly different sensitivity for a low-mass broadband capacitive haloscope. Hence we ask the question, can understanding which one is the correct one for axion dark matter detection, be considered under the framework of the Abraham-Minkowski controversy? In reality, this should be confirmed by experiment when the axion is detected. However, many electrodynamic experiments have ruled in favour of the Minkowski Poynting vector when considering the canonical momentum in dielectric media. In light of this, we show that the axion modified Minkowski Poynting vector should indeed be taken seriously for sensitivity calculation for low-mass axion haloscope detectors in the quasi static limit, and predict orders of magnitude better sensitivity than the Abraham Poynting vector equivalent.
On the Cartan decomposition for classical random matrix ensembles

We complete Dyson’s dream by cementing the links between symmetric spaces and classical random matrix ensembles. Previous work has focused on a one-to-one correspondence between symmetric spaces and many but not all of the classical random matrix ensembles. This work shows that we can completely capture all of the classical random matrix ensembles from Cartan’s symmetric spaces through the use of alternative coordinate systems. In the end, we have to let go of the notion of a one-to-one correspondence. We emphasize that the KAK decomposition traditionally favored by mathematicians is merely one coordinate system on the symmetric space, albeit a beautiful one. However, other matrix factorizations, especially the generalized singular value decomposition from numerical linear algebra, reveal themselves to be perfectly valid coordinate systems that one symmetric space can lead to many classical random matrix theories. We establish the connection between this numerical linear algebra viewpoint and the theory of generalized Cartan decompositions. This, in turn, allows us to produce yet more random matrix theories from a single symmetric space. Yet, again, these random matrix theories arise from matrix factorizations, though ones that we are not aware have appeared in the literature.
Log-Spectral Matching GAN: PPG-Based Atrial Fibrillation Detection can be Enhanced by GAN-Based Data Augmentation With Integration of Spectral Loss

Photoplethysmography (PPG) is a ubiquitous physiological measurement that detects beat-to-beat pulsatile blood volume changes and hence has a potential for monitoring cardiovascular conditions, particularly in ambulatory settings. A PPG dataset that is created for a particular use case is often imbalanced, due to a low prevalence of the pathological condition it targets to predict and the paroxysmal nature of the condition as well. To tackle this problem, we propose log-spectral matching GAN (LSM-GAN), a generative model that can be used as a data augmentation technique to alleviate the class imbalance in a PPG dataset to train a classifier. LSM-GAN utilizes a novel generator that generates a synthetic signal without a up-sampling process of input white noises, as well as adds the mismatch between real and synthetic signals in frequency domain to the conventional adversarial loss. In this study, experiments are designed focusing on examining how the influence of LSM-GAN as a data augmentation technique on one specific classification task - atrial fibrillation (AF) detection using PPG. We show that by taking spectral information into consideration, LSM-GAN as a data augmentation solution can generate more realistic PPG signals.
Kinetic time-inhomogeneous L{\'e}vy-driven model

We study a one-dimensional kinetic stochastic model driven by a L{\'e}vy process with a non-linear time-inhomogeneous drift. More precisely, the process $(V,X)$ is considered, where $X$ is the position of the particle and its velocity $V$ is the solution of a stochastic differential equation with a drift of the form $t^{-\beta}F(v)$. The driving process can be a stable L{\'e}vy process of index $\alpha$ or a general L{\'e}vy process under appropriate assumptions. The function $F$ satisfies a homogeneity condition and $\beta$ is non-negative. The behavior in large time of the process $(V,X)$ is proved and the precise rate of convergence is pointed out by using stochastic analysis tools. To this end, we compute the moment estimates of the velocity process.
Encoding Weights of Irregular Sparsity for Fixed-to-Fixed Model Compression

Even though fine-grained pruning techniques achieve a high compression ratio, conventional sparsity representations (such as CSR) associated with irregular sparsity degrade parallelism significantly. Practical pruning methods, thus, usually lower pruning rates (by structured pruning) to improve parallelism. In this paper, we study fixed-to-fixed (lossless) encoding architecture/algorithm to support fine-grained pruning methods such that sparse neural networks can be stored in a highly regular structure. We first estimate the maximum compression ratio of encoding-based compression using entropy. Then, as an effort to push the compression ratio to the theoretical maximum (by entropy), we propose a sequential fixed-to-fixed encoding scheme. We demonstrate that our proposed compression scheme achieves almost the maximum compression ratio for the Transformer and ResNet-50 pruned by various fine-grained pruning methods.
Variational Policy Propagation for Multi-agent Reinforcement Learning

We propose a \emph{collaborative} multi-agent reinforcement learning algorithm named variational policy propagation (VPP) to learn a \emph{joint} policy through the interactions over agents. We prove that the joint policy is a Markov Random Field under some mild conditions, which in turn reduces the policy space effectively. We integrate the variational inference as special differentiable layers in policy such that the actions can be efficiently sampled from the Markov Random Field and the overall policy is differentiable. We evaluate our algorithm on several large scale challenging tasks and demonstrate that it outperforms previous state-of-the-arts.