Miracle-dz/UniFAR-FTUs huggingface dataset:
An Improved Classical Singular Value Transformation for Quantum Machine Learning

We study quantum speedups in quantum machine learning (QML) by analyzing the quantum singular value transformation (QSVT) framework. QSVT, introduced by [GSLW, STOC'19, arXiv:1806.01838], unifies all major types of quantum speedup; in particular, a wide variety of QML proposals are applications of QSVT on low-rank classical data. We challenge these proposals by providing a classical algorithm that matches the performance of QSVT in this regime up to a small polynomial overhead. We show that, given a matrix $A \in \mathbb{C}^{m\times n}$, a vector $b \in \mathbb{C}^{n}$, a bounded degree-$d$ polynomial $p$, and linear-time pre-processing, we can output a description of a vector $v$ such that $\|v - p(A) b\| \leq \varepsilon\|b\|$ in $\widetilde{\mathcal{O}}(d^{11} \|A\|_{\mathrm{F}}^4 / (\varepsilon^2 \|A\|^4 ))$ time. This improves upon the best known classical algorithm [CGLLTW, STOC'20, arXiv:1910.06151], which requires $\widetilde{\mathcal{O}}(d^{22} \|A\|_{\mathrm{F}}^6 /(\varepsilon^6 \|A\|^6 ) )$ time, and narrows the gap with QSVT, which, after linear-time pre-processing to load input into a quantum-accessible memory, can estimate the magnitude of an entry $p(A)b$ to $\varepsilon\|b\|$ error in $\widetilde{\mathcal{O}}(d\|A\|_{\mathrm{F}}/(\varepsilon \|A\|))$ time. Our key insight is to combine the Clenshaw recurrence, an iterative method for computing matrix polynomials, with sketching techniques to simulate QSVT classically. We introduce several new classical techniques in this work, including (a) a non-oblivious matrix sketch for approximately preserving bi-linear forms, (b) a new stability analysis for the Clenshaw recurrence, and (c) a new technique to bound arithmetic progressions of the coefficients appearing in the Chebyshev series expansion of bounded functions, each of which may be of independent interest.
Dodging the Double Descent in Deep Neural Networks

Finding the optimal size of deep learning models is very actual and of broad impact, especially in energy-saving schemes. Very recently, an unexpected phenomenon, the "double descent", has caught the attention of the deep learning community. As the model’s size grows, the performance gets first worse and then goes back to improving. It raises serious questions about the optimal model’s size to maintain high generalization: the model needs to be sufficiently over-parametrized, but adding too many parameters wastes training resources. Is it possible to find, in an efficient way, the best trade-off? Our work shows that the double descent phenomenon is potentially avoidable with proper conditioning of the learning problem, but a final answer is yet to be found. We empirically observe that there is hope to dodge the double descent in complex scenarios with proper regularization, as a simple ℓ2 regularization is already positively contributing to such a perspective.
Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization

Numerically stable algorithms are given for updating the GramSchmidt QR factorization of an m X n matrix A (m > n) when A is modified by a matrix of rank one, or when a row or column is inserted or deleted. The algorithms require O(mn) operations per update, and are based on the use of elementary two-by-two reflection matrices and the Gram-Schmidt process with reorthogonalization. An error analysis of the reorthogonalization process provides rigorous justification for the corresponding ALGOL procedures.
Parallel and Distributed Exact Single-Source Shortest Paths with Negative Edge Weights

This paper presents parallel and distributed algorithms for single-source shortest paths when edges can have negative weights (negative-weight SSSP). We show a framework that reduces negative-weight SSSP in either setting to $n^{o(1)}$ calls to any SSSP algorithm that works with a virtual source. More specifically, for a graph with $m$ edges, $n$ vertices, undirected hop-diameter $D$, and polynomially bounded integer edge weights, we show randomized algorithms for negative-weight SSSP with (i) $W_{SSSP}(m,n)n^{o(1)}$ work and $S_{SSSP}(m,n)n^{o(1)}$ span, given access to an SSSP algorithm with $W_{SSSP}(m,n)$ work and $S_{SSSP}(m,n)$ span in the parallel model, (ii) $T_{SSSP}(n,D)n^{o(1)}$, given access to an SSSP algorithm that takes $T_{SSSP}(n,D)$ rounds in $\mathsf{CONGEST}$. This work builds off the recent result of [Bernstein, Nanongkai, Wulff-Nilsen, FOCS'22], which gives a near-linear time algorithm for negative-weight SSSP in the sequential setting. Using current state-of-the-art SSSP algorithms yields randomized algorithms for negative-weight SSSP with (i) $m^{1+o(1)}$ work and $n^{1/2+o(1)}$ span in the parallel model, (ii) $(n^{2/5}D^{2/5} + \sqrt{n} + D)n^{o(1)}$ rounds in $\mathsf{CONGEST}$. Our main technical contribution is an efficient reduction for computing a low-diameter decomposition (LDD) of directed graphs to computations of SSSP with a virtual source. Efficiently computing an LDD has heretofore only been known for undirected graphs in both the parallel and distributed models. The LDD is a crucial step of the algorithm in [Bernstein, Nanongkai, Wulff-Nilsen, FOCS'22], and we think that its applications to other problems in parallel and distributed models are far from being exhausted.
The greedy side of the LASSO: New algorithms for weighted sparse recovery via loss function-based orthogonal matching pursuit

We propose a class of greedy algorithms for weighted sparse recovery by considering new loss function-based generalizations of Orthogonal Matching Pursuit (OMP). Given a (regularized) loss function, the proposed algorithms alternate the iterative construction of the signal support via greedy index selection and a signal update based on solving a local data-fitting problem restricted to the current support. We show that greedy selection rules associated with popular weighted sparsity-promoting loss functions admit explicitly computable and simple formulas. Specifically, we consider $ \ell^0 $- and $ \ell^1 $-based versions of the weighted LASSO (Least Absolute Shrinkage and Selection Operator), the Square-Root LASSO (SR-LASSO) and the Least Absolute Deviations LASSO (LAD-LASSO). Through numerical experiments on Gaussian compressive sensing and high-dimensional function approximation, we demonstrate the effectiveness of the proposed algorithms and empirically show that they inherit desirable characteristics from the corresponding loss functions, such as SR-LASSO's noise-blind optimal parameter tuning and LAD-LASSO's fault tolerance. In doing so, our study sheds new light on the connection between greedy sparse recovery and convex relaxation.
High-dimensional analysis of double descent for linear regression with random projections

We consider linear regression problems with a varying number of random projections, where we provably exhibit a double descent curve for a fixed prediction problem, with a high-dimensional analysis based on random matrix theory. We first consider the ridge regression estimator and review earlier results using classical notions from non-parametric statistics, namely degrees of freedom, also known as effective dimensionality. We then compute asymptotic equivalents of the generalization performance (in terms of squared bias and variance) of the minimum norm least-squares fit with random projections, providing simple expressions for the double descent phenomenon.
Distortion Minimization with Age of Information and Cost Constraints

We consider a source node deployed in a real-time monitoring application that needs to sample a stochastic process and convey its state timely and accurately to a destination over a wireless ON/OFF channel. The source can either process a raw sample to determine its current state and transmit that information or transmit the raw sample and let the destination determine the state. The source is subjected to an average cost constraint, and it cannot sample, process, and transmit at all the time instants due to the associated costs. When the destination does not receive information, it uses the previous information as an estimate of the current state, which, if it matches the actual state at the source, the distortion is considered to be zero. The objective is to minimize average expected distortion subject to constraints on the average expected age of information (AoI) of states of interest and costs incurred by the source, where the AoI of a state increases if no status update is received, else drops to unity. We derive a stationary randomized policy (SRP) to solve the formulated problem, for which we obtain the expression for the expected AoI under the SRP using a lumpability argument on the two-dimensional discrete-time Markov chain formed using AoI and instantaneous distortion as states. We extensively study the impact of the system parameters on the average distortion under the SRP and draw significant conclusions.
X-Ray2EM: Uncertainty-Aware Cross-Modality Image Reconstruction from X-Ray to Electron Microscopy in Connectomics

Comprehensive, synapse-resolution imaging of the brain will be crucial for understanding neuronal computations and function. In connectomics, this has been the sole purview of volume electron microscopy (EM), which entails an excruciatingly difficult process because it requires cutting tissue into many thin, fragile slices that then need to be imaged, aligned, and reconstructed. Unlike EM, hard X-ray imaging is compatible with thick tissues, eliminating the need for thin sectioning, and delivering fast acquisition, intrinsic alignment, and isotropic resolution. Unfortunately, current state-of-the-art X-ray microscopy provides much lower resolution, to the extent that segmenting membranes is very challenging. We propose an uncertainty-aware 3D reconstruction model that translates X-ray images to EM-like images with enhanced membrane segmentation quality, showing its potential for developing simpler, faster, and more accurate X-ray based connectomics pipelines.
Tight Risk Bounds for Gradient Descent on Separable Data

We study the generalization properties of unregularized gradient methods applied to separable linear classification -- a setting that has received considerable attention since the pioneering work of Soudry et al. (2018). We establish tight upper and lower (population) risk bounds for gradient descent in this setting, for any smooth loss function, expressed in terms of its tail decay rate. Our bounds take the form $\Theta(r_{\ell,T}^2 / \gamma^2 T + r_{\ell,T}^2 / \gamma^2 n)$, where $T$ is the number of gradient steps, $n$ is size of the training set, $\gamma$ is the data margin, and $r_{\ell,T}$ is a complexity term that depends on the (tail decay rate) of the loss function (and on $T$). Our upper bound matches the best known upper bounds due to Shamir (2021); Schliserman and Koren (2022), while extending their applicability to virtually any smooth loss function and relaxing technical assumptions they impose. Our risk lower bounds are the first in this context and establish the tightness of our upper bounds for any given tail decay rate and in all parameter regimes. The proof technique used to show these results is also markedly simpler compared to previous work, and is straightforward to extend to other gradient methods; we illustrate this by providing analogous results for Stochastic Gradient Descent.
The Point to Which Soft Actor-Critic Converges

Soft actor-critic is a successful successor over soft Q-learning. While lived under maximum entropy framework, their relationship is still unclear. In this paper, we prove that in the limit they converge to the same solution. This is appealing since it translates the optimization from an arduous to an easier way. The same justification can also be applied to other regularizers such as KL divergence.
Teaching quantum communications through a hands-on laboratory

Teaching quantum communication is a challenging task when involving different technical and engineering backgrounds. The use of an approach that exploits the knowledge of these profiles, as well as other technological resources available for demonstrations or exercises, enhances this teaching. This paper presents as an example the “Quantum Communications Lab” that took place at the 6th INFIERI Summer School in 2021. In this lab, the access to the Madrid Quantum Communication Infrastructure (MadQCI) was an important resource available.
Q-Profile: Profiling Tool for Quantum Control Stacks applied to the Quantum Approximate Optimization Algorithm

Scaling up the number of qubits and speeding up the execution of quantum algorithms are important steps towards reaching quantum advantage. This poses heavy demands particularly on the control stack, as pulses need to be distributed to an increasing number of control channels and variational algorithms require rapid interleaving of quantum and classical computation. Assessing the bottlenecks in the control stack is therefore key to making it ready for reaching quantum advantage. However, existing benchmark suites suffer from lack of detail due to indirect access to the control hardware. In this work, we present Q-Profile, a tool to profile quantum control stacks that circumvents these issues by utilizing a direct connection from the host CPU to the control stack, providing fine accuracy in measuring the runtime and allowing to identify performance bottlenecks. We demonstrate the use of our tool by benchmarking the Quantum Approximate Optimization Algorithm (QAOA) on a Qblox Cluster for a virtual 4 to 14-qubit transmon system. Our results identify the major execution bottlenecks in the passive qubit reset and communication overhead. We estimate a 1.40x~speedup with respect to the total runtime by using an active qubit reset, instead of passive reset, and demonstrate a further speedup of 1.37x by parallel initialization of the control modules. The presented method of profiling is applicable to other control-stack providers, as well as to other benchmarks, while still providing detailed information beyond a single metric. By extension, this tool will enable identifying and eliminating bottlenecks for future quantum acceleration. The profiling tool is included in the open-source Quantify quantum control software, which allows support for multiple back-ends.
On the prior probability in the theory of sampling

1. If a class consists of n members of which r have the property φ, and we wish to estimate r by the process of sampling, the distribution of probability among values of r, given the composition of the sample, necessarily depends to some extent on our previous knowledge. This is expressed by saying that the prior probability of a particular value of r is f(r). According to Laplace's theory f(r) is constant. It is obvious that there are cases where the previous knowledge is such as to ensure that f(r) is not constant; but the question remains whether such cases should be considered the exception or the rule.
A Notion of Feature Importance by Decorrelation and Detection of Trends by Random Forest Regression

In many studies, we want to determine the influence of certain features on a dependent variable. More specifically, we are interested in the strength of the influence -- i.e., is the feature relevant? -- and, if so, how the feature influences the dependent variable. Recently, data-driven approaches such as \emph{random forest regression} have found their way into applications (Boulesteix et al., 2012). These models allow to directly derive measures of feature importance, which are a natural indicator of the strength of the influence. For the relevant features, the correlation or rank correlation between the feature and the dependent variable has typically been used to determine the nature of the influence. More recent methods, some of which can also measure interactions between features, are based on a modeling approach. In particular, when machine learning models are used, SHAP scores are a recent and prominent method to determine these trends (Lundberg et al., 2017). In this paper, we introduce a novel notion of feature importance based on the well-studied Gram-Schmidt decorrelation method. Furthermore, we propose two estimators for identifying trends in the data using random forest regression, the so-called absolute and relative transversal rate. We empirically compare the properties of our estimators with those of well-established estimators on a variety of synthetic and real-world datasets.
Improved Segmentation of Deep Sulci in Cortical Gray Matter Using a Deep Learning Framework Incorporating Laplace's Equation

When developing tools for automated cortical segmentation, the ability to produce topologically correct segmentations is important in order to compute geometrically valid morphometry measures. In practice, accurate cortical segmentation is challenged by image artifacts and the highly convoluted anatomy of the cortex itself. To address this, we propose a novel deep learning-based cortical segmentation method in which prior knowledge about the geometry of the cortex is incorporated into the network during the training process. We design a loss function which uses the theory of Laplace's equation applied to the cortex to locally penalize unresolved boundaries between tightly folded sulci. Using an ex vivo MRI dataset of human medial temporal lobe specimens, we demonstrate that our approach outperforms baseline segmentation networks, both quantitatively and qualitatively.
A Visual-Thermal Image Sequence Registration Method Based on Motion Status Statistic Feature Multi-Resolution Analysis

Multi-sensor registration is an important and basic problem of intelligent surveillance. A novel visual-thermal image sequence registration method based on motion statistics feature multi-resolution analysis is proposed. In this method, motion statistics feature is utilized to select corresponding point pairs from visual-thermal synchronous video sequence. Then, multi-resolution analysis of motion statistic feature is done to choose proper scale. Finally, outliners are removed by RANSAC, and the geometry transformation parameters are optimized by LM algorithm. By using motion statistics feature, this method avoids the difficult problem of extracting invariant feature from two different image sensor and doesn’t depend on precise motion detection. Through multi-resolution analysis, the proposed approach can resolve the registration under the change of large scale. The performance was demonstrated on three groups of dataset, the results showed that our algorithm carried out precise image registration under the change of translation, scale and rotation.
OPE-SR: Orthogonal Position Encoding for Designing a Parameter-free Upsampling Module in Arbitrary-scale Image Super-Resolution

Arbitrary-scale image super-resolution (SR) is often tackled using the implicit neural representation (INR) approach, which relies on a position encoding scheme to im-prove its representation ability. In this paper, we introduce orthogonal position encoding (OPE), an extension of po-sition encoding, and an OPE-Upscale module to replace the INR-based upsampling module for arbitrary-scale im-age super-resolution. Our OPE-Upscale module takes 2D coordinates and latent code as inputs, just like INR, but does not require any training parameters. This parameter-free feature allows the OPE-Upscale module to directly perform linear combination operations, resulting in con-tinuous image reconstruction and achieving arbitrary-scale image reconstruction. As a concise SR framework, our method is computationally efficient and consumes less mem-ory than state-of-the-art methods, as confirmed by exten-sive experiments and evaluations. In addition, our method achieves comparable results with state-of-the-art methods in arbitrary-scale image super-resolution. Lastly, we show that OPE corresponds to a set of orthogonal basis, validating our design principle.11Project page: https://github.com/gaochao-s/ope-sr
Excitation Functions for (p, n) Reactions with Titanium, Vanadium, Chromium, Iron and Nickel up to Ep=14 MeV

The absolute ( p , n ) cross sections on Ti 47 , Ti 48 , V 51 , Cr 52 , Fe 56 , Fe 57 , Ni 61 and Ni 64 were measured by the activation method at proton energies up to 14 MeV. The experimental results were compared with the predictions based on statistical model in terms of σ( p , n )/σ total , and it was shown that the predictions based on this simple model are not necessarily in disagreement with the experiments.
HasChor: Functional Choreographic Programming for All (Functional Pearl)

Choreographic programming is an emerging paradigm for programming distributed systems. In choreographic programming, the programmer describes the behavior of the entire system as a single, unified program -- a choreography -- which is then compiled to individual programs that run on each node, via a compilation step called endpoint projection. We present a new model for functional choreographic programming where choreographies are expressed as computations in a monad. Our model supports cutting-edge choreographic programming features that enable modularity and code reuse: in particular, it supports higher-order choreographies, in which a choreography may be passed as an argument to another choreography, and location-polymorphic choreographies, in which a choreography can abstract over nodes. Our model is implemented in a Haskell library, HasChor, which lets programmers write choreographic programs while using the rich Haskell ecosystem at no cost, bringing choreographic programming within reach of everyday Haskellers. Moreover, thanks to Haskell's abstractions, the implementation of the HasChor library itself is concise and understandable, boiling down endpoint projection to its short and simple essence.
An augmented mixed FEM for the convective Brinkman-Forchheimer problem: a priori and a posteriori error analysis

We propose and analyze an augmented mixed finite element method for the pseudostress-velocity formulation of the stationary convective Brinkman-Forchheimer problem in $\mathrm{R}^d$, $d\in \{2,3\}$. Since the convective and Forchheimer terms forces the velocity to live in a smaller space than usual, we augment the variational formulation with suitable Galerkin type terms. The resulting augmented scheme is written equivalently as a fixed point equation, so that the well-known Schauder and Banach theorems, combined with the Lax-Milgram theorem, allow to prove the unique solvability of the continuous problem. The finite element discretization involves Raviart-Thomas spaces of order $k\geq 0$ for the pseudostress tensor and continuous piecewise polynomials of degree $\le k + 1$ for the velocity. Stability, convergence, and a priori error estimates for the associated Galerkin scheme are obtained. In addition, we derive two reliable and efficient residual-based a posteriori error estimators for this problem on arbitrary polygonal and polyhedral regions. The reliability of the proposed estimators draws mainly upon the uniform ellipticity of the form involved, a suitable assumption on the data, a stable Helmholtz decomposition, and the local approximation properties of the Cl\'ement and Raviart-Thomas operators. In turn, inverse inequalities, the localization technique based on bubble functions, and known results from previous works, are the main tools yielding the efficiency estimate. Finally, some numerical examples illustrating the performance of the mixed finite element method, confirming the theoretical rate of convergence and the properties of the estimators, and showing the behaviour of the associated adaptive algorithms, are reported. In particular, the case of flow through a $2$D porous media with fracture networks is considered.