Miracle-dz/UniFAR-FTUs huggingface dataset:
Exact Recovery and Sharp Thresholds of Stochastic Ising Block Model

The stochastic block model (SBM) is a random graph model in which the edges are generated according to the underlying cluster structure on the vertices. The (ferromagnetic) Ising model, on the other hand, assigns ±1 labels to vertices according to an underlying graph structure in a way that if two vertices are connected in the graph then they are more likely to be assigned the same label. In SBM, one aims to recover the underlying clusters from the graph structure while in Ising model, an extensively-studied problem is to recover the underlying graph structure based on i.i. d. samples (labelings of the vertices). In this paper, we propose a natural composition of SBM and the Ising model, which we call the Stochastic Ising Block Model (SIBM). In SIBM, we take SBM in its simplest form, where <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> vertices are divided into two equal-sized clusters and the edges are connected independently with probability <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> within clusters and <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> across clusters. Then we use the graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> generated by the SBM as the underlying graph of the Ising model and draw <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> i.i. d. samples from it. The objective is to exactly recover the two clusters in SBM from the samples generated by the Ising model, without observing the graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula>. As the main result of this paper, we establish a sharp threshold <inline-formula> <tex-math notation="LaTeX">$m^\ast $ </tex-math></inline-formula> on the sample complexity of this exact recovery problem in a properly chosen regime, where <inline-formula> <tex-math notation="LaTeX">$m^\ast $ </tex-math></inline-formula> can be calculated from the parameters of SIBM. We show that when <inline-formula> <tex-math notation="LaTeX">$m\ge m^\ast $ </tex-math></inline-formula>, one can recover the clusters from <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> samples in <inline-formula> <tex-math notation="LaTeX">$O(n)$ </tex-math></inline-formula> time as the number of vertices <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> goes to infinity. When <inline-formula> <tex-math notation="LaTeX">$m < m^\ast $ </tex-math></inline-formula>, we further show that for almost all choices of parameters of SIBM, the success probability of any recovery algorithms approaches 0 as <inline-formula> <tex-math notation="LaTeX">$n\to \infty $ </tex-math></inline-formula>.
Unsupervised Facial Action Unit Intensity Estimation via Differentiable Optimization

The automatic intensity estimation of facial action units (AUs) from a single image plays a vital role in facial analysis systems. One big challenge for data-driven AU intensity estimation is the lack of sufficient AU label data. Due to the fact that AU annotation requires strong domain expertise, it is expensive to construct an extensive database to learn deep models. The limited number of labeled AUs as well as identity differences and pose variations further increases the estimation difficulties. Considering all these difficulties, we propose an unsupervised framework GE-Net for facial AU intensity estimation from a single image, without requiring any annotated AU data. Our framework performs differentiable optimization, which iteratively updates the facial parameters (i.e., head pose, AU parameters and identity parameters) to match the input image. GE-Net consists of two modules: a generator and a feature extractor. The generator learns to "render" a face image from a set of facial parameters in a differentiable way, and the feature extractor extracts deep features for measuring the similarity of the rendered image and input real image. After the two modules are trained and fixed, the framework searches optimal facial parameters by minimizing the differences of the extracted features between the rendered image and the input image. Experimental results demonstrate that our method can achieve state-of-the-art results compared with existing methods.
The Energetic Thermonuclear Bursts in SAX J1712.6–3739

The neutron star low-mass X-ray binary SAX J1712.6–3739 is known for its long and hard thermonuclear X-ray bursts from previous observations. Its thermonuclear bursts are so distinct as they can last for tens of minutes, as seen with Swift/BAT (E > 15 keV). To explore the origin of these extreme bursts and the nature of SAX J1712.6–3739, we analyzed the observations of all four bursts that were captured by Swift/BAT and derived the peak flux and the fluence of these bursts from joint studies with Swift/XRT and Swift/BAT. The derived bolometric peak fluxes observed by Swift set the distance of SAX J1712.6–3739 to be 4.6–5.6 kpc, while the derived absolute magnitude and average accretion rate agree with its ultracompact nature. Our measurements of the effective duration of these bursts conclude that the 2010 burst corresponds to a normal X-ray burst, the 2011 burst is consistent with an intermediate-duration burst, while the 2014 and the 2018 bursts are more energetic than common intermediate-duration bursts but less energetic than those known superbursts. We estimated that the average mass accretion rate of SAX J1712.6–3739 was about only 0.4%–0.7% . Current theory predicts no carbon production in the bursters under such low accretion rate. If true, the 2014 and 2018 bursts are then deep helium bursts instead of carbon bursts. The thermonuclear bursts of SAX J1712.6–3739 have shown a very wide range of durations. The ignition model predicts that the diverse burst durations are induced by variable accretion rates, but current results provide only weak support to this inference.
Optimal Control of Droplets on a Solid Surface using Distributed Contact Angles.

Controlling the shape and position of moving and pinned droplets on a solid surface is an important feature often found in microfluidic applications. However, automating them, e.g., for high-throughput applications, does rarely involve model-based optimal control strategies. In this work, we demonstrate the optimal control of both the shape and position of a droplet sliding on an inclined surface. This basic test case is a fundamental building block in plenty of microfluidic designs. The static contact angle between the solid surface, the surrounding gas, and the liquid droplet serves as the control variable. By using several control patches, e.g., like done in electrowetting, the contact angles are allowed to vary in space and time. In computer experiments, we are able to calculate mathematically optimal contact angle distributions using gradient-based optimization. The dynamics of the droplet are described by the Cahn-Hilliard-Navier-Stokes equations. We anticipate our demonstration to be the starting point for more sophisticated optimal design and control concepts.
Dense Registration and Mosaicking of Fingerprints by Training an End-to-End Network

Dense registration of fingerprints is a challenging task due to elastic skin distortion, low image quality, and self-similarity of ridge pattern. To overcome the limitation of handcraft features, we propose to train an end-to-end network to directly output pixel-wise displacement field between two fingerprints. The proposed network includes a siamese network for feature embedding, and a following encoder-decoder network for regressing displacement field. By applying displacement fields reliably estimated by tracing high quality fingerprint videos to challenging fingerprints, we synthesize a large number of training fingerprint pairs with ground truth displacement fields. In addition, based on the proposed registration algorithm, we propose a fingerprint mosaicking method based on optimal seam selection. Registration and matching experiments on FVC2004 databases, Tsinghua Distorted Fingerprint (TDF) database, and NIST SD27 latent fingerprint database show that our registration method outperforms previous dense registration methods in accuracy. Mosaicking experiments on FVC2004 DB1_A and a small fingerprint database demonstrate that the proposed algorithm produced higher quality fingerprints and led to higher matching accuracy, which also validates the performance of our registration algorithm.
DLMP-based Coordination Procedure for Decentralized Demand Response under Distribution Network Constraints

Load aggregators are independent private entities whose goal is to optimize energy consumption flexibilities offered by multiple residential consumers. Although aggregators optimize their decisions in a decentralized way, they are indirectly linked together if their respective consumers belong to the same distribution grid. This is an important issue for a distribution system operator (DSO), in charge of the reliability of the distribution network, it has to ensure that decentralized decisions taken do not violate the grid constraints and do not increase the global system costs. From the information point of view,the network state and characteristics are confidential to the DSO, which makes a decentralized solution even more relevant. To address this issue, we propose a decentralized coordination mechanism between the DSO and multiple aggregators that computes the optimal demand response profiles while solving the optimal power flow problem. The procedure, based on distribution locational marginal prices (DLMP), preserves the decentralized structure of information and decisions, and lead to a feasible and optimal solution for both the aggregators and the DSO. The procedure is analyzed from a mechanism design perspective, and different decentralized methods that could be used to implement this procedure are presented.
Analysis of The Ratio of $\ell_1$ and $\ell_2$ Norms in Compressed Sensing

We first propose a novel criterion that guarantees that an $s$-sparse signal is the local minimizer of the $\ell_1/\ell_2$ objective; our criterion is interpretable and useful in practice. We also give the first uniform recovery condition using a geometric characterization of the null space of the measurement matrix, and show that this condition is easily satisfied for a class of random matrices. We also present analysis on the stability of the procedure when noise pollutes data. Numerical experiments are provided that compare $\ell_1/\ell_2$ with some other popular non-convex methods in compressed sensing. Finally, we propose a novel initialization approach to accelerate the numerical optimization procedure. We call this initialization approach \emph{support selection}, and we demonstrate that it empirically improves the performance of existing $\ell_1/\ell_2$ algorithms.
Sequence Model Design for Code Completion in the Modern IDE

Code completion plays a prominent role in modern integrated development environments (IDEs). Machine learning has become ubiquitous in analogous natural language writing and search software, surfacing more relevant autocompletions and search suggestions in fewer keystrokes. Prior research has reported training high-accuracy, deep neural networks for modeling source code, but little attention has been given to the practical constraints imposed by interactive developer tools. In particular, neural language models for source code modeling like the one described in Maybe Deep Neural Networks are the Best Choice for Modeling Source Code are framed around code completion, but only report accuracy of next-token prediction. However, in order for a language model (LM) to work well within real-world code completion systems, it must also always make suggestions that produce valid code that typechecks to support code completion's role in correctness-checking; return instantaneous results to help programmers code more efficiently in fewer keystrokes; and be small enough to fit comfortably on disk and in memory on developer workstations, since virtually all modern IDEs run locally and support offline usage. To meet these additional requirements, we propose a novel design for predicting top-k next tokens that combines static analysis' ability to enumerate all valid keywords and in-scope identifiers with the ability of a language model to place a probability distribution over them. Our model mixes character-level input representation with token output to represent out-of-vocabulary (OOV) tokens meaningfully and minimize prediction latency. OOV tokens can be predicted through detection of local repetition common in software. This design achieves state-of-art accuracy in source code modeling and fits the constraints imposed by real-world code completion implementations in modern IDEs.
Spatially-Attentive Patch-Hierarchical Network for Adaptive Motion Deblurring

This paper tackles the problem of motion deblurring of dynamic scenes. Although end-to-end fully convolutional designs have recently advanced the state-of-the-art in non-uniform motion deblurring, their performance-complexity trade-off is still sub-optimal. Existing approaches achieve a large receptive field by increasing the number of generic convolution layers and kernel-size, but this comesat the expense of of the increase in model size and inference speed. In this work, we propose an efficient pixel adaptive and feature attentive design for handling large blur variations across different spatial locations and process each test image adaptively. We also propose an effective content-aware global-local filtering module that significantly improves performance by considering not only global dependencies but also by dynamically exploiting neighboring pixel information. We use a patch-hierarchical attentive architecture composed of the above module that implicitly discovers the spatial variations in the blur present in the input image and in turn, performs local and global modulation of intermediate features. Extensive qualitative and quantitative comparisons with prior art on deblurring benchmarks demonstrate that our design offers significant improvements over the state-of-the-art in accuracy as well as speed.
A Simple Randomized O(n log n)-Time Closest-Pair Algorithm in Doubling Metrics

Consider a metric space $(P,dist)$ with $N$ points whose doubling dimension is a constant. We present a simple, randomized, and recursive algorithm that computes, in $O(N \log N)$ expected time, the closest-pair distance in $P$. To generate recursive calls, we use previous results of Har-Peled and Mendel, and Abam and Har-Peled for computing a sparse annulus that separates the points in a balanced way.
Fast and Effective Techniques for T-Count Reduction via Spider Nest Identities

In fault-tolerant quantum computing systems, realising (approximately) universal quantum computation is usually described in terms of realising Clifford+T operations, which is to say a circuit of CNOT, Hadamard, and $\pi/2$-phase rotations, together with T operations ($\pi/4$-phase rotations). For many error correcting codes, fault-tolerant realisations of Clifford operations are significantly less resource-intensive than those of T gates, which motivates finding ways to realise the same transformation involving T-count (the number of T gates involved) which is as low as possible. Investigations into this problem [arXiv:1206.0758, 1303.2042, 1308.4134, 1601.07363, 1606.01904, 1701.00140] has led to observations that this problem is closely related to NP-hard tensor decomposition problems [arXiv:1712.01557] and is tantamount to the difficult problem of decoding exponentially long Reed-Muller codes [arXiv:1601.07363]. This problem then presents itself as one for which must be content in practise with approximate optimisation, in which one develops an array of tactics to be deployed through some pragmatic strategy. In this vein, we describe techniques to reduce the T-count, based on the effective application of "spider nest identities": easily recognised products of parity-phase operations which are equivalent to the identity operation. We demonstrate the effectiveness of such techniques by obtaining improvements in the T-counts of a number of circuits, in run-times which are typically less than the time required to make a fresh cup of coffee.
Optical clocks based on the 
Cf15+
 and 
Cf17+
 ions

Recent experimental progress in cooling, trapping, and quantum logic spectroscopy of highly charged ions (HCIs) made HCIs accessible for high-resolution spectroscopy and precision fundamental studies. Based on these achievements, we explore a possibility to develop optical clocks using transitions between the ground and a low-lying excited state in ${\mathrm{Cf}}^{15+}$ and ${\mathrm{Cf}}^{17+}$ ions. Using a high-accuracy relativistic method of calculation, we predicted the wavelengths of clock transitions, calculated relevant atomic properties, and analyzed a number of systematic effects (such as the electric quadrupole, micromotion, and quadratic Zeeman shifts of the clock transitions) that affect the accuracy and stability of the optical clocks. We also calculated magnetic dipole hyperfine-structure constants of the clock states and the blackbody radiation shifts of the clock transitions.
Crystalline shielding mitigates structural rearrangement and localizes memory in jammed systems under oscillatory shear

Amorphous materials store spatially heterogeneous memories of shear direction in particles buried inside crystal grains. The nature of yield in amorphous materials under stress has yet to be fully elucidated. In particular, understanding how microscopic rearrangement gives rise to macroscopic structural and rheological signatures in disordered systems is vital for the prediction and characterization of yield and the study of how memory is stored in disordered materials. Here, we investigate the evolution of local structural homogeneity on an individual particle level in amorphous jammed two-dimensional (athermal) systems under oscillatory shear and relate this evolution to rearrangement, memory, and macroscale rheological measurements. We define the structural metric crystalline shielding, and show that it is predictive of rearrangement propensity and structural volatility of individual particles under shear. We use this metric to identify localized regions of the system in which the material’s memory of its preparation is preserved. Our results contribute to a growing understanding of how local structure relates to dynamic response and memory in disordered systems.
At the Interface of Algebra and Statistics

This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals recover classical marginal probabilities. In general, these reduced densities will have rank higher than one, and their eigenvalues and eigenvectors will contain extra information that encodes subsystem interactions governed by statistics. We decode this information, and show it is akin to conditional probability, and then investigate the extent to which the eigenvectors capture "concepts" inherent in the original joint distribution. The theory is then illustrated with an experiment that exploits these ideas. Turning to a more theoretical application, we also discuss a preliminary framework for modeling entailment and concept hierarchy in natural language, namely, by representing expressions in the language as densities. Finally, initial inspiration for this thesis comes from formal concept analysis, which finds many striking parallels with the linear algebra. The parallels are not coincidental, and a common blueprint is found in category theory. We close with an exposition on free (co)completions and how the free-forgetful adjunctions in which they arise strongly suggest that in certain categorical contexts, the "fixed points" of a morphism with its adjoint encode interesting information.
Unified Multi-Criteria Chinese Word Segmentation with BERT

Multi-Criteria Chinese Word Segmentation (MCCWS) aims at finding word boundaries in a Chinese sentence composed of continuous characters while multiple segmentation criteria exist. The unified framework has been widely used in MCCWS and shows its effectiveness. Besides, the pre-trained BERT language model has been also introduced into the MCCWS task in a multi-task learning framework. In this paper, we combine the superiority of the unified framework and pretrained language model, and propose a unified MCCWS model based on BERT. Moreover, we augment the unified BERT-based MCCWS model with the bigram features and an auxiliary criterion classification task. Experiments on eight datasets with diverse criteria demonstrate that our methods could achieve new state-of-the-art results for MCCWS.
When Does Unsupervised Machine Translation Work?

Despite the reported success of unsupervised machine translation (MT), the field has yet to examine the conditions under which the methods succeed and fail. We conduct an extensive empirical evaluation using dissimilar language pairs, dissimilar domains, and diverse datasets. We find that performance rapidly deteriorates when source and target corpora are from different domains, and that stochasticity during embedding training can dramatically affect downstream results. We additionally find that unsupervised MT performance declines when source and target languages use different scripts, and observe very poor performance on authentic low-resource language pairs. We advocate for extensive empirical evaluation of unsupervised MT systems to highlight failure points and encourage continued research on the most promising paradigms. We release our preprocessed dataset to encourage evaluations that stress-test systems under multiple data conditions.