Miracle-dz/UniFAR-FTUs huggingface dataset:
Linearized Wasserstein dimensionality reduction with approximation guarantees

We introduce LOT Wassmap, a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space. The algorithm is motivated by the observation that many datasets are naturally interpreted as probability measures rather than points in $\mathbb{R}^n$, and that finding low-dimensional descriptions of such datasets requires manifold learning algorithms in the Wasserstein space. Most available algorithms are based on computing the pairwise Wasserstein distance matrix, which can be computationally challenging for large datasets in high dimensions. Our algorithm leverages approximation schemes such as Sinkhorn distances and linearized optimal transport to speed-up computations, and in particular, avoids computing a pairwise distance matrix. We provide guarantees on the embedding quality under such approximations, including when explicit descriptions of the probability measures are not available and one must deal with finite samples instead. Experiments demonstrate that LOT Wassmap attains correct embeddings and that the quality improves with increased sample size. We also show how LOT Wassmap significantly reduces the computational cost when compared to algorithms that depend on pairwise distance computations.
Qualitative Data Augmentation for Performance Prediction in VLSI circuits

Various studies have shown the advantages of using Machine Learning (ML) techniques for analog and digital IC design automation and optimization. Data scarcity is still an issue for electronic designs, while training highly accurate ML models. This work proposes generating and evaluating artificial data using generative adversarial networks (GANs) for circuit data to aid and improve the accuracy of ML models trained with a small training data set. The training data is obtained by various simulations in the Cadence Virtuoso, HSPICE, and Microcap design environment with TSMC 180nm and 22nm CMOS technology nodes. The artificial data is generated and tested for an appropriate set of analog and digital circuits. The experimental results show that the proposed artificial data generation significantly improves ML models and reduces the percentage error by more than 50\% of the original percentage error, which were previously trained with insufficient data. Furthermore, this research aims to contribute to the extensive application of AI/ML in the field of VLSI design and technology by relieving the training data availability-related challenges.
Improved stabilising conditions for model predictive control

It is known that stability of a model predictive control system is ensured if the terminal conditions of the optimal control problem solved online satisfy certain criteria. The usual requirement is that the terminal cost function is a control Lyapunov function defined on the terminal constraint set. Conventionally the terminal cost function is chosen, when the system being controlled is linear, to be the value function for the infinite horizon unconstrained optimal control problem and the terminal constraint set is chosen to be the output admissible set for the closed-loop system using the optimal unconstrained controller u=-Kx. The purpose of the paper is to relax these terminal conditions thereby facilitating online solution of the optimal control problem. Using some earlier results, we present alternative conditions that employ, as the terminal cost, the infinite horizon cost resulting from a nonlinear controller u=-sat(Kx) and, as the terminal constraint set, the set in which this controller is optimal for the infinite horizon constrained optimal control problem. It is shown that this solution provides a considerably larger terminal constraint set.
Towards Optimal Compression: Joint Pruning and Quantization

Model compression is instrumental in optimizing deep neural network inference on resource-constrained hardware. The prevailing methods for network compression, namely quantization and pruning, have been shown to enhance efficiency at the cost of performance. Determining the most effective quantization and pruning strategies for individual layers and parameters remains a challenging problem, often requiring computationally expensive and ad hoc numerical optimization techniques. This paper introduces FITCompress, a novel method integrating layer-wise mixed-precision quantization and unstructured pruning using a unified heuristic approach. By leveraging the Fisher Information Metric and path planning through compression space, FITCompress optimally selects a combination of pruning mask and mixed-precision quantization configuration for a given pre-trained model and compression constraint. Experiments on computer vision and natural language processing benchmarks demonstrate that our proposed approach achieves a superior compression-performance trade-off compared to existing state-of-the-art methods. FITCompress stands out for its principled derivation, making it versatile across tasks and network architectures, and represents a step towards achieving optimal compression for neural networks.
Unsupervised Hashing with Similarity Distribution Calibration

Unsupervised hashing methods typically aim to preserve the similarity between data points in a feature space by mapping them to binary hash codes. However, these methods often overlook the fact that the similarity between data points in the continuous feature space may not be preserved in the discrete hash code space, due to the limited similarity range of hash codes. The similarity range is bounded by the code length and can lead to a problem known as similarity collapse. That is, the positive and negative pairs of data points become less distinguishable from each other in the hash space. To alleviate this problem, in this paper a novel Similarity Distribution Calibration (SDC) method is introduced. SDC aligns the hash code similarity distribution towards a calibration distribution (e.g., beta distribution) with sufficient spread across the entire similarity range, thus alleviating the similarity collapse problem. Extensive experiments show that our SDC outperforms significantly the state-of-the-art alternatives on coarse category-level and instance-level image retrieval. Code is available at https://github.com/kamwoh/sdc.
Over-parametrization via Lifting for Low-rank Matrix Sensing: Conversion of Spurious Solutions to Strict Saddle Points

This paper studies the role of over-parametrization in solving non-convex optimization problems. The focus is on the important class of low-rank matrix sensing, where we propose an infinite hierarchy of non-convex problems via the lifting technique and the Burer-Monteiro factorization. This contrasts with the existing over-parametrization technique where the search rank is limited by the dimension of the matrix and it does not allow a rich over-parametrization of an arbitrary degree. We show that although the spurious solutions of the problem remain stationary points through the hierarchy, they will be transformed into strict saddle points (under some technical conditions) and can be escaped via local search methods. This is the first result in the literature showing that over-parametrization creates a negative curvature for escaping spurious solutions. We also derive a bound on how much over-parametrization is requited to enable the elimination of spurious solutions.
ESTIMATION OF AND INFERENCE ABOUT THE EXPECTED SHORTFALL FOR TIME SERIES WITH INFINITE VARIANCE

We study estimation and inference of the expected shortfall for time series with infinite variance. Both the smoothed and nonsmoothed estimators are investigated. The rate of convergence is determined by the tail thickness parameter, and the limiting distribution is in the stable class with parameters depending on the tail thickness parameter of the time series and on the dependence structure, which makes inference complicated. A subsampling procedure is proposed to carry out statistical inference. We also analyze a nonparametric estimator of the conditional expected shortfall. A Monte Carlo experiment is conducted to evaluate the finite sample performance of the proposed inference procedure, and an empirical application to emerging market exchange rates (from October 1997 to October 2008) is conducted to highlight the proposed study.
SynGraphy: Succinct Summarisation of Large Networks via Small Synthetic Representative Graphs

We describe SynGraphy, a method for visually summarising the structure of large network datasets that works by drawing smaller graphs generated to have similar structural properties to the input graphs. Visualising complex networks is crucial to understand and make sense of networked data and the relationships it represents. Due to the large size of many networks, visualisation is extremely difficult; the simple method of drawing large networks like those of Facebook or Twitter leads to graphics that convey little or no information. While modern graph layout algorithms can scale computationally to large networks, their output tends to a common"hairball"look, which makes it difficult to even distinguish different graphs from each other. Graph sampling and graph coarsening techniques partially address these limitations but they are only able to preserve a subset of the properties of the original graphs. In this paper we take the problem of visualising large graphs from a novel perspective: we leave the original graph's nodes and edges behind, and instead summarise its properties such as the clustering coefficient and bipartivity by generating a completely new graph whose structural properties match that of the original graph. To verify the utility of this approach as compared to other graph visualisation algorithms, we perform an experimental evaluation in which we repeatedly asked experimental subjects (professionals in graph mining and related areas) to determine which of two given graphs has a given structural property and then assess which visualisation algorithm helped in identifying the correct answer. Our summarisation approach SynGraphy compares favourably to other techniques on a variety of networks.
Signatures of van Hove singularities in the anisotropic in-plane optical conductivity of the topological semimetal Nb$_3$SiTe$_6$

We present a temperature-dependent infrared spectroscopy study on the layered topological semimetal Nb$_3$SiTe$_6$ combined with density-functional theory (DFT) calculations of the electronic band structure and optical conductivity. Our results reveal an anisotropic behavior of the in-plane ($ac$-plane) optical conductivity, with three pronounced excitations located at around 0.15, 0.28, and 0.41~eV for the polarization of the incident radiation along the $c$ axis. These excitations are well reproduced in the theoretical spectra. Based on the \textit{ab initio} results, the excitations around 0.15 eV and 0.28 eV are interpreted as fingerprints of van Hove singularities in the electronic band structure and compared to the findings for other topological semimetals.
Similarity, Compression and Local Steps: Three Pillars of Efficient Communications for Distributed Variational Inequalities

Variational inequalities are a broad and flexible class of problems that includes minimization, saddle point, fixed point problems as special cases. Therefore, variational inequalities are used in a variety of applications ranging from equilibrium search to adversarial learning. Today's realities with the increasing size of data and models demand parallel and distributed computing for real-world machine learning problems, most of which can be represented as variational inequalities. Meanwhile, most distributed approaches has a significant bottleneck - the cost of communications. The three main techniques to reduce both the total number of communication rounds and the cost of one such round are the use of similarity of local functions, compression of transmitted information and local updates. In this paper, we combine all these approaches. Such a triple synergy did not exist before for variational inequalities and saddle problems, nor even for minimization problems. The methods presented in this paper have the best theoretical guarantees of communication complexity and are significantly ahead of other methods for distributed variational inequalities. The theoretical results are confirmed by adversarial learning experiments on synthetic and real datasets.
Properties of the nuclei of Centaurs Chiron and Chariklo

We analyze visible, infrared, radio and spectroscopic observations of 2060 Chiron in a synthetic way to determine the physical properties of its nucleus. From visible observations performed from 1969 to 2001, we determine an absolute V magnitude for the nucleus of $7.28\pm0.08$ with an amplitude of $0.16\pm0.03$, implying a nearly spherical nucleus with a ratio of semi-axes $a/b=1.16\pm0.03$. Infrared observations at 25, 60, 100 and 160 μ m (i.e., covering the broad maximum of the spectral energy distribution) obtained with the Infrared Space Observatory Photometer (ISOPHOT) in June 1996 when Chiron was near its perihelion are analyzed with a thermal model which considers an intimate mixture of water ice and refractory materials and includes heat conduction into the interior of the nucleus. We find a very low thermal inertia of $3^{+5}_{-3}$ J K -1 m -2 s -1/2 and a radius of $71\pm5$ km. Combining the visible and infrared observations, we derive a geometric albedo of $0.11\pm0.02$. We find that the observed spectra of Chiron can be fitted by a mixture of water ice (~30%) and refractory ( ∼ 70%) grains, and that this surface model has a geometric albedo consistent with the above value. We also analyze the visible, infrared and radio observations of Chariklo (1997 CU26) and derive a radius of $118\pm6$ km, a geometric albedo of $0.07\pm0.01$ and a thermal inertia of 0$^{+2}_{-0}$ J K -1 m -2 s -1/2 . A mixture of water ice ($\sim $20%) and refractory ($\sim $80%) grains is compatible with the near-infrared spectrum and the above albedo.
Crystal symmetry protected gapless vortex line phases in superconducting Dirac semimetals

Vortex lines in superconducting Dirac semimetals realize crystal-symmetry-protected gapless vortex-line phases in which gapless excitations propagate inside a vortex line, in the presence of appropriate crystal symmetry, spin-orbit coupling, and multi-band structures. Here we present a general scheme to classify possible gapless vortex-line phases in superconducting Dirac semimetals with rotation (or screw) symmetry and inversion symmetry, assuming that the rotation (screw) axis is parallel to the vortex line. The rotation (screw)-symmetry-protected gapless modes are stable as long as they have different rotation (screw) eigenvalues. The underlying mechanism for the formation of gapless vortex bound states depends on irreducible representations of rotation (screw) symmetry subject to a vortex field and is classified into three types: (i) accidental band crossing of two vortex bound-state modes under rotation symmetry; (ii) accidental and (iii) enforced band crossing of four vortex bound-state modes under screw symmetry. We present a tight-binding model of screw-symmetry-protected Dirac semimetal with an $s$-wave pair potential, demonstrating a gapless vortex-line phase of type (ii). We obtain four gapless modes of vortex bound states whose gapless points (Majorana zero modes) pinned at a time-reversal invariant momentum (TRIM) when the Fermi energy is close to the Dirac points. As the Fermi energy is moved away from the Dirac points, the four gapless modes are split into a pair of two gapless modes with vanishing excitation energy at non-TRIMs. In closing, we discuss Nb$_3$Pt as a candidate material with the four-fold screw-symmetry-protected Dirac cones that can host a gapless vortex-line phase.
Free Extreme points of free spectrahedrops and generalized free spectrahedra

Matrix convexity generalizes convexity to the dimension free setting and has connections to many mathematical and applied pursuits including operator theory, quantum information, noncommutative optimization, and linear control systems. In the setting of classical convex sets, extreme points are central objects which exhibit many important properties. For example, the Minkowski theorem shows that any element of a closed bounded convex set can be expressed as a convex combination of extreme points. Extreme points are also of great interest in the dimension free setting of matrix convex sets; however, here the situation requires more nuance. In the dimension free setting, there are many different types of extreme points. Of particular importance are free extreme points, a highly restricted type of extreme point that is closely connected to the dilation theoretic Arveson boundary. If free extreme points span a matrix convex set through matrix convex combinations, then they satisfy a strong notion of minimality in doing so. However, not all closed bounded matrix convex sets even have free extreme points. Thus, a major goal is to determine which matrix convex sets are spanned by their free extreme points. Building on a recent work of J. W. Helton and the author which shows that free spectrahedra, i.e., dimension free solution sets to linear matrix inequalities, are spanned by their free extreme points, we establish two additional classes of matrix convex sets which are the matrix convex hull of their free extreme points. Namely, we show that closed bounded free spectrahedrops, i.e, closed bounded projections of free spectrahedra, are the span of their free extreme points. Furthermore, we show that if one considers linear operator inequalities that have compact operator defining tuples, then the resulting ``generalized"free spectrahedra are spanned by their free extreme points.
Spin-strain coupling in nanodiamonds as a unique cluster identifier

Fluorescent nanodiamonds have been used to a large extent in various biological systems due to their robust nature, their inert properties, and the relative ease of modifying their surface for attachment to different functional groups. Within a given batch, however, each nanodiamond is indistinguishable from its neighbors and, so far, one could only rely on fluorescence statistics for some global information about the ensemble. Here, we propose and measure the possibility of adding another layer of unique information, relying on the coupling between the strain in the nanodiamond and the spin degree-of-freedom in the nitrogen-vacancy center in diamond. We show that the large variance in axial and transverse strain can be encoded to an individual radio frequency identity for a cluster of nanodiamonds. When using single nanodiamonds, this unique fingerprint can then be potentially tracked in real-time in, e.g., cells, as their size is compatible with metabolism intake. From a completely different aspect, in clusters of nanodiamonds, this can already serve as a platform for anti-counterfeiting measures.
ScatterShot: Interactive In-context Example Curation for Text Transformation

The in-context learning capabilities of LLMs like GPT-3 allow annotators to customize an LLM to their specific tasks with a small number of examples. However, users tend to include only the most obvious patterns when crafting examples, resulting in underspecified in-context functions that fall short on unseen cases. Further, it is hard to know when “enough” examples have been included even for known patterns. In this work, we present ScatterShot, an interactive system for building high-quality demonstration sets for in-context learning. ScatterShot iteratively slices unlabeled data into task-specific patterns, samples informative inputs from underexplored or not-yet-saturated slices in an active learning manner, and helps users label more efficiently with the help of an LLM and the current example set. In simulation studies on two text perturbation scenarios, ScatterShot sampling improves the resulting few-shot functions by 4-5 percentage points over random sampling, with less variance as more examples are added. In a user study, ScatterShot greatly helps users in covering different patterns in the input space and labeling in-context examples more efficiently, resulting in better in-context learning and less user effort.
A validated finite element model for room acoustic treatments with edge absorbers

Porous acoustic absorbers have excellent properties in the low-frequency range when positioned in room edges, therefore they are a common method for reducing low-frequency reverberation. However, standard room acoustic simulation methods such as ray tracing and mirror sources are invalid for low frequencies in general which is a consequence of using geometrical methods, yielding a lack of simulation tools for these so-called edge absorbers. In this article, a validated finite element simulation model is presented, which is able to predict the effect of an edge absorber on the acoustic field. With this model, the interaction mechanisms between room and absorber can be studied by high-resolved acoustic field visualizations in both room and absorber. The finite element model is validated against transfer function data computed from impulse response measurements in a reverberation chamber in style of ISO 354. The absorber made of Basotect® is modeled using the Johnson-Champoux-Allard-Lafarge model, which is fitted to impedance tube measurements using the four-microphone transfer matrix method. It is shown that the finite element simulation model is able to predict the influence of different edge absorber configurations on the measured transfer functions to a high degree of accuracy. The evaluated third-octave band error exhibits deviations of 3.3–4.1 dB computed from third-octave band averaged spectra.
Large-scale structures in a forced turbulent mixing layer

The large-scale structures that occur in a forced turbulent mixing layer at moderately high Reynolds numbers have been modelled by linear inviscid stability theory incorporating first-order corrections for slow spatial variations of the mean flow. The perturbation stream function for a spatially growing time-periodic travelling wave has been numerically evaluated for the measured linearly diverging mean flow. In an accompanying experiment periodic oscillations were imposed on the turbulent mixing layer by the motion of a small flap at the trailing edge of the splitter plate that separated the two uniform streams of different velocity. The results of the numerical computations are compared with experimental measurements. When the comparison between experimental data and the computational model was made on a purely local basis, agreement in both the amplitude and phase distribution across the mixing layer was excellent. Comparisons on a global scale revealed, not unexpectedly, less good accuracy in predicting the overall amplification.