Miracle-dz/UniFAR-FTUs huggingface dataset:
A dichotomy for succinct representations of homomorphisms

The task of computing homomorphisms between two finite relational structures $\mathcal{A}$ and $\mathcal{B}$ is a well-studied question with numerous applications. Since the set $\operatorname{Hom}(\mathcal{A},\mathcal{B})$ of all homomorphisms may be very large having a method of representing it in a succinct way, especially one which enables us to perform efficient enumeration and counting, could be extremely useful. One simple yet powerful way of doing so is to decompose $\operatorname{Hom}(\mathcal{A},\mathcal{B})$ using union and Cartesian product. Such data structures, called d-representations, have been introduced by Olteanu and Zavodny in the context of database theory. Their results also imply that if the treewidth of the left-hand side structure $\mathcal{A}$ is bounded, then a d-representation of polynomial size can be found in polynomial time. We show that for structures of bounded arity this is optimal: if the treewidth is unbounded then there are instances where the size of any d-representation is superpolynomial. Along the way we develop tools for proving lower bounds on the size of d-representations, in particular we define a notion of reduction suitable for this context and prove an almost tight lower bound on the size of d-representations of all $k$-cliques in a graph.
Synthesizing Annotated Image and Video Data Using a Rendering-Based Pipeline for Improved License Plate Recognition

An insufficient number of training samples is a common problem in neural network applications. While data augmentation methods require at least a minimum number of samples, we propose a novel, rendering-based pipeline for synthesizing annotated data sets. Our method does not modify existing samples but synthesizes entirely new samples. The proposed rendering-based pipeline is capable of generating and annotating synthetic and partly-real image and video data in a fully automatic procedure. Moreover, the pipeline can aid the acquisition of real data. The proposed pipeline is based on a rendering process. This process generates synthetic data. Partly-real data bring the synthetic sequences closer to reality by incorporating real cameras during the acquisition process. The benefits of the proposed data generation pipeline, especially for machine learning scenarios with limited available training data, are demonstrated by an extensive experimental validation in the context of automatic license plate recognition. The experiments demonstrate a significant reduction of the character error rate and miss rate from 73.74% and 100% to 14.11% and 41.27% respectively, compared to an OCR algorithm trained on a real data set solely. These improvements are achieved by training the algorithm on synthesized data solely. When additionally incorporating real data, the error rates can be decreased further. Thereby, the character error rate and miss rate can be reduced to 11.90% and 39.88% respectively. All data used during the experiments as well as the proposed rendering-based pipeline for the automated data generation is made publicly available under (URL will be revealed upon publication).
SymmNeRF: Learning to Explore Symmetry Prior for Single-View View Synthesis

We study the problem of novel view synthesis of objects from a single image. Existing methods have demonstrated the potential in single-view view synthesis. However, they still fail to recover the fine appearance details, especially in self-occluded areas. This is because a single view only provides limited information. We observe that manmade objects usually exhibit symmetric appearances, which introduce additional prior knowledge. Motivated by this, we investigate the potential performance gains of explicitly embedding symmetry into the scene representation. In this paper, we propose SymmNeRF, a neural radiance field (NeRF) based framework that combines local and global conditioning under the introduction of symmetry priors. In particular, SymmNeRF takes the pixel-aligned image features and the corresponding symmetric features as extra inputs to the NeRF, whose parameters are generated by a hypernetwork. As the parameters are conditioned on the image-encoded latent codes, SymmNeRF is thus scene-independent and can generalize to new scenes. Experiments on synthetic and real-world datasets show that SymmNeRF synthesizes novel views with more details regardless of the pose transformation, and demonstrates good generalization when applied to unseen objects. Code is available at: https://github.com/xingyi-li/SymmNeRF.
Lattice Linear Algorithms ∗

This paper focuses on analyzing and diﬀerentiating between lattice linear problems and algorithms. It introduces a new class of algorithms called (fully) lattice linear algorithms . A property of these algorithms is that they induce a partial order among all states and form multiple lattices . An initial state locks in one of these lattices. We present a lattice linear self-stabilizing algorithm for minimal dominating set.
Equivariant maps from invariant functions

In equivariant machine learning the idea is to restrict the learning to a hypothesis class where all the functions are equivariant with respect to some group action. Irreducible representations or invariant theory are typically used to parameterize the space of such functions. In this note, we explicate a general procedure, attributed to Malgrange, to express all polynomial maps between linear spaces that are equivariant with respect to the action of a group G , given a characterization of the invariant polynomials on a bigger space. The method also parametrizes smooth equivariant maps in the case that G is a compact Lie group.
Gerador de malhas de elementos finitos para a simulação numérica de propagação de ondas marítimas

The mesh generator GMALHA was developed for the construction of non-structured triangular meshes used in sea wave propagation finite element models. For a given coastal zone delimited by a boundary line and characterised by its bathymetry, GMALHA generates an optimal triangular mesh. The boundary, which sometimes can be very complex, includes a coastline with port infrastructures, beaches, marinas, islands, etc. . Based on that boundary and bathymetric information within it, GMALHA, first generates a rough triangular mesh that fills the domain. The mesh is then subjected to post-processing, such as: local refinement and optimization (control of elements uniformity, repositioning of points to correct angles and edge swaps to correct node valence). This paper describes the generation, refinement and optimization algorithms of GMALHA. The advantages of this generator are also illustrated with some practical cases of sea wave propagation in coastal areas.
Radio Emission of Nearby Early-type Galaxies in the Low and Very Low Radio Luminosity Range

We analyze radio continuum emission of early-type galaxies with dynamical measurements of central supermassive black hole (SMBH) masses and well-characterized large-scale environments, but regardless of the exact level of the nuclear activity. The 1.4 GHz radio fluxes collected with ∼arcmin resolution for 62 nearby targets (distances ≲153 Mpc) correspond to low and very low monochromatic luminosities of L r ∼ 1035–1041 erg s−1. We quantify possible correlations between the radio properties with the main parameters of SMBHs, host galaxies, and hot gaseous halos, finding a general bimodality in the radio luminosity distribution, with the borderline between radio-bright and radio-dim populations at logLr/LEdd≃−8.5 . We analyze the far-infrared data for the targets, finding that all radio-bright and over a half of the radio-dim sources are overluminous in radio wavelengths with respect to the far-infrared–radio correlation. High-resolution radio maps reveal that the overwhelming majority of radio-dim sources is unresolved on the arcsecond scale, while the bulk of radio-bright sources display extended jets and lobes of low- and intermediate-power radio galaxies; these jets dominate the radio emission of radio-bright objects. Regarding the origin of the radio emission of radio-dim sources, we discuss two main possibilities. One possibility is the advection-dominated accretion flow model, in which the radio and nuclear X-ray radiative outputs at very low accretion rates are both dominated by unresolved jets. The other possibility is that the radio-dim sources, unlike the radio-bright ones, are characterized by low values of SMBH spins, so that their radio emission is not related to the jets, but instead is due to a combination of star-forming processes and previous nuclear outbursts.
On the Fourier dimension and a modification

We give a sufficient condition for the Fourier dimension of a countable union of sets to equal the supremum of the Fourier dimensions of the sets in the union, and show by example that the Fourier dimension is not countably stable in general. A natural approach to finite stability of the Fourier dimension for sets would be to try to prove that the Fourier dimension for measures is finitely stable, but we give an example showing that it is not in general. We also describe some situations where the Fourier dimension for measures is stable or is stable for all but one value of some parameter. Finally we propose a way of modifying the definition of the Fourier dimension so that it becomes countably stable, and show that a measure has modified Fourier dimension greater than or equal to $s$ if and only if it annihilates all sets with modified Fourier dimension less than $s$.
THE STAR FORMATION HISTORY OF LEO T FROM HUBBLE SPACE TELESCOPE IMAGING

We present the star formation history (SFH) of the faintest known star-forming galaxy, Leo T, based on deep imaging taken with the Hubble Space Telescope (HST) Wide Field Planetary Camera 2 (WFPC2). The HST/WFPC2 color–magnitude diagram (CMD) of Leo T is exquisitely deep, extending ∼2 mag below the oldest main-sequence turnoff, permitting excellent constraints on star formation at all ages. We use a maximum likelihood CMD fitting technique to measure the SFH of Leo T assuming three different sets of stellar evolution models: Padova (solar-scaled metallicity) and BaSTI (both solar-scaled and α-enhanced metallicities). The resulting SFHs are remarkably consistent at all ages, indicating that our derived SFH is robust to the choice of stellar evolution model. From the lifetime SFH of Leo T, we find that 50% of the total stellar mass formed prior to z ∼ 1 (7.6 Gyr ago). Subsequent to this epoch, the SFH of Leo T is roughly constant until the most recent ∼25 Myr, where the SFH shows an abrupt drop. This decrease could be due to a cessation of star formation or stellar initial mass function sampling effects, but we are unable to distinguish between the two scenarios. Overall, our measured SFH is consistent with previously derived SFHs of Leo T. However, the HST-based solution provides improved age resolution and reduced uncertainties at all epochs. The SFH, baryonic gas fraction, and location of Leo T are unlike any of the other recently discovered faint dwarf galaxies in the Local Group, and instead bear strong resemblance to gas-rich dwarf galaxies (irregular or transition), suggesting that gas-rich dwarf galaxies may share common modes of star formation over a large range of stellar mass (∼105–109 M☉).
Multi-Robot Coordination and Cooperation with Task Precedence Relationships

We propose a new formulation for the multi-robot task planning and allocation problem that incorporates (a) precedence relationships between tasks; (b) coordination for tasks allowing multiple robots to achieve increased efficiency; and (c) cooperation through the formation of robot coalitions for tasks that cannot be performed by individual robots alone. In our formulation, the tasks and the relationships between the tasks are specified by a task graph. We define a set of reward functions over the task graph's nodes and edges. These functions model the effect of robot coalition size on task performance while incorporating the influence of one task's performance on a dependent task. Solving this problem optimally is NP-hard. However, using the task graph formulation allows us to leverage min-cost network flow approaches to obtain approximate solutions efficiently. Additionally, we explore a mixed integer programming approach, which gives optimal solutions for small instances of the problem but is computationally expensive. We also develop a greedy heuristic algorithm as a baseline. Our modeling and solution approaches result in task plans that leverage task precedence relationships and robot coordination and cooperation to achieve high mission performance, even in large missions with many agents.
Robust Bayesian Non-segmental Detection of Multiple Change-points

Change-points detection has long been important and active research areas with broad application in economics, medical research, genetics, social science, etc. It includes themes of the number, locations, and jump sizes of change-points. However, most existing methods focus on segment parameters or features, regardless of Bayesian or frequentist. We propose an innovative non-segmental approach to detect multiple change-points by concentrating the abrupt changes into a global distributional parameter, which is characterized by a function of states of the system. We construct a class of discrete spike and Cauchy-slab variate prior, which distinguishes from existing such two-group mixture priors by a dynamic rate of a latent indicator. A 3-sigma discrimination criterion of change-points is built with sigma being the standard deviation of the sequence of diﬀerences between marginal maximum a posteriori estimates on two adjacent discretized states. It intrinsically guarantees reasonable false positive rate to prevent over-detection. The proposed method is powerful and robust to unveil structure changes of the autoregression model for house prices in London and the linear regression model for age-speciﬁc fertility in US, not to mention consistent detection results of shifts of mean or scale on known data sets. Abundant simulations demonstrate that the proposed method outperforms state-of-the-art others in ﬁnite-sample performance. An R package BaRDCP is developed for detecting changes in mean, scale, and the regression or autocorrelation coeﬃcient.
Batch Normalization Explained

A critically important, ubiquitous, and yet poorly understood ingredient in modern deep networks (DNs) is batch normalization (BN), which centers and normalizes the feature maps. To date, only limited progress has been made understanding why BN boosts DN learning and inference performance; work has focused exclusively on showing that BN smooths a DN's loss landscape. In this paper, we study BN theoretically from the perspective of function approximation; we exploit the fact that most of today's state-of-the-art DNs are continuous piecewise affine (CPA) splines that fit a predictor to the training data via affine mappings defined over a partition of the input space (the so-called"linear regions"). {\em We demonstrate that BN is an unsupervised learning technique that -- independent of the DN's weights or gradient-based learning -- adapts the geometry of a DN's spline partition to match the data. } BN provides a"smart initialization"that boosts the performance of DN learning, because it adapts even a DN initialized with random weights to align its spline partition with the data. We also show that the variation of BN statistics between mini-batches introduces a dropout-like random perturbation to the partition boundaries and hence the decision boundary for classification problems. This per mini-batch perturbation reduces overfitting and improves generalization by increasing the margin between the training samples and the decision boundary.
CompNet: A Designated Model to Handle Combinations of Images and Designed features

Convolutional neural networks (CNNs) are one of the most popular models of Artificial Neural Networks (ANN)s in Computer Vision (CV). A variety of CNN-based structures were developed by researchers to solve problems like image classification, object detection, and image similarity measurement. Although CNNs have shown their value in most cases, they still have a downside: they easily overfit when there are not enough samples in the dataset. Most medical image datasets are examples of such a dataset. Additionally, many datasets also contain both designed features and images, but CNNs can only deal with images directly. This represents a missed opportunity to leverage additional information. For this reason, we propose a new structure of CNN-based model: CompNet, a composite convolutional neural network. This is a specially designed neural network that accepts combinations of images and designed features as input in order to leverage all available information. The novelty of this structure is that it uses learned features from images to weight designed features in order to gain all information from both images and designed features. With the use of this structure on classification tasks, the results indicate that our approach has the capability to significantly reduce overfitting. Furthermore, we also found several similar approaches proposed by other researchers that can combine images and designed features. To make comparison, we first applied those similar approaches on LIDC and compared the results with the CompNet results, then we applied our CompNet on the datasets that those similar approaches originally used in their works and compared the results with the results they proposed in their papers. All these comparison results showed that our model outperformed those similar approaches on classification tasks either on LIDC dataset or on their proposed datasets.
Biological connectomes as a representation for the Architecture of Artificial Neural Networks

Grand efforts in neuroscience are working toward mapping the connectomes of many new species, including the near completion of the Drosophila melanogaster. It is important to ask whether these models could benefit artificial intelligence. In this work we ask two fundamental questions: (1) where and when biological connectomes can provide use in machine learning, (2) which design principles are necessary for extracting a good representation of the connectome. Toward this end, we translate the motor circuit of the C. Elegans nematode into artificial neural networks at varying levels of biophysical realism and evaluate the outcome of training these networks on motor and non-motor behavioral tasks. We demonstrate that biophysical realism need not be upheld to attain the advantages of using biological circuits. We also establish that, even if the exact wiring diagram is not retained, the architectural statistics provide a valuable prior. Finally, we show that while the C. Elegans locomotion circuit provides a powerful inductive bias on locomotion problems, its structure may hinder performance on tasks unrelated to locomotion such as visual classification problems.
Clinical Language Understanding Evaluation (CLUE)

Clinical language processing has received a lot of attention in recent years, resulting in new models or methods for disease phenotyping, mortality prediction, and other tasks. Unfortunately, many of these approaches are tested under different experimental settings (e.g., data sources, training and testing splits, metrics, evaluation criteria, etc.) making it difficult to compare approaches and determine state-of-the-art. To address these issues and facilitate reproducibility and comparison, we present the Clinical Language Understanding Evaluation (CLUE) benchmark with a set of four clinical language understanding tasks, standard training, development, validation and testing sets derived from MIMIC data, as well as a software toolkit. It is our hope that these data will enable direct comparison between approaches, improve reproducibility, and reduce the barrier-to-entry for developing novel models or methods for these clinical language understanding tasks.
META-STORM: Generalized Fully-Adaptive Variance Reduced SGD for Unbounded Functions

We study the application of variance reduction (VR) techniques to general non-convex stochastic optimization problems. In this setting, the recent work STORM [3] overcomes the drawback of having to compute gradients of “mega-batches” that earlier VR methods rely on. There, STORM utilizes recursive momentum to achieve the VR effect and is then later made fully adaptive in STORM+ [13], where full-adaptivity removes the requirement for obtaining certain problem-specific parameters such as the smoothness of the objective and bounds on the variance and norm of the stochastic gradients in order to set the step size. However, STORM+ crucially relies on the assumption that the function values are bounded, excluding a large class of useful functions. In this work, we propose META-STORM, a generalized framework of STORM+ that removes this bounded function values assumption while still attaining the optimal convergence rate for non-convex optimization. META-STORM not only maintains full-adaptivity, removing the need to obtain problem specific parameters, but also improves the convergence rate’s dependency on the problem parameters. Furthermore, META-STORM can utilize a large range of parameter settings that subsumes previous methods allowing for more flexibility in a wider range of settings. Finally, we demonstrate the effectiveness of META-STORM through experiments across common deep learning tasks. Our algorithm improves upon the previous work STORM+ and is competitive with widely used algorithms after the addition of per-coordinate update and exponential moving average heuristics.
Using Multivariate Linear Regression for Biochemical Oxygen Demand Prediction in Waste Water

There exist opportunities for Multivariate Linear Regression (MLR) in the prediction of Biochemical Oxygen Demand (BOD) in waste water, using the diverse water quality parameters as the input variables. The goal of this work is to examine the capability of MLR in prediction of BOD in waste water through four input variables: Dissolved Oxygen (DO), Nitrogen, Fecal Coliform and Total Coliform. The four input variables have higher correlation strength to BOD out of the seven parameters examined for the strength of correlation. Machine Learning (ML) was done with both 80% and 90% of the data as the training set and 20% and 10% as the test set respectively. MLR performance was evaluated through the coefficient of correlation (r), Root Mean Square Error (RMSE) and the percentage accuracy in prediction of BOD. The performance indices for the input variables of Dissolved Oxygen, Nitrogen, Fecal Coliform and Total Coliform in prediction of BOD are: RMSE=6.77mg/L, r=0.60 and accuracy 70.3% for training dataset of 80% and RMSE=6.74mg/L, r=0.60 and accuracy of 87.5% for training set of 90% of the dataset. It was found that increasing the percentage of the training set above 80% of the dataset improved the accuracy of the model only but did not have a significant impact on the prediction capacity of the model. The results showed that MLR model could be successfully employed in the estimation of BOD in waste water using appropriately selected input parameters.
A Two-Stage Method for Chinese AMR Parsing

In this paper, we provide a detailed description of our system at CAMRP-2022 evaluation. We firstly propose a two-stage method to conduct Chinese AMR Parsing with alignment generation, which includes Concept-Prediction and Relation-Prediction stages. Our model achieves 0.7756 and 0.7074 Align-Smatch F1 scores on the CAMR 2.0 test set and the blind-test set of CAMRP-2022 individually. We also analyze the result and the limitation such as the error propagation and class imbalance problem we conclude in the current method. Code and the trained models are released at https://github.com/PKUnlp-icler/Two-Stage-CAMRP for reproduction.