Miracle-dz/UniFAR-FTUs huggingface dataset:
Deep Point Cloud Reconstruction

Point cloud obtained from 3D scanning is often sparse, noisy, and irregular. To cope with these issues, recent studies have been separately conducted to densify, denoise, and complete inaccurate point cloud. In this paper, we advocate that jointly solving these tasks leads to significant improvement for point cloud reconstruction. To this end, we propose a deep point cloud reconstruction network consisting of two stages: 1) a 3D sparse stacked-hourglass network as for the initial densification and denoising, 2) a refinement via transformers converting the discrete voxels into 3D points. In particular, we further improve the performance of transformer by a newly proposed module called amplified positional encoding. This module has been designed to differently amplify the magnitude of positional encoding vectors based on the points' distances for adaptive refinements. Extensive experiments demonstrate that our network achieves state-of-the-art performance among the recent studies in the ScanNet, ICL-NUIM, and ShapeNetPart datasets. Moreover, we underline the ability of our network to generalize toward real-world and unmet scenes.
A Systematic Study of Isomorphism Invariants of Finite Groups via the Weisfeiler-Leman Dimension

We investigate the relationship between various isomorphism invariants for finite groups. Specifically, we use the Weisfeiler-Leman dimension (WL) to characterize, compare and quantify the effectiveness and complexity of invariants for group isomorphism. It turns out that a surprising number of invariants and characteristic subgroups that are classic to group theory can be detected and identified by a low dimensional Weisfeiler-Leman algorithm. These include the center, the inner automorphism group, the commutator subgroup and the derived series, the abelian radical, the solvable radical, the Fitting group and $\pi$-radicals. A low dimensional WL algorithm additionally determines the isomorphism type of the socle as well as the factors in the derived series and the upper and lower central series. We also analyze the behavior of the WL algorithm for group extensions and prove that a low dimensional WL algorithm determines the isomorphism types of the composition factors of a group. Finally we develop a new tool to define a canonical maximal central decomposition for groups. This allows us to show that the Weisfeiler-Leman dimension of a group is at most one larger than the dimensions of its direct indecomposable factors. In other words the Weisfeiler-Leman dimension increases by at most 1 when taking direct products.
Schedule Based Temporal Difference Algorithms

Learning the value function of a given policy from data samples is an important problem in Reinforcement Learning. TD <tex>$(\lambda)$</tex> is a popular class of algorithms to solve this problem. However, the weights assigned to different <tex>$n$</tex> -step returns in TD <tex>$(\lambda)$</tex>, controlled by the parameter <tex>$\lambda$</tex>, decrease exponentially with increasing <tex>$n$</tex>. In this paper, we present a <tex>$\lambda$</tex> -schedule procedure that generalizes the TD <tex>$(\lambda)$</tex> algorithm to the case when the parameter <tex>$\lambda$</tex> could vary with time-step. This allows flexibility in weight assignment, i.e., the user can specify the weights assigned to different <tex>$n$</tex> -step returns by choosing a sequence <tex>$\{\lambda_{t}\}_{t\geq 1}$</tex>. Based on this procedure, we propose an on-policy algorithm - TD <tex>$(\lambda)\text{-}$</tex> schedule, and two off-policy algorithms - GTD <tex>$(\lambda)$</tex> -schedule and TDC <tex>$(\lambda)$</tex> -schedule, respectively. We provide proofs of almost sure convergence for all three algorithms under a general Markov noise framework.
Adversarial Sampling for Solving Differential Equations with Neural Networks

Neural network-based methods for solving differential equations have been gaining traction. They work by improving the differential equation residuals of a neural network on a sample of points in each iteration. However, most of them employ standard sampling schemes like uniform or perturbing equally spaced points. We present a novel sampling scheme which samples points adversarially to maximize the loss of the current solution estimate. A sampler architecture is described along with the loss terms used for training. Finally, we demonstrate that this scheme outperforms pre-existing schemes by comparing both on a number of problems.
Satisfiability of Constrained Horn Clauses on Algebraic Data Types: A Transformation-based Approach

We address the problem of checking the satisfiability of Constrained Horn Clauses (CHCs) defined on Algebraic Data Types (ADTs), such as lists and trees. We propose a new technique for transforming CHCs defined on ADTs into CHCs where the arguments of the predicates have only basic types, such as integers and booleans. Thus, our technique avoids, during satisfiability checking, the explicit use of proof rules based on induction over the ADTs. The main extension over previous techniques for ADT removal is a new transformation rule, called differential replacement, which allows us to introduce auxiliary predicates, whose definitions correspond to lemmas that are used when making inductive proofs. We present an algorithm that performs the automatic removal of ADTs by applying the new rule, together with the traditional folding/unfolding rules. We prove that, under suitable hypotheses, the set of the transformed clauses is satisfiable if and only if so is the set of the original clauses. By an experimental evaluation, we show that the use of the new rule significantly improves the effectiveness of ADT removal. We also show that our approach is competitive with respect to tools that extend CHC solvers with the use of inductive rules.
Quasiuniversal scaling in mouse-brain neuronal activity stems from edge-of-instability critical dynamics

The brain is in a state of perpetual reverberant neural activity, even in the absence of specific tasks or stimuli. Shedding light on the origin and functional significance of such a dynamical state is essential to understanding how the brain transmits, processes, and stores information. An inspiring, albeit controversial, conjecture proposes that some statistical characteristics of empirically observed neuronal activity can be understood by assuming that brain networks operate in a dynamical regime near the edge of a phase transition. Moreover, the resulting critical behavior, with its concomitant scale invariance, is assumed to carry crucial functional advantages. Here, we present a data-driven analysis based on simultaneous high-throughput recordings of the activity of thousands of individual neurons in various regions of the mouse brain. To analyze these data, we synergistically combine cutting-edge methods for the study of brain activity (such as a phenomenological renormalization group approach and techniques that infer the general dynamical state of a neural population), while designing complementary tools. This strategy allows us to uncover strong signatures of scale invariance that is ”quasi-universal” across brain regions and reveal that all these areas operate, to a greater or lesser extent, near the edge of instability. Furthermore, this framework allows us to distinguish between quasi-universal background activity and non-universal input-related activity. Taken together, this study provides strong evidence that brain networks actually operate in a critical regime which, among other functional advantages, provides them with a scale-invariant substrate of activity covariances that can sustain optimal input representations.
On Data-centric Myths

The community lacks theory-informed guidelines for building good data sets. We analyse theoretical directions relating to what aspects of the data matter and conclude that the intuitions derived from the existing literature are incorrect and misleading. Using empirical counter-examples, we show that 1) data dimension should not necessarily be minimised and 2) when manipulating data, preserving the distribution is inessential. This calls for a more data-aware theoretical understanding. Although not explored in this work, we propose the study of the impact of data modification on learned representations as a promising research direction.
On quasi-2-transitive actions of branch groups

An action of a group G on a set X is said to be quasi-n-transitive if the diagonal action of G on Xn has only finitely many orbits. We show that branch groups, a special class of groups of automorphisms of rooted trees, cannot act quasi-2-transitively on infinite sets.
Glueballs at physical pion mass

Glueballs are investigated through gluonic operators on two RBC/UKQCD gauge ensembles at the physical pion mass. The statistical errors of glueball correlation functions are considerably reduced through the cluster decomposition error reduction (CDER) method. The Bethe-Salpeter wave functions are obtained for the scalar, tensor, and pseudoscalar glueballs by using spatially extended glueball operators defined through the gauge potential in the Coulomb gauge. These wave functions exhibit similar features of non-relativistic two-gluon systems and are used to optimize the signals of the related correlation functions at the early time regions, where the ground state masses are extracted. These masses are close to those from the quenched approximation and indicate the possible existence of glueballs at the physical point. The resonance feature of glueballs and the mixing with conventional mesons and multi-hadron systems should be considered in a more systematic lattice study.
Image Based Reconstruction of Liquids from 2D Surface Detections

In this work, we present a solution to the challenging problem of reconstructing liquids from image data. The challenges in reconstructing liquids, which is not faced in previous reconstruction works on rigid and deforming surfaces, lies in the inability to use depth sensing and color features due the variable index of refraction, opacity, and environmental reflections. Therefore, we limit ourselves to only surface detections (i.e. binary mask) of liquids as observations and do not assume any prior knowledge on the liquids properties. A novel optimization problem is posed which reconstructs the liquid as particles by minimizing the error between a rendered surface from the particles and the surface detections while satisfying liquid constraints. Our solvers to this optimization problem are presented and no training data is required to apply them. We also propose a dynamic prediction to seed the reconstruction optimization from the previous time-step. We test our proposed methods in simulation and on two new liquid datasets which we open source11https://github.com/ucsdarclab/liquid_reconstruction so the broader research community can continue developing in this under explored area.
Weakly-Supervised Cloud Detection with Fixed-Point GANs

The detection of clouds in satellite images is an essential preprocessing task for big data in remote sensing. Convolutional neural networks (CNNs) have greatly advanced the state-of-the-art in the detection of clouds in satellite images, but existing CNN-based methods are costly as they require large amounts of training images with expensive pixel-level cloud labels. To alleviate this cost, we propose Fixed-Point GAN for Cloud Detection (FCD), a weakly-supervised approach. Training with only image-level labels, we learn fixed-point translation between clear and cloudy images, so only clouds are affected during translation. Doing so enables our approach to predict pixel-level cloud labels by translating satellite images to clear ones and setting a threshold to the difference between the two images. Moreover, we propose FCD+, where we exploit the label-noise robustness of CNNs to refine the prediction of FCD, leading to further improvements. We demonstrate the effectiveness of our approach on the Landsat-8 Biome cloud detection dataset, where we obtain performance close to existing fully-supervised methods that train with expensive pixel-level labels. By fine-tuning our FCD+ with just 1% of the available pixel-level labels, we match the performance of fully-supervised methods. Our source code is publicly available at https://github.com/jnyborg/fcd.
Optimizing Pricing, Repositioning, En-Route Time, and Idle Time in Ride-Hailing Systems

In ride-hailing systems, en-route time refers to the time that elapses from the moment a car is dispatched to pick up a rider until the rider is picked up. A fundamental phenomenon in ride-hailing systems is that there is a trade-off between en-route time and the time that a car waits for a dispatch. In short, if cars spend little time idle waiting for a dispatch, then few cars are available when a rider makes a request, and thus the mean distance between a rider and the closest available car is long, which means that en-route time is long. This phenomenon is of great importance in ride-hailing, because en-route time increases rapidly as the number of idle cars decreases, and every minute that a car spends en-route is one minute less that the car can transport riders. In spite of this, the existing literature on price optimization for ride-hailing, and on repositioning optimization for ride-hailing, ignores en-route time. Initial attempts to take this trade-off for the mean en-route time into account when considering price optimization or repositioning optimization all resulted in intractable optimization problems. Then we found a way to reformulate a simultaneous price and repositioning optimization problem, that takes this trade-off for the distribution of en-route time into account, as a tractable convex optimization problem. We show how the optimal solution can be used to construct policies that perform much better in simulations than the policies proposed in previous papers. 1 ar X iv :2 11 1. 11 55 1v 1 [ m at h. O C ] 2 2 N ov 2 02 1
Assessing students’ learning of primary science in the multicultural context of Singapore: Considerations influencing task selection for formative assessment

This research reports the considerations influencing task selection for formative assessment among 30 primary school science teachers. Education and assessment are high stake enterprises in this multicultural city-state of Singapore. The 39 participants were chosen through random sampling from six primary schools located at different parts of Singapore. The participants responded to an instrument comprising of activities on the concepts of electrical circuits and conductors. The activities, set in different contexts but based on the same learning outcomes, were presented to the participants as possible tasks to assess students’ learning. The participants’ responses to the questions were analysed. The findings revealed that the teachers prioritised students’ abilities and their learning over and above other factors. The writers argued that the teachers’ focus on students’ abilities may work against the current initiative of inquiry approach towards teaching and learning. While studies on teachers’ conceptions on assessment have been undertaken, the contribution of this paper lies in illuminating influences on the implementation of formative assessment in Singapore primary science classrooms.
Probing the Structure of String Theory Vacua with Genetic Algorithms and Reinforcement Learning

Identifying string theory vacua with desired physical properties at low energies requires searching through high-dimensional solution spaces - collectively referred to as the string landscape. We highlight that this search problem is amenable to reinforcement learning and genetic algorithms. In the context of flux vacua, we are able to reveal novel features (suggesting previously unidentified symmetries) in the string theory solutions required for properties such as the string coupling. In order to identify these features robustly, we combine results from both search methods, which we argue is imperative for reducing sampling bias.
Component Transfer Learning for Deep RL Based on Abstract Representations

In this work we investigate a specific transfer learning approach for deep reinforcement learning in the context where the internal dynamics between two tasks are the same but the visual representations differ. We learn a low-dimensional encoding of the environment, meant to capture summarizing abstractions, from which the internal dynamics and value functions are learned. Transfer is then obtained by freezing the learned internal dynamics and value functions, thus reusing the shared low-dimensional embedding space. When retraining the encoder for transfer, we make several observations: (i) in some cases, there are local minima that have small losses but a mismatching embedding space, resulting in poor task performance and (ii) in the absence of local minima, the output of the encoder converges in our experiments to the same embedding space, which leads to a fast and efficient transfer as compared to learning from scratch. The local minima are caused by the reduced degree of freedom of the optimization process caused by the frozen models. We also find that the transfer performance is heavily reliant on the base model; some base models often result in a successful transfer, whereas other base models often result in a failing transfer.
Uniqueness in determining binary grating profiles and refractive indices with a single incoming wave

We investigate inverse diffraction problems for penetrable gratings in a piecewise constant medium. In the TE polarization case, it is proved that a binary grating profile together with the refractive index beneath it can be uniquely determined by the near-field observation data incited by a single plane wave and measured on a line segment above the grating. Our approach relies on the expansion of solutions to the Helmholtz equation and the corner singularity analysis of solutions to the inhomogeneous Laplace equation with a piecewise continuous source term in a sector. This paper also contributes to corner scattering theory for the Helmholtz equation in a special non-convex domain.
A Modular Framework for Centrality and Clustering in Complex Networks

The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important such network analysis techniques, namely, centrality and clustering. An information-flow based model is adopted for clustering, which itself builds upon an information theoretic measure for computing centrality. Our principal contributions include (1) a generalized model of Markov entropic centrality with the flexibility to tune the importance of node degrees, edge weights and directions, with a closed-form asymptotic analysis, which (2) leads to a novel two-stage graph clustering algorithm. The centrality analysis helps reason about the suitability of our approach to cluster a given graph, and determine ‘query’ nodes, around which to explore local community structures, leading to an agglomerative clustering mechanism. Our clustering algorithm naturally inherits the flexibility to accommodate edge directionality, as well as different interpretations and interplay between edge weights and node degrees. Extensive benchmarking experiments are provided, using both real-world networks with ground truth and synthetic networks.
Columnar Formats for Schemaless LSM-based Document Stores

In the last decade, document store database systems have gained more traction for storing and querying large volumes of semi-structured data. However, the flexibility of the document stores' data models has limited their ability to store data in a column-major layout --- making them less performant for analytical workloads than column store relational databases. In this paper, we propose several techniques based on piggy-backing on Log-Structured Merge (LSM) tree events and tailored to document stores to store data in a columnar layout. We first extend the Dremel format, a popular on-disk columnar format for semi-structured data, to comply with document stores' flexible data model. We then introduce a new columnar layout for organizing and storing data in LSM-based storage. We also highlight the potential of using query compilation techniques for document stores, where values' types are known only at runtime. We have implemented and evaluated our techniques to measure their impact on storage, data ingestion, and query performance in Apache AsterixDB. Our experiments show significant performance gains, improving the query execution time by orders of magnitude while minimally impacting ingestion performance.
Interpolating Population Distributions using Public-Use Data: An Application to Income Segregation using American Community Survey Data

Abstract The presence of income inequality is an important problem to demographers, policy makers, economists, and social scientists. A causal link has been hypothesized between income inequality and income segregation, which measures how much households with similar incomes cluster. The information theory index is used to measure income segregation, however, critics have suggested the divergence index instead. Motivated by this, we construct both indices using American Community Survey (ACS) estimates of features of the income distribution. Since the elimination of the decennial census long form, methods of computing these indices must be updated to interpolate ACS estimates and account for survey error. We propose a novel model-based method to do this which improves on previous approaches by using more types of estimates, and by providing uncertainty quantification. We apply this method to estimate U.S. census tract-level income distributions, and in turn use these to construct both income segregation indices. We find major differences between the two indices and find evidence that the information index underestimates the relationship between income inequality and income segregation. The literature suggests interventions designed to reduce income inequality by reducing income segregation, or vice versa, so using the information index implicitly understates the value of these interventions. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
Tuning Cooperative Behavior in Games With Nonlinear Opinion Dynamics

We examine the tuning of cooperative behavior in repeated multi-agent games using an analytically tractable, continuous-time, nonlinear model of opinion dynamics. Each modeled agent updates its real-valued opinion about each available strategy in response to payoffs and other agents’ opinions, as observed over a network. We show how the model provides a principled and systematic means to investigate behavior of agents that select strategies using rationality and reciprocity, key features of human decision-making in social dilemmas. For two-strategy games, we use bifurcation analysis to prove conditions for the bistability of two equilibria and conditions for the first (second) equilibrium to reflect all agents favoring the first (second) strategy. We prove how model parameters, e.g., level of attention to opinions of others, network structure, and payoffs, influence dynamics and, notably, the size of the region of attraction to each stable equilibrium. We provide insights by examining the tuning of the bistability of mutual cooperation and mutual defection and their regions of attraction for the repeated prisoner’s dilemma and the repeated multi-agent public goods game. Our results generalize to games with more strategies, heterogeneity, and additional feedback dynamics, such as those designed to elicit cooperation or coordination.