Miracle-dz/UniFAR-FTUs huggingface dataset:
Unbiased Library of k-regular, n-sized, Connected, Small Graphs

The past decade highlighted the usefulness of social network simulations that run on k-regular, n-size, connected graphs. These can be seen as small-scale models of human social networks of large societies. By narrowing down onto k-regular graphs, the degree variation can be eliminated from the research question, which allows a focus on the isolated impact by other variables, for instance, by the clustering coefficient or the size of the network. This paper describes the generation of a random graph library that uses a random walk graph creation algorithm that starts from the"chain of caves", which is the structure in which the clustering coefficient is at its maximum. This method finds mid and high clustering coefficient graphs, while Wolfram`s RandomGraph was useful for finding low ones. The merge of the two samples proved to be somewhat biased. After eliminating a host of network measures, the paper focused on mean graph distance as a further variable and created an unbiased subsample for each size and clustering coefficient bin.
Microscopic triaxial cranking model: preliminary predictions for oscillator potential and light nuclei

The conventional cranking model for uniaxial and triaxial rotation (CCRM3) is frequently used to study rotational features in deformed nuclei. However, CCRM3 is semi-classical and phenomenological because it uses a constant angular velocity, resulting in a number of Hamiltonian symmetry breakings. To investigate the effect of a dynamic angular velocity, a quantal, microscopic, D2, signature, and time-reversal invariant cranking model for triaxial rotation (MSCRM3) is derived exactly from a unitary rigid-flow-velocity-field rotation transformation of the nuclear Schrodinger equation and Hartree-Fock method. Except for a microscopically-determined angular velocity and normally-small residual terms, the MSCRM3 and CCRM3 Schrodinger equations are identical in form. The microscopic angular velocity emerges from the HF variation, and the residual terms may become significant for triaxial rotation at high spins and in back-bending regions where and undergo large changes. A preliminary application of MSCRM3 and CCRM3 to the light nuclei 20Ne, 24Mg, and 28Si using the simple self-consistent deformed harmonic oscillator potential predicts some interesting differences between the rotational features and phenomena predicted by the two models. These differences are attributable to the impact of the dynamic angular velocity. It is important to investigate and understand these differences for the simple and realistic nuclear interactions.
BAVS: Bootstrapping Audio-Visual Segmentation by Integrating Foundation Knowledge

Given an audio-visual pair, audio-visual segmentation (AVS) aims to locate sounding sources by predicting pixel-wise maps. Previous methods assume that each sound component in an audio signal always has a visual counterpart in the image. However, this assumption overlooks that off-screen sounds and background noise often contaminate the audio recordings in real-world scenarios. They impose significant challenges on building a consistent semantic mapping between audio and visual signals for AVS models and thus impede precise sound localization. In this work, we propose a two-stage bootstrapping audio-visual segmentation framework by incorporating multi-modal foundation knowledge. In a nutshell, our BAVS is designed to eliminate the interference of background noise or off-screen sounds in segmentation by establishing the audio-visual correspondences in an explicit manner. In the first stage, we employ a segmentation model to localize potential sounding objects from visual data without being affected by contaminated audio signals. Meanwhile, we also utilize a foundation audio classification model to discern audio semantics. Considering the audio tags provided by the audio foundation model are noisy, associating object masks with audio tags is not trivial. Thus, in the second stage, we develop an audio-visual semantic integration strategy (AVIS) to localize the authentic-sounding objects. Here, we construct an audio-visual tree based on the hierarchical correspondence between sounds and object categories. We then examine the label concurrency between the localized objects and classified audio tags by tracing the audio-visual tree. With AVIS, we can effectively segment real-sounding objects. Extensive experiments demonstrate the superiority of our method on AVS datasets, particularly in scenarios involving background noise. Our project website is https://yenanliu.github. io/AVSS.github. io/.
On the impossibility of discovering a formula for primes using AI

In the present work we use maximum entropy methods to derive several theorems in probabilistic number theory, including a version of the Hardy-Ramanujan Theorem. We also provide a theoretical argument explaining the experimental observations of Y. -H. He about the learnability of primes, and posit that the Erd\H{o}s-Kac law would very unlikely be discovered by current machine learning techniques. Numerical experiments that we perform corroborate our theoretical findings.
Simulating Hydrogen-poor Interaction-powered Supernovae with CHIPS

We present the updated open-source code Complete History of Interaction-Powered Supernovae (CHIPS) that can be applied to modeling supernovae (SNe) arising from an interaction with the massive circumstellar medium (CSM) as well as the formation process of the CSM. Our update mainly concerns extensions to hydrogen-poor SNe from stripped progenitors, targeting the modeling of interaction-powered SNe Ibc, such as Type Ibn and Icn SNe. We successfully reproduce the basic properties of the light curves of these types of SNe that occur after the partial eruption of the outermost layer with a mass of 0.01–0.1 M ⊙ at ≲1 year before explosion. We also find that the luminosity of the observed precursors can be naturally explained by the outburst that creates the dense CSM, given that the energy of the outburst is efficiently dissipated by collision with an external material, possibly generated by a previous mass eruption. We discuss possible scenarios causing eruptive mass loss based on our results.
Thompson Sampling for Real-Valued Combinatorial Pure Exploration of Multi-Armed Bandit

We study the real-valued combinatorial pure exploration of the multi-armed bandit (R-CPE-MAB) problem. In R-CPE-MAB, a player is given stochastic arms, and the reward of each arm follows an unknown distribution. In each time step, a player pulls a single arm and observes its reward. The player's goal is to identify the optimal action from a finite-sized real-valued action set with as few arm pulls as possible. Previous methods in the R-CPE-MAB require enumerating all of the feasible actions of the combinatorial optimization problem one is considering. In general, since the size of the action set grows exponentially large with respect to the number of arms, this is almost practically impossible when the number of arms is large. We introduce an algorithm named the Generalized Thompson Sampling Explore (GenTS-Explore) algorithm, which is the first algorithm that can work even when the size of the action set is exponentially large with respect to the number of arms. We also introduce a novel problem-dependent sample complexity lower bound of the R-CPE-MAB problem, and show that the GenTS-Explore algorithm achieves the optimal sample complexity up to a problem-dependent constant factor.
GBM-based Bregman Proximal Algorithms for Constrained Learning

As the complexity of learning tasks surges, modern machine learning encounters a new constrained learning paradigm characterized by more intricate and data-driven function constraints. Prominent applications include Neyman-Pearson classification (NPC) and fairness classification, which entail specific risk constraints that render standard projection-based training algorithms unsuitable. Gradient boosting machines (GBMs) are among the most popular algorithms for supervised learning; however, they are generally limited to unconstrained settings. In this paper, we adapt the GBM for constrained learning tasks within the framework of Bregman proximal algorithms. We introduce a new Bregman primal-dual method with a global optimality guarantee when the learning objective and constraint functions are convex. In cases of nonconvex functions, we demonstrate how our algorithm remains effective under a Bregman proximal point framework. Distinct from existing constrained learning algorithms, ours possess a unique advantage in their ability to seamlessly integrate with publicly available GBM implementations such as XGBoost (Chen and Guestrin, 2016) and LightGBM (Ke et al., 2017), exclusively relying on their public interfaces. We provide substantial experimental evidence to showcase the effectiveness of the Bregman algorithm framework. While our primary focus is on NPC and fairness ML, our framework holds significant potential for a broader range of constrained learning applications. The source code is currently freely available at https://github.com/zhenweilin/ConstrainedGBM}{https://github.com/zhenweilin/ConstrainedGBM.
Soils for Fine Wines

1. Soil and the Environment 2. The Makeup of Soil 3. The Vine Root Habitat 4. How the Soil Supplies Nutrients 5. Nutrients for Healthy Vines and Good Wines 6. Soil-Water-Vine Relationships and Water Management 7. Soil Quality in Vineyards 8. Site Selection and Soil Preparation 9. Soil and Wine Appendices References Index
Cost-Efficient Online Decision Making: A Combinatorial Multi-Armed Bandit Approach

Online decision making plays a crucial role in numerous real-world applications. In many scenarios, the decision is made based on performing a sequence of tests on the incoming data points. However, performing all tests can be expensive and is not always possible. In this paper, we provide a novel formulation of the online decision making problem based on combinatorial multi-armed bandits and take the (possibly stochastic) cost of performing tests into account. Based on this formulation, we provide a new framework for cost-efficient online decision making which can utilize posterior sampling or BayesUCB for exploration. We provide a theoretical analysis of Thompson Sampling for cost-efficient online decision making, and present various experimental results that demonstrate the applicability of our framework to real-world problems.
Scaling up Discovery of Latent Concepts in Deep NLP Models

Despite the revolution caused by deep NLP models, they remain black boxes, necessitating research to understand their decision-making processes. A recent work by Dalvi et al. (2022) carried out representation analysis through the lens of clustering latent spaces within pre-trained models (PLMs), but that approach is limited to small scale due to the high cost of running Agglomerative hierarchical clustering. This paper studies clustering algorithms in order to scale the discovery of encoded concepts in PLM representations to larger datasets and models. We propose metrics for assessing the quality of discovered latent concepts and use them to compare the studied clustering algorithms. We found that K-Means-based concept discovery significantly enhances efficiency while maintaining the quality of the obtained concepts. Furthermore, we demonstrate the practicality of this newfound efficiency by scaling latent concept discovery to LLMs and phrasal concepts.
Decentralized Riemannian Conjugate Gradient Method on the Stiefel Manifold

The conjugate gradient method is a crucial first-order optimization method that generally converges faster than the steepest descent method, and its computational cost is much lower than that of second-order methods. However, while various types of conjugate gradient methods have been studied in Euclidean spaces and on Riemannian manifolds, there is little study for those in distributed scenarios. This paper proposes a decentralized Riemannian conjugate gradient descent (DRCGD) method that aims at minimizing a global function over the Stiefel manifold. The optimization problem is distributed among a network of agents, where each agent is associated with a local function, and the communication between agents occurs over an undirected connected graph. Since the Stiefel manifold is a non-convex set, a global function is represented as a finite sum of possibly non-convex (but smooth) local functions. The proposed method is free from expensive Riemannian geometric operations such as retractions, exponential maps, and vector transports, thereby reducing the computational complexity required by each agent. To the best of our knowledge, DRCGD is the first decentralized Riemannian conjugate gradient algorithm to achieve global convergence over the Stiefel manifold.
A Survey on Fairness in Large Language Models

Large Language Models (LLMs) have shown powerful performance and development prospects and are widely deployed in the real world. However, LLMs can capture social biases from unprocessed training data and propagate the biases to downstream tasks. Unfair LLM systems have undesirable social impacts and potential harms. In this paper, we provide a comprehensive review of related research on fairness in LLMs. Considering the influence of parameter magnitude and training paradigm on research strategy, we divide existing fairness research into oriented to medium-sized LLMs under pre-training and fine-tuning paradigms and oriented to large-sized LLMs under prompting paradigms. First, for medium-sized LLMs, we introduce evaluation metrics and debiasing methods from the perspectives of intrinsic bias and extrinsic bias, respectively. Then, for large-sized LLMs, we introduce recent fairness research, including fairness evaluation, reasons for bias, and debiasing methods. Finally, we discuss and provide insight on the challenges and future directions for the development of fairness in LLMs.
The phenomenon of revivals on complex potential Schr\"odinger's equation

The mysterious phenomena of revivals in linear dispersive periodic equations was discovered first experimentally in optics in the 19th century, then rediscovered several times by theoretical and experimental investigations. While the term has been used systematically and consistently by many authors, there is no consensus on a rigorous definition. In this paper, we describe revivals modulo a regularity condition in a large class of Schr\"odinger's equations with complex bounded potentials. As we show, at rational times the solution is given explicitly by finite linear combinations of translations and dilations of the initial datum, plus an additional continuous term.
Integrated Sensing and Communications for 3D Object Imaging via Bilinear Inference

We consider an uplink integrated sensing and communications (ISAC) scenario where the detection of data symbols from multiple user equipment (UEs) occurs simultaneously with a three-dimensional (3D) estimation of the environment, extracted from the scattering features present in the channel state information (CSI) and utilizing the same physical layer communications air interface, as opposed to radar technologies. By exploiting a discrete (voxelated) representation of the environment, two novel ISAC schemes are derived with purpose-built message passing (MP) rules for the joint estimation of data symbols and status (filled/empty) of the discretized environment. The first relies on a modular feedback structure in which the data symbols and the environment are estimated alternately, whereas the second leverages a bilinear inference framework to estimate both variables concurrently. Both contributed methods are shown via simulations to outperform the state-of-the-art (SotA) in accurately recovering the transmitted data as well as the 3D image of the environment. An analysis of the computational complexities of the proposed methods reveals distinct advantages of each scheme, namely, that the bilinear solution exhibits a superior robustness to short pilots and channel blockages, while the alternating solution offers lower complexity with large number of UEs and superior performance in ideal conditions.
Anisotropic Fractional Cosmology: K-Essence Theory

In the particular configuration of the scalar field k-essence in the Wheeler–DeWitt quantum equation, for some age in the Bianchi type I anisotropic cosmological model, a fractional differential equation for the scalar field arises naturally. The order of the fractional differential equation is β=2α2α−1. This fractional equation belongs to different intervals depending on the value of the barotropic parameter; when ωX∈[0,1], the order belongs to the interval 1≤β≤2, and when ωX∈[−1,0), the order belongs to the interval 0<β≤1. In the quantum scheme, we introduce the factor ordering problem in the variables (Ω,ϕ) and its corresponding momenta (ΠΩ,Πϕ), obtaining a linear fractional differential equation with variable coefficients in the scalar field equation, then the solution is found using a fractional power series expansion. The corresponding quantum solutions are also given. We found the classical solution in the usual gauge N obtained in the Hamiltonian formalism and without a gauge. In the last case, the general solution is presented in a transformed time T(τ); however, in the dust era we found a closed solution in the gauge time τ.
Measuring the Effect of Causal Disentanglement on the Adversarial Robustness of Neural Network Models

Causal Neural Network models have shown high levels of robustness to adversarial attacks as well as an increased capacity for generalisation tasks such as few-shot learning and rare-context classification compared to traditional Neural Networks. This robustness is argued to stem from the disentanglement of causal and confounder input signals. However, no quantitative study has yet measured the level of disentanglement achieved by these types of causal models or assessed how this relates to their adversarial robustness. Existing causal disentanglement metrics are not applicable to deterministic models trained on real-world datasets. We, therefore, utilise metrics of content/style disentanglement from the field of Computer Vision to measure different aspects of the causal disentanglement for four state-of-the-art causal Neural Network models. By re-implementing these models with a common ResNet18 architecture we are able to fairly measure their adversarial robustness on three standard image classification benchmarking datasets under seven common white-box attacks. We find a strong association (r=0.820, p=0.001) between the degree to which models decorrelate causal and confounder signals and their adversarial robustness. Additionally, we find a moderate negative association between the pixel-level information content of the confounder signal and adversarial robustness (r=-0.597, p=0.040).
CXL Memory as Persistent Memory for Disaggregated HPC: A Practical Approach

In the landscape of High-Performance Computing (HPC), the quest for efficient and scalable memory solutions remains paramount. The advent of Compute Express Link (CXL) introduces a promising avenue with its potential to function as a Persistent Memory (PMem) solution in the context of disaggregated HPC systems. This paper presents a comprehensive exploration of CXL memory’s viability as a candidate for PMem, supported by physical experiments conducted on cutting-edge multi-NUMA nodes equipped with CXL-attached memory prototypes. Our study not only benchmarks the performance of CXL memory but also illustrates the seamless transition from traditional PMem programming models to CXL, reinforcing its practicality. To substantiate our claims, we establish a tangible CXL prototype using an FPGA card embodying CXL 1.1/2.0 compliant endpoint designs (Intel FPGA CXL IP). Performance evaluations, executed through the STREAM and STREAM-PMem benchmarks, showcase CXL memory’s ability to mirror PMem characteristics in App-Direct and Memory Mode while achieving impressive bandwidth metrics with Intel 4th generation Xeon (Sapphire Rapids) processors. The results elucidate the feasibility of CXL memory as a persistent memory solution, outperforming previously established benchmarks. In contrast to published DCPMM results, our CXL-DDR4 memory module offers comparable bandwidth to local DDR4 memory configurations, albeit with a moderate decrease in performance. The modified STREAM-PMem application underscores the ease of transitioning programming models from PMem to CXL, thus underscoring the practicality of adopting CXL memory. The sources of this work are available at: https://github.com/Scientific-Computing-Lab-NRCN/STREAMer.
Affine Hecke algebras and symmetric quasi-polynomial duality

In a recent paper with Sahi and Stokman, we introduced quasi-polynomial generalizations of Macdonald polynomials for arbitrary root systems via a new class of representations of the double affine Hecke algebra. These objects depend on a deformation parameter $q$, Hecke parameters, and an additional torus parameter. In this paper, we study $\textit{antisymmetric}$ and $\textit{symmetric}$ quasi-polynomial analogs of Macdonald polynomials in the $q \rightarrow \infty$ limit. We provide explicit decomposition formulas for these objects in terms of classical Demazure-Lusztig operators and partial symmetrizers, and relate them to Macdonald polynomials with prescribed symmetry in the same limit. We also provide a complete characterization of (anti-)symmetric quasi-polynomials in terms of partially (anti-)symmetric polynomials. As an application, we obtain formulas for metaplectic spherical Whittaker functions associated to arbitrary root systems. For $GL_{r}$, this recovers some recent results of Brubaker, Buciumas, Bump, and Gustafsson, and proves a precise statement of their conjecture about a ``parahoric-metaplectic"duality.
Finding emergence in data by maximizing effective information

Quantifying emergence and modeling emergent dynamics in a data-driven manner for complex dynamical systems is challenging due to the lack of direct observations at the micro-level. Thus, it's crucial to develop a framework to identify emergent phenomena and capture emergent dynamics at the macro-level using available data. Inspired by the theory of causal emergence (CE), this paper introduces a machine learning framework to learn macro-dynamics in an emergent latent space and quantify the degree of CE. The framework maximizes effective information, resulting in a macro-dynamics model with enhanced causal effects. Experimental results on simulated and real data demonstrate the effectiveness of the proposed framework. It quantifies degrees of CE effectively under various conditions and reveals distinct influences of different noise types. It can learn a one-dimensional coarse-grained macro-state from fMRI data, to represent complex neural activities during movie clip viewing. Furthermore, improved generalization to different test environments is observed across all simulation data.