Miracle-dz/UniFAR-FTUs huggingface dataset:
FRW Cosmology with a Varying Cubic Deceleration Parameter

In this work a new law of varying deceleration parameter of third degree have been proposed. The solutions of the modified field equations have been derived under the newly proposed law of the deceleration parameter. Model exhibits the Big-bang singularity at cosmic time ($t=0$) and shows Big Rip at ($t=n$) then it re-enter the phase of initial singularity at $t=2n$ and ends its cyclic behavior at $t=3n$. The evolution of the physical and dynamical parameters of the Universe have been studied and the graphical representation has also been shown. Further $Om(z)$ diagnostic parameter and the energy conditions have also been studied together with their graphical representations.
Adam Can Converge Without Any Modification on Update Rules

Ever since Reddi et al. 2018 pointed out the divergence issue of Adam, many new variants have been designed to obtain convergence. However, vanilla Adam remains exceptionally popular and it works well in practice. Why is there a gap between theory and practice? We point out there is a mismatch between the settings of theory and practice: Reddi et al. 2018 pick the problem after picking the hyperparameters of Adam, i.e., $(\beta_1, \beta_2)$; while practical applications often fix the problem first and then tune $(\beta_1, \beta_2)$. Due to this observation, we conjecture that the empirical convergence can be theoretically justified, only if we change the order of picking the problem and hyperparameter. In this work, we confirm this conjecture. We prove that, when $\beta_2$ is large and $\beta_1<\sqrt{\beta_2}<1$, Adam converges to the neighborhood of critical points. The size of the neighborhood is propositional to the variance of stochastic gradients. Under an extra condition (strong growth condition), Adam converges to critical points. It is worth mentioning that our results cover a wide range of hyperparameters: as $\beta_2$ increases, our convergence result can cover any $\beta_1 \in [0,1)$ including $\beta_1=0.9$, which is the default setting in deep learning libraries. To our knowledge, this is the first result showing that Adam can converge without any modification on its update rules. Further, our analysis does not require assumptions of bounded gradients or bounded 2nd-order momentum. When $\beta_2$ is small, we further point out a large region of $(\beta_1,\beta_2)$ where Adam can diverge to infinity. Our divergence result considers the same setting as our convergence result, indicating a phase transition from divergence to convergence when increasing $\beta_2$. These positive and negative results can provide suggestions on how to tune Adam hyperparameters.
Prompt-Matched Semantic Segmentation

The objective of this work is to explore how to effectively and efficiently adapt pre-trained visual foundation models to various downstream tasks of semantic segmentation. Previous methods usually fine-tuned the entire networks for each specific dataset, which will be burdensome to store massive parameters of these networks. A few recent works attempted to insert some extra trainable parameters into the frozen networks to learn visual prompts for parameter-efficient tuning. However, these works showed poor generality as they were designed specifically for Transformers. Moreover, using limited information in these schemes, they exhibited a poor capacity to learn beneficial prompts. To alleviate these issues, we propose a novel Stage-wise Prompt-Matched Framework for generic and effective visual prompt tuning. Specifically, to ensure generality, we divide the pre-trained backbone with frozen parameters into multiple stages and perform prompt learning between different stages, which makes the proposed scheme applicable to various architectures of CNN and Transformer. For effective tuning, a lightweight Semantic-aware Prompt Matcher (SPM) is designed to progressively learn reasonable prompts with a recurrent mechanism, guided by the rich information of interim semantic maps. Working as deep matched filter of representation learning, the proposed SPM can well transform the output of the previous stage into a desirable input for the next stage, thus achieving the better matching/stimulating for the pre-trained knowledge. Extensive experiments on four benchmarks demonstrate that the proposed scheme can achieve a promising trade-off between parameter efficiency and performance effectiveness. Our code and models will be released.
Learning Correlated Equilibria in Mean-Field Games

The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an N -player game typically grows exponentially with N , standard game theoretic analysis becomes effectively infeasible beyond a low number of players. Recent approaches have gone around this limitation by instead considering Mean-Field games, an approximation of anonymous N -player games, where the number of players is infinite and the population’s state distribution, instead of every individual player’s state, is the object of interest. The practical computability of Mean-Field Nash equilibria, the most studied Mean-Field equilibrium to date, however, typically depends on beneficial non-generic structural properties such as monotonicity [61] or contraction properties [43], which are required for known algorithms to converge. In this work, we provide an alternative route for studying Mean-Field games, by developing the concepts of Mean-Field correlated and coarse-correlated equilibria. We show that they can be efficiently learnt in all games, without requiring any additional assumption on the structure of the game, using three classical algorithms. Furthermore, we establish correspondences between our notions and those already present in the literature, derive optimality bounds for the Mean-Field N -player transition, and empirically demonstrate the convergence of these algorithms on simple games. Keywords— Mean Field Games, Correlated equilibrium, Coarse Correlated equilibrium, Regret minimization
Predicting the protein-ligand affinity from molecular dynamics trajectories

Accurate protein-ligand binding aﬃnity prediction is essential in drug design and many other molecular recognition problems. Despite many advances in aﬃnity prediction based on machine learning techniques, they are still limited since the protein-ligand binding is determined by the dynamics of atoms and molecules. To this end, we curated an MD dataset containing 3,218 dynamic protein-ligand complexes and further developed Dynaformer, a graph-based deep learning framework. Dynaformer can fully capture the dynamic binding modes by considering various geometric characteristics of the interaction. Our method shows superior performance on the benchmark dataset over the methods hitherto reported. Moreover, we performed virtual drug-screening on heat shock protein 90 (HSP90) by integrating our model with structure-based docking. We benchmarked our performance against the conventional knowledge-based approach, demonstrating that our method can identify two lead compounds with submicromolar activity (0.207 µ M and 0.517 µ M). We antici-pate that large-scale MD dataset and machine learning models will form a new synergy, providing a new route toward accelerated drug discovery.
Seiberg-Witten Theory and Monstrous Moonshine

We study the relation between the instanton expansion of the Seiberg-Witten prepotential for D = 4, N = 2 SU (2) SUSY gauge theory for N f = 0 and 1 and the monstrous moonshine. By utilizing a newly developed simple method to obtain the SW prepotential, it is shown that the coeﬃcients of the expansion of q = e 2 πτ in terms of A 2 = Λ 2 16 a 2 ( N f = 0) or Λ 2 16 √ 2 a 2 ( N f = 1) are all integer coeﬃcient polynomials of the moonshine coeﬃcients of the modular j -function. A relationship between the AGT c = 25 Liouville CFT and the c = 24 vertex operator algebra CFT of the moonshine module is also suggested.
MolGraph: a Python package for the implementation of small molecular graphs and graph neural networks with TensorFlow and Keras

Molecular machine learning (ML) has proven important for tackling various molecular problems, such as predicting molecular properties based on molecular descriptors or fingerprints. Since relatively recently, graph neural network (GNN) algorithms have been implemented for molecular ML, showing comparable or superior performance to descriptor or fingerprint-based approaches. Although various tools and packages exist to apply GNNs in molecular ML, a new GNN package, named MolGraph, was developed in this work with the motivation to create GNN model pipelines highly compatible with the TensorFlow and Keras application programming interface (API). MolGraph also implements a chemistry module to accommodate the generation of small molecular graphs, which can be passed to a GNN algorithm to solve a molecular ML problem. To validate the GNNs, they were benchmarked against the datasets of MoleculeNet, as well as three chromatographic retention time datasets. The results on these benchmarks illustrate that the GNNs performed as expected. Additionally, the GNNs proved useful for molecular identification and improved interpretability of chromatographic retention time data. MolGraph is available at https://github.com/akensert/molgraph. Installation, tutorials and implementation details can be found at https://molgraph.readthedocs. io/en/latest/.
Where Shall I Touch? Vision-Guided Tactile Poking for Transparent Object Grasping

Picking up transparent objects is still a challenging task for robots. The visual properties of transparent objects such as reflection and refraction make the current grasping methods that rely on camera sensing fail to detect and localize them. However, humans can handle the transparent object well by first observing its coarse profile and then poking an area of interest to get a fine profile for grasping. Inspired by this, we propose a novel framework of vision-guided tactile poking for transparent objects grasping. In the proposed framework, a segmentation network is first used to predict the horizontal upper regions named as poking regions, where the robot can poke the object to obtain a good tactile reading, while leading to minimal disturbance to the object's state. A poke is then performed with a high-resolution GelSight tactile sensor. Given the local profiles improved with the tactile reading, a heuristic grasp is planned for grasping the transparent object. To mitigate the limitations of real-world data collection and labeling for transparent objects, a large-scale realistic synthetic dataset was constructed. Extensive experiments demonstrate that our proposed segmentation network can predict the potential poking region with a high mean average precision (mAP) of 0.360, and the vision-guided tactile poking can enhance the grasping success rate significantly from 38.9% to 85.2%. Thanks to its simplicity, our proposed approach could also be adopted by other force or tactile sensors and could be used for grasping of other challenging objects.
PointDP: Diffusion-driven Purification against Adversarial Attacks on 3D Point Cloud Recognition

3D Point cloud is becoming a critical data representation in many real-world applications like autonomous driving, robotics, and medical imaging. Although the success of deep learning further accelerates the adoption of 3D point clouds in the physical world, deep learning is notorious for its vulnerability to adversarial attacks. In this work, we first identify that the state-of-the-art empirical defense, adversarial training, has a major limitation in applying to 3D point cloud models due to gradient obfuscation. We further propose PointDP, a purification strategy that leverages diffusion models to defend against 3D adversarial attacks. We extensively evaluate PointDP on six representative 3D point cloud architectures, and leverage 10+ strong and adaptive attacks to demonstrate its lower-bound robustness. Our evaluation shows that PointDP achieves significantly better robustness than state-of-the-art purification methods under strong attacks. Results of certified defenses on randomized smoothing combined with PointDP will be included in the near future.
Rate-Splitting Multiple Access for Intelligent Reflecting Surface-Aided Secure Transmission

In this letter, we study a rate-splitting multiple access (RSMA)-based intelligent reflecting surface (IRS)-aided multi-user multiple-input single-output (MISO) secure communication system with a potential eavesdropper (Eve). Aiming to maximize the minimum secrecy rate (SR) among all the legitimate users (LUs), a design problem for jointly optimizing the transmit beamforming with artificial noise (AN), the IRS beamforming, and the secrecy common rate allocation is formulated. Since the design problem is highly non-convex with coupled optimization variables, we develop a computationally efficient algorithm based on the alternating optimization (AO) technique to solve it suboptimally. Numerical results demonstrate that the proposed design can significantly improve the max-min SR over the benchmark schemes without IRS or adopting other multiple access techniques. In particular, employing the RSMA strategy can substantially reduce the required numbers of IRS elements for achieving a target level of secrecy performance compared with the benchmark schemes.
Determining Parameter Ranges for High Accuracy Large Eddy Simulation by Lax-Wendroff Method

The analysis of Lax-Wendroff (LW) method is performed by the generic modified differential equation (MDE) approach in the spectral plane using Fourier transform. In this approach, the concept of dispersion relation plays a major role relating spatial and temporal dependence of the governing differential equation, including initial and boundary conditions in developing high accuracy schemes. Such dispersion relation preserving schemes are calibrated in the spectral plane using the global spectral analysis for the numerical method in the full domain. In this framework, the numerical methods are calibrated by studying convection and diffusion as the underlying physical processes for this canonical model problem. In the LW method spatial and temporal discretizations are considered together, with time derivatives replaced by corresponding spatial derivatives using the governing equation. Here the LW method is studied for the convection-diffusion equation (CDE) to establish limits for numerical parameters for an explicit central difference scheme that invokes third and fourth spatial derivatives in the MDE, in its general form. Thus, for the LW method, two different MDEs are obtained, depending on whether the LW method is applied only on the convection operator, or both on the convection and diffusion operators. Motivated by a one-to-one correspondence of the Navier-Stokes equation with the linear CDE established in"Effects of numerical anti-diffusion in closed unsteady flows governed by two-dimensional Navier-Stokes equation- Suman et al. Comput. Fluids, 201, 104479 (2020)", an assessment is made here to solve flow problems by these two variants of the LW method. Apart from mapping the numerical properties for performing large eddy simulation for the LW methods, simulations of the canonical lid-driven cavity problem are performed for a super-critical Reynolds number for a uniform grid.
A Diverse Large-Scale Building Dataset and a Novel Plug-and-Play Domain Generalization Method for Building Extraction

In this article, we introduce a new building dataset and propose a novel domain generalization method to facilitate the development of building extraction from high-resolution remote sensing images. The problem with the current building datasets involves that they lack diversity to train a practical learning model with good generalization ability, and the quality of the labels is unsatisfactory. To address these issues, we built a diverse, large-scale, and high-quality building dataset named the WHU-Mix building dataset, which is more practice-oriented. The WHU-Mix building dataset consists of a training/validation set containing 43 727 diverse images collected from all over the world, and a test set containing 8402 images from five other cities on five continents. In addition, to further improve the generalization ability of a building extraction model, we propose a domain generalization method named batch style mixing (BSM), which can be embedded as an efficient plug-and-play module in the front-end of a building extraction model, providing the model with a progressively larger data distribution to learn data-invariant knowledge. The experiments conducted in this article confirmed the potential of the WHU-Mix building dataset to improve the performance of a building extraction model, resulting in a 6–36% improvement in mean intersection over union (mIoU), compared to the other existing datasets. The adverse impact of the inaccurate labels in the other datasets can cause about 20% intersection over union decrease. The experiments also confirmed the high performance of the proposed BSM module in enhancing the generalization ability and robustness of a model, exceeding the baseline model without domain generalization by 13% and the recent domain generalization methods by 4–15% in mIoU. The WHU-Mix dataset is available at http://gpcv.whu. edu.cn/data.
An O(k log n) Time Fourier Set Query Algorithm

Fourier transformation is an extensively studied problem in many research fields. It has many applications in machine learning, signal processing, compressed sensing, and so on. In many real-world applications, approximated Fourier transformation is sufficient and we only need to do the Fourier transform on a subset of coordinates. Given a vector $x \in \mathbb{C}^{n}$, an approximation parameter $\epsilon$ and a query set $S \subset [n]$ of size $k$, we propose an algorithm to compute an approximate Fourier transform result $x'$ which uses $O(\epsilon^{-1} k \log(n/\delta))$ Fourier measurements, runs in $O(\epsilon^{-1} k \log(n/\delta))$ time and outputs a vector $x'$ such that $\| ( x' - \widehat{x} )_S \|_2^2 \leq \epsilon \| \widehat{x}_{\bar{S}} \|_2^2 + \delta \| \widehat{x} \|_1^2 $ holds with probability of at least $9/10$.
Problem-size-independent angles for a Grover-driven quantum approximate optimization algorithm

The Quantum Approximate Optimization Algorithm (QAOA) requires that circuit parameters are determined that allow one to sample from high-quality solutions to combinatorial optimization problems. Such parameters can be obtained using either costly outer-loop optimization procedures and repeated calls to a quantum computer or, alternatively, via analytical means. In this work we demonstrate that if one knows the probability density function describing how the objective function of a problem is distributed, that the calculation of the expectation of such a problem Hamiltonian under a Grover-driven, QAOA-prepared state can be performed independently of system size. Such calculations can help deliver insights into the performance of and predictability of angles in QAOA in the limit of large problem sizes, in particular, for the number partitioning problem.
High-dimensional composite quantile regression: Optimal statistical guarantees and fast algorithms

The composite quantile regression (CQR) was introduced by Zou and Yuan [Ann. Statist. 36 (2008) 1108--1126] as a robust regression method for linear models with heavy-tailed errors while achieving high efficiency. Its penalized counterpart for high-dimensional sparse models was recently studied in Gu and Zou [IEEE Trans. Inf. Theory 66 (2020) 7132--7154], along with a specialized optimization algorithm based on the alternating direct method of multipliers (ADMM). Compared to the various first-order algorithms for penalized least squares, ADMM-based algorithms are not well-adapted to large-scale problems. To overcome this computational hardness, in this paper we employ a convolution-smoothed technique to CQR, complemented with iteratively reweighted $\ell_1$-regularization. The smoothed composite loss function is convex, twice continuously differentiable, and locally strong convex with high probability. We propose a gradient-based algorithm for penalized smoothed CQR via a variant of the majorize-minimization principal, which gains substantial computational efficiency over ADMM. Theoretically, we show that the iteratively reweighted $\ell_1$-penalized smoothed CQR estimator achieves near-minimax optimal convergence rate under heavy-tailed errors without any moment constraint, and further achieves near-oracle convergence rate under a weaker minimum signal strength condition than needed in Gu and Zou (2020). Numerical studies demonstrate that the proposed method exhibits significant computational advantages without compromising statistical performance compared to two state-of-the-art methods that achieve robustness and high efficiency simultaneously.
MUDGUARD: Taming Malicious Majorities in Federated Learning using Privacy-Preserving Byzantine-Robust Clustering

Byzantine-robust Federated Learning (FL) aims to counter malicious clients and train an accurate global model while maintaining an extremely low attack success rate. Most existing systems, however, are only robust when most of the clients are honest. FLTrust (NDSS '21) and Zeno++ (ICML '20) do not make such an honest majority assumption but can only be applied to scenarios where the server is provided with an auxiliary dataset used to filter malicious updates. FLAME (USENIX '22) and EIFFeL (CCS '22) maintain the semi-honest majority assumption to guarantee robustness and the confidentiality of updates. It is therefore currently impossible to ensure Byzantine robustness and confidentiality of updates without assuming a semi-honest majority. To tackle this problem, we propose a novel Byzantine-robust and privacy-preserving FL system, called MUDGUARD, that can operate under malicious minority \emph{or majority} in both the server and client sides. Based on DBSCAN, we design a new method for extracting features from model updates via pairwise adjusted cosine similarity to boost the accuracy of the resulting clustering. To thwart attacks from a malicious majority, we develop a method called \textit{Model Segmentation}, that aggregates together only the updates from within a cluster, sending the corresponding model only to the clients of the corresponding cluster. The fundamental idea is that even if malicious clients are in their majority, their poisoned updates cannot harm benign clients if they are confined only within the malicious cluster. We also leverage multiple cryptographic tools to conduct clustering without sacrificing training correctness and updates confidentiality. We present a detailed security proof and empirical evaluation along with a convergence analysis for MUDGUARD.