Miracle-dz/UniFAR-FTUs huggingface dataset:
I-Love-Q in Einstein-aether Theory

Although Lorentz symmetry is a staple of General Relativity (GR), there are several reasons to believe it may not hold in a more advanced theory of gravity, such as quantum gravity. Einstein-aether theory is a modified theory of gravity that breaks Lorentz symmetry by introducing a dynamical vector field called the aether. The theory has four coupling constants that characterize deviations from GR and that must be determined through observations. Although three of the four parameters have been constrained by various empirical observations and stability requirements, one, called $c_\omega$, remains essentially unconstrained. The aim of this work is to see if a constraint on $c_\omega$ can be derived from the I-Love-Q universal relations for neutron stars, which connect the neutron star moment of inertia (I), the tidal Love number (Love), and the quadrupole moment (Q) in a way that is insensitive to uncertainties in the neutron star equation-of-state. To understand if the theory can be constrained through such relations, we model slowly-rotating or weakly tidally-deformed neutron stars in Einstein-aether theory, derive their I-Love-Q relations, and study how they depend on $c_\omega$. We find that the I-Love-Q relations in Einstein-aether theory are insensitive to $c_\omega$ and that they are close to the relations in GR. This means that the I-Love-Q relations in Einstein-aether theory remain universal but cannot be used to constrain the theory. These results indicate that to constrain the theory with neutron stars, it is necessary to investigate relations involving other observables.
More PAC-Bayes bounds: From bounded losses, to losses with general tail behaviors, to anytime-validity

In this paper, we present new high-probability PAC-Bayes bounds for different types of losses. Firstly, for losses with a bounded range, we present a strengthened version of Catoni's bound that holds uniformly for all parameter values. This leads to new fast rate and mixed rate bounds that are interpretable and tighter than previous bounds in the literature. Secondly, for losses with more general tail behaviors, we introduce two new parameter-free bounds: a PAC-Bayes Chernoff analogue when the loss' cumulative generating function is bounded, and a bound when the loss' second moment is bounded. These two bounds are obtained using a new technique based on a discretization of the space of possible events for the"in probability"parameter optimization problem. Finally, we extend all previous results to anytime-valid bounds using a simple technique applicable to any existing bound.
MimiC: Combating Client Dropouts in Federated Learning by Mimicking Central Updates

Federated learning (FL) is a promising framework for privacy-preserving collaborative learning, where model training tasks are distributed to clients and only the model updates need to be collected at a server. However, when being deployed at mobile edge networks, clients may have unpredictable availability and drop out of the training process, which hinders the convergence of FL. This paper tackles such a critical challenge. Specifically, we first investigate the convergence of the classical FedAvg algorithm with arbitrary client dropouts. We find that with the common choice of a decaying learning rate, FedAvg oscillates around a stationary point of the global loss function, which is caused by the divergence between the aggregated and desired central update. Motivated by this new observation, we then design a novel training algorithm named MimiC, where the server modifies each received model update based on the previous ones. The proposed modification of the received model updates mimics the imaginary central update irrespective of dropout clients. The theoretical analysis of MimiC shows that divergence between the aggregated and central update diminishes with proper learning rates, leading to its convergence. Simulation results further demonstrate that MimiC maintains stable convergence performance and learns better models than the baseline methods.
Understanding human mobility patterns in Chicago: an analysis of taxi data using clustering techniques

Understanding human mobility patterns is important in applications as diverse as urban planning, public health, and political organizing. One rich source of data on human mobility is taxi ride data. Using the city of Chicago as a case study, we examine data from taxi rides in 2016 with the goal of understanding how neighborhoods are interconnected. This analysis will provide a sense of which neighborhoods individuals are using taxis to travel between, suggesting regions to focus new public transit development efforts. Additionally, this analysis will map traffic circulation patterns and provide an understanding of where in the city people are traveling from and where they are heading to - perhaps informing traffic or road pollution mitigation efforts. For the first application, representing the data as an undirected graph will suffice. Transit lines run in both directions so simply a knowledge of which neighborhoods have high rates of taxi travel between them provides an argument for placing public transit along those routes. However, in order to understand the flow of people throughout a city, we must make a distinction between the neighborhood from which people are departing and the areas to which they are arriving - this requires methods that can deal with directed graphs. All developed codes can be found at https://github.com/Nikunj-Gupta/Spectral-Clustering-Directed-Graphs.
Geometric Pooling: maintaining more useful information

Graph Pooling technology plays an important role in graph node classification tasks. Sorting pooling technologies maintain large-value units for pooling graphs of varying sizes. However, by analyzing the statistical characteristic of activated units after pooling, we found that a large number of units dropped by sorting pooling are negative-value units that contain useful information and can contribute considerably to the final decision. To maintain more useful information, a novel pooling technology, called Geometric Pooling (GP), was proposed to contain the unique node features with negative values by measuring the similarity of all node features. We reveal the effectiveness of GP from the entropy reduction view. The experiments were conducted on TUdatasets to show the effectiveness of GP. The results showed that the proposed GP outperforms the SOTA graph pooling technologies by 1%\sim5% with fewer parameters.
A Chain of AI-based Solutions for Resolving FQNs and Fixing Syntax Errors in Partial Code

API documentation, technical blogs and programming Q&A sites contain numerous partial code that can be reused in programming tasks, but often these code are uncompilable due to unresolved names and syntax errors. To facilitate partial code reuse, we propose the Partial Code Reuse Chain (PCR-Chain) for resolving fully-qualified names (FQNs) and fixing last-mile syntax errors in partial code based on a giant large language model (LLM) like ChatGPT. Methodologically, PCR-Chain is backed up by the underlying global-level prompt architecture (which combines three design ideas: hierarchical task breakdown, prompt composition, and a mix of prompt-based AI and non-AI units) and the local-level prompt design. Technically, we propose PCR-Chain, which employs in-context learning rather than symbolic, costly training methods. Experimental results demonstrate that in dynamically-typed languages (Python), PCR-Chain outperforms current state-of-the-art (SOTA) 5% accuracy like RING. For statically-type languages (Java), our approach achieves high accuracy of 80.5% in resolving both non-FQNs and last-mile syntax errors, surpassing SOTA methods (RING) that can only address last-mile syntax errors. The correct execution of the unit, module, and PCR-Chain demonstrates the effectiveness of the prompt design, composition, and architecture and opens up possibilities for building software engineering tools based on LLMs, replacing traditional program analysis methods.
Addressing the Rank Degeneration in Sequential Recommendation via Singular Spectrum Smoothing

Sequential recommendation (SR) investigates the dynamic user preferences modeling and generates the next-item prediction. The next item preference is typically generated by the affinity between the sequence and item representations. However, both sequence and item representations suffer from the rank degeneration issue due to the data sparsity problem. The rank degeneration issue significantly impairs the representations for SR. This motivates us to measure how severe is the rank degeneration issue and alleviate the sequence and item representation rank degeneration issues simultaneously for SR. In this work, we theoretically connect the sequence representation degeneration issue with the item rank degeneration, particularly for short sequences and cold items. We also identify the connection between the fast singular value decay phenomenon and the rank collapse issue in transformer sequence output and item embeddings. We propose the area under the singular value curve metric to evaluate the severity of the singular value decay phenomenon and use it as an indicator of rank degeneration. We further introduce a novel singular spectrum smoothing regularization to alleviate the rank degeneration on both sequence and item sides, which is the Singular sPectrum sMoothing for sequential Recommendation (SPMRec). We also establish a correlation between the ranks of sequence and item embeddings and the rank of the user-item preference prediction matrix, which can affect recommendation diversity. We conduct experiments on four benchmark datasets to demonstrate the superiority of SPMRec over the state-of-the-art recommendation methods, especially in short sequences. The experiments also demonstrate a strong connection between our proposed singular spectrum smoothing and recommendation diversity.
PriorBand: Practical Hyperparameter Optimization in the Age of Deep Learning

Hyperparameters of Deep Learning (DL) pipelines are crucial for their downstream performance. While a large number of methods for Hyperparameter Optimization (HPO) have been developed, their incurred costs are often untenable for modern DL. Consequently, manual experimentation is still the most prevalent approach to optimize hyperparameters, relying on the researcher's intuition, domain knowledge, and cheap preliminary explorations. To resolve this misalignment between HPO algorithms and DL researchers, we propose PriorBand, an HPO algorithm tailored to DL, able to utilize both expert beliefs and cheap proxy tasks. Empirically, we demonstrate PriorBand's efficiency across a range of DL benchmarks and show its gains under informative expert input and robustness against poor expert beliefs
Fr\'echet Covariance and MANOVA Tests for Random Objects in Multiple Metric Spaces

In this manuscript we consider random objects being measured in multiple metric spaces, which may arise when those objects may be measured in multiple distinct ways. In this new multivariate setting, we define a Fr\'echet covariance and Fr\'echet correlation in two metric spaces, and a Fr\'echet covariance matrix and Fr\'echet correlation matrix in an arbitrary number of metric spaces. We prove consistency for the sample Fr\'echet covariance, and propose several tests to compare the means and covariance matrices between two or more groups. Lastly, we investigate the power and Type I error of each test under a variety of scenarios.
Decoupled Boundary Handling in SPH

Particle-based boundary representations are frequently used in smoothed particle hydrodynamics (SPH) due to their simple integration into fluid solvers. Commonly, incompressible fluid solvers estimate the current density and corresponding forces in case the current density exceeds the rest density to push fluid particles apart. Close to the boundary, the calculation of the fluid particles’ density involves both neighboring fluid and neighboring boundary particles, yielding an overestimation of density, and, subsequently, wrong pressure forces and wrong velocities leading to the disturbed fluid particles’ behavior in the vicinity of the boundary. In this paper, we present a detailed explanation of this disturbed fluid particle behavior, which is mainly due to the combined or coupled handling of the fluid–fluid particle and the fluid–boundary particle interaction. We propose the decoupled handling of both interaction types, leading to two densities for a given fluid particle, i.e., fluid-induced density and boundary-induced density. In our approach, we alternately apply the corresponding fluid-induced and boundary-induced forces during pressure estimation. This separation avoids force overestimation and reduces unintended fluid dynamics near the boundary, as well as a inconsistent fluid–boundary distance across different fluid amounts and different particle-based boundary handling methods. We compare our method with two regular state-of-the-art methods in different experiments and show how our method handles detailed boundary shapes.
Persuading Farsighted Receivers in MDPs: the Power of Honesty

Bayesian persuasion studies the problem faced by an informed sender who strategically discloses information to influence the behavior of an uninformed receiver. Recently, a growing attention has been devoted to settings where the sender and the receiver interact sequentially, in which the receiver's decision-making problem is usually modeled as a Markov decision process (MDP). However, previous works focused on computing optimal information-revelation policies (a.k.a. signaling schemes) under the restrictive assumption that the receiver acts myopically, selecting actions to maximize the one-step utility and disregarding future rewards. This is justified by the fact that, when the receiver is farsighted and thus considers future rewards, finding an optimal Markovian signaling scheme is NP-hard. In this paper, we show that Markovian signaling schemes do not constitute the"right"class of policies. Indeed, differently from most of the MDPs settings, we prove that Markovian signaling schemes are not optimal, and general history-dependent signaling schemes should be considered. Moreover, we also show that history-dependent signaling schemes circumvent the negative complexity results affecting Markovian signaling schemes. Formally, we design an algorithm that computes an optimal and {\epsilon}-persuasive history-dependent signaling scheme in time polynomial in 1/{\epsilon} and in the instance size. The crucial challenge is that general history-dependent signaling schemes cannot be represented in polynomial space. Nevertheless, we introduce a convenient subclass of history-dependent signaling schemes, called promise-form, which are as powerful as general history-dependent ones and efficiently representable. Intuitively, promise-form signaling schemes compactly encode histories in the form of honest promises on future receiver's rewards.
λFS: A Scalable and Elastic Distributed File System Metadata Service using Serverless Functions

The metadata service (MDS) sits on the critical path for distributed file system (DFS) operations, and therefore it is key to the overall performance of a large-scale DFS. Common"serverful"MDS architectures, such as a single server or cluster of servers, have a significant shortcoming: either they are not scalable, or they make it difficult to achieve an optimal balance of performance, resource utilization, and cost. A modern MDS requires a novel architecture that addresses this shortcoming. To this end, we design and implement $\lambda$FS, an elastic, high-performance metadata service for large-scale DFSes. $\lambda$FS scales a DFS metadata cache elastically on a FaaS (Function-as-a-Service) platform and synthesizes a series of techniques to overcome the obstacles that are encountered when building large, stateful, and performance-sensitive applications on FaaS platforms. $\lambda$FS takes full advantage of the unique benefits offered by FaaS $\unicode{x2013}$ elastic scaling and massive parallelism $\unicode{x2013}$ to realize a highly-optimized metadata service capable of sustaining up to 4.13$\times$ higher throughput, 90.40% lower latency, 85.99% lower cost, 3.33$\times$ better performance-per-cost, and better resource utilization and efficiency than a state-of-the-art DFS for an industrial workload.
Entropic characterization of optimal rates for learning Gaussian mixtures

We consider the question of estimating multi-dimensional Gaussian mixtures (GM) with compactly supported or subgaussian mixing distributions. Minimax estimation rate for this class (under Hellinger, TV and KL divergences) is a long-standing open question, even in one dimension. In this paper we characterize this rate (for all constant dimensions) in terms of the metric entropy of the class. Such characterizations originate from seminal works of Le Cam (1973); Birge (1983); Haussler and Opper (1997); Yang and Barron (1999). However, for GMs a key ingredient missing from earlier work (and widely sought-after) is a comparison result showing that the KL and the squared Hellinger distance are within a constant multiple of each other uniformly over the class. Our main technical contribution is in showing this fact, from which we derive entropy characterization for estimation rate under Hellinger and KL. Interestingly, the sequential (online learning) estimation rate is characterized by the global entropy, while the single-step (batch) rate corresponds to local entropy, paralleling a similar result for the Gaussian sequence model recently discovered by Neykov (2022) and Mourtada (2023). Additionally, since Hellinger is a proper metric, our comparison shows that GMs under KL satisfy the triangle inequality within multiplicative constants, implying that proper and improper estimation rates coincide.
High Throughput Open-Source Implementation of Wi-Fi 6 and WiMAX LDPC Encoder and Decoder

This paper describes the design and C99 implementation of a free and open-source Low-Density Parity-Check (LDPC) codes encoder and decoder focused primarily on the Quasi-Cyclic LDPC (QCLDPC) codes utilized in the IEEE 802.11ax-2021 (Wi-Fi 6) and IEEE 802.16-2017 (WiMAX) standards. The encoder is designed in two variants: the first one universal, the other a minimal memory usage design. The decoder provides a single- and multi- threaded implementation of the layered singlescan min-sum LDPC decoding algorithm both for floating point and fixed-point arithmetic. Both encoder and decoder are directly callable from MATLAB using the provided MEX wrappers but are designed to be simply used in any C project. A comparison of throughput and error performance with the recent commercial closed-source MEX implementation of an LDPC encoder and decoder introduced in MATLAB R2021b Communications Toolbox is provided. Source code portability to alternative nonx86 architectures is facilitated by using only the standard C99 constructs, GNU tools, and POSIX libraries. The implementation maintains low-memory requirements, enabling its deployment in a constrained-architecture in the context of Internet of Things. All source codes are freely available on GitHub under a permissive BSD license.
Stochastic homogenization of nondegenerate viscous HJ equations in 1d

We prove homogenization for a nondegenerate viscous Hamilton-Jacobi equation in dimension one in stationary ergodic environments with a superlinear (nonconvex) Hamiltonian of fairly general type. The version of the paper herein posted is identical to the one submitted to the journal *** for publication on the 26th of February, 2024. One of the crucial idea for the proof corresponds to Theorem 4.2. This theorem, together with its proof, already appeared, in essential identical form, in the ArXiv e-print 2306.12145, version 1 (posted on the 21st of June 2023), see Theorem 4.5 therein.
UMM: Unsupervised Mean-difference Maximization

Many brain-computer interfaces make use of brain signals that are elicited in response to a visual, auditory or tactile stimulus, so-called event-related potentials (ERPs). In visual ERP speller applications, sets of letters shown on a screen are flashed randomly, and the participant attends to the target letter they want to spell. When this letter flashes, the resulting ERP is different compared to when any other non-target letter flashes. We propose a new unsupervised approach to detect this attended letter. In each trial, for every available letter our approach makes the hypothesis that it is in fact the attended letter, and calculates the ERPs based on each of these hypotheses. We leverage the fact that only the true hypothesis produces the largest difference between the class means. Note that this unsupervised method does not require any changes to the underlying experimental paradigm and therefore can be employed in almost any ERP-based setup. To deal with limited data, we use a block-Toeplitz regularized covariance matrix that models the background activity. We implemented the proposed novel unsupervised mean-difference maximization (UMM) method and evaluated it in offline replays of brain-computer interface visual speller datasets. For a dataset that used 16 flashes per symbol per trial, UMM correctly classifies 3651 out of 3654 letters ($99.92\,\%$) across 25 participants. In another dataset with fewer and shorter trials, 7344 out of 7383 letters ($99.47\,\%$) are classified correctly across 54 participants with two sessions each. Even in more challenging datasets obtained from patients with amyotrophic lateral sclerosis ($77.86\,\%$) or when using auditory ERPs ($82.52\,\%$), the obtained classification rates obtained by UMM are competitive. In addition, UMM provides stable confidence measures which can be used to monitor convergence.
Fast Segment Anything

The recently proposed segment anything model (SAM) has made a significant influence in many computer vision tasks. It is becoming a foundation step for many high-level tasks, like image segmentation, image caption, and image editing. However, its huge computation costs prevent it from wider applications in industry scenarios. The computation mainly comes from the Transformer architecture at high-resolution inputs. In this paper, we propose a speed-up alternative method for this fundamental task with comparable performance. By reformulating the task as segments-generation and prompting, we find that a regular CNN detector with an instance segmentation branch can also accomplish this task well. Specifically, we convert this task to the well-studied instance segmentation task and directly train the existing instance segmentation method using only 1/50 of the SA-1B dataset published by SAM authors. With our method, we achieve a comparable performance with the SAM method at 50 times higher run-time speed. We give sufficient experimental results to demonstrate its effectiveness. The codes and demos will be released at https://github.com/CASIA-IVA-Lab/FastSAM.
A theoretical and numerical study of the estimators for the parameters of a random signal with unknown moments of appearance and disappearance

Algorithms for estimating the expected value, magnitude of the power spectrum, arrival time, and duration (moments of appearance and disappearance) of a Gaussian signal are constructed. Asymptotically exact expressions for the characteristics of the estimators are found. The results of a stochastic numerical simulation of the estimators are presented.