Miracle-dz/UniFAR-FTUs huggingface dataset:
Van der Corput and metric theorems for geometric progressions for self-similar measures

We prove a van der Corput lemma for non-atomic self-similar measures $\mu$. As an application, we show that the correlations of all finite orders of $( x^n \mod 1 )_{n\geq 1}$ converge to the Poissonian model for $\mu$-a.e. $x$, assuming $x>1$. We also complete a recent result of Algom, Rodriguez Hertz, and Wang (obtained simultaneously by Baker and Banaji), showing that any self-conformal measure with respect to a non-affine real analytic IFS has polynomial Fourier decay.
Xorbits: Automating Operator Tiling for Distributed Data Science

Data science pipelines commonly utilize dataframe and array operations for tasks such as data preprocessing, analysis, and machine learning. The most popular tools for these tasks are pandas and NumPy. However, these tools are limited to executing on a single node, making them unsuitable for processing large-scale data. Several systems have attempted to distribute data science applications to clusters while maintaining interfaces similar to single-node libraries, enabling data scientists to scale their workloads without significant effort. However, existing systems often struggle with processing large datasets due to Out-of-Memory (OOM) problems caused by poor data partitioning. To overcome these challenges, we develop Xorbits, a high-performance, scalable data science framework specifically designed to distribute data science workloads across clusters while retaining familiar APIs. The key differentiator of Xorbits is its ability to dynamically switch between graph construction and graph execution. Xorbits has been successfully deployed in production environments with up to 5k CPU cores. Its applications span various domains, including user behavior analysis and recommendation systems in the e-commerce sector, as well as credit assessment and risk management in the finance industry. Users can easily scale their data science workloads by simply changing the import line of their pandas and NumPy code. Our experiments demonstrate that Xorbits can effectively process very large datasets without encountering OOM or data-skewing problems. Over the fastest state-of-the-art solutions, Xorbits achieves an impressive 2.66* speedup on average. In terms of API coverage, Xorbits attains a compatibility rate of 96.7%, surpassing the fastest framework by an impressive margin of 60 percentage points. Xorbits is available at https://github.com/xorbitsai/xorbits.
An Out-of-Equilibrium 1D Particle System Undergoing Perfectly Plastic Collisions

At time zero, there are $N$ identical point particles in the line (1D) which are characterized by their positions and velocities. Both values are given randomly and independently from each other, with arbitrary probability densities. Each particle evolves at constant velocity until eventually they meet. When this happens, a perfectly-plastic collision is produced, resulting in a new particle composed by the sum of their masses and the weighted average velocity.The merged particles evolve indistinguishably from the non-merged ones, i.e. they move at constant velocity until a new plastic collision eventually happens. As in any open system, the particles are not confined to any region or reservoir, so as time progresses, they go on to infinity. From this non-equilibrium process, the number of (now, non-identical) final particles, $\tilde{X}_N$, the distribution of masses of these final particles and the kinetic energy loss from all plastic collisions, is studied. Counterintuitively, the way to achieve the number of final particles and each of their masses does not need to rely on evolving the particle system; this result can be obtained by simply considering the initial conditions. Moreover, they can also be used to obtain an accurate approximation of the energy loss. Finally, I will also present strong evidence for the validity of the following conjecture: $\langle \tilde{X}_N \rangle=\sum_{k=1}^{N} \frac{1}{k}$ (which behaves as $log(N)+\gamma$ for large $N$), additionally an explicit expression for the variance will also be given.
Linking tracklets over the years in large datasets

We present a new procedure to identify observations of known objects in large data sets of unlinked detections. It begins with a Keplerian integrals method that allows us to link two tracklets, computing preliminary orbits, even when the tracklets are separated in time by a few years. In the second step, we represent the results in a `graph' where the tracklets are the nodes and the preliminary orbits are the edges. Then, acceptable `3-cycles' are identified and a least squares orbit is computed for each of them. Finally, we construct sequences of $n \geq 4$ tracklets by searching through the orbits of nearby 3-cycles and attempting to attribute the remaining tracklets. We calculate the technique's efficiency at identifying unknown objects using real detections that attempt to mimic key parameters of the Minor Planet Center's Isolated Tracklet File (ITF) and then apply the procedure to the ITF to identify tens of thousands of new objects.
Optimal Rates of Kernel Ridge Regression under Source Condition in Large Dimensions

Motivated by the studies of neural networks (e.g.,the neural tangent kernel theory), we perform a study on the large-dimensional behavior of kernel ridge regression (KRR) where the sample size $n \asymp d^{\gamma}$ for some $\gamma>0$. Given an RKHS $\mathcal{H}$ associated with an inner product kernel defined on the sphere $\mathbb{S}^{d}$, we suppose that the true function $f_{\rho}^{*} \in [\mathcal{H}]^{s}$, the interpolation space of $\mathcal{H}$ with source condition $s>0$. We first determined the exact order (both upper and lower bound) of the generalization error of kernel ridge regression for the optimally chosen regularization parameter $\lambda$. We then further showed that when $01$, KRR is not minimax optimal (a.k.a. he saturation effect). Our results illustrate that the curves of rate varying along $\gamma$ exhibit the periodic plateau behavior and the multiple descent behavior and show how the curves evolve with $s>0$. Interestingly, our work provides a unified viewpoint of several recent works on kernel regression in the large-dimensional setting, which correspond to $s=0$ and $s=1$ respectively.
The geometry of large charge multi-traces in $\mathcal{N}=4$ SYM

We construct a one-parameter family of half-BPS solutions of type IIB supergravity using a consistent truncation to gauged five-dimensional supergravity. For small values of the parameter, the solution reduces to the linear perturbation of AdS$_5\times S^5$ dual to the chiral primary operator in the stress-tensor multiplet, and we give evidence that the geometry is regular and asymptotes AdS in a normalisable way for arbitrarily large values of the parameter. We conjecture that the solution is the gravity dual of a ``heavy"multi-trace operator in $\mathcal{N}=4$ $SU(N)$ Super Yang-Mills made by $p$ copies of the stress-tensor chiral primary operator, with $p$ of order $N^2$ in the large $N$ limit. We perform some holographic checks supporting this duality map.
Efficient Parallel Audio Generation using Group Masked Language Modeling

We present a fast and high-quality codec language model for parallel audio generation. While SoundStorm, a state-of-the-art parallel audio generation model, accelerates inference speed compared to autoregressive models, it still suffers from slow inference due to iterative sampling. To resolve this problem, we propose Group-Masked Language Modeling~(G-MLM) and Group Iterative Parallel Decoding~(G-IPD) for efficient parallel audio generation. Both the training and sampling schemes enable the model to synthesize high-quality audio with a small number of iterations by effectively modeling the group-wise conditional dependencies. In addition, our model employs a cross-attention-based architecture to capture the speaker style of the prompt voice and improves computational efficiency. Experimental results demonstrate that our proposed model outperforms the baselines in prompt-based audio generation.
Masked Modeling for Self-supervised Representation Learning on Vision and Beyond

As the deep learning revolution marches on, self-supervised learning has garnered increasing attention in recent years thanks to its remarkable representation learning ability and the low dependence on labeled data. Among these varied self-supervised techniques, masked modeling has emerged as a distinctive approach that involves predicting parts of the original data that are proportionally masked during training. This paradigm enables deep models to learn robust representations and has demonstrated exceptional performance in the context of computer vision, natural language processing, and other modalities. In this survey, we present a comprehensive review of the masked modeling framework and its methodology. We elaborate on the details of techniques within masked modeling, including diverse masking strategies, recovering targets, network architectures, and more. Then, we systematically investigate its wide-ranging applications across domains. Furthermore, we also explore the commonalities and differences between masked modeling methods in different fields. Toward the end of this paper, we conclude by discussing the limitations of current techniques and point out several potential avenues for advancing masked modeling research. A paper list project with this survey is available at \url{https://github.com/Lupin1998/Awesome-MIM}.
Boosting Transformer's Robustness and Efficacy in PPG Signal Artifact Detection with Self-Supervised Learning

Recent research at CHU Sainte Justine's Pediatric Critical Care Unit (PICU) has revealed that traditional machine learning methods, such as semi-supervised label propagation and K-nearest neighbors, outperform Transformer-based models in artifact detection from PPG signals, mainly when data is limited. This study addresses the underutilization of abundant unlabeled data by employing self-supervised learning (SSL) to extract latent features from these data, followed by fine-tuning on labeled data. Our experiments demonstrate that SSL significantly enhances the Transformer model's ability to learn representations, improving its robustness in artifact classification tasks. Among various SSL techniques, including masking, contrastive learning, and DINO (self-distillation with no labels)-contrastive learning exhibited the most stable and superior performance in small PPG datasets. Further, we delve into optimizing contrastive loss functions, which are crucial for contrastive SSL. Inspired by InfoNCE, we introduce a novel contrastive loss function that facilitates smoother training and better convergence, thereby enhancing performance in artifact classification. In summary, this study establishes the efficacy of SSL in leveraging unlabeled data, particularly in enhancing the capabilities of the Transformer model. This approach holds promise for broader applications in PICU environments, where annotated data is often limited.
High-dimensional FGM-ResNet modelling of turbulent spray combustion: Effects of evaporation non-adiabacity and scalar correlation

In the stratified or partially premixed piloted jet flames, previous experimental and priori studies have identified a strong correlation between mixture fraction and progress variable. In the framework of large-eddy simulation (LES) and flamelet-generated manifolds (FGM) approach, a joint probability density function (PDF) method is constructed to characterize subgrid correlations. To pave the way for high dimensional tabulation modeling, a deep residual network (ResNet) is trained, dramatically reducing the memory footprint of tabulation. The Message Passing Interface (MPI) shared memory technique is applied to load the original chemical table during parallel computations. Application of LES to a partially pre-vaporized ethanol spray flame demonstrates good agreement with experimental results. Consideration of the subgrid correlation results in a noticeable improvement in temperature prediction. Calculations using ResNet show a notable consistency with those using chemical tables. Visualization of enthalpy highlights the significance of non-adiabatic tabulation in modeling liquid fuel combustion. The unscaled progress variable is selected to better describe the chemical reaction rate in the blending zone of an air stream and a pilot stream with the product of a fully burnt lean fuel mixture. The impact of the source term due to evaporation in the transport equation of the progress variable is validated. The correlation coefficient is found to significantly influence the chemical reaction rate. The subgrid-scale interaction between liquid fuel evaporation and subgrid correlation is elucidated.
Fixing Your Own Smells: Adding a Mistake-Based Familiarisation Step When Teaching Code Refactoring

Programming problems can be solved in a multitude of functionally correct ways, but the quality of these solutions (e.g. readability, maintainability) can vary immensely. When code quality is poor, symptoms emerge in the form of 'code smells', which are specific negative characteristics (e.g. duplicate code) that can be resolved by applying refactoring patterns. Many undergraduate computing curricula train students on this software engineering practice, often doing so via exercises on unfamiliar instructor-provided code. Our observation, however, is that this makes it harder for novices to internalise refactoring as part of their own development practices. In this paper, we propose a new approach to teaching refactoring, in which students must first complete a programming exercise constrained to ensure they will produce a code smell. This simple intervention is based on the idea that learning refactoring is easier if students are familiar with the code (having built it), that it brings refactoring closer to their regular development practice, and that it presents a powerful opportunity to learn from a 'mistake'. We designed and conducted a study with 35 novice undergraduates in which they completed various refactoring exercises alternately taught using a traditional and our 'mistake-based' approach, finding that students were significantly more effective and confident at completing exercises using the latter.
First-passage time of a Brownian searcher with stochastic resetting to random positions

We study the effect of a resetting point randomly distributed around the origin on the mean first passage time of a Brownian searcher moving in one dimension. We compare the search efficiency with that corresponding to reset to the origin and find that the mean first passage time of the latter can be larger or smaller than the distributed case, depending on whether the resetting points are symmetrically or asymmetrically distributed. In particular, we prove the existence of an optimal reset rate that minimizes the mean first-passage time for distributed resetting to a finite interval if the target is located outside this interval. When the target position belongs to the resetting interval or it is infinite then no optimal reset rate exists, but there is an optimal resetting interval width or resetting characteristic scale which minimizes the mean first-passage time. We also show that the first-passage density averaged over the resetting points depends on its first moment only. As a consequence, there is an equivalent point such that the first-passage problem with resetting to that point is statistically equivalent to the case of distributed resetting. We end our study by analyzing the fluctuations of the first-passage times for these cases. All our analytical results are verified through numerical simulations.
Hybrid Internal Model: Learning Agile Legged Locomotion with Simulated Robot Response

Robust locomotion control depends on accurate state estimations. However, the sensors of most legged robots can only provide partial and noisy observations, making the estimation particularly challenging, especially for external states like terrain frictions and elevation maps. Inspired by the classical Internal Model Control principle, we consider these external states as disturbances and introduce Hybrid Internal Model (HIM) to estimate them according to the response of the robot. The response, which we refer to as the hybrid internal embedding, contains the robot's explicit velocity and implicit stability representation, corresponding to two primary goals for locomotion tasks: explicitly tracking velocity and implicitly maintaining stability. We use contrastive learning to optimize the embedding to be close to the robot's successor state, in which the response is naturally embedded. HIM has several appealing benefits: It only needs the robot's proprioceptions, i.e., those from joint encoders and IMU as observations. It innovatively maintains consistent observations between simulation reference and reality that avoids information loss in mimicking learning. It exploits batch-level information that is more robust to noises and keeps better sample efficiency. It only requires 1 hour of training on an RTX 4090 to enable a quadruped robot to traverse any terrain under any disturbances. A wealth of real-world experiments demonstrates its agility, even in high-difficulty tasks and cases never occurred during the training process, revealing remarkable open-world generalizability.
Memory Gym: Towards Endless Tasks to Benchmark Memory Capabilities of Agents

Memory Gym presents a suite of 2D partially observable environments, namely Mortar Mayhem, Mystery Path, and Searing Spotlights, designed to benchmark memory capabilities in decision-making agents. These environments, originally with finite tasks, are expanded into innovative, endless formats, mirroring the escalating challenges of cumulative memory games such as ``I packed my bag''. This progression in task design shifts the focus from merely assessing sample efficiency to also probing the levels of memory effectiveness in dynamic, prolonged scenarios. To address the gap in available memory-based Deep Reinforcement Learning baselines, we introduce an implementation that integrates Transformer-XL (TrXL) with Proximal Policy Optimization. This approach utilizes TrXL as a form of episodic memory, employing a sliding window technique. Our comparative study between the Gated Recurrent Unit (GRU) and TrXL reveals varied performances across different settings. TrXL, on the finite environments, demonstrates superior sample efficiency in Mystery Path and outperforms in Mortar Mayhem. However, GRU is more efficient on Searing Spotlights. Most notably, in all endless tasks, GRU makes a remarkable resurgence, consistently outperforming TrXL by significant margins. Website and Source Code: https://github.com/MarcoMeter/endless-memory-gym/
Solving partial differential equations with waveguide-based metatronic networks

Photonic computing has recently become an interesting paradigm for high-speed calculation of computing processes using light-matter interactions. Here, we propose and study an electromagnetic wave-based structure with the ability to calculate the solution of partial differential equations in the form of the Helmholtz wave equation. To do this, we make use of a network of interconnected waveguides filled with dielectric inserts. In so doing, it is shown how the proposed network can mimic the response of a network of T-circuit elements formed by two series and a parallel impedance, i.e., the waveguide network effectively behaves as a metatronic network. An in-depth theoretical analysis of the proposed metatronic structure is presented showing how the governing equation for the currents and impedances of the metatronic network resembles that of the finite difference representation of the Helmholtz wave equation. Different studies are then discussed including the solution of partial differential equations for Dirichlet and open boundary value problems, demonstrating how the proposed metatronic-based structure has the ability to calculate their solutions.
Exploring the relationships between psychological variables and loot box engagement, part 2: exploratory analyses of complex relationships

In a pre-registered survey linked to this paper (Exploring the relationships between psychological variables and loot box engagement, part 1: pre-registered hypotheses), we confirmed bivariate associations between engagement with loot boxes (purchasable randomized rewards in video games) and measures of problem gambling, problem video gaming, impulsivity, gambling cognitions, experiences of game-related ‘flow’, psychological distress and reduced wellbeing. However, these variables have complex relationships, so to gain further insights, we analysed the dataset (1495 gamers who purchase loot boxes and 1223 purchasers of non-randomized content) in a series of Bayesian mixed-effects multiple regressions with a zero-inflation component. The results challenge some well-established results in the literature, including associations between loot box engagement and problematic gambling measures, instead suggesting that this relationship might be underpinned by shared variance with problem video gaming and gambling-related cognitions. An entirely novel discovery revealed a complex interaction between experiences of flow and loot box engagement. Distress and wellbeing are both (somewhat contradictorily) predictive of participants engaging with loot boxes, but neither correlate with increasing loot box risky engagement/spend (among those who engage). Our findings unravel some of the nuances underpinning loot box engagement, yet remain consistent with narratives that policy action on loot boxes will have benefits for harm minimization.
More Than Meets the AI: Evaluating the performance of GPT-4 on Computer Graphics assessment questions

Recent studies have showcased the exceptional performance of LLMs (Large Language Models) on assessment questions across various discipline areas. This can be helpful if used to support the learning process, for example by enabling students to quickly generate and contrast alternative solution approaches. However, concerns about student over-reliance and inappropriate use of LLMs in education are common. Understanding the capabilities of LLMs is essential for instructors to make informed decisions on question choices for learning and assessment tasks. In CS (Computer Science), previous evaluations of LLMs have focused on CS1 and CS2 questions, and little is known about how well LLMs perform for assessment questions in upper-level CS courses such as CG (Computer Graphics), which covers a wide variety of concepts and question types. To address this gap, we compiled a dataset of past assessment questions used in a final-year undergraduate course about introductory CG, and evaluated the performance of GPT-4 on this dataset. We also classified assessment questions and evaluated the performance of GPT-4 for different types of questions. We found that the performance tended to be best for simple mathematical questions, and worst for questions requiring creative thinking, and those with complex descriptions and/or images. We share our benchmark dataset with the community and provide new insights into the capabilities of GPT-4 in the context of CG courses. We highlight opportunities for teaching staff to improve student learning by guiding the use of LLMs for CG questions, and inform decisions around question choices for assessment tasks.