Miracle-dz/UniFAR-FTUs huggingface dataset:
Characterizing the minimax rate of nonparametric regression under bounded convex constraints

We quantify the minimax rate for a nonparametric regression model over a convex function class $\mathcal{F}$ with bounded diameter. We obtain a minimax rate of ${\varepsilon^{\ast}}^2\wedge\mathrm{diam}(\mathcal{F})^2$ where \[\varepsilon^{\ast} =\sup\{\varepsilon>0:n\varepsilon^2 \le \log M_{\mathcal{F}}^{\operatorname{loc}}(\varepsilon,c)\},\] where $M_{\mathcal{F}}^{\operatorname{loc}}(\cdot, c)$ is the local metric entropy of $\mathcal{F}$ and our loss function is the squared population $L_2$ distance over our input space $\mathcal{X}$. In contrast to classical works on the topic [cf. Yang and Barron, 1999], our results do not require functions in $\mathcal{F}$ to be uniformly bounded in sup-norm. In addition, we prove that our estimator is adaptive to the true point, and to the best of our knowledge this is the first such estimator in this general setting. This work builds on the Gaussian sequence framework of Neykov [2022] using a similar algorithmic scheme to achieve the minimax rate. Our algorithmic rate also applies with sub-Gaussian noise. We illustrate the utility of this theory with examples including multivariate monotone functions, linear functionals over ellipsoids, and Lipschitz classes.
Mise en évidence d'une phase climatique holocène extrêmement aride dans l'Altiplano central, par la présence de la polyhalite dans le salar de Uyuni (Bolivie)

An extremely severe drought hit the Bolivian central Altiplano during the Holocene for at least 2,000 years. The climate was similar to that prevailing today in the Atacama Desert (Chile), one of the most arid areas in the world. This phase is likely to be contemporaneous with those detected between 7,000 and 2,000 year B.P. on other areas of South America
Multifidelity domain decomposition-based physics-informed neural networks for time-dependent problems

Multiscale problems are challenging for neural network-based discretizations of differential equations, such as physics-informed neural networks (PINNs). This can be (partly) attributed to the so-called spectral bias of neural networks. To improve the performance of PINNs for time-dependent problems, a combination of multifidelity stacking PINNs and domain decomposition-based finite basis PINNs are employed. In particular, to learn the high-fidelity part of the multifidelity model, a domain decomposition in time is employed. The performance is investigated for a pendulum and a two-frequency problem as well as the Allen-Cahn equation. It can be observed that the domain decomposition approach clearly improves the PINN and stacking PINN approaches.
Predicting heteropolymer interactions: demixing and hypermixing of disordered protein sequences

Cells contain multiple condensates which spontaneously form due to the heterotypic interactions between their components. Although the proteins and disordered region sequences that are responsible for condensate formation have been extensively studied, the rule of interactions between the components that allow demixing, i.e., the coexistence of multiple condensates, is yet to be elucidated. Here we construct an effective theory of the interaction between heteropolymers by fitting it to the molecular dynamics simulation results obtained for more than 200 sequences sampled from the disordered regions of human proteins. We find that the sum of amino acid pair interactions across two heteropolymers predicts the Boyle temperature qualitatively well, which can be quantitatively improved by the dimer pair approximation, where we incorporate the effect of neighboring amino acids in the sequences. The improved theory, combined with the finding of a metric that captures the effective interaction strength between distinct sequences, allowed the selection of up to three disordered region sequences that demix with each other in multicomponent simulations, as well as the generation of artificial sequences that demix with a given sequence. The theory points to a generic sequence design strategy to demix or hypermix thanks to the low dimensional nature of the space of the interactions that we identify. As a consequence of the geometric arguments in the space of interactions, we find that the number of distinct sequences that can demix with each other is strongly constrained, irrespective of the choice of the coarse-grained model. Altogether, we construct a theoretical basis for methods to estimate the effective interaction between heteropolymers, which can be utilized in predicting phase separation properties as well as rules of assignment in the localization and functions of disordered proteins.
A comment on the impact of CMD-3 $e^+e^- \to \pi^+\pi^-$ cross section measurement on the SM $g_\mu-2$ value

We estimated an impact of the recent CMD-3 measurement of the $e^+e^- \to \pi^+\pi^-$ total cross section at $0.3<\sqrt{s}<1.2$ GeV on the leading order hadronic contribution $a_\mu^{had,LO}$ to the muon anomalous magnetic moment $a_\mu = (g_\mu-2)/2$, in presence of comparably precise ISR measurements of the cross section by BaBar and KLOE experiments being in significant tension with the CMD-3. Assuming that all the experiments are affected by yet unidentified systematic effects, to account for the latter, we scaled the experimental uncertainties following the PDG prescription, thus facilitating a consistent joint fit of the world data on the $e^+e^- \to \pi^+\pi^-$ total cross section. The same procedure was applied in all $e^+e^- \to hadrons$ channels contributing to the dispersive estimate of $a_\mu^{had,LO}$. Despite an inclusion of the new CMD-3 $\pi^+\pi^-$ data, our estimate $a_\mu^{had,LO}(e^+e^-) = (696.2 \pm 2.9) \times 10^{-10}$ is consistent with $a_\mu^{had,LO}(e^+e^-)$ values obtained by other authors before publication of the CMD-3 result. Including our $a_\mu^{had,LO}$ value into the SM prediction for $a_\mu$, we obtain $a_\mu^{SM} = (11~659~184 \pm 4_{\mathrm{tot}}) \times 10^{-10}$ which is by $4.7\sigma$ smaller than the world average for the experimental value $a_\mu^{exp} = (11~659~205.9 \pm 2.2) \times 10^{-10}$. We confirm the observation by the CMD-3 authors that their $\sigma(e^+e^- \to \pi^+\pi^-)$ measurement, when taken alone, implies the $a_\mu^{SM}$ prediction consistent with the $a_\mu^{exp}$ at $\sim 1\sigma$ level.
The non-decreasing condition on g-vectors

The non-decreasing condition on g-vectors is introduced. Our study shows that this condition is both necessary and sufficient to ensure that the generically indecomposable direct summands of a given g-vector are linearly independent. Additionally, we prove that for any finite dimensional algebra $\Lambda$, under the non-decreasing condition, the number of generically indecomposable irreducible components that appear in the decomposition of a given generically $\tau$-reduced component is lower than or equal to $|\Lambda|$. This solves the conjecture concerning the cardinality of component clusters by Cerulli-Labardini-Schr\"oer, in a reasonable generality. Lastly, we study numerical criteria to check the wildness of g-vectors.
Uncovering the Full Potential of Visual Grounding Methods in VQA

Visual Grounding (VG) methods in Visual Question Answering (VQA) attempt to improve VQA performance by strengthening a model's reliance on question-relevant visual information. The presence of such relevant information in the visual input is typically assumed in training and testing. This assumption, however, is inherently flawed when dealing with imperfect image representations common in large-scale VQA, where the information carried by visual features frequently deviates from expected ground-truth contents. As a result, training and testing of VG-methods is performed with largely inaccurate data, which obstructs proper assessment of their potential benefits. In this study, we demonstrate that current evaluation schemes for VG-methods are problematic due to the flawed assumption of availability of relevant visual information. Our experiments show that these methods can be much more effective when evaluation conditions are corrected. Code is provided on GitHub.
Intersective sets for sparse sets of integers

For $E \subset \mathbb{N}$, a subset $R \subset \mathbb{N}$ is $E$-intersective if for every $A \subset E$ having positive upper relative density, we have $R \cap (A - A) \neq \varnothing$. On the other hand, $R$ is chromatically $E$-intersective if for every finite partition $E=\bigcup_{i=1}^k E_i$, there exists $i$ such that $R\cap (E_i-E_i)\neq\varnothing$. When $E=\mathbb{N}$, we recover the usual notions of intersectivity and chromatic intersectivity. In this article, we investigate to which extent known intersectivity results hold in the relative setting when $E = \mathbb{P}$, the set of primes, or other sparse subsets of $\mathbb{N}$. Among other things, we prove: -There exists an intersective set that is not $\mathbb{P}$-intersective. -However, every $\mathbb{P}$-intersective set is intersective. -There exists a chromatically $\mathbb{P}$-intersective set which is not intersective (and therefore not $\mathbb{P}$-intersective). -The set of shifted Chen primes $\mathbb{P}_{\mathrm{Chen}} + 1$ is $\mathbb{P}$-intersective (and therefore intersective).
Dual-View Data Hallucination with Semantic Relation Guidance for Few-Shot Image Recognition

Learning to recognize novel concepts from just a few image samples is very challenging as the learned model is easily overfitted on the few data and results in poor generalizability. One promising but underexplored solution is to compensate the novel classes by generating plausible samples. However, most existing works of this line exploit visual information only, rendering the generated data easy to be distracted by some challenging factors contained in the few available samples. Being aware of the semantic information in the textual modality that reflects human concepts, this work proposes a novel framework that exploits semantic relations to guide dual-view data hallucination for few-shot image recognition. The proposed framework enables generating more diverse and reasonable data samples for novel classes through effective information transfer from base classes. Specifically, an instance-view data hallucination module hallucinates each sample of a novel class to generate new data by employing local semantic correlated attention and global semantic feature fusion derived from base classes. Meanwhile, a prototype-view data hallucination module exploits semantic-aware measure to estimate the prototype of a novel class and the associated distribution from the few samples, which thereby harvests the prototype as a more stable sample and enables resampling a large number of samples. We conduct extensive experiments and comparisons with state-of-the-art methods on several popular few-shot benchmarks to verify the effectiveness of the proposed framework.
X-ray Polarisation in Magnetar Atmospheres - Effects of Mode Conversion

Magnetars, the most strongly magnetised neutron stars, are among the most promising targets for X-ray polarimetry. The Imaging X-ray Polarimetry Explorer (IXPE), the first satellite devoted to exploring the sky in polarised X-rays, has observed four magnetars to date. A proper interpretation of IXPE results requires the development of new atmospheric models that can take into proper account the effects of the magnetised vacuum on par with those of the plasma. Here we investigate the effects of mode conversion at the vacuum resonance on the polarisation properties of magnetar emission by computing plane-parallel atmospheric models under varying conditions of magnetic field strength/orientation, effective temperature and allowing for either complete or partial adiabatic mode conversion. Complete mode conversion results in a switch of the dominant polarisation mode, from the extraordinary (X) to the ordinary (O) one, below an energy that decreases with increasing magnetic field strength, occurring at ≈0.5 keV for a magnetic field strength of B = 1014 G. Partial adiabatic mode conversion results in a reduced polarisation degree when compared with a standard plasma atmosphere. No dominant mode switch occurs for B = 1014 G while there are two switches for lower fields of B = 3 × 1013 G. Finally, by incorporating our models in a ray-tracing code, we computed the expected polarisation signal at infinity for different emitting regions on the star surface and for different viewing geometries. The observability of QED signatures with IXPE and with future soft X-ray polarimeters as REDSoX is discussed.
Enhancing Document-level Translation of Large Language Model via Translation Mixed-instructions

Existing large language models (LLMs) for machine translation are typically fine-tuned on sentence-level translation instructions and achieve satisfactory performance at the sentence level. However, when applied to document-level translation, these models face a significant challenge, particularly when dealing with documents containing over 512 tokens. This challenge arises from the issue of sentence-level coverage, where subsequent sentences in the document remain untranslated. As a result, the document-level translation capability of LLMs fine-tuned on sentence-level translation instructions is significantly limited. We conjecture that the primary cause of LLMs' weak document-level translation performance is the absence of document-to-document mapping ability. To address the issue, we propose an approach that combines sentence-level and document-level translation instructions of varying lengths to fine-tune LLMs. Our proposed translation mixed-instructions enable LLMs (Llama-2~7B and 13B) to maintain consistent translation performance from the sentence level to documents containing as many as 2048 tokens. Extensive experimental results show that the proposed approach significantly enhances the document-level translation capabilities of LLMs on 10 language pairs, effectively mitigating the sentence-level coverage issue in document-level translation. Experimentation on discourse phenomena has demonstrated that our document-level translation approach significantly improves translation quality, both in terms of BLEU score and discourse coherence.
Machine Learning Applications in Gravitational Wave Astronomy

Gravitational wave astronomy has emerged as a new branch of observational astronomy, since the first detection of gravitational waves in 2015. The current number of $O(100)$ detections is expected to grow by several orders of magnitude over the next two decades. As a result, current computationally expensive detection algorithms will become impractical. A solution to this problem, which has been explored in the last years, is the application of machine-learning techniques to accelerate the detection and parameter estimation of gravitational wave sources. In this chapter, several different applications are summarized, including the application of artificial neural networks and autoenconders in accelerating the computation of surrogate models, deep residual networks in achieving rapid detections with high sensitivity, as well as artificial neural networks for accelerating the construction of neutron star models in an alternative theory of gravity.
A Survey on Statistical Theory of Deep Learning: Approximation, Training Dynamics, and Generative Models

In this article, we review the literature on statistical theories of neural networks from three perspectives. In the first part, results on excess risks for neural networks are reviewed in the nonparametric framework of regression or classification. These results rely on explicit constructions of neural networks, leading to fast convergence rates of excess risks, in that tools from the approximation theory are adopted. Through these constructions, the width and depth of the networks can be expressed in terms of sample size, data dimension, and function smoothness. Nonetheless, their underlying analysis only applies to the global minimizer in the highly non-convex landscape of deep neural networks. This motivates us to review the training dynamics of neural networks in the second part. Specifically, we review papers that attempt to answer ``how the neural network trained via gradient-based methods finds the solution that can generalize well on unseen data. '' In particular, two well-known paradigms are reviewed: the Neural Tangent Kernel (NTK) paradigm, and Mean-Field (MF) paradigm. In the last part, we review the most recent theoretical advancements in generative models including Generative Adversarial Networks (GANs), diffusion models, and in-context learning (ICL) in the Large Language Models (LLMs). The former two models are known to be the main pillars of the modern generative AI era, while ICL is a strong capability of LLMs in learning from a few examples in the context. Finally, we conclude the paper by suggesting several promising directions for deep learning theory.
PokerGPT: An End-to-End Lightweight Solver for Multi-Player Texas Hold'em via Large Language Model

Poker, also known as Texas Hold'em, has always been a typical research target within imperfect information games (IIGs). IIGs have long served as a measure of artificial intelligence (AI) development. Representative prior works, such as DeepStack and Libratus heavily rely on counterfactual regret minimization (CFR) to tackle heads-up no-limit Poker. However, it is challenging for subsequent researchers to learn CFR from previous models and apply it to other real-world applications due to the expensive computational cost of CFR iterations. Additionally, CFR is difficult to apply to multi-player games due to the exponential growth of the game tree size. In this work, we introduce PokerGPT, an end-to-end solver for playing Texas Hold'em with arbitrary number of players and gaining high win rates, established on a lightweight large language model (LLM). PokerGPT only requires simple textual information of Poker games for generating decision-making advice, thus guaranteeing the convenient interaction between AI and humans. We mainly transform a set of textual records acquired from real games into prompts, and use them to fine-tune a lightweight pre-trained LLM using reinforcement learning human feedback technique. To improve fine-tuning performance, we conduct prompt engineering on raw data, including filtering useful information, selecting behaviors of players with high win rates, and further processing them into textual instruction using multiple prompt engineering techniques. Through the experiments, we demonstrate that PokerGPT outperforms previous approaches in terms of win rate, model size, training time, and response speed, indicating the great potential of LLMs in solving IIGs.
AutoTAB: An Algorithm to Track Bipolar Magnetic Regions and Initial results from the Tracked BMRs

AutoTAB is a state-of-the-art, fully automatic algorithm that tracks the Bipolar Magnetic Regions (BMRs) in magnetogram observations. AutoTAB employs identified BMR regions from Line-of-Sight magnetograms from MDI and HMI (1996--2022) to track the BMRs through their evolution on the nearside of the Sun. AutoTAB enables us to create a comprehensive and unique catalog of tracked information of 9232 BMRs in the mentioned time period. This dataset is used to study the collective statistical properties of BMRs and particularly to identify the correct theory for the BMR formation. Here, we discuss the algorithm's functionality and the initial findings obtained from the AutoTAB BMRs catalog.
Singular limit of BSDEs and optimal control of two scale systems with jumps in infinite dimensional spaces

The paper is devoted to a stochastic optimal control problem for a two scale, infinite dimensional, stochastic system. The state of the system consists of slow and fast component and its evolution is driven by both continuous Wiener noises and discontinuous Poisson-type noises. The presence of discontinuous noises is the main feature of the present work. We use the theory of backward stochastic differential equations (BSDEs) to prove that, as the speed of the fast component diverges, the value function of the control problem converges to the solution of a reduced forward backward system that, in turn, is related to a reduced stochastic optimal control problem.
Gradient conformal stationarity and the CMC condition in LRS spacetimes

We study the existence of gradient conformal Killing vectors (CKVs) in LRS spacetimes, and investigate some implications for the evolutionary character of marginally outer trapped surfaces. We first study existence of gradient CKVs via the obtention of a relationship between the Ricci curvature and the gradient of the divergence of the CKV. This provides an alternative set of equations, for which the integrability condition is obtained, to analyze the existence of gradient CKVs. A uniqueness result is obtained in the case of perfect fluids, where it is demonstrated that the Robertson-Walker solution is the unique perfect fluid solution with a nonvanishing pressure, admitting a timelike gradient CKV. The constant mean curvature condition for LRS spacetimes is also obtained, characterized by three distinct conditions which are specified by a set of three scalars. Linear combinations of these scalars, whose vanishing define the constant mean curvature condition, turn out to be related to the evolutions of null expansions of 2-sphere along their null normal directions. As such, some implications for the existence of black holes and the character of the associated horizons are obtained. It is further shown that dynamical black holes of increasing area, with a non-vanishing heat flux across the horizon, will be in equilibrium, with respect to the frame of the conformal observers.
Understanding the ADMM Algorithm via High-Resolution Differential Equations

In the fields of statistics, machine learning, image science, and related areas, there is an increasing demand for decentralized collection or storage of large-scale datasets, as well as distributed solution methods. To tackle this challenge, the alternating direction method of multipliers (ADMM) has emerged as a widely used approach, particularly well-suited to distributed convex optimization. However, the iterative behavior of ADMM has not been well understood. In this paper, we employ dimensional analysis to derive a system of high-resolution ordinary differential equations (ODEs) for ADMM. This system captures an important characteristic of ADMM, called the $\lambda$-correction, which causes the trajectory of ADMM to deviate from the constrained hyperplane. To explore the convergence behavior of the system of high-resolution ODEs, we utilize Lyapunov analysis and extend our findings to the discrete ADMM algorithm. Through this analysis, we identify that the numerical error resulting from the implicit scheme is a crucial factor that affects the convergence rate and monotonicity in the discrete ADMM algorithm. In addition, we further discover that if one component of the objective function is assumed to be strongly convex, the iterative average of ADMM converges strongly with a rate $O(1/N)$, where $N$ is the number of iterations.