Miracle-dz/UniFAR-FTUs huggingface dataset:
Efficient Algorithms for Sum-of-Minimum Optimization

In this work, we propose a novel optimization model termed ``sum-of-minimum"optimization. This model computes the sum (or average) of $N$ values where each is the minimum of the $k$ results of applying a distinct objective function to the same set of $k$ variables, and the model seeks to minimize this sum (or average) over those $k$ variables. When the $N$ functions are distance measures, we recover the $k$-means clustering problem by treating the $k$ variables as $k$ cluster centroids and the sum as the total distance of the input points to their nearest centroids. Therefore, the sum-of-minimum model embodies a clustering functionality with more general measurements instead of just distances. We develop efficient algorithms for sum-of-minimum optimization by generalizing a randomized initialization algorithm for classic $k$-means (Arthur&Vassilvitskii, 2007) and Lloyd's algorithm (Lloyd, 1982). We establish a new tight bound for the generalized initialization algorithm and prove a gradient-descent-like convergence rate for the generalized Lloyd's algorithm. The efficiency of our algorithms is numerically examined on multiple tasks including generalized principal component analysis, mixed linear regression, and small-scale neural network training. Our approach compares favorably to previous ones that are based on simpler but less precise optimization reformulations.
Variación de las concentraciones foliares de nutrientes según la edad fisiológica de las hojas de la palma de aceite en dos localidades de Colombia Variation in Oil Palm Leaf Nutrient Concentrations with Leaf Physiological Age in Two Locations in Colombia

El analisis foliar es una herramienta fundamental para el manejo nutricional y el establecimiento de los programas de fertilizacion de la palma de aceite (Elaeis guineensis Jacq.). La confiabilidad de los analisis foliares depende de muchos factores, entre ellos, los relacionados con la seleccion de la hoja de la palma que se toma como muestra, dado que los niveles foliares de nutrientes cambian con la edad fisiologica de la hoja y el patron de cambios es diferente entre nutrientes. Por lo anterior, es conveniente conocer como cambia la concentracion de cada elemento esencial segun la edad de la hoja, aspecto que esta documentado en la literatura internacional solo para algunos nutrientes y sin incluir datos de Colombia. Con este objetivo, se adelanto un estudio en dos localidades de Colombia, en el cual se determino la variacion de la concentracion de 12 nutrientes en el follaje de la palma haciendo mediciones en hojas de cinco edades fisiologicas. Los resultados permitieron agrupar los elementos en tres categorias segun el patron de su comportamiento. Los datos sobre los micronutrientes potasio (K), fosforo (P), calcio (Ca) y magnesio (Mg) permitieron lo consignado en la literatura para otras localidades del mundo. Se obtuvo informacion no disponible respecto al comportamiento de los micronutrientes y a la sumatoria de las bases (Ca + Mg + K) y la relacion entre ellas [(Ca + Mg)/ K] en funcion de la edad de la hoja. Con base en los resultados, se hicieron inferencias sobre la movilidad de los micronutrientes en la palma. Los resultados ratifican la importancia de una adecuada seleccion de la hoja a muestrear para analisis foliares porque de ello depende la aplicabilidad de los resultados.
Affine term structure models driven by independent L\'evy processes

We characterize affine term structure models of non-negative short rate $R$ which may be obtained as solutions of autonomous SDEs driven by independent, one-dimensional L\'evy martingales, that is equations of the form $$ dR(r)=F(R(t))dt+\sum_{i=1}^{d}G_i(R(t-))dZ_i(t), \quad R(0)=r_0\geq 0, \quad t>0, \quad (1)$$ with deterministic real functions $F,G_1,. ,G_d$ and independent one-dimensional L\'evy martingales $Z_1,. ,Z_d$. Using a general result on the form of the generators of affine term structure models due to Filipovi\'c, it is shown, under the assumption that the Laplace transforms of the driving noises are regularly varying, that all possible solutions $R$ of (1) may be obtained also as solutions of autonomous SDEs driven by independent stable processes with stability indices in the range $(1,2]$. The obtained models include in particular the $\alpha$-CIR model, introduced by Jiao et al., which proved to be still simple yet more reliable than the classical CIR model. Results on heavy tails of $R$ and its limit distribution in terms of the stability indices are proven. Finally, results of numerical calibration of the obtained models to the market term structure of interest rates are presented and compared with the CIR and $\alpha$-CIR models.
Interactive singing melody extraction based on active adaptation

Extraction of predominant pitch from polyphonic audio is one of the fundamental tasks in the field of music information retrieval and computational musicology. To accomplish this task using machine learning, a large amount of labeled audio data is required to train the model. However, a classical model pre-trained on data from one domain (source), e.g., songs of a particular singer or genre, may not perform comparatively well in extracting melody from other domains (target). The performance of such models can be boosted by adapting the model using very little annotated data from the target domain. In this work, we propose an efficient interactive melody adaptation method. Our method selects the regions in the target audio that require human annotation using a confidence criterion based on normalized true class probability. The annotations are used by the model to adapt itself to the target domain using meta-learning. Our method also provides a novel meta-learning approach that handles class imbalance, i.e., a few representative samples from a few classes are available for adaptation in the target domain. Experimental results show that the proposed method outperforms other adaptive melody extraction baselines. The proposed method is model-agnostic and hence can be applied to other non-adaptive melody extraction models to boost their performance. Also, we released a Hindustani Alankaar and Raga (HAR) dataset containing 523 audio files of about 6.86 hours of duration intended for singing melody extraction tasks.
Whispers in the Machine: Confidentiality in LLM-integrated Systems

Large Language Models (LLMs) are increasingly integrated with external tools. While these integrations can significantly improve the functionality of LLMs, they also create a new attack surface where confidential data may be disclosed between different components. Specifically, malicious tools can exploit vulnerabilities in the LLM itself to manipulate the model and compromise the data of other services, raising the question of how private data can be protected in the context of LLM integrations. In this work, we provide a systematic way of evaluating confidentiality in LLM-integrated systems. For this, we formalize a"secret key"game that can capture the ability of a model to conceal private information. This enables us to compare the vulnerability of a model against confidentiality attacks and also the effectiveness of different defense strategies. In this framework, we evaluate eight previously published attacks and four defenses. We find that current defenses lack generalization across attack strategies. Building on this analysis, we propose a method for robustness fine-tuning, inspired by adversarial training. This approach is effective in lowering the success rate of attackers and in improving the system's resilience against unknown attacks.
Investigating the M1 radiative decay behaviors and the magnetic moments of the predicted triple-charm molecular-type pentaquarks

In this work, we systematically study the electromagnetic properties including the M1 radiative decay widths and the magnetic moments of the isoscalar $\Xi_{c c} D^{(*)}$, $\Xi_{cc}D_{1}$, and $\Xi_{cc}D_{2}^{*}$ triple-charm molecular-type pentaquark candidates, where we adopt the constituent quark model and consider both the $S$-$D$ wave mixing effect and the coupled channel effect. Our numerical results suggest that the M1 radiative decay widths and the magnetic moments of the isoscalar $\Xi_{c c} D^{(*)}$, $\Xi_{cc}D_{1}$, and $\Xi_{cc}D_{2}^{*}$ triple-charm molecular-type pentaquark candidates can reflect their inner structures, and the study of the electromagnetic properties is the important step to construct the family of the triple-charm molecular-type pentaquarks. With the accumulation of the experimental data during the high-luminosity phase of LHC, we expect that the present work combined with the corresponding mass spectrum information can encourage the experimental colleagues at LHCb to focus on the isoscalar $\Xi_{c c} D^{(*)}$, $\Xi_{cc}D_{1}$, and $\Xi_{cc}D_{2}^{*}$ triple-charm molecular-type pentaquark candidates.
Magnetism and superconductivity in the $t-J$ model of $La_3Ni_2O_7$ under multiband Gutzwiller approximation

The recent discovery of possible high temperature superconductivity in single crystals of $La_3Ni_2O_7$ under pressure renews the interest in research on nickelates. The DFT calculations reveal that both $d_{z^2}$ and $d_{x^2-y^2}$ orbitals are active, which suggests a minimal two-orbital model to capture the low-energy physics of this system. In this work, we study a bilayer two-orbital $t-J$ model within multiband Gutzwiller approximation, and discuss the magnetism as well as the superconductivity over a wide range of the hole doping. Owing to the inter-orbital super-exchange process between $d_{z^2}$ and $d_{x^2-y^2}$ orbitals, the induced ferromagnetic coupling within layers competes with the conventional antiferromagnetic coupling, and leads to complicated hole doping dependence for the magnetic properties in the system. With increasing hole doping, the system transfers to A-AFM state from the starting G-AFM state. We also find the inter-layer superconducting pairing of $d_{x^2-y^2}$ orbitals dominates due to the large hopping parameter of $d_{z^2}$ along the vertical inter-layer bonds and significant Hund's coupling between $d_{z^2}$ and $d_{x^2-y^2}$ orbitals. Meanwhile, the G-AFM state and superconductivity state can coexist in the low hole doping regime. To take account of the pressure, we also analyze the impacts of inter-layer hopping amplitude on the system properties.
Constraining CP violating nucleon-nucleon long range interactions in diatomic eEDM searches

The searches for CP violating effects in diatomic molecules, such as $\text{HfF}^+$ and ThO, are typically interpreted as a probe of the electron's electric dipole moment ($e\text{EDM}$), a new electron-nucleon interaction, and a new electron-electron interaction. However, in the case of a non-vanishing nuclear spin, a new CP violating nucleon-nucleon long range force will also affect the measurement. Here, we use the $\text{HfF}^+$ $e\text{EDM}$ search and derive a new bound on this hypothetical interaction, which is the most stringent from terrestrial experiments in the 1 eV-10 keV mass range. These multiple new physics sources motivate independent searches in different molecular species for CP violation at low energy that result in model independent bounds, which are insensitive to cancellation among them.
Geodesic X-ray transform and streaking artifacts on simple surfaces or on spaces of constant curvature

The X-ray transform on the plane or on the three-dimensional Euclidean space can be considered as the measurements of CT scanners for normal human tissue. If the human body contains metal regions such as dental implants, stents in blood vessels, metal bones, etc., the beam hardening effect for the energy level of the X-ray causes streaking artifacts in its CT image. More precisely, if there are two strictly convex metal regions contained in the cross-section of normal human tissue, then streaking artifacts occur along the common tangent lines of the two regions. In this paper we study the geodesic X-ray transform and streaking artifacts on nontrapping simple compact Riemannian manifolds with strictly convex boundaries. We show that the streaking artifacts result from the propagation of conormal singularities on the boundary of metal regions along the common tangent geodesics under the strong and seemingly strange assumption that the manifolds are two dimensional or spaces of constant curvature. This condition ensures that every Jacobi field takes the form of the product of a scalar function and parallel transport along the geodesic. Our results clarify the geometric meaning of the theory, which was imperceptible in the known results on the Euclidean space.
On Computationally Efficient Multi-Class Calibration

Consider a multi-class labelling problem, where the labels can take values in $[k]$, and a predictor predicts a distribution over the labels. In this work, we study the following foundational question: Are there notions of multi-class calibration that give strong guarantees of meaningful predictions and can be achieved in time and sample complexities polynomial in $k$? Prior notions of calibration exhibit a tradeoff between computational efficiency and expressivity: they either suffer from having sample complexity exponential in $k$, or needing to solve computationally intractable problems, or give rather weak guarantees. Our main contribution is a notion of calibration that achieves all these desiderata: we formulate a robust notion of projected smooth calibration for multi-class predictions, and give new recalibration algorithms for efficiently calibrating predictors under this definition with complexity polynomial in $k$. Projected smooth calibration gives strong guarantees for all downstream decision makers who want to use the predictor for binary classification problems of the form: does the label belong to a subset $T \subseteq [k]$: e.g. is this an image of an animal? It ensures that the probabilities predicted by summing the probabilities assigned to labels in $T$ are close to some perfectly calibrated binary predictor for that task. We also show that natural strengthenings of our definition are computationally hard to achieve: they run into information theoretic barriers or computational intractability. Underlying both our upper and lower bounds is a tight connection that we prove between multi-class calibration and the well-studied problem of agnostic learning in the (standard) binary prediction setting.
Recent results on large gaps between primes

The present paper is devoted to the discussion of some important results on large gaps between primes and the appearance of such gaps containing $k$-th powers of primes of various types. These results are based on important breakthrough results due to Goldston-Pintz-Yildirim and Maynard on small gaps between primes which are discussed shortly. They are achieved by a combination of the large gap result of K. Ford, B. Green, J. Maynard and T. Tao as well as the matrix method of Maier.
The rational HK-conjecture: transformation groupoids and a revised version

We prove the rational HK-conjecture for a large class of transformation groupoids in the case when the relevant action has torsion-free stabilizers. A revised version of the rational HK-conjecture in the case of (possibly) torsion stabilizers is introduced and proved for a large class of transformation groupoids. In particular, this revised version holds for Scarparo's counterexamples to the original rational HK-conjecture. The key tools used are the Baum-Connes conjecture and a Chern character defined by Raven.
Tighter Bounds on the Information Bottleneck with Application to Deep Learning

Deep Neural Nets (DNNs) learn latent representations induced by their downstream task, objective function, and other parameters. The quality of the learned representations impacts the DNN's generalization ability and the coherence of the emerging latent space. The Information Bottleneck (IB) provides a hypothetically optimal framework for data modeling, yet it is often intractable. Recent efforts combined DNNs with the IB by applying VAE-inspired variational methods to approximate bounds on mutual information, resulting in improved robustness to adversarial attacks. This work introduces a new and tighter variational bound for the IB, improving performance of previous IB-inspired DNNs. These advancements strengthen the case for the IB and its variational approximations as a data modeling framework, and provide a simple method to significantly enhance the adversarial robustness of classifier DNNs.
Discipline and Label: A WEIRD Genealogy and Social Theory of Data Annotation

Data annotation remains the sine qua non of machine learning and AI. Recent empirical work on data annotation has begun to highlight the importance of rater diversity for fairness, model performance, and new lines of research have begun to examine the working conditions for data annotation workers, the impacts and role of annotator subjectivity on labels, and the potential psychological harms from aspects of annotation work. This paper outlines a critical genealogy of data annotation; starting with its psychological and perceptual aspects. We draw on similarities with critiques of the rise of computerized lab-based psychological experiments in the 1970's which question whether these experiments permit the generalization of results beyond the laboratory settings within which these results are typically obtained. Do data annotations permit the generalization of results beyond the settings, or locations, in which they were obtained? Psychology is overly reliant on participants from Western, Educated, Industrialized, Rich, and Democratic societies (WEIRD). Many of the people who work as data annotation platform workers, however, are not from WEIRD countries; most data annotation workers are based in Global South countries. Social categorizations and classifications from WEIRD countries are imposed on non-WEIRD annotators through instructions and tasks, and through them, on data, which is then used to train or evaluate AI models in WEIRD countries. We synthesize evidence from several recent lines of research and argue that data annotation is a form of automated social categorization that risks entrenching outdated and static social categories that are in reality dynamic and changing. We propose a framework for understanding the interplay of the global social conditions of data annotation with the subjective phenomenological experience of data annotation work.
Intrinsic Task-based Evaluation for Referring Expression Generation

Recently, a human evaluation study of Referring Expression Generation (REG) models had an unexpected conclusion: on \textsc{webnlg}, Referring Expressions (REs) generated by the state-of-the-art neural models were not only indistinguishable from the REs in \textsc{webnlg} but also from the REs generated by a simple rule-based system. Here, we argue that this limitation could stem from the use of a purely ratings-based human evaluation (which is a common practice in Natural Language Generation). To investigate these issues, we propose an intrinsic task-based evaluation for REG models, in which, in addition to rating the quality of REs, participants were asked to accomplish two meta-level tasks. One of these tasks concerns the referential success of each RE; the other task asks participants to suggest a better alternative for each RE. The outcomes suggest that, in comparison to previous evaluations, the new evaluation protocol assesses the performance of each REG model more comprehensively and makes the participants' ratings more reliable and discriminable.
Convection and Stratification of Temperature and Concentration

The paper is devoted to the study of natural convection and the formation of delamination in an incompressible liquid due to convective laminar flows in a closed region heated from the side. Weak, medium and intensive modes of stationary laminar thermal, concentration and hemoconcentration (thermohaline) convection are considered, in which nonlinear flow features are manifested that can radically change the flow structure and characteristics of heat and mass transfer. Nonmonotonic dependences of temperature and concentration segregation in the center of the square region on the Grashof number (an intensity of flow) were found. The features of the formation of a nonstationary periodic structure of thermal convection in boundary layers and in the core of a convective flow in a closed region are shown. Details of the formation of countercurrents inside the region with the direction opposite to the main convective flow are given. The influence of vertical and horizontal vibrations on oscillatory convection is shown.
For Better or For Worse? Learning Minimum Variance Features With Label Augmentation

Data augmentation has been pivotal in successfully training deep learning models on classification tasks over the past decade. An important subclass of data augmentation techniques - which includes both label smoothing and Mixup - involves modifying not only the input data but also the input label during model training. In this work, we analyze the role played by the label augmentation aspect of such methods. We prove that linear models on linearly separable data trained with label augmentation learn only the minimum variance features in the data, while standard training (which includes weight decay) can learn higher variance features. An important consequence of our results is negative: label smoothing and Mixup can be less robust to adversarial perturbations of the training data when compared to standard training. We verify that our theory reflects practice via a range of experiments on synthetic data and image classification benchmarks.
Summing Up the Facts: Additive Mechanisms Behind Factual Recall in LLMs

How do transformer-based large language models (LLMs) store and retrieve knowledge? We focus on the most basic form of this task -- factual recall, where the model is tasked with explicitly surfacing stored facts in prompts of form `Fact: The Colosseum is in the country of'. We find that the mechanistic story behind factual recall is more complex than previously thought. It comprises several distinct, independent, and qualitatively different mechanisms that additively combine, constructively interfering on the correct attribute. We term this generic phenomena the additive motif: models compute through summing up multiple independent contributions. Each mechanism's contribution may be insufficient alone, but summing results in constructive interfere on the correct answer. In addition, we extend the method of direct logit attribution to attribute an attention head's output to individual source tokens. We use this technique to unpack what we call `mixed heads' -- which are themselves a pair of two separate additive updates from different source tokens.
Show Me How It's Done: The Role of Explanations in Fine-Tuning Language Models

Our research demonstrates the significant benefits of using fine-tuning with explanations to enhance the performance of language models. Unlike prompting, which maintains the model's parameters, fine-tuning allows the model to learn and update its parameters during a training phase. In this study, we applied fine-tuning to various sized language models using data that contained explanations of the output rather than merely presenting the answers. We found that even smaller language models with as few as 60 million parameters benefited substantially from this approach. Interestingly, our results indicated that the detailed explanations were more beneficial to smaller models than larger ones, with the latter gaining nearly the same advantage from any form of explanation, irrespective of its length. Additionally, we demonstrate that the inclusion of explanations enables the models to solve tasks that they were not able to solve without explanations. Lastly, we argue that despite the challenging nature of adding explanations, samples that contain explanations not only reduce the volume of data required for training but also promote a more effective generalization by the model. In essence, our findings suggest that fine-tuning with explanations significantly bolsters the performance of large language models.