Miracle-dz/UniFAR-FTUs huggingface dataset:
A Risk Management Perspective on Statistical Estimation and Generalized Variational Inference

Generalized variational inference (GVI) provides an optimization-theoretic framework for statistical estimation that encapsulates many traditional estimation procedures. The typical GVI problem is to compute a distribution of parameters that maximizes the expected payoff minus the divergence of the distribution from a specified prior. In this way, GVI enables likelihood-free estimation with the ability to control the influence of the prior by tuning the so-called learning rate. Recently, GVI was shown to outperform traditional Bayesian inference when the model and prior distribution are misspecified. In this paper, we introduce and analyze a new GVI formulation based on utility theory and risk management. Our formulation is to maximize the expected payoff while enforcing constraints on the maximizing distribution. We recover the original GVI distribution by choosing the feasible set to include a constraint on the divergence of the distribution from the prior. In doing so, we automatically determine the learning rate as the Lagrange multiplier for the constraint. In this setting, we are able to transform the infinite-dimensional estimation problem into a two-dimensional convex program. This reformulation further provides an analytic expression for the optimal density of parameters. In addition, we prove asymptotic consistency results for empirical approximations of our optimal distributions. Throughout, we draw connections between our estimation procedure and risk management. In fact, we demonstrate that our estimation procedure is equivalent to evaluating a risk measure. We test our procedure on an estimation problem with a misspecified model and prior distribution, and conclude with some extensions of our approach.
Magnetized AdS/BCFT Correspondence in Horndeski Gravity

This work presents a study of the thermodynamics and hydrodynamics of a five-dimensional black hole in the presence of an external magnetic field. The solution is the gravity dual to the Anti-de Sitter/Boundary Conformal Field Theory correspondence, and with it, we will study the properties of an anisotropic fluid. Using holographic renormalization, we compute the free energy and {the} holographic stress tensor residing on the boundary {$Q$}. From the point of view of the fluid/gravity correspondence, we have a class of boundary extensions existing in $Q$, for which the stress-energy tensor describes a magnetizing conformal fluid. We discuss the characteristics of this special solution and its thermodynamic properties, for example, the bulk and shear viscosity, the square of the speed of sound, as well as the anisotropic properties produced by the magnetic field in the magnetized conformal plasma.
Model-theoretic properties of nilpotent groups and Lie algebras

We give a systematic study of the model theory of generic nilpotent groups and Lie algebras. We show that the Fra\"iss\'e limit of 2-nilpotent groups of exponent $p$ studied by Baudisch is 2-dependent and NSOP$_{1}$. We prove that the class of $c$-nilpotent Lie algebras over an arbitrary field, in a language with predicates for a Lazard series, is closed under free amalgamation. We show that for $2<c$, the generic $c$-nilpotent Lie algebra over $\mathbb{F}_{p}$ is strictly NSOP$_{4}$ and $c$-dependent. Via the Lazard correspondence, we obtain the same result for $c$-nilpotent groups of exponent $p$, for an odd prime $p>c$.
Snake Graphs and Caldero-Chapoton Functions from Triangulated Orbifolds

Generalized cluster algebras from orbifolds were defined by Chekhov and Shapiro to give a combinatorial description of their Teichm\"uller spaces. One can also assign a gentle algebra to a triangulated orbifold, as in the work of Labardini-Fragoso and Mou. In this work, we show that the Caldero-Chapoton map and the snake graph expansion map agree for arcs in triangulated orbifolds and arc modules, and similarly for closed curves and certain band modules. As a consequence, we have a bijection between some indecomposable modules over a gentle algebra and cluster variables in a generalized cluster algebra where both algebras arise from the same triangulated orbifold.
Incorporating Probing Signals into Multimodal Machine Translation via Visual Question-Answering Pairs

This paper presents an in-depth study of multimodal machine translation (MMT), examining the prevailing understanding that MMT systems exhibit decreased sensitivity to visual information when text inputs are complete. Instead, we attribute this phenomenon to insufficient cross-modal interaction, rather than image information redundancy. A novel approach is proposed to generate parallel Visual Question-Answering (VQA) style pairs from the source text, fostering more robust cross-modal interaction. Using Large Language Models (LLMs), we explicitly model the probing signal in MMT to convert it into VQA-style data to create the Multi30K-VQA dataset. An MMT-VQA multitask learning framework is introduced to incorporate explicit probing signals from the dataset into the MMT training process. Experimental results on two widely-used benchmarks demonstrate the effectiveness of this novel approach. Our code and data would be available at: \url{https://github.com/libeineu/MMT-VQA}.
Predicting Patient No-Shows in Community Health Clinics: A Case Study in Designing a Data Analytic Product

The data science revolution has highlighted the varying roles that data analytic products can play in a different industries and applications. There has been particular interest in using analytic products coupled with algorithmic prediction models to aid in human decision-making. However, detailed descriptions of the decision-making process that leads to the design and development of analytic products are lacking in the statistical literature, making it difficult to accumulate a body of knowledge where students interested in the field of data science may look to learn about this process. In this paper, we present a case study describing the development of an analytic product for predicting whether patients will show up for scheduled appointments at a community health clinic. We consider the stakeholders involved and their interests, along with the real-world analytical and technical trade-offs involved in developing and deploying the product. Our goal here is to highlight the decisions made and evaluate them in the context of possible alternatives. We find that although this case study has some unique characteristics, there are lessons to be learned that could translate to other settings and applications.
Multiband $k \cdot p$ theory for hexagonal germanium

The direct bandgap found in hexagonal germanium and some of its alloys with silicon allows for an optically active material within the group-IV semiconductor family with various potential technological applications. However, there remain some unanswered questions regarding several aspects of the band structiure, including the strength of the electric dipole transitions at the center of the Brillouin zone. Using the $\mathbf{k\cdot p}$ method near the $\Gamma$ point, including 10 bands, and taking spin-orbit coupling into account, we obtain a self-consistent model that produces the correct band curvatures, with previously unknown inverse effective mass parameters, to describe 2H-Ge via fitting to {\it ab initio} data and to calculate effective masses for electrons and holes. To understand the weak dipole coupling between the lowest conduction band and the top valance band, we start from a spinless 12-band model and show that when adding spin-orbit coupling, the lowest conduction band hybridizes with a higher-lying conduction band, which cannot be explained by the spinful 10-band model. With the help of L\"owdin's partitioning, we derive the effective low-energy Hamiltonian for the conduction bands for the possible spin dynamics and nanostructure studies and in a similar manner, we give the best fit parameters for the valance-band-only model that can be used in the transport studies. Finally, using the self-consistent 10-band model, we include the effects of a magnetic field and predict the electron and hole g-factor of the conduction and valance bands.
Primordial Black Holes with QCD Color Charge

We describe a realistic mechanism whereby black holes with significant QCD color charge could have formed during the early universe. Primordial black holes (PBHs) could make up a significant fraction of the dark matter if they formed well before the QCD confinement transition. Such PBHs would form by absorbing unconfined quarks and gluons, and hence could acquire a net color charge. We estimate the number of PBHs per Hubble volume with near-extremal color charge for various scenarios, and discuss possible phenomenological implications.
Combating Representation Learning Disparity with Geometric Harmonization

Self-supervised learning (SSL) as an effective paradigm of representation learning has achieved tremendous success on various curated datasets in diverse scenarios. Nevertheless, when facing the long-tailed distribution in real-world applications, it is still hard for existing methods to capture transferable and robust representation. Conventional SSL methods, pursuing sample-level uniformity, easily leads to representation learning disparity where head classes dominate the feature regime but tail classes passively collapse. To address this problem, we propose a novel Geometric Harmonization (GH) method to encourage category-level uniformity in representation learning, which is more benign to the minority and almost does not hurt the majority under long-tailed distribution. Specially, GH measures the population statistics of the embedding space on top of self-supervised learning, and then infer an fine-grained instance-wise calibration to constrain the space expansion of head classes and avoid the passive collapse of tail classes. Our proposal does not alter the setting of SSL and can be easily integrated into existing methods in a low-cost manner. Extensive results on a range of benchmark datasets show the effectiveness of GH with high tolerance to the distribution skewness. Our code is available at https://github.com/MediaBrain-SJTU/Geometric-Harmonization.
FMMRec: Fairness-aware Multimodal Recommendation

Recently, multimodal recommendations have gained increasing attention for effectively addressing the data sparsity problem by incorporating modality-based representations. Although multimodal recommendations excel in accuracy, the introduction of different modalities (e.g., images, text, and audio) may expose more users' sensitive information (e.g., gender and age) to recommender systems, resulting in potentially more serious unfairness issues. Despite many efforts on fairness, existing fairness-aware methods are either incompatible with multimodal scenarios, or lead to suboptimal fairness performance due to neglecting sensitive information of multimodal content. To achieve counterfactual fairness in multimodal recommendations, we propose a novel fairness-aware multimodal recommendation approach (dubbed as FMMRec) to disentangle the sensitive and non-sensitive information from modal representations and leverage the disentangled modal representations to guide fairer representation learning. Specifically, we first disentangle biased and filtered modal representations by maximizing and minimizing their sensitive attribute prediction ability respectively. With the disentangled modal representations, we mine the modality-based unfair and fair (corresponding to biased and filtered) user-user structures for enhancing explicit user representation with the biased and filtered neighbors from the corresponding structures, followed by adversarially filtering out sensitive information. Experiments on two real-world public datasets demonstrate the superiority of our FMMRec relative to the state-of-the-art baselines. Our source code is available at https://anonymous.4open. science/r/FMMRec.
Physician Detection of Clinical Harm in Machine Translation: Quality Estimation Aids in Reliance and Backtranslation Identifies Critical Errors

A major challenge in the practical use of Machine Translation (MT) is that users lack guidance to make informed decisions about when to rely on outputs. Progress in quality estimation research provides techniques to automatically assess MT quality, but these techniques have primarily been evaluated in vitro by comparison against human judgments outside of a specific context of use. This paper evaluates quality estimation feedback in vivo with a human study simulating decision-making in high-stakes medical settings. Using Emergency Department discharge instructions, we study how interventions based on quality estimation versus backtranslation assist physicians in deciding whether to show MT outputs to a patient. We find that quality estimation improves appropriate reliance on MT, but backtranslation helps physicians detect more clinically harmful errors that QE alone often misses.
A boundary projection for the dilation order

Motivated by Arveson's conjecture, we introduce a notion of hyperrigidity for a partial order on the state space of a $C^*$-algebra $B$. We show how this property is equivalent to the existence of a boundary: a subset of the pure states which completely encodes maximality in the given order. In the classical case where $B$ is commutative, such boundaries are known to exist when the partial order is induced by some well-behaved cone. However, the relevant order for the purposes of Arveson's conjecture is the dilation order, which is not known to fit into this framework. Our main result addresses this difficulty by showing that the dilation maximal states are stable under absolute continuity. Consequently, we obtain the existence of a boundary projection in the bidual $B^{**}$, on which all dilation maximal states must be concentrated. The topological regularity of this boundary projection is shown to lie at the heart of Arveson's conjecture. Our techniques do not require $B$ to be commutative.
Quantifying the Transit Light Source Effect: Measurements of Spot Temperature and Coverage on the Photosphere of AU Microscopii with High-resolution Spectroscopy and Multicolor Photometry

AU Microscopii (AU Mic) is an active 24 ± 3 Myr pre-main-sequence M dwarf in the stellar neighborhood (d = 9.7 pc) with a rotation period of 4.86 days. The two transiting planets orbiting AU Mic, AU Mic b and c, are warm sub-Neptunes on 8.5 and 18.9 day periods and are targets of interest for atmospheric observations of young planets. Here we study AU Mic’s unocculted starspots using ground-based photometry and spectra in order to complement current and future transmission spectroscopy of its planets. We gathered multicolor Las Cumbres Observatory (LCO) 0.4 m SBIG photometry to study the star's rotational modulations and LCO Network of Robotic Echelle Spectrographs high-resolution spectra to measure the different spectral components within the integrated spectrum of the star, parameterized by three spectral components and their coverage fractions. We find AU Mic’s surface has at least two spectral components: a T amb = 4003 − 14 + 15 K ambient photosphere and cool spots that have a temperature of T spot = 3003 − 71 + 63 K, covering a globally averaged area of 39% ± 4% which increases and decreases by 5.1% ± 0.3% from the average throughout a rotation. We also detect a third flux component with a filling factor less than 0.5% and a largely uncertain temperature between 8500 and 10,000 K that we attribute to flare flux not entirely omitted when time averaging the spectra. We include measurements of spot characteristics using a two-temperature model, which we find agree strongly with the three-temperature results. Our expanded use of various techniques to study starspots will help us better understand this system and may have applications for interpreting the transmission spectra for exoplanets transiting stars of a wide range of activity levels.
Minimal group codes over alternating groups

In this work we show that every minimal code in a semisimple group algebra $\mathbb{F}_qG$ is essential if $G$ is a simple group. Since the alternating group $A_n$ is simple if $n=3$ or $n\geq 5$, we present some examples of minimal codes in $\mathbb{F}_qA_n$. For this purpose, if $char(\mathbb{F}_q)>n$, we present the Wedderburn-Artin decomposition of $\mathbb{F}_qS_n$ and $\mathbb{F}_qA_n$ and explicit some of the centrally primitive idempotents of $\mathbb{F}_qS_n$ and $\mathbb{F}_qA_n$.
An Open Source Data Contamination Report for Llama Series Models

Data contamination in language model evaluation is increasingly prevalent as the popularity of large language models. It allows models to "cheat" via memorisation instead of displaying true capabilities. Therefore, contamination analysis has became an crucial part of reliable model evaluation to validate results. However, existing contamination analysis is usually conducted internally by LLM developers and often lacks transparency and completeness. This paper present an open source data contamination reports for the Llama series models. We analyse six popular multi-choice QA benchmarks and quantify their overlapping with the training set of Llama. Various levels of contamination ranging from 1% to 8.7% are found across benchmarks. Our comparison also reveals that Llama models can gain over 5% higher accuracy on contaminated subsets versus clean subsets. Data and code are available at: https://github.com/liyucheng09/ Contamination_Detector .
Transformers Learn Higher-Order Optimization Methods for In-Context Learning: A Study with Linear Models

Transformers are remarkably good at in-context learning (ICL) -- learning from demonstrations without parameter updates -- but how they perform ICL remains a mystery. Recent work suggests that Transformers may learn in-context by internally running Gradient Descent, a first-order optimization method. In this paper, we instead demonstrate that Transformers learn to implement higher-order optimization methods to perform ICL. Focusing on in-context linear regression, we show that Transformers learn to implement an algorithm very similar to Iterative Newton's Method, a higher-order optimization method, rather than Gradient Descent. Empirically, we show that predictions from successive Transformer layers closely match different iterations of Newton's Method linearly, with each middle layer roughly computing 3 iterations. In contrast, exponentially more Gradient Descent steps are needed to match an additional Transformers layer; this suggests that Transformers have an comparable rate of convergence with high-order methods such as Iterative Newton, which are exponentially faster than Gradient Descent. We also show that Transformers can learn in-context on ill-conditioned data, a setting where Gradient Descent struggles but Iterative Newton succeeds. Finally, we show theoretical results which support our empirical findings and have a close correspondence with them: we prove that Transformers can implement $k$ iterations of Newton's method with $\mathcal{O}(k)$ layers.
Global hypoellipticity of $G$-invariant operators on homogeneous vector bundles

We establish necessary and sufficient conditions for the global hypoellipticity of $G$-invariant operators on homogeneous vector bundles. These criteria are established in terms of the corresponding matrix-valued symbols as developed by Ruzhansky and Turunen and extended in [7] to homogeneous vector-bundles.
2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects

We introduce a novel geometrically frustrated classical Ising model, dubbed the"spin vorticity model", whose ground state manifold is a novel classical spin liquid, a"2-form Coulomb phase". We study the thermodynamics of this model both analytically and numerically, exposing the presence of algebraically decaying correlations and demonstrating an extensive ground state entropy, and give a comprehensive account of its ground state properties and excitations. Each classical ground state may be decomposed into collections of closed 2-dimensional membranes, supporting fractionalized string excitations attached to the boundaries of open membranes. At finite temperature, the model can then be described as a gas of closed strings in a background of fluctuating membranes. We demonstrate that the emergent gauge structure of the low-temperature phase is naturally captured in the formalism of 2-form electrodynamics, which describes 1-dimensional charged strings coupled to a rank-2 anti-symmetric gauge field. After establishing the classical spin vorticity model, we consider perturbing it with quantum exchange interactions, from which we derive an effective membrane exchange model of the quantum dynamics of these membranes, which maps to a frustrated 2-form U(1) lattice gauge theory. We show the existence of a fine-tuned Rokhsar-Kivelson point where the quantum ground state is an equal weight superposition of all classical ground state configurations. We further demonstrate how to quantize the string excitations, by coupling a 1-form string field to the emergent 2-form U(1) gauge field, thus mapping a quantum spin model to a 2-form gauge-Higgs model. We discuss the stability of the gapless deconfined phase of this gauge theory and the possibility of realizing a novel class of phases of quantum matter: 2-form U(1) quantum spin liquids.
A minimax optimal control approach for robust neural ODEs

In this paper, we address the adversarial training of neural ODEs from a robust control perspective. This is an alternative to the classical training via empirical risk minimization, and it is widely used to enforce reliable outcomes for input perturbations. Neural ODEs allow the interpretation of deep neural networks as discretizations of control systems, unlocking powerful tools from control theory for the development and the understanding of machine learning. In this specific case, we formulate the adversarial training with perturbed data as a minimax optimal control problem, for which we derive first order optimality conditions in the form of Pontryagin's Maximum Principle. We provide a novel interpretation of robust training leading to an alternative weighted technique, which we test on a low-dimensional classification task.
Neural Distributed Compressor Discovers Binning

We consider lossy compression of an information source when the decoder has lossless access to a correlated one. This setup, also known as the Wyner-Ziv problem, is a special case of distributed source coding. To this day, practical approaches for the Wyner-Ziv problem have neither been fully developed nor heavily investigated. We propose a data-driven method based on machine learning that leverages the universal function approximation capability of artificial neural networks. We find that our neural network-based compression scheme, based on variational vector quantization, recovers some principles of the optimum theoretical solution of the Wyner-Ziv setup, such as binning in the source space as well as optimal combination of the quantization index and side information, for exemplary sources. These behaviors emerge although no structure exploiting knowledge of the source distributions was imposed. Binning is a widely used tool in information theoretic proofs and methods, and to our knowledge, this is the first time it has been explicitly observed to emerge from data-driven learning.