Miracle-dz/UniFAR-FTUs huggingface dataset:
Input-agnostic Certified Group Fairness via Gaussian Parameter Smoothing

Only recently, researchers attempt to provide classification algorithms with provable group fairness guarantees. Most of these algorithms suffer from harassment caused by the requirement that the training and deployment data follow the same distribution. This paper proposes an input-agnostic certified group fairness algorithm, FairSmooth, for improving the fairness of classification models while maintaining the remarkable prediction accuracy. A Gaussian parameter smoothing method is developed to transform base classifiers into their smooth versions. An optimal individual smooth classifier is learnt for each group with only the data regarding the group and an overall smooth classifier for all groups is generated by averaging the parameters of all the individual smooth ones. By leveraging the theory of nonlinear functional analysis, the smooth classifiers are reformulated as output functions of a Nemytskii operator. Theoretical analysis is conducted to derive that the Nemytskii operator is smooth and induces a Frechet differentiable smooth manifold. We theoretically demonstrate that the smooth manifold has a global Lipschitz constant that is independent of the domain of the input data, which derives the input-agnostic certified group fairness.
Misinformation Mitigation under Differential Propagation Rates and Temporal Penalties

We propose an information propagation model that captures important temporal aspects that have been well observed in the dynamics of fake news diffusion, in contrast with the diffusion of truth. The model accounts for differential propagation rates of truth and misinformation and for user reaction times. We study a time-sensitive variant of the misinformation mitigation problem, where k seeds are to be selected to activate a truth campaign so as to minimize the number of users that adopt misinformation propagating through a social network. We show that the resulting objective is non-submodular and employ a sandwiching technique by defining submodular upper and lower bounding functions, providing data-dependent guarantees. In order to enable the use of a reverse sampling framework, we introduce a weighted version of reverse reachability sets that captures the associated differential propagation rates and establish a key equivalence between weighted set coverage probabilities and mitigation with respect to the sandwiching functions. Further, we propose an offline reverse sampling framework that provides (1 - 1/ e - ϵ)-approximate solutions to our bounding functions and introduce an importance sampling technique to reduce the sample complexity of our solution. Finally, we show how our framework can provide an anytime solution to the problem. Experiments over five datasets show that our approach outperforms previous approaches and is robust to uncertainty in the model parameters.
ModMax meets GCA

A maximally symmetric non-linear extension of Maxwell's theory in four dimensions called ModMax has been recently introduced in the literature. This theory preserves both electromagnetic duality and conformal invariance of the linear theory. In this short paper, we introduce a Galilean cousin of the ModMax theory, written in a covariant formalism, that is explicitly shown to be invariant under Galilean Conformal Symmetries. We discuss the construction of such a theory involving Galilean electromagnetic invariants, and show how the classical structure of the theory is invariant under the action of Galilean Conformal Algebra (GCA).
Low-Rank Mirror-Prox for Nonsmooth and Low-Rank Matrix Optimization Problems

Low-rank and nonsmooth matrix optimization problems capture many fundamental tasks in statistics and machine learning. While significant progress has been made in recent years in developing efficient methods for smooth low-rank optimization problems that avoid maintaining high-rank matrices and computing expensive high-rank SVDs, advances for nonsmooth problems have been slow paced. In this paper we consider standard convex relaxations for such problems. Mainly, we prove that under a strict complementarity condition and under the relatively mild assumption that the nonsmooth objective can be written as a maximum of smooth functions, approximated variants of two popular mirror-prox methods: the Euclidean extragradient method and mirror-prox with matrix exponentiated gradient updates, when initialized with a “warm-start”, converge to an optimal solution with rate O(1/t), while requiring only two low-rank SVDs per iteration. Moreover, for the extragradient method we also consider relaxed versions of strict complementarity which yield a trade-off between the rank of the SVDs required and the radius of the ball in which we need to initialize the method. We support our theoretical results with empirical experiments on several nonsmooth low-rank matrix recovery tasks, demonstrating both the plausibility of the strict complementarity assumption, and the efficient convergence of our proposed low-rank mirror-prox variants.
On Pre-Training for Federated Learning

In most of the literature on federated learning (FL), neural networks are initialized with random weights. In this paper, we present an empirical study on the effect of pre-training on FL. Speciﬁcally, we aim to investigate if pre-training can alleviate the drastic accuracy drop when clients’ decentralized data are non-IID. We focus on F ED A VG , the fundamental and most widely used FL algorithm. We found that pre-training does largely close the gap between F ED A VG and centralized learning under non-IID data, but this does not come from alleviating the well-known model drifting problem in F ED A VG ’s local training. Instead, how pre-training helps F ED A VG is by making F ED A VG ’s global aggregation more stable. When pre-training using real data is not feasible for FL, we propose a novel approach to pre-train with synthetic data. On various image datasets (including one for segmentation), our approach with synthetic pre-training leads to a notable gain, essentially a critical step toward scaling up federated learning for real-world applications.
Learning Viewpoint-Agnostic Visual Representations by Recovering Tokens in 3D Space

Humans are remarkably flexible in understanding viewpoint changes due to visual cortex supporting the perception of 3D structure. In contrast, most of the computer vision models that learn visual representation from a pool of 2D images often fail to generalize over novel camera viewpoints. Recently, the vision architectures have shifted towards convolution-free architectures, visual Transformers, which operate on tokens derived from image patches. However, these Transformers do not perform explicit operations to learn viewpoint-agnostic representation for visual understanding. To this end, we propose a 3D Token Representation Layer (3DTRL) that estimates the 3D positional information of the visual tokens and leverages it for learning viewpoint-agnostic representations. The key elements of 3DTRL include a pseudo-depth estimator and a learned camera matrix to impose geometric transformations on the tokens, trained in an unsupervised fashion. These enable 3DTRL to recover the 3D positional information of the tokens from 2D patches. In practice, 3DTRL is easily plugged-in into a Transformer. Our experiments demonstrate the effectiveness of 3DTRL in many vision tasks including image classification, multi-view video alignment, and action recognition. The models with 3DTRL outperform their backbone Transformers in all the tasks with minimal added computation. Our code is available at https://github.com/elicassion/3DTRL.
Grain boundary-induced martensitic transformations: A phase-field study of nucleation, size-effect, triple junction-effect, microstructures, and compatibility at the nanoscale

An original thermodynamically consistent large strains-based multiphase phase-field (PF) approach of Ginzburg-Landau type is developed for studying the grain boundary (GB)-induced martensitic transformations (MTs) in polycrystalline materials at the nanoscale considering the structural stresses within the interfaces. In this general PF approach, N independent order parameters are used for describing the austenite (A)↔martensite (M) transformations and N(> 1) martensitic variants, and another M independent order parameters are considered for describing M(> 1) grains in the polycrystalline samples. The change in the GB energy due to its structural rearrangement during MTs is considered using variable energy for the GB(s) as a function of the order parameter related to the A ↔ M transformation. A rich plot for the temperatures of transformations between the A, premartensite, and M in a bicrystal with a symmetric planar tilt GB are plotted for the varying austenitic GB width. The strong effects of the parameters, including the austenitic GB width, change in GB energy due to MTs, GB misorientation, applied strains, and sample size on heterogeneous nucleation of the phases and the subsequent complex martensitic microstructures evolution are explored in various bicrystals with symmetric or asymmetric planar or circular tilt GBs during the forward and reverse transformations. The triple junction (TJ) energy and the energy and width of the adjacent GBs are also shown to strongly influence the nucleation and microstructures using the tricrystals having three symmetric planar tilt GBs meeting at 120◦ dihedral angles. The compatibility of the microstructures across the GBs is studied. The elastic and structural stresses across the GBs and TJ regions are plotted, which is essential for understanding the role of GBs and TJs in materials failure. The plausible reasons for the nonintuitive behaviour of the GBs on martensite nucleation observed in experiments and atomistic simulations are explained.
Dynamic Scene Deblurring Base on Continuous Cross-Layer Attention Transmission

—The deep convolutional neural networks (CNNs) using attention mechanism have achieved great success for dynamic scene deblurring. In most of these networks, only the features refined by the attention maps can be passed to the next layer and the attention maps of different layers are separated from each other, which does not make full use of the attention information from different layers in the CNN. To address this problem, we introduce a new continuous cross-layer attention transmission (CCLAT) mechanism that can exploit hierarchical attention information from all the convolutional layers. Based on the CCLAT mechanism, we use a very simple attention module to construct a novel residual dense attention fusion block (RDAFB). In RDAFB, the attention maps inferred from the outputs of the preceding RDAFB and each layer are directly connected to the subsequent ones, leading to a CRLAT mechanism. Taking RDAFB as the building block, we design an effective architecture for dynamic scene deblurring named RDAFNet. The experiments on benchmark datasets show that the proposed model outperforms the state-of-the-art deblurring approaches, and demonstrate the effectiveness of CCLAT mechanism. The source code is available on: https://github.com/xjmz6/RDAFNet.
Marginal quenches and drives in Tomonaga-Luttinger liquids

We study Tomonaga-Luttinger liquids thrown out of equilibrium by marginal deformations in the form of interaction modulations. This is modeled by quenching or periodically driving the Luttinger parameter or, equivalently, the compactification radius of the free boson conformal field theory between two different values. We obtain exact analytical results for the evolution of the Loschmidt echo and observables such as the particle and energy densities. Starting from generic initial states, the quench dynamics are shown to exhibit revivals and temporal orthogonalities. For the periodic drive, we show stability or instability of time-evolved physical quantities dependent on the drive parameters. We also compare the corresponding marginally deformed thermal density matrices by non-perturbatively evaluating their Rényi divergence as a Euclidean quench. All the dynamics are shown to be crucially dependent on the ratio of the Luttinger parameters, which corresponds to the Zamolodchikov distance in the space of marginal deformations. Our setup is equivalently interpreted as the dynamics of the bosonic string upon instantaneous changes of the target-space radius.
Community Recovery in the Geometric Block Model

To capture the inherent geometric features of many community detection problems, we propose to use a new random graph model of communities that we call a Geometric Block Model. The geometric block model builds on the random geometric graphs (Gilbert, 1961), one of the basic models of random graphs for spatial networks, in the same way that the well-studied stochastic block model builds on the Erd\H{o}s-R\'{en}yi random graphs. It is also a natural extension of random community models inspired by the recent theoretical and practical advancements in community detection. To analyze the geometric block model, we first provide new connectivity results for random annulus graphs which are generalizations of random geometric graphs. The connectivity properties of geometric graphs have been studied since their introduction, and analyzing them has been more difficult than their Erd\H{o}s-R\'{en}yi counterparts due to correlated edge formation. We then use the connectivity results of random annulus graphs to provide necessary and sufficient conditions for efficient recovery of communities for the geometric block model. We show that a simple triangle-counting algorithm to detect communities in the geometric block model is near-optimal. For this we consider the following two regimes of graph density. In the regime where the average degree of the graph grows logarithmically with the number of vertices, we show that our algorithm performs extremely well, both theoretically and practically. In contrast, the triangle-counting algorithm is far from being optimum for the stochastic block model in the logarithmic degree regime. We simulate our results on both real and synthetic datasets to show superior performance of both the new model as well as our algorithm.
Microscopic foundation of the $\mu$(I) rheology for dense granular flows on inclined planes

Macroscopic and microscopic properties of dense granular layers flowing down inclined planes are obtained from Discrete-Element-Method simulations for both frictionless and frictional grains. Three fundamental observations for dense granular flows are recovered, namely the occurrence of a critical stress, the Bagnold velocity profile, as well as well-defined friction and dilatancy laws. The microscopic aspects of the grain motion highlight the formation of transient clusters. From this microscopic picture, we derive a theoretical scaling model without any empirical input that explains quantitatively the fundamental laws of dense granular flows in incline plane and shear geometries. The adequacy between the model and the observed results suggests that granular flows can be viewed as flows from thermal fluids of hard spheres.
Curious Exploration via Structured World Models Yields Zero-Shot Object Manipulation

It has been a long-standing dream to design artificial agents that explore their environment efficiently via intrinsic motivation, similar to how children perform curious free play. Despite recent advances in intrinsically motivated reinforcement learning (RL), sample-efficient exploration in object manipulation scenarios remains a significant challenge as most of the relevant information lies in the sparse agent-object and object-object interactions. In this paper, we propose to use structured world models to incorporate relational inductive biases in the control loop to achieve sample-efficient and interaction-rich exploration in compositional multi-object environments. By planning for future novelty inside structured world models, our method generates free-play behavior that starts to interact with objects early on and develops more complex behavior over time. Instead of using models only to compute intrinsic rewards, as commonly done, our method showcases that the self-reinforcing cycle between good models and good exploration also opens up another avenue: zero-shot generalization to downstream tasks via model-based planning. After the entirely intrinsic task-agnostic exploration phase, our method solves challenging downstream tasks such as stacking, flipping, pick&place, and throwing that generalizes to unseen numbers and arrangements of objects without any additional training.
Graph potentials and symplectic geometry of moduli spaces of vector bundles

We give the rst examples of Fano manifolds with multiple optimal tori, i.e. we construct monotone Lagrangian tori 𝐿 , such that the weighted number of holomorphic Maslovindextwodiscswithboundaryon 𝐿 equalstheupperboundgivenbythesymplectic invariant limsup 𝑛 ([ 𝑚 0 ( 𝐿 ) 𝑛 ] 𝑥 0 ) 1 / 𝑛 , where 𝑚 0 ( 𝐿 ) is the Floer potential. Toeverytrivalentgraph 𝛾 ofgenus 𝑔 weassociateanoptimaltorus 𝐿 𝛾 onthecelebrated symplectic Fano manifold N 𝑔 (of complex dimension 3 𝑔 − 3) given by the character variety of rank 2 on a genus 𝑔 surface with prescribed odd monodromy at a puncture, We moreover show that all pairs ( N 𝑔 ,𝐿 𝛾 ) are pairwise non-isotopic. In particular, we conrm a form of mirror symmetry between the A-model of the pairs ( N 𝑔 ,𝐿 𝛾 ) and B-model of graph potentials, a family of Laurent polynomials we introduced in earlier work. A crucial input from outside of symplectic geometry is an analysis of Manon’s toric degenerations of algebro-geometric models M 𝐶 ( 2 , L ) for the spaces N 𝑔 , as moduli spaces of stable rank 2 bundles on an algebraic curve with a xed determinant, constructed using conformal eld theory.
Video PreTraining (VPT): Learning to Act by Watching Unlabeled Online Videos

Pretraining on noisy, internet-scale datasets has been heavily studied as a technique for training models with broad, general capabilities for text, images, and other modalities. However, for many sequential decision domains such as robotics, video games, and computer use, publicly available data does not contain the labels required to train behavioral priors in the same way. We extend the internet-scale pretraining paradigm to sequential decision domains through semi-supervised imitation learning wherein agents learn to act by watching online unlabeled videos. Specifically, we show that with a small amount of labeled data we can train an inverse dynamics model accurate enough to label a huge unlabeled source of online data -- here, online videos of people playing Minecraft -- from which we can then train a general behavioral prior. Despite using the native human interface (mouse and keyboard at 20Hz), we show that this behavioral prior has nontrivial zero-shot capabilities and that it can be fine-tuned, with both imitation learning and reinforcement learning, to hard-exploration tasks that are impossible to learn from scratch via reinforcement learning. For many tasks our models exhibit human-level performance, and we are the first to report computer agents that can craft diamond tools, which can take proficient humans upwards of 20 minutes (24,000 environment actions) of gameplay to accomplish.
Obj2Sub: Unsupervised Conversion of Objective to Subjective Questions

Exams are conducted to test the learner's understanding of the subject. To prevent the learners from guessing or exchanging solutions, the mode of tests administered must have sufficient subjective questions that can gauge whether the learner has understood the concept by mandating a detailed answer. Hence, in this paper, we propose a novel hybrid unsupervised approach leveraging rule-based methods and pre-trained dense retrievers for the novel task of automatically converting the objective questions to subjective questions. We observe that our approach outperforms the existing data-driven approaches by 36.45% as measured by Recall@k and Precision@k.
The Effective Sample Size in Bayesian Information Criterion for Level-Specific Fixed and Random Effects Selection in a Two-Level Nested Model

Popular statistical software provides Bayesian information criterion (BIC) for multilevel models or linear mixed models. However, it has been observed that the combination of statistical literature and software documentation has led to discrepancies in the formulas of the BIC and uncertainties of the proper use of the BIC in selecting a multilevel model with respect to level-specific fixed and random effects. These discrepancies and uncertainties result from different specifications of sample size in the BIC's penalty term for multilevel models. In this study, we derive the BIC's penalty term for level-specific fixed and random effect selection in a two-level nested design. In this new version of BIC, called BIC_E, this penalty term is decomposed into two parts if the random effect variance-covariance matrix has full rank: (a) a term with the log of average sample size per cluster whose multiplier involves the overlapping number of dimensions between the column spaces of the random and fixed effect design matrices and (b) the total number of parameters times the log of the total number of clusters. Furthermore, we study the behavior of BIC_E in the presence of redundant random effects. The use of BIC_E is illustrated with a textbook example data set and a numerical demonstration shows that the derived formulae adheres to empirical values.
The Maximality Principle in Singular Control with Absorption and Its Applications to the Dividend Problem

Motivated by a new formulation of the classical dividend problem, we show that Peskir's maximality principle can be transferred to singular stochastic control problems with 2-dimensional degenerate dynamics and absorption along the diagonal of the state space. We construct an optimal control as a Skorokhod reflection along a moving barrier, where the barrier can be computed analytically as the smallest solution to a certain non-linear ordinary differential equation. Contrarily to the classical 1-dimensional formulation of the dividend problem, our framework produces a non-trivial solution when the firm's (pre-dividend) equity capital evolves as a geometric Brownian motion. Such solution is also qualitatively different from the one traditionally obtained for the arithmetic Brownian motion.
Quantifying NV-center Spectral Diffusion by Symmetry

The spectrally narrow, spin-dependent optical transitions of nitrogen vacancy (NV) center defects in diamond can be harnessed for quantum networking applications. Key to such networking schemes is the generation of indistinguishable photons. Two challenges limit scalability in such systems: defect-to-defect variations of the optical transition frequencies caused by local strain variation, and spectral diﬀusion of the optical frequencies on repeated measurement caused by photoexcitation of nearby charge traps. In this experimental study we undertake a group theoretic approach to quantifying spectral diﬀusion and strain, decomposing each into components corresponding to Jahn-Teller symmetries of the NV center. We investigate correlations between the components of strain, spectral diﬀusion, and depth from surface, ﬁnding that strain and spectral diﬀusion are each dominated by longitudinal perturbations. We also ﬁnd a weak negative correlation between transverse static strain and total spectral diﬀusion suggesting that transverse strain provides some degree of protection from spectral diﬀusion. Additionally, we ﬁnd that spectral diﬀusion becomes more pronounced with increasing depth in the diamond bulk. Our symmetry-decomposed technique for quantifying spectral diﬀusion can be valuable for understanding how a given nanoscale charge trap environment inﬂuences spectral diﬀusion and for developing strategies of mitigation.