Miracle-dz/UniFAR-FTUs huggingface dataset:
On the optimality of target-data-dependent kernel greedy interpolation in Sobolev Reproducing Kernel Hilbert Spaces

Kernel interpolation is a versatile tool for the approximation of functions from data, and it can be proven to have some optimality properties when used with kernels related to certain Sobolev spaces. In the context of interpolation, the selection of optimal function sampling locations is a central problem, both from a practical perspective, and as an interesting theoretical question. Greedy interpolation algorithms provide a viable solution for this task, being efficient to run and provably accurate in their approximation. In this paper we close a gap that is present in the convergence theory for these algorithms by employing a recent result on general greedy algorithms. This modification leads to new convergence rates which match the optimal ones when restricted to the $P$-greedy target-data-independent selection rule, and can additionally be proven to be optimal when they fully exploit adaptivity ($f$-greedy). Other than closing this gap, the new results have some significance in the broader setting of the optimality of general approximation algorithms in Reproducing Kernel Hilbert Spaces, as they allow us to compare adaptive interpolation with non-adaptive best nonlinear approximation.
An efficient displacement-based isogeometric formulation for geometrically exact viscoelastic beams

We propose a novel approach to the linear viscoelastic problem of shear-deformable geometrically exact beams. The generalized Maxwell model for one-dimensional solids is here efficiently extended to the case of arbitrarily curved beams undergoing finite displacement and rotations. High efficiency is achieved by combining a series of distinguishing features, that are i) the formulation is displacement-based, therefore no additional unknowns, other than incremental displacements and rotations, are needed for the internal variables associated with the rate-dependent material; ii) the governing equations are discretized in space using the isogeometric collocation method, meaning that elements integration is totally bypassed; iii) finite rotations are updated using the incremental rotation vector, leading to two main benefits: minimum number of rotation unknowns (the three components of the incremental rotation vector) and no singularity problems; iv) the same $\rm SO(3)$-consistent linearization of the governing equations and update procedures as for non-rate-dependent linear elastic material can be used; v) a standard second-order accurate time integration scheme is made consistent with the underlying geometric structure of the kinematic problem. Moreover, taking full advantage of the isogeometric analysis features, the formulation permits accurately representing beams and beam structures with highly complex initial shape and topology, paving the way for a large number of potential applications in the field of architectured materials, meta-materials, morphing/programmable objects, topological optimizations, etc. Numerical applications are finally presented in order to demonstrate attributes and potentialities of the proposed formulation.
Efficient Non-Learning Similar Subtrajectory Search

Similar subtrajectory search is a finer-grained operator that can better capture the similarities between one query trajectory and a portion of a data trajectory than the traditional similar trajectory search, which requires that the two checking trajectories are similar in their entirety. Many real applications (e.g., trajectory clustering and trajectory join) utilize similar subtrajectory search as a basic operator. It is considered that the time complexity is O ( mn 2 ) for exact algorithms to solve the similar subtrajectory search problem under most trajectory distance functions in the existing studies, where m is the length of the query trajectory and n is the length of the data trajectory. In this paper, to the best of our knowledge, we are the first to propose an exact algorithm to solve the similar subtrajectory search problem in O ( mn ) time for most of widely used trajectory distance functions (e.g., WED, DTW, ERP, EDR and Frechet distance). Through extensive experiments on three real datasets, we demonstrate the efficiency and effectiveness of our proposed algorithms.
TUNeS: A Temporal U-Net with Self-Attention for Video-based Surgical Phase Recognition

To enable context-aware computer assistance in the operating room of the future, cognitive systems need to understand automatically which surgical phase is being performed by the medical team. The primary source of information for surgical phase recognition is typically video, which presents two challenges: extracting meaningful features from the video stream and effectively modeling temporal information in the sequence of visual features. For temporal modeling, attention mechanisms have gained popularity due to their ability to capture long-range dependencies. In this paper, we explore design choices for attention in existing temporal models for surgical phase recognition and propose a novel approach that uses attention more effectively and does not require hand-crafted constraints: TUNeS, an efficient and simple temporal model that incorporates self-attention at the core of a convolutional U-Net structure. In addition, we propose to train the feature extractor, a standard CNN, together with an LSTM on preferably long video segments, i.e., with long temporal context. In our experiments, almost all temporal models performed better on top of feature extractors that were trained with longer temporal context. On these contextualized features, TUNeS achieves state-of-the-art results on the Cholec80 and AutoLaparo datasets.
Geometry in global coordinates in mechanics and optimal transport

For a manifold embedded in an inner product space, we express geometric quantities such as {\it Hamilton vector fields, affine and Levi-Civita connections, curvature} in global coordinates. Instead of coordinate indices, the global formulas for most quantities are expressed as {\it operator-valued} expressions, using an {\it affine projection} to the tangent bundle. For a submersion image of an embedded manifold, we introduce {\it liftings} of Hamilton vector fields, allowing us to use embedded coordinates on horizontal bundles. We derive a {\it Gauss-Codazzi equation} for affine connections on vector bundles. This approach allows us to evaluate geometric expressions globally, and could be used effectively with modern numerical frameworks in applications. Examples considered include rigid body mechanics and Hamilton mechanics on Grassmann manifolds. We show explicitly the cross-curvature (MTW-tensor) for the {\it Kim-McCann} metric with a reflector antenna-type cost function on the space of positive-semidefinite matrices of fixed rank has nonnegative cross-curvature, while the corresponding cost could have negative cross-curvature on Grassmann manifolds, except for projective spaces.
Optical taxonomic signal

Scattering of light by biological tissue has hindered applications of spectroscopy to medical diagnosis. We describe here a combination of feature selection techniques and several discriminant statistics that may mitigate this problem. In the particular case of spectroscopy, a useful feature should have linewidth, which in practice means that the discriminant statistic should have significant values on several contiguous pixels of the detector. We also suggest a definition for optical taxonomic signal as a measure of how efficacious a particular combination may be and how much other variables such as source-detector separation and fiber width may affect discrimination.
Generalization Error Bounds for Noisy, Iterative Algorithms via Maximal Leakage

We adopt an information-theoretic framework to analyze the generalization behavior of the class of iterative, noisy learning algorithms. This class is particularly suitable for study under information-theoretic metrics as the algorithms are inherently randomized, and it includes commonly used algorithms such as Stochastic Gradient Langevin Dynamics (SGLD). Herein, we use the maximal leakage (equivalently, the Sibson mutual information of order infinity) metric, as it is simple to analyze, and it implies both bounds on the probability of having a large generalization error and on its expected value. We show that, if the update function (e.g., gradient) is bounded in $L_2$-norm and the additive noise is isotropic Gaussian noise, then one can obtain an upper-bound on maximal leakage in semi-closed form. Furthermore, we demonstrate how the assumptions on the update function affect the optimal (in the sense of minimizing the induced maximal leakage) choice of the noise. Finally, we compute explicit tight upper bounds on the induced maximal leakage for other scenarios of interest.
Simple Deterministic Approximation for Submodular Multiple Knapsack Problem

Submodular maximization has been a central topic in theoretical computer science and combinatorial optimization over the last decades. Plenty of well-performed approximation algorithms have been designed for the problem over a variety of constraints. In this paper, we consider the submodular multiple knapsack problem (SMKP). In SMKP, the profits of each subset of elements are specified by a monotone submodular function. The goal is to find a feasible packing of elements over multiple bins (knapsacks) to maximize the profit. Recently, Fairstein et al.~[ESA20] proposed a nearly optimal $(1-e^{-1}-\epsilon)$-approximation algorithm for SMKP. Their algorithm is obtained by combining configuration LP, a grouping technique for bin packing, and the continuous greedy algorithm for submodular maximization. As a result, the algorithm is somewhat sophisticated and inherently randomized. In this paper, we present an arguably simple deterministic combinatorial algorithm for SMKP, which achieves a $(1-e^{-1}-\epsilon)$-approximation ratio. Our algorithm is based on very different ideas compared with Fairstein et al.~[ESA20].
Quantifying Network Similarity using Graph Cumulants

How might one test the hypothesis that networks were sampled from the same distribution? Here, we compare two statistical tests that use subgraph counts to address this question. The first uses the empirical subgraph densities themselves as estimates of those of the underlying distribution. The second test uses a new approach that converts these subgraph densities into estimates of the \textit{graph cumulants} of the distribution (without any increase in computational complexity). We demonstrate -- via theory, simulation, and application to real data -- the superior statistical power of using graph cumulants. In summary, when analyzing data using subgraph/motif densities, we suggest using the corresponding graph cumulants instead.
RoCOCO: Robustness Benchmark of MS-COCO to Stress-test Image-Text Matching Models

In this paper, we propose a robustness benchmark for image-text matching models to assess their vulnerabilities. To this end, we insert adversarial texts and images into the search pool (i.e., gallery set) and evaluate models with the adversarial data. Specifically, we replace a word in the text to change the meaning of the text and mix images with different images to create perceptible changes in pixels. We assume that such explicit alterations would not deceive a robust model, as they should understand the holistic meaning of texts and images simultaneously. However, in our evaluations on the proposed benchmark, many state-of-the-art models show significant performance degradation, e.g., Recall@1: 81.9% $\rightarrow$ 64.5% in BLIP, 66.1% $\rightarrow$ 37.5% in VSE$\infty$, where the models favor adversarial texts/images over the original ones. This reveals the current vision-language models may not account for subtle changes or understand the overall context of texts and images. Our findings can provide insights for improving the robustness of the vision-language models and devising more diverse stress-test methods in cross-modal retrieval task. Source code and dataset will be available at https://github.com/pseulki/rococo.
Spuriosity Didn't Kill the Classifier: Using Invariant Predictions to Harness Spurious Features

To avoid failures on out-of-distribution data, recent works have sought to extract features that have a stable or invariant relationship with the label across domains, discarding the"spurious"or unstable features whose relationship with the label changes across domains. However, unstable features often carry complementary information about the label that could boost performance if used correctly in the test domain. Our main contribution is to show that it is possible to learn how to use these unstable features in the test domain without labels. In particular, we prove that pseudo-labels based on stable features provide sufficient guidance for doing so, provided that stable and unstable features are conditionally independent given the label. Based on this theoretical insight, we propose Stable Feature Boosting (SFB), an algorithm for: (i) learning a predictor that separates stable and conditionally-independent unstable features; and (ii) using the stable-feature predictions to adapt the unstable-feature predictions in the test domain. Theoretically, we prove that SFB can learn an asymptotically-optimal predictor without test-domain labels. Empirically, we demonstrate the effectiveness of SFB on real and synthetic data.
A Passivity-based Approach for Variable Stiffness Control with Dynamical Systems

In this paper, we present a controller that combines motion generation and control in one loop, to endow robots with reactivity and safety. In particular, we propose a control approach that enables to follow the motion plan of a first order Dynamical System (DS) with a variable stiffness profile, in a closed loop configuration where the controller is always aware of the current robot state. This allows the robot to follow a desired path with an interactive behavior dictated by the desired stiffness. We also present two solutions to enable a robot to follow the desired velocity profile, in a manner similar to trajectory tracking controllers, while maintaining the closed-loop configuration. Additionally, we exploit the concept of energy tanks in order to guarantee the passivity during interactions with the environment, as well as the asymptotic stability in free motion, of our closed-loop system. The developed approach is evaluated extensively in simulation, as well as in real robot experiments, in terms of performance and safety both in free motion and during the execution of physical interaction tasks.
XSkill: Cross Embodiment Skill Discovery

Human demonstration videos are a widely available data source for robot learning and an intuitive user interface for expressing desired behavior. However, directly extracting reusable robot manipulation skills from unstructured human videos is challenging due to the big embodiment difference and unobserved action parameters. To bridge this embodiment gap, this paper introduces XSkill, an imitation learning framework that 1) discovers a cross-embodiment representation called skill prototypes purely from unlabeled human and robot manipulation videos, 2) transfers the skill representation to robot actions using conditional diffusion policy, and finally, 3) composes the learned skill to accomplish unseen tasks specified by a human prompt video. Our experiments in simulation and real-world environments show that the discovered skill prototypes facilitate both skill transfer and composition for unseen tasks, resulting in a more general and scalable imitation learning framework. The benchmark, code, and qualitative results are on https://xskill.cs. columbia.edu/
Sparse estimation of parameter support sets for generalized vector autoregressions by resampling and model aggregation

The central problem we address in this work is estimation of the parameter support set S, the set of indices corresponding to nonzero parameters, in the context of a sparse parametric likelihood model for count-valued multivariate time series. We develop a computationally-intensive algorithm that performs the estimation by aggregating support sets obtained by applying the LASSO to data subsamples. Our approach is to identify several well-fitting candidate models and estimate S by the most frequently-used parameters, thus \textit{aggregating} candidate models rather than selecting a single candidate deemed optimal in some sense. While our method is broadly applicable to any selection problem, we focus on the generalized vector autoregressive model class, and in particular the Poisson case, due to (i) the difficulty of the support estimation problem due to complex dependence in the data, (ii) recent work applying the LASSO in this context, and (iii) interesting applications in network recovery from discrete multivariate time series. We establish benchmark methods based on the LASSO and present empirical results demonstrating the superior performance of our method. Additionally, we present an application estimating ecological interaction networks from paleoclimatology data.
Semi-Linear All-Polarization-Maintaining Yb-Doped Fiber Laser Oscillator Manifesting Dual Operation Regime at Net Anomalous Dispersion

Ultrafast all-fiber Yb-doped fiber oscillators are usually associated with all-normal-dispersion cavities, which operate in a dissipative soliton regime, quintessential for pulsed operation at the wavelength of 1 $\mu$m. This work presents an all-polarization-maintaining Yb-doped fiber laser oscillator that operates in a dispersion-managed dissipative soliton regime, thanks to incorporating a chirped fiber Bragg grating. The oscillator, mode-locked via a nonlinear optical loop mirror, has an unconventional semi-linear cavity of net anomalous dispersion. Unlike in standard ring resonators, the ultrashort pulse undergoes amplification twice per cavity roundtrip. Additionally, we report a duality of pulsed operation states depending on the pumping power. Strikingly, the oscillator can work in a subregime similar to the standard dissipative soliton, facilitating further energy scaling at anomalous dispersion. We characterize the low-noise setup capable of delivering pulse energy as high as 6.4 nJ using standard single-mode polarization-maintaining optical fibers.
Analyzing large scale political discussions on Twitter: the use case of the Greek wiretapping scandal (#ypoklopes)

In this paper, we study the Greek wiretappings scandal, which has been revealed in 2022 and attracted a lot of attention by press and citizens. Specifically, we propose a methodology for collecting data and analyzing patterns of online public discussions on Twitter. We apply our methodology to the Greek wiretappings use case, and present findings related to the evolution of the discussion over time, its polarization, and the role of the media. The methodology can be of wider use and replicated to other topics. Finally, we provide publicly an open dataset, and online resources with the results.
Bayesian compound poisson mixed models for longitudinal semi-continuous data with non-ignorable missingness

Longitudinal semi-continuous data, which contain a fair amount of zeros along with positive values, is common in biomedical, econometric and health research. The existence of missing values in this kind of data creates additional difficulty in analysis. This thesis proposes a Compound Poisson mixed model to analyse the semicontinuous data with missing data using a selection-model approach. In the literature, the two-part model has been used most frequently to analyse semi-continuous data. In the two-part model, the zero values and positive responses from the same subject are modeled separately (Liu et al., 2012). This separation of zero and non-zero values is likely to destroy the serial dependence structure among the repeated responses within subjects. Therefore, we modelled the zero and positive responses together of the semi-continuous data while considering multilevel random effects. Our work is motivated by Ma et al. (2007) and Hasan et al. (2009). They have proposed a multilevel random effects zero inflated Poisson model for the clustered count data with excess zeros. Furthermore they use patten-mixture model to deal with the dropouts in the longitudinal unbalanced data. Recently, Yan et al. (2016) also analyse the semi-continuous longitudinal data with Tweedie’s compound Poisson based on orthodox best linear unbiased predictor (BLUP) of the random effects given the data. This thesis applies a Tweedie’s compound Poisson mixed model for longitudinal
Deep Reinforcement Learning for ESG financial portfolio management

This paper investigates the application of Deep Reinforcement Learning (DRL) for Environment, Social, and Governance (ESG) financial portfolio management, with a specific focus on the potential benefits of ESG score-based market regulation. We leveraged an Advantage Actor-Critic (A2C) agent and conducted our experiments using environments encoded within the OpenAI Gym, adapted from the FinRL platform. The study includes a comparative analysis of DRL agent performance under standard Dow Jones Industrial Average (DJIA) market conditions and a scenario where returns are regulated in line with company ESG scores. In the ESG-regulated market, grants were proportionally allotted to portfolios based on their returns and ESG scores, while taxes were assigned to portfolios below the mean ESG score of the index. The results intriguingly reveal that the DRL agent within the ESG-regulated market outperforms the standard DJIA market setup. Furthermore, we considered the inclusion of ESG variables in the agent state space, and compared this with scenarios where such data were excluded. This comparison adds to the understanding of the role of ESG factors in portfolio management decision-making. We also analyze the behaviour of the DRL agent in IBEX 35 and NASDAQ-100 indexes. Both the A2C and Proximal Policy Optimization (PPO) algorithms were applied to these additional markets, providing a broader perspective on the generalization of our findings. This work contributes to the evolving field of ESG investing, suggesting that market regulation based on ESG scoring can potentially improve DRL-based portfolio management, with significant implications for sustainable investing strategies.
U-CE: Uncertainty-aware Cross-Entropy for Semantic Segmentation

Deep neural networks have shown exceptional performance in various tasks, but their lack of robustness, reliability, and tendency to be overconfident pose challenges for their deployment in safety-critical applications like autonomous driving. In this regard, quantifying the uncertainty inherent to a model's prediction is a promising endeavour to address these shortcomings. In this work, we present a novel Uncertainty-aware Cross-Entropy loss (U-CE) that incorporates dynamic predictive uncertainties into the training process by pixel-wise weighting of the well-known cross-entropy loss (CE). Through extensive experimentation, we demonstrate the superiority of U-CE over regular CE training on two benchmark datasets, Cityscapes and ACDC, using two common backbone architectures, ResNet-18 and ResNet-101. With U-CE, we manage to train models that not only improve their segmentation performance but also provide meaningful uncertainties after training. Consequently, we contribute to the development of more robust and reliable segmentation models, ultimately advancing the state-of-the-art in safety-critical applications and beyond.
Combining Dependency, Grades, and Adjoint Logic

We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then generalize this system to support many graded systems connected by many modal operators through the introduction of modes from Adjoint Logic. Finally, we prove several meta-theoretic properties of these two systems including graded substitution.