We address in this work the question of identifying the failure conditions of a given image classifier. To do so, we exploit the capacity of producing controllable distributions of high quality image data made available by recent Generative Adversarial Networks (StyleGAN2): the failure conditions are expressed as directions of strong performance degradation in the generative model latent space. This strategy of analysis is used to discover corner cases that combine multiple sources of corruption, and to compare in more details the behavior of different classifiers. The directions of degradation can also be rendered visually by generating data for better interpretability. Some degradations such as image quality can affect all classes, whereas other ones such as shape are more class-specific. The approach is demonstrated on the MNIST dataset that has been completed by two sources of corruption: noise and blur, and shows a promising way to better understand and control the risks of exploiting Artificial Intelligence components for safety-critical applications.
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One of the questions in Rigidity Theory is whether a realization of the vertices of a graph in the plane is flexible, namely, if it allows a continuous deformation preserving the edge lengths. A flexible realization of a connected graph in the plane exists if and only if the graph has a so called NAC-coloring, which is surjective edge coloring by two colors such that for each cycle either all the edges have the same color or there are at least two edges of each color. The question whether a graph has a NAC-coloring, and hence also the existence of a flexible realization, has been proven to be NP-complete. We show that this question is also NP-complete on graphs with maximum degree five and on graphs with the average degree at most $4+\varepsilon$ for every fixed $\varepsilon >0$. The existence of a NAC-coloring is fixed parameter tractable when parametrized by treewidth. Since the only existing implementation of checking the existence of a NAC-coloring is rather naive, we propose new algorithms along with their implementation, which is significantly faster. We also focus on searching all NAC-colorings of a graph, since they provide useful information about its possible flexible realizations.
Combining microstructural mechanical models with experimental data enhances our understanding of the mechanics of soft tissue, such as tendons. In previous work, a Bayesian framework was used to infer constitutive parameters from uniaxial stress-strain experiments on horse tendons, specifically the superficial digital flexor tendon (SDFT) and common digital extensor tendon (CDET), on a per-experiment basis. Here, we extend this analysis to investigate the natural variation of these parameters across a population of horses. Using a Bayesian mixed effects model, we infer population distributions of these parameters. Given that the chosen hyperelastic model does not account for tendon damage, careful data selection is necessary. Avoiding ad hoc methods, we introduce a hierarchical Bayesian data selection method. This two-stage approach selects data per experiment, and integrates data weightings into the Bayesian mixed effects model. Our results indicate that the CDET is stiffer than the SDFT, likely due to a higher collagen volume fraction. The modes of the parameter distributions yield estimates of the product of the collagen volume fraction and Young's modulus as 811.5 MPa for the SDFT and 1430.2 MPa for the CDET. This suggests that positional tendons have stiffer collagen fibrils and/or higher collagen volume density than energy-storing tendons.
The stability number of a graph, defined as the cardinality of the largest set of pairwise non-adjacent vertices, is NP-hard to compute. The exact subgraph hierarchy (ESH) provides a sequence of increasingly tighter upper bounds on the stability number, starting with the Lov\'asz theta function at the first level and including all exact subgraph constraints of subgraphs of order $k$ into the semidefinite program to compute the Lov\'asz theta function at level $k$. In this paper, we investigate the ESH for Paley graphs, a class of strongly regular, vertex-transitive graphs. We show that for Paley graphs, the bounds obtained from the ESH remain the Lov\'asz theta function up to a certain threshold level, i.e., the bounds of the ESH do not improve up to a certain level. To overcome this limitation, we introduce the local ESH for the stable set problem for vertex-transitive graphs such as Paley graphs. We prove that this new hierarchy provides upper bounds on the stability number of vertex-transitive graphs that are at least as tight as those obtained from the ESH. Additionally, our computational experiments reveal that the local ESH produces superior bounds compared to the ESH for Paley graphs.
The proposed two-dimensional geometrically exact beam element extends our previous work by including the effects of shear distortion, and also of distributed forces and moments acting along the beam. The general flexibility-based formulation exploits the kinematic equations combined with the inverted sectional equations and the integrated form of equilibrium equations. The resulting set of three first-order differential equations is discretized by finite differences and the boundary value problem is converted into an initial value problem using the shooting method. Due to the special structure of the governing equations, the scheme remains explicit even though the first derivatives are approximated by central differences, leading to high accuracy. The main advantage of the adopted approach is that the error can be efficiently reduced by refining the computational grid used for finite differences at the element level while keeping the number of global degrees of freedom low. The efficiency is also increased by dealing directly with the global centerline coordinates and sectional inclination with respect to global axes as the primary unknowns at the element level, thereby avoiding transformations between local and global coordinates. Two formulations of the sectional equations, referred to as the Reissner and Ziegler models, are presented and compared. In particular, stability of an axially loaded beam/column is investigated and the connections to the Haringx and Engesser stability theories are discussed. Both approaches are tested in a series of numerical examples, which illustrate (i) high accuracy with quadratic convergence when the spatial discretization is refined, (ii) easy modeling of variable stiffness along the element (such as rigid joint offsets), (iii) efficient and accurate characterization of the buckling and post-buckling behavior.
In this paper, we reported our experiments with various strategies to improve code-mixed humour and sarcasm detection. We did all of our experiments for Hindi-English code-mixed scenario, as we have the linguistic expertise for the same. We experimented with three approaches, namely (i) native sample mixing, (ii) multi-task learning (MTL), and (iii) prompting very large multilingual language models (VMLMs). In native sample mixing, we added monolingual task samples in code-mixed training sets. In MTL learning, we relied on native and code-mixed samples of a semantically related task (hate detection in our case). Finally, in our third approach, we evaluated the efficacy of VMLMs via few-shot context prompting. Some interesting findings we got are (i) adding native samples improved humor (raising the F1-score up to 6.76%) and sarcasm (raising the F1-score up to 8.64%) detection, (ii) training MLMs in an MTL framework boosted performance for both humour (raising the F1-score up to 10.67%) and sarcasm (increment up to 12.35% in F1-score) detection, and (iii) prompting VMLMs couldn't outperform the other approaches. Finally, our ablation studies and error analysis discovered the cases where our model is yet to improve. We provided our code for reproducibility.
Climate models struggle to accurately simulate precipitation, particularly extremes and the diurnal cycle. Here, we present a hybrid model that is trained directly on satellite-based precipitation observations. Our model runs at 2.8$^\circ$ resolution and is built on the differentiable NeuralGCM framework. The model demonstrates significant improvements over existing general circulation models, the ERA5 reanalysis, and a global cloud-resolving model in simulating precipitation. Our approach yields reduced biases, a more realistic precipitation distribution, improved representation of extremes, and a more accurate diurnal cycle. Furthermore, it outperforms the mid-range precipitation forecast of the ECMWF ensemble. This advance paves the way for more reliable simulations of current climate and demonstrates how training on observations can be used to directly improve GCMs.
Motivated by the Iowa Fluoride Study (IFS) dataset, which comprises zero-inflated multi-level ordinal responses on tooth fluorosis, we develop an estimation scheme leveraging generalized estimating equations (GEEs) and James-Stein shrinkage. Previous analyses of this cohort study primarily focused on caries (count response) or employed a Bayesian approach to the ordinal fluorosis outcome. This study is based on the expanded dataset that now includes observations for age 23, whereas earlier works were restricted to ages 9, 13, and/or 17 according to the participants' ages at the time of measurement. The adoption of a frequentist perspective enhances the interpretability to a broader audience. Over a choice of several covariance structures, separate models are formulated for the presence (zero versus non-zero score) and severity (non-zero ordinal scores) of fluorosis, which are then integrated through shared regression parameters. This comprehensive framework effectively identifies risk or protective effects of dietary and non-dietary factors on dental fluorosis.
A discrete spatial lattice can be cast as a network structure over which spatially-correlated outcomes are observed. A second network structure may also capture similarities among measured features, when such information is available. Incorporating the network structures when analyzing such doubly-structured data can improve predictive power, and lead to better identification of important features in the data-generating process. Motivated by applications in spatial disease mapping, we develop a new doubly regularized regression framework to incorporate these network structures for analyzing high-dimensional datasets. Our estimators can be easily implemented with standard convex optimization algorithms. In addition, we describe a procedure to obtain asymptotically valid confidence intervals and hypothesis tests for our model parameters. We show empirically that our framework provides improved predictive accuracy and inferential power compared to existing high-dimensional spatial methods. These advantages hold given fully accurate network information, and also with networks which are partially misspecified or uninformative. The application of the proposed method to modeling COVID-19 mortality data suggests that it can improve prediction of deaths beyond standard spatial models, and that it selects relevant covariates more often.
Deep Neural Networks are vulnerable to adversarial examples, i.e., carefully crafted input samples that can cause models to make incorrect predictions with high confidence. To mitigate these vulnerabilities, adversarial training and detection-based defenses have been proposed to strengthen models in advance. However, most of these approaches focus on a single data modality, overlooking the relationships between visual patterns and textual descriptions of the input. In this paper, we propose a novel defense, Multi-Shield, designed to combine and complement these defenses with multi-modal information to further enhance their robustness. Multi-Shield leverages multi-modal large language models to detect adversarial examples and abstain from uncertain classifications when there is no alignment between textual and visual representations of the input. Extensive evaluations on CIFAR-10 and ImageNet datasets, using robust and non-robust image classification models, demonstrate that Multi-Shield can be easily integrated to detect and reject adversarial examples, outperforming the original defenses.
Leveraging the large body of work devoted in recent years to describe redundancy and synergy in multivariate interactions among random variables, we propose a novel approach to quantify cooperative effects in feature importance, one of the most used techniques for explainable artificial intelligence. In particular, we propose an adaptive version of a well-known metric of feature importance, named Leave One Covariate Out (LOCO), to disentangle high-order effects involving a given input feature in regression problems. LOCO is the reduction of the prediction error when the feature under consideration is added to the set of all the features used for regression. Instead of calculating the LOCO using all the features at hand, as in its standard version, our method searches for the multiplet of features that maximize LOCO and for the one that minimize it. This provides a decomposition of the LOCO as the sum of a two-body component and higher-order components (redundant and synergistic), also highlighting the features that contribute to building these high-order effects alongside the driving feature. We report the application to proton/pion discrimination from simulated detector measures by GEANT.
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