Physical parameterizations are used as representations of unresolved subgrid processes within weather and global climate models or coarse-scale turbulent models, whose resolutions are too coarse to resolve small-scale processes. These parameterizations are typically grounded on physically-based, yet empirical, representations of the underlying small-scale processes. Machine learning-based parameterizations have recently been proposed as an alternative and have shown great promises to reduce uncertainties associated with small-scale processes. Yet, those approaches still show some important mismatches that are often attributed to stochasticity in the considered process. This stochasticity can be due to noisy data, unresolved variables or simply to the inherent chaotic nature of the process. To address these issues, we develop a new type of parameterization (closure) which is based on a Bayesian formalism for neural networks, to account for uncertainty quantification, and includes memory, to account for the non-instantaneous response of the closure. To overcome the curse of dimensionality of Bayesian techniques in high-dimensional spaces, the Bayesian strategy is based on a Hamiltonian Monte Carlo Markov Chain sampling strategy that takes advantage of the likelihood function and kinetic energy's gradients with respect to the parameters to accelerate the sampling process. We apply the proposed Bayesian history-based parameterization to the Lorenz '96 model in the presence of noisy and sparse data, similar to satellite observations, and show its capacity to predict skillful forecasts of the resolved variables while returning trustworthy uncertainty quantifications for different sources of error. This approach paves the way for the use of Bayesian approaches for closure problems.

Standard few-shot benchmarks are often built upon simplifying assumptions on the query sets, which may not always hold in practice. In particular, for each task at testing time, the classes effectively present in the unlabeled query set are known a priori, and correspond exactly to the set of classes represented in the labeled support set. We relax these assumptions and extend current benchmarks, so that the query-set classes of a given task are unknown, but just belong to a much larger set of possible classes. Our setting could be viewed as an instance of the challenging yet practical problem of extremely imbalanced K-way classification, K being much larger than the values typically used in standard benchmarks, and with potentially irrelevant supervision from the support set. Expectedly, our setting incurs drops in the performances of state-of-the-art methods. Motivated by these observations, we introduce a PrimAl Dual Minimum Description LEngth (PADDLE) formulation, which balances data-fitting accuracy and model complexity for a given few-shot task, under supervision constraints from the support set. Our constrained MDL-like objective promotes competition among a large set of possible classes, preserving only effective classes that befit better the data of a few-shot task. It is hyperparameter free, and could be applied on top of any base-class training. Furthermore, we derive a fast block coordinate descent algorithm for optimizing our objective, with convergence guarantee, and a linear computational complexity at each iteration. Comprehensive experiments over the standard few-shot datasets and the more realistic and challenging i-Nat dataset show highly competitive performances of our method, more so when the numbers of possible classes in the tasks increase. Our code is publicly available at https://github.com/SegoleneMartin/PADDLE.

Continuum robots have the potential to enable new applications in medicine, inspection, and countless other areas due to their unique shape, compliance, and size. Excellent progess has been made in the mechanical design and dynamic modelling of continuum robots, to the point that there are some canonical designs, although new concepts continue to be explored. In this paper, we turn to the problem of state estimation for continuum robots that can been modelled with the common Cosserat rod model. Sensing for continuum robots might comprise external camera observations, embedded tracking coils or strain gauges. We repurpose a Gaussian process (GP) regression approach to state estimation, initially developed for continuous-time trajectory estimation in $SE(3)$. In our case, the continuous variable is not time but arclength and we show how to estimate the continuous shape (and strain) of the robot (along with associated uncertainties) given discrete, noisy measurements of both pose and strain along the length. We demonstrate our approach quantitatively through simulations as well as through experiments. Our evaluations show that accurate and continuous estimates of a continuum robot's shape can be achieved, resulting in average end-effector errors between the estimated and ground truth shape as low as 3.5mm and 0.016$^\circ$ in simulation or 3.3mm and 0.035$^\circ$ for unloaded configurations and 6.2mm and 0.041$^\circ$ for loaded ones during experiments, when using discrete pose measurements.

We show that the $\ell_2$ norm of a static sense embedding encodes information related to the frequency of that sense in the training corpus used to learn the sense embeddings. This finding can be seen as an extension of a previously known relationship for word embeddings to sense embeddings. Our experimental results show that, in spite of its simplicity, the $\ell_2$ norm of sense embeddings is a surprisingly effective feature for several word sense related tasks such as (a) most frequent sense prediction, (b) Word-in-Context (WiC), and (c) Word Sense Disambiguation (WSD). In particular, by simply including the $\ell_2$ norm of a sense embedding as a feature in a classifier, we show that we can improve WiC and WSD methods that use static sense embeddings.

Decoding emotional states from human brain activity plays an important role in brain-computer interfaces. Existing emotion decoding methods still have two main limitations: one is only decoding a single emotion category from a brain activity pattern and the decoded emotion categories are coarse-grained, which is inconsistent with the complex emotional expression of human; the other is ignoring the discrepancy of emotion expression between the left and right hemispheres of human brain. In this paper, we propose a novel multi-view multi-label hybrid model for fine-grained emotion decoding (up to 80 emotion categories) which can learn the expressive neural representations and predicting multiple emotional states simultaneously. Specifically, the generative component of our hybrid model is parametrized by a multi-view variational auto-encoder, in which we regard the brain activity of left and right hemispheres and their difference as three distinct views, and use the product of expert mechanism in its inference network. The discriminative component of our hybrid model is implemented by a multi-label classification network with an asymmetric focal loss. For more accurate emotion decoding, we first adopt a label-aware module for emotion-specific neural representations learning and then model the dependency of emotional states by a masked self-attention mechanism. Extensive experiments on two visually evoked emotional datasets show the superiority of our method.

In order to identify expertise, forecasters should not be tested by their calibration score, which can always be made arbitrarily small, but rather by their Brier score. The Brier score is the sum of the calibration score and the refinement score; the latter measures how good the sorting into bins with the same forecast is, and thus attests to "expertise." This raises the question of whether one can gain calibration without losing expertise, which we refer to as "calibeating." We provide an easy way to calibeat any forecast, by a deterministic online procedure. We moreover show that calibeating can be achieved by a stochastic procedure that is itself calibrated, and then extend the results to simultaneously calibeating multiple procedures, and to deterministic procedures that are continuously calibrated.

Researchers investigating example hardness have increasingly focused on the dynamics by which neural networks learn and forget examples throughout training. Popular metrics derived from these dynamics include (i) the epoch at which examples are first correctly classified; (ii) the number of times their predictions flip during training; and (iii) whether their prediction flips if they are held out. However, these metrics do not distinguish among examples that are hard for distinct reasons, such as membership in a rare subpopulation, being mislabeled, or belonging to a complex subpopulation. In this paper, we propose $second$-$split$ $forgetting$ $time$ (SSFT), a complementary metric that tracks the epoch (if any) after which an original training example is forgotten as the network is fine-tuned on a randomly held out partition of the data. Across multiple benchmark datasets and modalities, we demonstrate that $mislabeled$ examples are forgotten quickly, and seemingly $rare$ examples are forgotten comparatively slowly. By contrast, metrics only considering the first split learning dynamics struggle to differentiate the two. At large learning rates, SSFT tends to be robust across architectures, optimizers, and random seeds. From a practical standpoint, the SSFT can (i) help to identify mislabeled samples, the removal of which improves generalization; and (ii) provide insights about failure modes. Through theoretical analysis addressing overparameterized linear models, we provide insights into how the observed phenomena may arise. Code for reproducing our experiments can be found here: https://github.com/pratyushmaini/ssft

Recent advances in contrastive representation learning over paired image-text data have led to models such as CLIP that achieve state-of-the-art performance for zero-shot classification and distributional robustness. Such models typically require joint reasoning in the image and text representation spaces for downstream inference tasks. Contrary to prior beliefs, we demonstrate that the image and text representations learned via a standard contrastive objective are not interchangeable and can lead to inconsistent downstream predictions. To mitigate this issue, we formalize consistency and propose CyCLIP, a framework for contrastive representation learning that explicitly optimizes for the learned representations to be geometrically consistent in the image and text space. In particular, we show that consistent representations can be learned by explicitly symmetrizing (a) the similarity between the two mismatched image-text pairs (cross-modal consistency); and (b) the similarity between the image-image pair and the text-text pair (in-modal consistency). Empirically, we show that the improved consistency in CyCLIP translates to significant gains over CLIP, with gains ranging from 10%-24% for zero-shot classification accuracy on standard benchmarks (CIFAR-10, CIFAR-100, ImageNet1K) and 10%-27% for robustness to various natural distribution shifts. The code is available at https://github.com/goel-shashank/CyCLIP.

Adversarial attacks pose serious challenges for deep neural network (DNN)-based analysis of various input signals. In the case of 3D point clouds, methods have been developed to identify points that play a key role in the network decision, and these become crucial in generating existing adversarial attacks. For example, a saliency map approach is a popular method for identifying adversarial drop points, whose removal would significantly impact the network decision. Generally, methods for identifying adversarial points rely on the deep model itself in order to determine which points are critically important for the model's decision. This paper aims to provide a novel viewpoint on this problem, in which adversarial points can be predicted independently of the model. To this end, we define 14 point cloud features and use multiple linear regression to examine whether these features can be used for model-free adversarial point prediction, and which combination of features is best suited for this purpose. Experiments show that a suitable combination of features is able to predict adversarial points of three different networks -- PointNet, PointNet++, and DGCNN -- significantly better than a random guess. The results also provide further insight into DNNs for point cloud analysis, by showing which features play key roles in their decision-making process.

In this paper, we tackle the problem of selecting the optimal model for a given structured pattern classification dataset. In this context, a model can be understood as a classifier and a hyperparameter configuration. The proposed meta-learning approach purely relies on machine learning and involves four major steps. Firstly, we present a concise collection of 62 meta-features that address the problem of information cancellation when aggregation measure values involving positive and negative measurements. Secondly, we describe two different approaches for synthetic data generation intending to enlarge the training data. Thirdly, we fit a set of pre-defined classification models for each classification problem while optimizing their hyperparameters using grid search. The goal is to create a meta-dataset such that each row denotes a multilabel instance describing a specific problem. The features of these meta-instances denote the statistical properties of the generated datasets, while the labels encode the grid search results as binary vectors such that best-performing models are positively labeled. Finally, we tackle the model selection problem with several multilabel classifiers, including a Convolutional Neural Network designed to handle tabular data. The simulation results show that our meta-learning approach can correctly predict an optimal model for 91% of the synthetic datasets and for 87% of the real-world datasets. Furthermore, we noticed that most meta-classifiers produced better results when using our meta-features. Overall, our proposal differs from other meta-learning approaches since it tackles the algorithm selection and hyperparameter tuning problems in a single step. Toward the end, we perform a feature importance analysis to determine which statistical features drive the model selection mechanism.