The majority of existing multimodal sequential learning methods focus on how to obtain powerful individual representations and neglect to effectively capture the multimodal joint representation. Bilinear attention network (BAN) is a commonly used integration method, which leverages tensor operations to associate the features of different modalities. However, BAN has a poor compatibility for more modalities, since the computational complexity of the attention map increases exponentially with the number of modalities. Based on this concern, we propose a new method called generalizable multi-linear attention network (MAN), which can associate more modalities in acceptable complexity with hierarchical approximation decomposition. Specifically, considering the fact that softmax attention kernels cannot be decomposed as linear operation directly, we adopt the addition random features mechanism to approximate the non-linear softmax functions with enough theoretical analysis. Furthermore, we also introduce the local sequential constraints, which can be combined with ARF conveniently, as positional information. We conduct extensive experiments on several datasets of corresponding tasks, the experimental results show that MAN could achieve competitive results compared with baseline methods, showcasing the effectiveness of our contributions.

Learning classifiers that are robust to adversarial examples has received a great deal of recent attention. A major drawback of the standard robust learning framework is there is an artificial robustness radius r that applies to all inputs. This ignores the fact that data may be highly heterogeneous, in which case it is plausible that robustness regions should be larger in some regions of data, and smaller in others. In this paper, we address this limitation by proposing a new limit classifier, called the neighborhood optimal classifier, that extends the Bayes optimal classifier outside its support by using the label of the closest in-support point. We then argue that this classifier maximizes the size of its robustness regions subject to the constraint of having accuracy equal to the Bayes optimal. We then present sufficient conditions under which general non-parametric methods that can be represented as weight functions converge towards this limit, and show that both nearest neighbors and kernel classifiers satisfy them under certain conditions.

What can linearized neural networks actually say about generalization? As mentioned in the main text, all our models are trained using the same scheme which was selected without any hyperparameter tuning, besides ensuring a good performance on CIFAR2 for the neural networks. Namely, we train using stochastic gradient descent (SGD) to optimize a binary crossentropy loss, with a decaying learning rate starting at 0.05 and momentum set to 0.9. Furthermore, we use a batch size of 128and train for a 100epochs. This is enough to obtain close-to-zero training losses for the neural networks, and converge to a stable test accuracy in the case of the linearized models1.

Expressing universal semantics common to all languages is helpful in understanding the meanings of complex and culture-specific sentences. The research theme underlying this scenario focuses on learning universal representations across languages with the usage of massive parallel corpora. However, due to the sparsity and scarcity of parallel data, there is still a big challenge in learning authentic "universals" for any two languages. In this paper, we propose EMMA-X: an EM-like Multilingual pre-training Algorithm, to learn (X)Cross-lingual universals with the aid of excessive multilingual non-parallel data.

In this paper, we comparatively analyze the Bures-Wasserstein (BW) geometry with the popular Affine-Invariant (AI) geometry for Riemannian optimization on the symmetric positive definite (SPD) matrix manifold. Our study begins with an observation that the BW metric has a linear dependence on SPD matrices in contrast to the quadratic dependence of the AI metric. We build on this to show that the BW metric is a more suitable and robust choice for several Riemannian optimization problems over ill-conditioned SPD matrices. We show that the BW geometry has a non-negative curvature, which further improves convergence rates of algorithms over the non-positively curved AI geometry. Finally, we verify that several popular cost functions, which are known to be geodesic convex under the AI geometry, are also geodesic convex under the BW geometry. Extensive experiments on various applications support our findings.