In real world scenarios, objects are often partially occluded. This requires a robustness for object recognition against these perturbations. Convolutional networks have shown good performances in classification tasks. The learned convolutional filters seem similar to receptive fields of simple cells found in the primary visual cortex. Alternatively, spiking neural networks are more biological plausible. We developed a two layer spiking network, trained on natural scenes with a biologically plausible learning rule. It is compared to two deep convolutional neural networks using a classification task of stepwise pixel erasement on MNIST. In comparison to these networks the spiking approach achieves good accuracy and robustness.

Recent research has made the surprising finding that state-of-the-art deep learning models sometimes fail to generalize to small variations of the input. Adversarial training has been shown to be an effective approach to overcome this problem. However, its application has been limited to enforcing invariance to analytically defined transformations like $\ell_p$-norm bounded perturbations. Such perturbations do not necessarily cover plausible real-world variations that preserve the semantics of the input (such as a change in lighting conditions). In this paper, we propose a novel approach to express and formalize robustness to these kinds of real-world transformations of the input. The two key ideas underlying our formulation are (1) leveraging disentangled representations of the input to define different factors of variations, and (2) generating new input images by adversarially composing the representations of different images. We use a StyleGAN model to demonstrate the efficacy of this framework. Specifically, we leverage the disentangled latent representations computed by a StyleGAN model to generate perturbations of an image that are similar to real-world variations (like adding make-up, or changing the skin-tone of a person) and train models to be invariant to these perturbations. Extensive experiments show that our method improves generalization and reduces the effect of spurious correlations.

Recent works have derived non - asymptotic upper bounds for convergence of underdamped Langevin MCMC. We revisit these bound and consider introducing scaling terms in the underlying underdamped Langevin equation. In particular, we provide conditions under which an appropria te scaling allows to improve the error bounds in terms of the condition number of the underlying density of interest.

We introduce a general method to extract knowledge from a recurrent neural network (Long Short Term Memory) that has learnt to detect if a given input sequence is valid or not, according to an unknown generative automaton. Based on the clustering of the hidden states, we explain how to build and validate an automaton that corresponds to the underlying (unknown) automaton, and allows to predict if a given sequence is valid or not. The method is illustrated on artificial grammars (Reber's grammar variations) as well as on a real use-case whose underlying grammar is unknown.

Stochastic Rank-One Bandits Katariya et al. (2017a,b) are a simple framework for regret minimization problems over rank-one matrices of arms. The initially proposed algorithms are proved to have logarithmic regret, but do not match the existing lower bound for this problem. We close this gap by first proving that rank-one bandits are a particular instance of unimodal bandits, and then providing a new analysis of Unimodal Thompson Sampling (UTS), initially proposed by Paladino et al. (2017). We prove an asymptotically optimal regret bound on the frequentist regret of UTS and we support our claims with simulations showing the significant improvement of our method compared to the state-of-the-art.

In classical machine learning, the data streamed to the algorithms is assumed to be independent and identically distributed. Otherwise, if the data distribution changes through time, the algorithm risks to remember only the data from the current state of the distribution and forget everything else. Continual learning is a sub-field of machine learning that aims to find automatic learning processes to solve non-iid problems. The main challenges of continual learning are two-fold. Firstly, to detect concept-drift in the distribution and secondly to remember what happened before a concept-drift. In this article, we study a specific case of continual learning approaches: \textit{the regularization method}. It consists of finding a smart regularization term that will protect important parameters from being modified to not forget. We show in this article, that in the context of multi-task learning for classification, this process does not learn to discriminate classes from different tasks. We propose theoretical reasoning to prove this shortcoming and illustrate it with examples and experiments with the "MNIST Fellowship" dataset.

Graph neural network (GNN) has shown superior performance in dealing with graphs, which has attracted considerable research attention recently. However, most of the existing GNN models are primarily designed for graphs in Euclidean spaces. Recent research has proven that the graph data exhibits non-Euclidean latent anatomy. Unfortunately, there was rarely study of GNN in non-Euclidean settings so far. To bridge this gap, in this paper, we study the GNN with attention mechanism in hyperbolic spaces at the first attempt. The research of hyperbolic GNN has some unique challenges: since the hyperbolic spaces are not vector spaces, the vector operations (e.g., vector addition, subtraction, and scalar multiplication) cannot be carried. To tackle this problem, we employ the gyrovector spaces, which provide an elegant algebraic formalism for hyperbolic geometry, to transform the features in a graph; and then we propose the hyperbolic proximity based attention mechanism to aggregate the features. Moreover, as mathematical operations in hyperbolic spaces could be more complicated than those in Euclidean spaces, we further devise a novel acceleration strategy using logarithmic and exponential mappings to improve the efficiency of our proposed model. The comprehensive experimental results on four real-world datasets demonstrate the performance of our proposed hyperbolic graph attention network model, by comparisons with other state-of-the-art baseline methods.

In this paper, we improve the PAC-Bayesian error bound for linear regression derived in Germain et al. [10]. The improvements are twofold. First, the proposed error bound is tighter, and converges to the generalization loss with a well-chosen temperature parameter. Second, the error bound also holds for training data that are not independently sampled. In particular, the error bound applies to certain time series generated by well-known classes of dynamical models, such as ARX models.

Spectral algorithms are graph partitioning algorithms that partition a node set of a graph into groups by using a spectral embedding map. Clustering techniques based on the algorithms are referred to as spectral clustering and are widely used in data analysis. To gain a better understanding of why spectral clustering is successful, Peng et al. (2015) and Kolev and Mehlhorn (2016) studied the behavior of a certain type of spectral algorithm for a class of graphs, called well-clustered graphs. Specifically, they put an assumption on graphs and showed the performance guarantee of the spectral algorithm under it. The algorithm they studied used the spectral embedding map developed by Shi and Malic (2000). In this paper, we improve on their results, giving a better performance guarantee under a weaker assumption. We also evaluate the performance of the spectral algorithm with the spectral embedding map developed by Ng et al. (2002).

Bayesian learning of model parameters in neural networks is important in scenarios where estimates with well-calibrated uncertainty are important. In this paper, we propose Bayesian quantized networks (BQNs), quantized neural networks (QNNs) for which we learn a posterior distribution over their discrete parameters. We provide a set of efficient algorithms for learning and prediction in BQNs without the need to sample from their parameters or activations, which not only allows for differentiable learning in QNNs, but also reduces the variance in gradients. We demonstrate BQNs achieve both lower predictive errors and better-calibrated uncertainties than E-QNN (with less than 20% of the negative log-likelihood). A Bayesian approach to deep learning considers the network's parameters to be random variables and seeks to infer their posterior distribution given the training data. Models trained this way, called Bayesian neural networks (BNNs) (Wang & Y eung, 2016), in principle have well-calibrated uncertainties when they make predictions, which is important in scenarios such as active learning and reinforcement learning (Gal, 2016). Furthermore, the posterior distribution over the model parameters provides valuable information for evaluation and compression of neural networks. There are three main challenges in using BNNs: (1) Intractable posterior: Computing and storing the exact posterior distribution over the network weights is intractable due to the complexity and high-dimensionality of deep networks. These challenges are typically addressed either by making simplifying assumptions about the distributions of the parameters and activations, or by using sampling-based approaches, which are expensive and unreliable (likely to overestimate the uncertainties in predictions). Our goal is to propose a sampling-free method which uses probabilistic propagation to deterministically learn BNNs. A seemingly unrelated area of deep learning research is that of quantized neural networks (QNNs), which offer advantages of computational and memory efficiency compared to continuous-valued models.