Mixture-of-Experts (MoE) with sparse conditional computation has been proved an effective architecture for scaling attention-based models to more parameters with comparable computation cost. In this paper, we propose Sparse-MLP, scaling the recent MLP-Mixer model with sparse MoE layers, to achieve a more computation-efficient architecture. We replace a subset of dense MLP blocks in the MLP-Mixer model with Sparse blocks. In each Sparse block, we apply two stages of MoE layers: one with MLP experts mixing information within channels along image patch dimension, one with MLP experts mixing information within patches along the channel dimension. Besides, to reduce computational cost in routing and improve expert capacity, we design Re-represent layers in each Sparse block. These layers are to re-scale image representations by two simple but effective linear transformations. When pre-training on ImageNet-1k with MoCo v3 algorithm, our models can outperform dense MLP models by 2.5\% on ImageNet Top-1 accuracy with fewer parameters and computational cost. On small-scale downstream image classification tasks, i.e. Cifar10 and Cifar100, our Sparse-MLP can still achieve better performance than baselines.

Common acquisition functions for active learning use either uncertainty or diversity sampling, aiming to select difficult and diverse data points from the pool of unlabeled data, respectively. In this work, leveraging the best of both worlds, we propose an acquisition function that opts for selecting \textit{contrastive examples}, i.e. data points that are similar in the model feature space and yet the model outputs maximally different predictive likelihoods. We compare our approach, CAL (Contrastive Active Learning), with a diverse set of acquisition functions in four natural language understanding tasks and seven datasets. Our experiments show that CAL performs consistently better or equal than the best performing baseline across all tasks, on both in-domain and out-of-domain data. We also conduct an extensive ablation study of our method and we further analyze all actively acquired datasets showing that CAL achieves a better trade-off between uncertainty and diversity compared to other strategies.

Combining a pretrained language model (PLM) with textual patterns has been shown to help in both zero- and few-shot settings. For zero-shot performance, it makes sense to design patterns that closely resemble the text seen during self-supervised pretraining because the model has never seen anything else. Supervised training allows for more flexibility. If we allow for tokens outside the PLM's vocabulary, patterns can be adapted more flexibly to a PLM's idiosyncrasies. Contrasting patterns where a "token" can be any continuous vector vs. those where a discrete choice between vocabulary elements has to be made, we call our method CONtinuous pAtterNs (CONAN). We evaluate CONAN on two established benchmarks for lexical inference in context (LIiC) a.k.a. predicate entailment, a challenging natural language understanding task with relatively small training sets. In a direct comparison with discrete patterns, CONAN consistently leads to improved performance, setting a new state of the art. Our experiments give valuable insights into the kind of pattern that enhances a PLM's performance on LIiC and raise important questions regarding our understanding of PLMs using text patterns.

We connect two random graph models, the Popularity Adjusted Block Model (PABM) and the Generalized Random Dot Product Graph (GRDPG), by demonstrating that the PABM is a special case of the GRDPG in which communities correspond to mutually orthogonal subspaces of latent vectors. This insight allows us to construct new algorithms for community detection and parameter estimation for the PABM, as well as improve an existing algorithm that relies on Sparse Subspace Clustering. Using established asymptotic properties of Adjacency Spectral Embedding for the GRDPG, we derive asymptotic properties of these algorithms. In particular, we demonstrate that the absolute number of community detection errors tends to zero as the number of graph vertices tends to infinity. Simulation experiments illustrate these properties.

Markov Chain Monte Carlo (MCMC) methods are promising solutions to sample from target distributions in high dimensions. While MCMC methods enjoy nice theoretical properties, like guaranteed convergence and mixing to the true target, in practice their sampling efficiency depends on the choice of the proposal distribution and the target at hand. This work considers using machine learning to adapt the proposal distribution to the target, in order to improve the sampling efficiency in the purely discrete domain. Specifically, (i) it proposes a new parametrization for a family of proposal distributions, called locally balanced proposals, (ii) it defines an objective function based on mutual information and (iii) it devises a learning procedure to adapt the parameters of the proposal to the target, thus achieving fast convergence and fast mixing. We call the resulting sampler as the Locally Self-Balancing Sampler (LSB). We show through experimental analysis on the Ising model and Bayesian networks that LSB is indeed able to improve the efficiency over a state-of-the-art sampler based on locally balanced proposals, thus reducing the number of iterations required to converge, while achieving comparable mixing performance.

This paper proposes a data-driven systematic, consistent and non-exhaustive approach to Model Selection, that is an extension of the classical agnostic PAC learning model. In this approach, learning problems are modeled not only by a hypothesis space $\mathcal{H}$, but also by a Learning Space $\mathbb{L}(\mathcal{H})$, a poset of subspaces of $\mathcal{H}$, which covers $\mathcal{H}$ and satisfies a property regarding the VC dimension of related subspaces, that is a suitable algebraic search space for Model Selection algorithms. Our main contributions are a data-driven general learning algorithm to perform regularized Model Selection on $\mathbb{L}(\mathcal{H})$ and a framework under which one can, theoretically, better estimate a target hypothesis with a given sample size by properly modeling $\mathbb{L}(\mathcal{H})$ and employing high computational power. A remarkable consequence of this approach are conditions under which a non-exhaustive search of $\mathbb{L}(\mathcal{H})$ can return an optimal solution. The results of this paper lead to a practical property of Machine Learning, that the lack of experimental data may be mitigated by a high computational capacity. In a context of continuous popularization of computational power, this property may help understand why Machine Learning has become so important, even where data is expensive and hard to get.

Representation learning constructs low-dimensional representations to summarize essential features of high-dimensional data. This learning problem is often approached by describing various desiderata associated with learned representations; e.g., that they be non-spurious, efficient, or disentangled. It can be challenging, however, to turn these intuitive desiderata into formal criteria that can be measured and enhanced based on observed data. In this paper, we take a causal perspective on representation learning, formalizing non-spuriousness and efficiency (in supervised representation learning) and disentanglement (in unsupervised representation learning) using counterfactual quantities and observable consequences of causal assertions. This yields computable metrics that can be used to assess the degree to which representations satisfy the desiderata of interest and learn non-spurious and disentangled representations from single observational datasets.

Generative approaches have been recently shown to be effective for both Entity Disambiguation and Entity Linking (i.e., joint mention detection and disambiguation). However, the previously proposed autoregressive formulation for EL suffers from i) high computational cost due to a complex (deep) decoder, ii) non-parallelizable decoding that scales with the source sequence length, and iii) the need for training on a large amount of data. In this work, we propose a very efficient approach that parallelizes autoregressive linking across all potential mentions and relies on a shallow and efficient decoder. Moreover, we augment the generative objective with an extra discriminative component, i.e., a correction term which lets us directly optimize the generator's ranking. When taken together, these techniques tackle all the above issues: our model is >70 times faster and more accurate than the previous generative method, outperforming state-of-the-art approaches on the standard English dataset AIDA-CoNLL. Source code available at https://github.com/nicola-decao/efficient-autoregressive-EL

A novel procedure to perform fuzzy clustering of multivariate time series generated from different dependence models is proposed. Different amounts of dissimilarity between the generating models or changes on the dynamic behaviours over time are some arguments justifying a fuzzy approach, where each series is associated to all the clusters with specific membership levels. Our procedure considers quantile-based cross-spectral features and consists of three stages: (i) each element is characterized by a vector of proper estimates of the quantile cross-spectral densities, (ii) principal component analysis is carried out to capture the main differences reducing the effects of the noise, and (iii) the squared Euclidean distance between the first retained principal components is used to perform clustering through the standard fuzzy C-means and fuzzy C-medoids algorithms. The performance of the proposed approach is evaluated in a broad simulation study where several types of generating processes are considered, including linear, nonlinear and dynamic conditional correlation models. Assessment is done in two different ways: by directly measuring the quality of the resulting fuzzy partition and by taking into account the ability of the technique to determine the overlapping nature of series located equidistant from well-defined clusters. The procedure is compared with the few alternatives suggested in the literature, substantially outperforming all of them whatever the underlying process and the evaluation scheme. Two specific applications involving air quality and financial databases illustrate the usefulness of our approach.

We introduce primed-PCA (pPCA), an extension of the recently proposed EigenGame algorithm for computing principal components in a large-scale setup. Our algorithm first runs EigenGame to get an approximation of the principal components, and then applies an exact PCA in the subspace they span. Since this subspace is of small dimension in any practical use of EigenGame, this second step is extremely cheap computationally. Nonetheless, it improves accuracy significantly for a given computational budget across datasets. In this setup, the purpose of EigenGame is to narrow down the search space, and prepare the data for the second step, an exact calculation. We show formally that pPCA improves upon EigenGame under very mild conditions, and we provide experimental validation on both synthetic and real large-scale datasets showing that it systematically translates to improved performance. In our experiments we achieve improvements in convergence speed by factors of 5-25 on the datasets of the original EigenGame paper.