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Convolutional networks almost always incorporate some form of spatial pooling, and very often it is alpha times alpha max-pooling with alpha=2. Max-pooling act on the hidden layers of the network, reducing their size by an integer…
Their vulnerability to small, imperceptible attacks limits the adoption of deep learning models to real-world systems. Adversarial training has proven to be one of the most promising strategies against these attacks, at the expense of a…
A well-trained Convolutional Neural Network can easily be pruned without significant loss of performance. This is because of unnecessary overlap in the features captured by the network's filters. Innovations in network architecture such as…
While many approaches exist in the literature to learn low-dimensional representations for data collections in multiple modalities, the generalizability of multi-modal nonlinear embeddings to previously unseen data is a rather overlooked…
In environmental applications of extreme value statistics, the underlying stochastic process is often modeled either as a max-stable process in continuous time/space or as a process in the domain of attraction of such a max-stable process.…
`Double descent' delineates the generalization behaviour of models depending on the regime they belong to: under- or over-parameterized. The current theoretical understanding behind the occurrence of this phenomenon is primarily based on…
The rapid recent progress in machine learning (ML) has raised a number of scientific questions that challenge the longstanding dogma of the field. One of the most important riddles is the good empirical generalization of overparameterized…
Dataset distillation has emerged as a strategy to overcome the hurdles associated with large datasets by learning a compact set of synthetic data that retains essential information from the original dataset. While distilled data can be used…
Recent advancements in machine learning have showcased its potential to significantly accelerate the discovery of new materials. Central to this progress is the development of rapidly computable property predictors, enabling the…
Mixup is a widely adopted strategy for training deep networks, where additional samples are augmented by interpolating inputs and labels of training pairs. Mixup has shown to improve classification performance, network calibration, and…
Interpolators -- estimators that achieve zero training error -- have attracted growing attention in machine learning, mainly because state-of-the art neural networks appear to be models of this type. In this paper, we study minimum $\ell_2$…
A \emph{fractal} is an object exhibiting complexity at arbitrarily small scales. In order to study and characterise fractals, one is often interested in quantifying how they fill up space on small scales. This gives rise to various notions…
Interpolation theory for complex polynomials is well understood. In the non-commutative quaternionic setting, the polynomials can be evaluated "on the left" and "on the right". If the interpolation problem involves interpolation conditions…
After training complex deep learning models, a common task is to compress the model to reduce compute and storage demands. When compressing, it is desirable to preserve the original model's per-example decisions (e.g., to go beyond top-1…
The problem of extrapolation and interpolation of asymptotic series is considered. Several new variants of improving the accuracy of the self-similar approximants are suggested. The methods are illustrated by examples typical of chemical…
Mixup is a regularization technique that artificially produces new samples using convex combinations of original training points. This simple technique has shown strong empirical performance, and has been heavily used as part of…
Transformer language models have demonstrated impressive generalization capabilities in natural language domains, yet we lack a fine-grained understanding of how such generalization arises. In this paper, we investigate length…
This paper describes applications of extrapolation for the computation of coefficients in an expansion of infrared divergent integrals. An extrapolation procedure is performed with respect to a parameter introduced by dimensional…
Recent work showed that there could be a large gap between the classical uniform convergence bound and the actual test error of zero-training-error predictors (interpolators) such as deep neural networks. To better understand this gap, we…
We analyze a class of norms defined via an optimal interpolation problem involving the composition of norms and a linear operator. This construction, known as infimal postcomposition in convex analysis, is shown to encompass various of…