Related papers: Modified difference ascent sequences and Fishburn …

A discriminatively trained neural net classifier can fit the training data perfectly if all information about its input other than class membership has been discarded prior to the output layer. Surprisingly, past research has discovered…

Memory is fundamental to intelligence, enabling learning, reasoning, and adaptability across biological and artificial systems. While Transformer architectures excel at sequence modeling, they face critical limitations in long-range context…

A permutation is (1-23-4)-avoiding if it contains no four entries, increasing left to right, with the middle two adjacent in the permutation. Here we give a 2-variable recurrence for the number of such permutations, improving on the…

We propose a novel data augmentation method for labeled sentences called conditional BERT contextual augmentation. Data augmentation methods are often applied to prevent overfitting and improve generalization of deep neural network models.…

The number of inversion sequences avoiding two patterns $101$ and $102$ is known to be the same as the number of permutations avoiding three patterns $2341$, $2431$, and $3241$. This sequence also counts the number of Schr\"{o}der paths…

Expansions of abelian categories are introduced. These are certain functors between abelian categories and provide a tool for induction/reduction arguments. Expansions arise naturally in the study of coherent sheaves on weighted projective…

We define and study odd analogues of classical geometric and combinatorial objects associated to permutations, namely odd Schubert varieties, odd diagrams, and odd inversion sets. We show that there is a bijection between odd inversion sets…

Backdoor adjustment is a technique in causal inference for estimating interventional quantities from purely observational data. For example, in medical settings, backdoor adjustment can be used to control for confounding and estimate the…

The task of learning to map an input set onto a permuted sequence of its elements is challenging for neural networks. Set-to-sequence problems occur in natural language processing, computer vision and structure prediction, where…

Unordered feature sets are a nonstandard data structure that traditional neural networks are incapable of addressing in a principled manner. Providing a concatenation of features in an arbitrary order may lead to the learning of spurious…

An oriented hypergraph is an oriented incidence structure that allows for the generalization of graph theoretic concepts to integer matrices through its locally signed graphic substructure. The locally graphic behaviors are formalized in…

Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen randomly proportionally to its weight. Under some assumptions on the sequence of…

A graphon is a limiting object used to describe the behaviour of large networks through a function that captures the probability of edge formation between nodes. Although the merits of graphons to describe large and unlabelled networks are…

Consider a bisexual population such that the set of females can be partitioned into finitely many different types indexed by $\{1,2,\dots,n\}$ and, similarly, that the male types are indexed by $\{1,2,\dots,\nu \}$. Recently an evolution…

Phylogenetic trees (i.e. evolutionary trees, additive trees or X-trees) play a key role in the processes of modeling and representing species evolution. Genome evolution of a given group of species is usually modeled by a species…

We present a framework to obtain valid inequalities for a reverse convex set: the set of points in a polyhedron that lie outside a given open convex set. Reverse convex sets arise in many models, including bilevel optimization and…

The training of deep residual neural networks (ResNets) with backpropagation has a memory cost that increases linearly with respect to the depth of the network. A way to circumvent this issue is to use reversible architectures. In this…

Deep learning research over the past years has shown that by increasing the scope or difficulty of the learning problem over time, increasingly complex learning problems can be addressed. We study incremental learning in the context of…

We improve the previously best known lower and upper bounds on the number n_g of numerical semigroups of genus g. Starting from a known recursive description of the tree T of numerical semigroups, we analyze some of its properties and use…

Next to scaling considerations, architectural design choices profoundly shape the solution space of transformers. In this work, we analyze the solutions simple transformer blocks implement when tackling the histogram task: counting items in…