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Continual learning is the ability to sequentially learn over time by accommodating knowledge while retaining previously learned experiences. Neural networks can learn multiple tasks when trained on them jointly, but cannot maintain…
These notes are dedicated to whom may be interested in algorithms, Markov chain, coupling, and graph theory etc. I present some preliminaries on coupling and explanations of the important formulas or phrases, which may be helpful for us to…
Contrastive learning is commonly used as a method of self-supervised learning with the "anchor" and "positive" being two random augmentations of a given input image, and the "negative" is the set of all other images. However, the…
This paper summarizes the results at the present moment about singularities with respect to the Mather-Jacobian log discrepancies over algebraically closed field of arbitrary characteristic. The basic point is the Inversion of Adjunction…
In this paper, we investigate how the initial models and the final models for the polynomial functors can be uniformly specified in matching logic.
We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…
Polynomial networks and factorization machines are two recently-proposed models that can efficiently use feature interactions in classification and regression tasks. In this paper, we revisit both models from a unified perspective. Based on…
Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path…
Why are classifiers in high dimension vulnerable to "adversarial" perturbations? We show that it is likely not due to information theoretic limitations, but rather it could be due to computational constraints. First we prove that, for a…
In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…
We present a categorical model for intuitionistic linear logic where objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally…
Several types of dependencies have been proposed for the static analysis of existential rule ontologies, promising insights about computational properties and possible practical uses of a given set of rules, e.g., in ontology-based query…
We count points on character varieties associated with punctured surfaces and regular semisimple generic conjugacy classes in reductive groups. We find that the number of points are palindromic polynomials. This suggests a $P=W$ conjecture…
We show that the question whether a term is typable is decidable for type systems combining inclusion polymorphism with parametric polymorphism provided the type constructors are at most unary. To prove this result we first reduce the…
We introduce a notion of compatibility between constraint encoding and compositional structure. Phrased in the language of category theory, it is given by a "composable constraint encoding". We show that every composable constraint encoding…
Over the past few years, deep learning has risen to the foreground as a topic of massive interest, mainly as a result of successes obtained in solving large-scale image processing tasks. There are multiple challenging mathematical problems…
These lecture notes provide a unified overview of most known canonical desingularization methods in characteristic zero. It starts with discussing the classical method, and then proceeds with the recently discovered ones: logarithmic…
We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from…
We construct efficient data structures that are resilient against a constant fraction of adversarial noise. Our model requires that the decoder answers most queries correctly with high probability and for the remaining queries, the decoder…
Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify…