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In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…

Over the last few decades, psychologists have developed sophisticated formal models of human categorization using simple artificial stimuli. In this paper, we use modern machine learning methods to extend this work into the realm of…

We are often interested in decomposing complex, structured data into simple components that explain the data. The linear version of this problem is well-studied as dictionary learning and factor analysis. In this work, we propose a…

Diffusion models are capable of generating photo-realistic images that combine elements which likely do not appear together in the training set, demonstrating the ability to \textit{compositionally generalize}. Nonetheless, the precise…

Neural networks are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this paper we build a category-theoretic formalism around a neural network system called…

We propose a transfer learning method that utilizes data representations in a semiparametric regression model. Our aim is to perform statistical inference on the parameter of primary interest in the target model while accounting for…

Transformers can generate predictions in two approaches: 1. auto-regressively by conditioning each sequence element on the previous ones, or 2. directly produce an output sequences in parallel. While research has mostly explored upon this…

Traditional approaches for complementary product recommendations rely on behavioral and non-visual data such as customer co-views or co-buys. However, certain domains such as fashion are primarily visual. We propose a framework that…

We introduce a method for deterministic decoupling of global features and show its applicability to improve data analysis performance, as well as to open new venues for feature transfer. We propose a new formalism that is based on defining…

Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled…

Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many applications where the data exhibit temporal dependencies…

Deep learning models learn to fit training data while they are highly expected to generalize well to testing data. Most works aim at finding such models by creatively designing architectures and fine-tuning parameters. To adapt to…

Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems. Although modern models are trained on massive datasets, they still cover only a tiny fraction of the…

Using the theory of group action, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the general notion of symmetry of a probabilistic model. This automorphism group…

Teaching requires distilling a rich category distribution into a small set of informative exemplars. Although prior work shows that humans consider both representativeness and diversity when teaching, the computational principles underlying…

The inference of deep hierarchical models is problematic due to strong dependencies between the hierarchies. We investigate a specific transformation of the model parameters based on the multivariate distributional transform. This…

Statistical learning relies upon data sampled from a distribution, and we usually do not care what actually generated it in the first place. From the point of view of causal modeling, the structure of each distribution is induced by…

Deep neural networks have demonstrated their ability to automatically extract meaningful features from data. However, in supervised learning, information specific to the dataset used for training, but irrelevant to the task at hand, may…

We introduce a novel self-supervised learning approach to learn representations of videos that are responsive to changes in the motion dynamics. Our representations can be learned from data without human annotation and provide a substantial…

We present the Topology Transformation Equivariant Representation learning, a general paradigm of self-supervised learning for node representations of graph data to enable the wide applicability of Graph Convolutional Neural Networks…