Related papers: Counting the learnable functions of structured dat…

Traditionally, for most machine learning settings, gaining some degree of explainability that tries to give users more insights into how and why the network arrives at its predictions, restricts the underlying model and hinders performance…

Reasoning, the ability to logically draw conclusions from existing knowledge, is a hallmark of human. Together with perception, they constitute the two major themes of artificial intelligence. While deep learning has pushed the limit of…

Understanding how convolutional neural networks (CNNs) can efficiently learn high-dimensional functions remains a fundamental challenge. A popular belief is that these models harness the local and hierarchical structure of natural data such…

We introduce a novel embedding method diverging from conventional approaches by operating within function spaces of finite dimension rather than finite vector space, thus departing significantly from standard knowledge graph embedding…

Compositional generalization (the ability to respond correctly to novel combinations of familiar components) is thought to be a cornerstone of intelligent behavior. Compositionally structured (e.g. disentangled) representations support this…

Deep neural networks have been the driving force behind the success in classification tasks, e.g., object and audio recognition. Impressive results and generalization have been achieved by a variety of recently proposed architectures, the…

Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…

We target open-world feature extrapolation problem where the feature space of input data goes through expansion and a model trained on partially observed features needs to handle new features in test data without further retraining. The…

We propose a novel architecture, the event-based GASSOM for learning and extracting invariant representations from event streams originating from neuromorphic vision sensors. The framework is inspired by feed-forward cortical models for…

Intelligent perception and interaction with the world hinges on internal representations that capture its underlying structure (''disentangled'' or ''abstract'' representations). Disentangled representations serve as world models, isolating…

We investigate how to model exchangeability with choice functions. Exchangeability is a structural assessment on a sequence of uncertain variables. We show how such assessments are a special indifference assessment, and how that leads to a…

A central challenge in machine learning is to distinguish genuine structure from chance correlations in high-dimensional data. In this work, we address this issue for the perceptron, a foundational model of neural computation. Specifically,…

A central question in computational neuroscience is how structure determines function in neural networks. The emerging high-quality large-scale connectomic datasets raise the question of what general functional principles can be gleaned…

Artificial neural networks show promising performance in detecting correlations within data that are associated with specific outcomes. However, the black-box nature of such models can hinder the knowledge advancement in research fields by…

We introduce a framework for reasoning about what meaning is captured by the neurons in a trained neural network. We provide a strategy for discovering meaning by training a second model (referred to as an observer model) to classify the…

The advent of comprehensive synaptic wiring diagrams of large neural circuits has created the field of connectomics and given rise to a number of open research questions. One such question is whether it is possible to reconstruct the…

Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…

Using representations of functional data can be more convenient and beneficial in subsequent statistical models than direct observations. These representations, in a lower-dimensional space, extract and compress information from individual…

We investigate partial functions and computability theory from within a constructive, univalent type theory. The focus is on placing computability into a larger mathematical context, rather than on a complete development of computability…

Discovering patterns in data that best describe the differences between classes allows to hypothesize and reason about class-specific mechanisms. In molecular biology, for example, this bears promise of advancing the understanding of…