Related papers: Counting the learnable functions of structured dat…

Do visual tasks have a relationship, or are they unrelated? For instance, could having surface normals simplify estimating the depth of an image? Intuition answers these questions positively, implying existence of a structure among visual…

A number of machine learning tasks entail a high degree of invariance: the data distribution does not change if we act on the data with a certain group of transformations. For instance, labels of images are invariant under translations of…

Ornaments aim at taming the multiplication of special-purpose datatype in dependently-typed theory. In its original form, the definition of ornaments is tied to a particular universe of datatypes. Being a type theoretic object,…

This paper develops a methodology for representing machine learning models as models of formal theories, grounded in the perspective that machine learning models are a form of database and that databases are models of theories in coherent…

We introduce a deep multitask architecture to integrate multityped representations of multimodal objects. This multitype exposition is less abstract than the multimodal characterization, but more machine-friendly, and thus is more precise…

An important characteristic of neural networks is their ability to learn representations of the input data with effective features for prediction, which is believed to be a key factor to their superior empirical performance. To better…

The success of neural networks builds to a large extent on their ability to create internal knowledge representations from real-world high-dimensional data, such as images, sound, or text. Approaches to extract and present these…

Deep learning models are used in critical applications, in which mistakes can have serious consequences. Therefore, it is crucial to understand how and why models generate predictions. This understanding provides useful information to check…

Learning representations that capture the underlying data generating process is a key problem for data efficient and robust use of neural networks. One key property for robustness which the learned representation should capture and which…

Counting cells in fluorescent microscopy is a tedious, time-consuming task that researchers have to accomplish to assess the effects of different experimental conditions on biological structures of interest. Although such objects are…

Census data provide detailed information about population characteristics at a coarse resolution. Nevertheless, fine-grained, high-resolution mappings of population counts are increasingly needed to characterize population dynamics and to…

The nerve theorem is a basic result of algebraic topology that plays a central role in computational and applied aspects of the subject. In topological data analysis, one often needs a nerve theorem that is functorial in an appropriate…

We propose the use of dilated filters to construct an aggregation module in a multicolumn convolutional neural network for perspective-free counting. Counting is a common problem in computer vision (e.g. traffic on the street or pedestrians…

Despite the remarkable empirical performance of Transformers, their theoretical understanding remains elusive. Here, we consider a deep multi-head self-attention network, that is closely related to Transformers yet analytically tractable.…

Transformers have revolutionized machine learning across diverse domains, yet understanding their behavior remains crucial, particularly in high-stakes applications. This paper introduces the contextual counting task, a novel toy problem…

Neural networks are powerful function estimators, leading to their status as a paradigm of choice for modeling structured data. However, unlike other structured representations that emphasize the modularity of the problem -- e.g., factor…

Exploiting data invariances is crucial for efficient learning in both artificial and biological neural circuits. Understanding how neural networks can discover appropriate representations capable of harnessing the underlying symmetries of…

We propose a new method to count objects of specific categories that are significantly smaller than the ground sampling distance of a satellite image. This task is hard due to the cluttered nature of scenes where different object categories…

We present a new approach for predictive modeling and its uncertainty quantification for mechanical systems, where coarse-grained models such as constitutive relations are derived directly from observation data. We explore the use of a…

Machine learning is a powerful tool to design accurate, highly non-local, exchange-correlation functionals for density functional theory. So far, most of those machine learned functionals are trained for systems with an integer number of…