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Despite their successes, deep learning models struggle with tasks requiring complex reasoning and function composition. We present a theoretical and empirical investigation into the limitations of Structured State Space Models (SSMs) and…

Representation is a core issue in artificial intelligence. Humans use discrete language to communicate and learn from each other, while machines use continuous features (like vector, matrix, or tensor in deep neural networks) to represent…

Neural networks have greatly boosted performance in computer vision by learning powerful representations of input data. The drawback of end-to-end training for maximal overall performance are black-box models whose hidden representations…

Deep neural networks have achieved impressive supervised classification performance in many tasks including image recognition, speech recognition, and sequence to sequence learning. However, this success has not been translated to…

Embedding of large but redundant data, such as images or text, in a hierarchy of lower-dimensional spaces is one of the key features of representation learning approaches, which nowadays provide state-of-the-art solutions to problems once…

Deep Learning (DL) models proved themselves to perform extremely well on a wide variety of learning tasks, as they can learn useful patterns from large data sets. However, purely data-driven models might struggle when very difficult…

The problem of extending a function $f$ defined on a training data $\mathcal{C}$ on an unknown manifold $\mathbb{X}$ to the entire manifold and a tubular neighborhood of this manifold is considered in this paper. For $\mathbb{X}$ embedded…

Recently, it has been shown that many functions on sets can be represented by sum decompositions. These decompositons easily lend themselves to neural approximations, extending the applicability of neural nets to set-valued inputs---Deep…

Deep learning, a branch of artificial intelligence, is a data-driven method that uses multiple layers of interconnected units or neurons to learn intricate patterns and representations directly from raw input data. Empowered by this…

One of the most prominent attributes of Neural Networks (NNs) constitutes their capability of learning to extract robust and descriptive features from high dimensional data, like images. Hence, such an ability renders their exploitation as…

The goal of supervised representation learning is to construct effective data representations for prediction. Among all the characteristics of an ideal nonparametric representation of high-dimensional complex data, sufficiency, low…

Neural networks have been very successful in many applications; we often, however, lack a theoretical understanding of what the neural networks are actually learning. This problem emerges when trying to generalise to new data sets. The…

Although deep neural networks have achieved remarkable results for the task of semantic segmentation, they usually fail to generalize towards new domains, especially when performing synthetic-to-real adaptation. Such domain shift is…

Objective functions that optimize deep neural networks play a vital role in creating an enhanced feature representation of the input data. Although cross-entropy-based loss formulations have been extensively used in a variety of supervised…

Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In…

Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role,…

Arguably the key reason for the success of deep neural networks is their ability to autonomously form non-linear combinations of the input features, which can be used in subsequent layers of the network. The analogon to this capability in…

Neural networks are versatile tools for computation, having the ability to approximate a broad range of functions. An important problem in the theory of deep neural networks is expressivity; that is, we want to understand the functions that…

Multitask learning, i.e. learning several tasks at once with the same neural network, can improve performance in each of the tasks. Designing deep neural network architectures for multitask learning is a challenge: There are many ways to…

Deep neural networks are increasingly being used in cognitive modeling as a means of deriving representations for complex stimuli such as images. While the predictive power of these networks is high, it is often not clear whether they also…