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The implicit bias induced by the training of neural networks has become a topic of rigorous study. In the limit of gradient flow and gradient descent with appropriate step size, it has been shown that when one trains a deep linear network…

Understanding the operation of biological and artificial networks remains a difficult and important challenge. To identify general principles, researchers are increasingly interested in surveying large collections of networks that are…

Many of the recent remarkable advances in computer vision and language models can be attributed to the success of transfer learning via the pre-training of large foundation models. However, a theoretical framework which explains this…

A fundamental feature of complex biological systems is the ability to form feedback interactions with their environment. A prominent model for studying such interactions is reservoir computing, where learning acts on low-dimensional…

Representations learned by pre-training a neural network on a large dataset are increasingly used successfully to perform a variety of downstream tasks. In this work, we take a closer look at how features are encoded in such pre-trained…

Recurrent and deep neural networks (RNNs/DNNs) are cornerstone architectures in machine learning. Remarkably, RNNs differ from DNNs only by weight sharing, as can be shown through unrolling in time. How does this structural similarity fit…

We study when geometric simplicity of decision boundaries, used here as a notion of interpretability, can conflict with accurate approximation of axis-aligned decision trees by shallow neural networks. Decision trees induce rule-based,…

Biologically, the brain does not rely on a single type of neuron that universally functions in all aspects. Instead, it acts as a sophisticated designer of task-based neurons. In this study, we address the following question: since the…

We study the expressivity of ReLU neural networks in the setting of a binary classification problem from a topological perspective. Recently, empirical studies showed that neural networks operate by changing topology, transforming a…

For classification tasks, the performance of a deep neural network is determined by the structure of its decision boundary, whose geometry directly affects essential properties of the model, including accuracy and robustness. Motivated by a…

Learning in neural systems arises from synaptic changes that reshape the representations underlying behavior. While low-rank recurrent neural networks (RNNs) have emerged as a powerful framework for linking connectivity to function, a…

We formalize and interpret the geometric structure of $d$-dimensional fully connected ReLU layers in neural networks. The parameters of a ReLU layer induce a natural partition of the input domain, such that the ReLU layer can be…

Contemporary wisdom based on empirical studies suggests that standard recurrent neural networks (RNNs) do not perform well on tasks requiring long-term memory. However, precise reasoning for this behavior is still unknown. This paper…

What has an Artificial Neural Network (ANN) learned after being successfully trained to solve a task - the set of training items or the relations between them? This question is difficult to answer for modern applied ANNs because of their…

It is well-known that overparametrized neural networks trained using gradient-based methods quickly achieve small training error with appropriate hyperparameter settings. Recent papers have proved this statement theoretically for highly…

The practice of deep learning has shown that neural networks generalize remarkably well even with an extreme number of learned parameters. This appears to contradict traditional statistical wisdom, in which a trade-off between model…

Generalization of deep neural networks remains one of the main open problems in machine learning. Previous theoretical works focused on deriving tight bounds of model complexity, while empirical works revealed that neural networks exhibit…

Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks as the curse of dimensionality (CoD) cannot be evaded when trying to approximate even a single ReLU neuron…

One of the central problems in the study of deep learning theory is to understand how the structure properties, such as depth, width and the number of nodes, affect the expressivity of deep neural networks. In this work, we show a new…

Working memory is a central cognitive ability crucial for intelligent decision-making. Recent experimental and computational work studying working memory has primarily used categorical (i.e., one-hot) inputs, rather than ecologically…