Related papers: Categorical Invariants of Learning Dynamics
The majority of computer vision algorithms fail to find higher-order (abstract) patterns in an image so are not robust against adversarial attacks, unlike human lateralized vision. Deep learning considers each input pixel in a homogeneous…
In this paper we develop a novel mathematical formalism for the modeling of neural information networks endowed with additional structure in the form of assignments of resources, either computational or metabolic or informational. The…
We provide a construction for categorical representation learning and introduce the foundations of "$\textit{categorifier}$". The central theme in representation learning is the idea of $\textbf{everything to vector}$. Every object in a…
Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…
Deep neural networks suffer from the major limitation of catastrophic forgetting old tasks when learning new ones. In this paper we focus on class incremental continual learning in semantic segmentation, where new categories are made…
Training neural networks is traditionally done by providing a sequence of random mini-batches sampled uniformly from the entire training data. In this work, we analyze the effect of curriculum learning, which involves the non-uniform…
Deep learning architectures based on convolutional neural networks tend to rely on continuous, smooth features. While this characteristics provides significant robustness and proves useful in many real-world tasks, it is strikingly…
It has been observed that the input space of deep neural network classifiers can exhibit `fragmentation', where the model function rapidly changes class as the input space is traversed. The severity of this fragmentation tends to follow the…
We propose and study a method for learning interpretable representations for the task of regression. Features are represented as networks of multi-type expression trees comprised of activation functions common in neural networks in addition…
Deep Learning has become interestingly popular in computer vision, mostly attaining near or above human-level performance in various vision tasks. But recent work has also demonstrated that these deep neural networks are very vulnerable to…
Despite the extreme popularity of deep learning in science and industry, its formal understanding is limited. This thesis puts forth notions of rank as key for developing a theory of deep learning, focusing on the fundamental aspects of…
According to a popular viewpoint, neural networks learn from data by first identifying low-dimensional representations, and subsequently fitting the best model in this space. Recent works provide a formalization of this phenomenon when…
Gradient descent typically converges to a single minimum of the training loss without mechanisms to explore alternative minima that may generalize better. Searching for diverse minima directly in high-dimensional parameter space is…
As deep neural networks are highly expressive, it is important to find solutions with small generalization gap (the difference between the performance on the training data and unseen data). Focusing on the stochastic nature of training, we…
Over the past decade, deep learning has proven to be a highly effective tool for learning meaningful features from raw data. However, it remains an open question how deep networks perform hierarchical feature learning across layers. In this…
Sequential training from task to task is becoming one of the major objects in deep learning applications such as continual learning and transfer learning. Nevertheless, it remains unclear under what conditions the trained model's…
This paper proposes a novel perspective on learning, positing it as the pursuit of dynamical invariants -- data combinations that remain constant or exhibit minimal change over time as a system evolves. This concept is underpinned by both…
Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…
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…
Geometric variations of objects, which do not modify the object class, pose a major challenge for object recognition. These variations could be rigid as well as non-rigid transformations. In this paper, we design a framework for training…