Related papers: Depth, Highness and DNR degrees

Novel dynamic programming algorithms to count the set $D(n)$ of zero-free degree sequences of length $n$, the set $D_c(n)$ of degree sequences of connected graphs on $n$ vertices and the set $D_b(n)$ of degree sequences of biconnected…

Generalization is essential for deep learning. In contrast to previous works claiming that Deep Neural Networks (DNNs) have an implicit regularization implemented by the stochastic gradient descent, we demonstrate explicitly Bayesian…

We compare classes of finite relational structures via monadic second-order transductions. More precisely, we study the preorder where we set C \subseteq K if, and only if, there exists a transduction {\tau} such that C\subseteq{\tau}(K).…

Deep SORT\cite{wojke2017simple} is a tracking-by-detetion approach to multiple object tracking with a detector and a RE-ID model. Both separately training and inference with the two model is time-comsuming. In this paper, we unify the…

We study the class of rational recursive sequences (ratrec) over the rational numbers. A ratrec sequence is defined via a system of sequences using mutually recursive equations of depth 1, where the next values are computed as rational…

In this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various deep neural network architectures which numerically predict…

For every $k\in \mathbb{N}$, we produce a set of integers which is $k$-recurrent but not $(k+1)$-recurrent. This extends a result of Furstenberg who produced a 1-recurrent set which is not 2-recurrent. We discuss a similar result for…

Deep neural networks (DNNs), especially deep convolutional neural networks (CNNs), have emerged as the powerful technique in various machine learning applications. However, the large model sizes of DNNs yield high demands on computation…

A residual network (or ResNet) is a standard deep neural net architecture, with state-of-the-art performance across numerous applications. The main premise of ResNets is that they allow the training of each layer to focus on fitting just…

We introduce a hierarchy of degree structures between the Medvedev and Muchnik lattices which allow varying amounts of non-uniformity. We use these structures to introduce the notion of the uniformity of a Muchnik reduction, which expresses…

A variation of ordered trees, where each rightmost edge might be marked or not, if it does not lead to an endnode, is investigated. These marked ordered trees were introduced by E. Deutsch et al.\ to model skew Dyck paths. We study the…

Why does Deep Learning work? What representations does it capture? How do higher-order representations emerge? We study these questions from the perspective of group theory, thereby opening a new approach towards a theory of Deep learning.…

We study the learning ability of linear recurrent neural networks with Gradient Descent. We prove the first theoretical guarantee on linear RNNs to learn any stable linear dynamic system using any a large type of loss functions. For an…

Deep neural networks (DNNs) are increasingly applied to safety-critical tasks in resource-constrained environments, such as video-based driver action and intention recognition. While last layer probabilistic deep learning (LL-PDL) methods…

Nowadays, neural networks play an important role in the task of relation classification. By designing different neural architectures, researchers have improved the performance to a large extent in comparison with traditional methods.…

Does the use of auto-differentiation yield reasonable updates for deep neural networks (DNNs)? Specifically, when DNNs are designed to adhere to neural ODE architectures, can we trust the gradients provided by auto-differentiation? Through…

Kernels derived from deep neural networks (DNNs) in the infinite-width regime provide not only high performance in a range of machine learning tasks but also new theoretical insights into DNN training dynamics and generalization. In this…

In the classification of complete first-order theories, many dividing lines have been defined in order to understand the complexity and the behavior of some classes of theories. In this paper, using the concept of patterns of consistency…

Finding parameters in a deep neural network (NN) that fit training data is a nonconvex optimization problem, but a basic first-order optimization method (gradient descent) finds a global optimizer with perfect fit (zero-loss) in many…

Neural Networks sequentially build high-level features through their successive layers. We propose here a new neural network model where each layer is associated with a set of candidate mappings. When an input is processed, at each layer,…