Related papers: Property Testing of Computational Networks
Random geometric graphs are widely used in modeling geometry and dependence structure in networks. In a random geometric graph, nodes are independently generated from some probability distribution $F$ over a metric space, and edges link…
We study the approximation of two-layer compositions $f(x) = g(\phi(x))$ via deep networks with ReLU activation, where $\phi$ is a geometrically intuitive, dimensionality reducing feature map. We focus on two intuitive and practically…
A fundamental advantage of neural models for NLP is their ability to learn representations from scratch. However, in practice this often means ignoring existing external linguistic resources, e.g., WordNet or domain specific ontologies such…
The growing research and industry interest in the Internet of Things and the edge computing paradigm has increased the need for cost-efficient virtual testbeds for large-scale distributed applications. Researchers, students, and…
The input space of a neural network with ReLU-like activations is partitioned into multiple linear regions, each corresponding to a specific activation pattern of the included ReLU-like activations. We demonstrate that this partition…
We study the approximation properties of random ReLU features through their reproducing kernel Hilbert space (RKHS). We first prove a universality theorem for the RKHS induced by random features whose feature maps are of the form of nodes…
We define the local complexity of a neural network with continuous piecewise linear activations as a measure of the density of linear regions over an input data distribution. We show theoretically that ReLU networks that learn…
The history of deep learning has shown that human-designed problem-specific networks can greatly improve the classification performance of general neural models. In most practical cases, however, choosing the optimal architecture for a…
Neural networks are powerful functions with widespread use, but the theoretical behaviour of these functions is not fully understood. Creating deep neural networks by stacking many layers has achieved exceptional performance in many…
A new network with super approximation power is introduced. This network is built with Floor ($\lfloor x\rfloor$) or ReLU ($\max\{0,x\}$) activation function in each neuron and hence we call such networks Floor-ReLU networks. For any…
We study quantum property testing for directed graphs with maximum in-degree and out-degree bounded by some universal constant $d$. For a proximity parameter $\varepsilon$, we show that any property that can be tested with…
Distribution testing deals with what information can be deduced about an unknown distribution over $\{1,\ldots,n\}$, where the algorithm is only allowed to obtain a relatively small number of independent samples from the distribution. In…
We investigate a graph probing problem in which an agent has only an incomplete view $G' \subsetneq G$ of the network and wishes to explore the network with least effort. In each step, the agent selects a node $u$ in $G'$ to probe. After…
Neural architecture search has attracted wide attentions in both academia and industry. To accelerate it, researchers proposed weight-sharing methods which first train a super-network to reuse computation among different operators, from…
Complex networks, modeled as large graphs, received much attention during these last years. However, data on such networks is only available through intricate measurement procedures. Until recently, most studies assumed that these…
For a property $P$ and a sub-property $P'$, we say that $P$ is $P'$-partially testable with $q$ queries if there exists an algorithm that distinguishes, with high probability, inputs in $P'$ from inputs $\epsilon$-far from $P$ by using $q$…
Network pruning techniques, including weight pruning and filter pruning, reveal that most state-of-the-art neural networks can be accelerated without a significant performance drop. This work focuses on filter pruning which enables…
Given Boolean functions \( f, g : \mathbb{F}_2^n \to \{-1,+1\} \), we say they are {\em linearly isomorphic} if there exists \( A \in \mathrm{GL}_n(\mathbb{F}_2) \) such that \( f(x)=g(Ax) \) for all \( x \). We study this problem in the…
The knowledge of the topology of a wired network is often of fundamental importance. For instance, in the context of Power Line Communications (PLC) networks it is helpful to implement data routing strategies, while in power distribution…
Network pruning reduces the computation costs of an over-parameterized network without performance damage. Prevailing pruning algorithms pre-define the width and depth of the pruned networks, and then transfer parameters from the unpruned…