Related papers: Scalar Solvability of Network Computation Problems…
The brain efficiently performs nonlinear computations through its intricate networks of spiking neurons, but how this is done remains elusive. While nonlinear computations can be implemented successfully in spiking neural networks, this…
In this paper, we generalize the minimum flow decomposition problem (MFD) to incorporate uncertain edge capacities and tackle it from the perspective of robust optimization. In the classical flow decomposition problem, a network flow is…
Networks are one of the most powerful structures for modeling problems in the real world. Downstream machine learning tasks defined on networks have the potential to solve a variety of problems. With link prediction, for instance, one can…
It has been hypothesized that some form of "modular" structure in artificial neural networks should be useful for learning, compositionality, and generalization. However, defining and quantifying modularity remains an open problem. We cast…
Linear programming has played a crucial role in shaping decision-making, resource allocation, and cost reduction in various domains. In this paper, we investigate the application of overparametrized neural networks and their implicit bias…
Computation codes in network information theory are designed for the scenarios where the decoder is not interested in recovering the information sources themselves, but only a function thereof. K\"orner and Marton showed for distributed…
An Ingletonian polymatroid satisfies, in addition to the polymatroid axioms, the inequalities of Ingleton (Combin. Math. Appln., 1971). These inequalities are required for a polymatroid to be representable. It is has been an open question…
Sum-networks are networks where all the terminals demand the sum of the symbols generated at the sources. It has been shown that for any finite set/co-finite set of prime numbers, there exists a sum-network which has a vector linear…
A sum-network is a directed acyclic network in which all terminal nodes demand the `sum' of the independent information observed at the source nodes. Many characteristics of the well-studied multiple-unicast network communication problem…
A sum-network is a directed acyclic network where each source independently generates one symbol from a given field $\mathbb F$ and each terminal wants to receive the sum $($over $\mathbb F)$ of the source symbols. For sum-networks with two…
Brain networks exhibit complications such as noise, neuron failures, and partial synaptic connectivity. These can make it difficult to model and analyze their behavior. This paper describes a way to address this difficulty, namely, breaking…
We study the complexity of functions computable by deep feedforward neural networks with piecewise linear activations in terms of the symmetries and the number of linear regions that they have. Deep networks are able to sequentially map…
Network visualization is essential for many scientific, societal, technological and artistic domains. The primary goal is to highlight patterns out of nodes interconnected by edges that are easy to understand, facilitate communication and…
Motivated by the trend to outsource work to commercial cloud computing services, we consider a variation of the streaming paradigm where a streaming algorithm can be assisted by a powerful helper that can provide annotations to the data…
We introduce linear network coding on parallel architecture for multi-source finite acyclic network. In this problem, different messages in diverse time periods are broadcast and every nonsource node in the network decodes and encodes the…
We consider tensors in the Hierarchical Tucker format and suppose the tensor data to be distributed among several compute nodes. We assume the compute nodes to be in a one-to-one correspondence with the nodes of the Hierarchical Tucker…
This paper studies the distributed linearly separable computation problem, which is a generalization of many existing distributed computing problems such as distributed gradient descent and distributed linear transform. In this problem, a…
A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is…
We consider uniquely-decodable coding for zero-error network function computation, where in a directed acyclic graph, the single sink node is required to compute with zero error a target function multiple times, whose arguments are the…
Rooted phylogenetic networks are often used to represent conflicting phylogenetic signals. Given a set of clusters, a network is said to represent these clusters in the "softwired" sense if, for each cluster in the input set, at least one…