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Found 11 papers, 2 papers with code
Depth-Bounds for Neural Networks via the Braid Arrangement
We contribute towards resolving the open question of how many hidden layers are required in ReLU networks for exactly representing all continuous and piecewise linear functions on $\mathbb{R}^d$.
Neural Networks and (Virtual) Extended Formulations
In an attempt to prove similar bounds also for general neural networks, we introduce the notion of virtual extension complexity $\mathrm{vxc}(P)$, which generalizes $\mathrm{xc}(P)$ and describes the number of inequalities needed to represent the linear optimization problem over $P$ as a difference of two linear programs.
Decomposition Polyhedra of Piecewise Linear Functions
Finally, we improve upon previous constructions of neural networks for a given convex CPWL function and apply our framework to obtain results in the nonconvex case.
Mode Connectivity in Auction Design
Mode connectivity has been recently investigated as an intriguing empirical and theoretically justifiable property of neural networks used for prediction problems.
Training Neural Networks is NP-Hard in Fixed Dimension
We also answer a question by Froese et al. [JAIR '22] proving W[1]-hardness for four ReLUs (or two linear threshold neurons) with zero training error.
Lower Bounds on the Depth of Integral ReLU Neural Networks via Lattice Polytopes
We prove that the set of functions representable by ReLU neural networks with integer weights strictly increases with the network depth while allowing arbitrary width.
Training Fully Connected Neural Networks is $\exists\mathbb{R}$-Complete
We consider the problem of finding weights and biases for a two-layer fully connected neural network to fit a given set of data points as well as possible, also known as EmpiricalRiskMinimization.
Towards Lower Bounds on the Depth of ReLU Neural Networks
We contribute to a better understanding of the class of functions that can be represented by a neural network with ReLU activations and a given architecture.
The Computational Complexity of ReLU Network Training Parameterized by Data Dimensionality
In particular, we extend a known polynomial-time algorithm for constant $d$ and convex loss functions to a more general class of loss functions, matching our running time lower bounds also in these cases.
ReLU Neural Networks of Polynomial Size for Exact Maximum Flow Computation
This paper studies the expressive power of artificial neural networks with rectified linear units.
Provably Good Solutions to the Knapsack Problem via Neural Networks of Bounded Size
The development of a satisfying and rigorous mathematical understanding of the performance of neural networks is a major challenge in artificial intelligence.
