The Computational Complexity of ReLU Network Training Parameterized by Data Dimensionality

Understanding the computational complexity of training simple neural networks with rectified linear units (ReLUs) has recently been a subject of intensive research. Closing gaps and complementing results from the literature, we present several results on the parameterized complexity of training two-...

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Veröffentlicht in:The Journal of artificial intelligence research Jg. 74; S. 1775 - 1790
Hauptverfasser: Froese, Vincent, Hertrich, Christoph, Niedermeier, Rolf
Format: Journal Article
Sprache:Englisch
Veröffentlicht: San Francisco AI Access Foundation 01.01.2022
Schlagworte:
Algorithms
Artificial intelligence
Complexity
Lower bounds
Neural networks
Parameterization
Parameters
Polynomials
Training
ISSN:1076-9757, 1076-9757, 1943-5037
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Abstract Understanding the computational complexity of training simple neural networks with rectified linear units (ReLUs) has recently been a subject of intensive research. Closing gaps and complementing results from the literature, we present several results on the parameterized complexity of training two-layer ReLU networks with respect to various loss functions. After a brief discussion of other parameters, we focus on analyzing the influence of the dimension d of the training data on the computational complexity. We provide running time lower bounds in terms of W[1]-hardness for parameter d and prove that known brute-force strategies are essentially optimal (assuming the Exponential Time Hypothesis). In comparison with previous work, our results hold for a broad(er) range of loss functions, including lp-loss for all p ∈ [0, ∞]. In particular, we improve 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.
AbstractList Understanding the computational complexity of training simple neural networks with rectified linear units (ReLUs) has recently been a subject of intensive research. Closing gaps and complementing results from the literature, we present several results on the parameterized complexity of training two-layer ReLU networks with respect to various loss functions. After a brief discussion of other parameters, we focus on analyzing the influence of the dimension d of the training data on the computational complexity. We provide running time lower bounds in terms of W[1]-hardness for parameter d and prove that known brute-force strategies are essentially optimal (assuming the Exponential Time Hypothesis). In comparison with previous work, our results hold for a broad(er) range of loss functions, including lp-loss for all p ∈ [0, ∞]. In particular, we improve 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.
Author Niedermeier, Rolf
Hertrich, Christoph
Froese, Vincent
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  surname: Niedermeier
  fullname: Niedermeier, Rolf
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Snippet Understanding the computational complexity of training simple neural networks with rectified linear units (ReLUs) has recently been a subject of intensive...
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StartPage 1775
SubjectTerms Algorithms
Artificial intelligence
Complexity
Lower bounds
Neural networks
Parameterization
Parameters
Polynomials
Training
Title The Computational Complexity of ReLU Network Training Parameterized by Data Dimensionality
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