83 citations
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Showing 2022Show all
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math.NA2022
Testing interval arithmetic libraries, including their IEEE-1788 compliance
Nathalie Revol, Luis Benet, Luca Ferranti +1
As developers of libraries implementing interval arithmetic, we faced the same difficulties when it came to testing our libraries. What must be tested? How can we devise relevant t…
cs.IT2022
Approximation speed of quantized vs. unquantized ReLU neural networks and beyond
Antoine Gonon, Nicolas Brisebarre, Rémi Gribonval +1
We deal with two complementary questions about approximation properties of ReLU networks. First, we study how the uniform quantization of ReLU networks with real-valued weights imp…
math.NA2022
Affine Iterations and Wrapping Effect: Various Approaches
Nathalie Revol
Affine iterations of the form x(n+1) = Ax(n) + b converge, using real arithmetic, if the spectral radius of the matrix A is less than 1. However, substituting interval arithmetic t…