Fig. 1: Representation of a k-\({\mathsf{ReLU}}\) gate within \({{\mathsf{bPTC}}}^{0}(k)\), constructed using multiple biased threshold gates (k-\({\mathsf{bT}}\)). | Nature Communications

Fig. 1: Representation of a k-\({\mathsf{ReLU}}\) gate within \({{\mathsf{bPTC}}}^{0}(k)\), constructed using multiple biased threshold gates (k-\({\mathsf{bT}}\)).

From: Unconditional advantage of noisy qudit quantum circuits over biased threshold circuits in constant depth

Fig. 1: Representation of a k- $${\mathsf{ReLU}}$$ ReLU gate within $${{\mathsf{bPTC}}}^{0}(k)$$ bPTC 0 ( k ) , constructed using multiple biased threshold gates (k- $${\mathsf{bT}}$$ bT ).

This gate is equivalent to a \({\mathsf{ReLU}}\) gate, defined as \(f(x)=\max \{0,x-c\}\) (where the center is shifted from 0 to c), up to an integer precision w for any input string with a Hamming weight bounded by k. Our scheme considers \({\mathsf{ReLU}}:{\{0,1\}}^{n}\mapsto \{0,n-c\}\), which takes n-bit strings as input and interprets their Hamming weight as the input x.

Back to article page