Question 1: Short answerhardAI-checkedOptimization & CalculusAdadelta updates st=ρst−1+(1−ρ)gt2\mathbf{s}_t = \rho\mathbf{s}_{t-1} + (1 - \rho)\mathbf{g}_t^2st=ρst−1+(1−ρ)gt2, gt′=Δxt−1+ϵst+ϵ⊙gt\mathbf{g}'_t = \frac{\sqrt{\Delta\mathbf{x}_{t-1} + \epsilon}}{\sqrt{\mathbf{s}_t + \epsilon}} \odot \mathbf{g}_tgt′=st+ϵΔxt−1+ϵ⊙gt, xt=xt−1−gt′\mathbf{x}_t = \mathbf{x}_{t-1} - \mathbf{g}'_txt=xt−1−gt′ and Δxt=ρΔxt−1+(1−ρ)gt′2\Delta\mathbf{x}_t = \rho\Delta\mathbf{x}_{t-1} + (1 - \rho)\mathbf{g}'^2_tΔxt=ρΔxt−1+(1−ρ)gt′2, with s0=Δx0=0\mathbf{s}_0 = \Delta\mathbf{x}_0 = 0s0=Δx0=0, ρ=0.9\rho = 0.9ρ=0.9 and ϵ=10−5\epsilon = 10^{-5}ϵ=10−5. For a scalar parameter with first gradient g1=5g_1 = 5g1=5, how large is the first step ∣g1′∣|g'_1|∣g1′∣?Your answera number, 4 decimals