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2644Why LayerNorm Is Attractive in Sequence and Online Settings 24Why is LayerNorm often preferred over BatchNorm in sequence models or online inference settings?机器学习中等essay未尝试面试订阅2645Why Global-Norm Clipping Preserves Direction 14Why does global-norm clipping change the magnitude of a gradient vector but not its direction whenever clipping is active?机器学习困难derivation未尝试面试订阅3241Directional Derivative Along a Unit DiagonalLet f(x,y)=1x 2+2y 2. Compute the directional derivative of f at (1,1) in the direction of the vector (1,1).数学中等derivation未尝试面试订阅3242Directional Derivative of a Quadratic BowlLet f(x,y)=2x 2+1y 2. Compute the directional derivative at (1,-1) in the direction of (3,4).数学中等derivation未尝试面试订阅3243Directional Derivative of a Product SurfaceLet f(x,y)=xy. Compute the directional derivative at (2,3) in the direction of (0,1).数学中等derivation未尝试面试订阅3244Directional Derivative of an Exponential PlaneLet f(x,y)=e x-y . Compute the directional derivative at the origin in the direction of (4,3).数学中等derivation未尝试面试订阅3245Directional Derivative of a Log LevelLet f(x,y)=\ln(x+y). Compute the directional derivative at (1,2) in the direction of (1,0).数学中等derivation未尝试面试订阅3251Tangent Plane to a Quadratic SurfaceFind the tangent plane to z=x 2+y 2 at the point (1,2,5).数学中等derivation未尝试面试订阅3252Linearization of an Exponential SurfaceFind the linearization of f(x,y)=e x+2y at (0,0).数学中等derivation未尝试面试订阅3253Tangent Plane to a Product SurfaceFind the tangent plane to z=xy at (2,3,6).数学中等derivation未尝试面试订阅3254Linearization of a Logarithmic SurfaceFind the linearization of f(x,y)=\ln(x+y) at (1,1).数学中等derivation未尝试面试订阅3255Tangent Plane to a Three-Variable SurfaceFind the tangent plane to w=x 2+y 2+z 2 at (1,1,2,6).数学中等derivation未尝试面试订阅3256Classify the Origin for x^2+2y^2Classify the critical point at the origin for f(x,y)=x 2+2y 2.数学中等derivation未尝试面试订阅3257Classify the Origin for x^2-y^2Classify the critical point at the origin for f(x,y)=x 2-y 2.数学中等derivation未尝试面试订阅3258Classify the Origin for -x^2-4y^2Classify the critical point at the origin for f(x,y)=-x 2-4y 2.数学中等derivation未尝试面试订阅3259Classify the Origin for x^2+xy+y^2Classify the critical point at the origin for f(x,y)=x 2+xy+y 2.数学中等derivation未尝试面试订阅3260Classify the Origin for -x^2+2xy-y^2Classify the critical point at the origin for f(x,y)=-x 2+2xy-y 2.数学困难derivation未尝试面试订阅3391Central-Difference Richardson Upgrade 1A second-order central-difference estimate of f'(x) is 1.28 at h=0.2 and 1.22 at h=0.1. Using an O(h 2) Richardson extrapolation, what improved estimate do you get?数学简单derivation未尝试面试订阅3392Second-Derivative Richardson Upgrade 2A second-order estimate of f''(x) is 5.8 at h=0.4 and 5.2 at h=0.2. Assuming an O(h 2) truncation error, what Richardson-extrapolated estimate do you get?数学简单derivation未尝试面试订阅3393First-Order Extrapolation From Two Forward MeshesA first-order one-sided derivative estimate is 2.6 at h=0.1 and 2.45 at h=0.05. Assuming an O(h) bias, what extrapolated estimate cancels the leading error?数学简单derivation未尝试面试订阅