One Exact Step

What One Step Is and Is Not

The finale keeps the boundary visible: one exact update is not a broader claim. The diagram's honesty note is required by the validator.

highlighted = computed this step

What is exact

This book computes one exact gradient-descent step with eta=1/2. Every displayed update is recomputed as old minus eta times the gradient.

wnew=wold−η∇ww_{\text{new}}=w_{\text{old}}-\eta\nabla w
One exact step boundaryExact update table with required boundary note.gradient descent update, η=1/2parameteroldgradientη·gradientneww111-2-12w121-4-23b1-1-2-10w211001w22-100-1b20000v11-4-23v21001c0-2-11w_new = w_old - η·gradientone exact step with η=1/2; NOT convergence, NOT the right η, NOT learning

What is outside the render

The required honesty note is part of the validated diagram. It states: one exact step with eta=1/2; NOT convergence, NOT the right eta, NOT learning.

one step≠ a broader claim\text{one step}\ne\text{ a broader claim}
One exact step boundaryExact update table with required boundary note.gradient descent update, η=1/2parameteroldgradientη·gradientneww111-2-12w121-4-23b1-1-2-10w211001w22-100-1b20000v11-4-23v21001c0-2-11w_new = w_old - η·gradientone exact step with η=1/2; NOT convergence, NOT the right η, NOT learning

What one step is and is not

This is ONE exact gradient-descent step with eta=1/2; the arithmetic is exact. It is NOT convergence, NOT the right eta, NOT training, NOT learning.

exact update, deferred claims explicit\text{exact update, deferred claims explicit}
One exact step boundaryExact update table with required boundary note.gradient descent update, η=1/2parameteroldgradientη·gradientneww111-2-12w121-4-23b1-1-2-10w211001w22-100-1b20000v11-4-23v21001c0-2-11w_new = w_old - η·gradientone exact step with η=1/2; NOT convergence, NOT the right η, NOT learning