Question at position 11 What if in a neural network implementation we use a learning rate that’s too large?Network will not convergeNetwork will convergeCan’t say单项选择题
A
Network will not converge
B
Network will converge
C
Can’t say

Question

Question at position 11 What if in a neural network implementation we use a learning rate that’s too large?Network will not convergeNetwork will convergeCan’t say

BlackTom AI · Accepted Answer

Gradient descent update: θ_{t+1} = θ_t − α ∇L(θ_t). If the learning rate α is too large, the parameter updates overshoot minima and cause divergence or sustained oscillation. 1) Relevant knowledge points and concepts - Gradient descent dynamics: update rule θ ← θ − α∇L(θ). - Convergence condition (for smooth convex/quadratic losses): α must be below a threshold related to the Lipschitz constant (largest eigenvalue of Hessian). - Consequences of large α: overshooting, oscillation, exploding loss, or numerical instability. 2) Complete reasoning process step by step Consider a simple quadratic loss L(θ) = 1/2 a θ^2 (a > 0). Then ∇L = a θ, and the update becomes: θ_{t+1} = θ_t − α a θ_t = (1 − α a) θ_t. This is a linear recurrence whose magnitude evolves by factor |1 − α a| each step. 3) Intermediate calculation steps Convergence requires |1 − α a| < 1. Solve: −1 < 1 − α a < 1 → 0 < α a < 2 → α < 2/a. If α ≥ 2/a, then |1 − α a| ≥ 1, so θ_t does not contract to zero; for α > 2/a it grows in magnitude (diverges), for α = 2/a it oscillates (period-2), and for α just below 2/a it may oscillate slowly but still converge. 4) Why the correct answer is correct A too-large learning rate violates the stability condition (α < 2/L), causing updates that do not reduce error reliably. In neural networks (nonlinear, high-dimensional), this manifests as exploding loss, oscillations around minima, or complete failure to converge. 5) Why other options are incorrect - "Network will converge": false because large α breaks stability; convergence is not guaranteed and typically fails. - "Can’t say": while edge cases exist (e.g., lucky initialization or adaptive methods), the general and expected outcome for an excessively large fixed learning rate is non-convergence, so "Can’t say" is not the correct general answer. 6) Conclusion Therefore the correct choice is "Network will not converge", which matches the provided answer.

Question at position 11 What if in a neural network implementation we use a learning rate that’s too large?Network will not convergeNetwork will convergeCan’t say单项选择题

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