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Dropout: Stochastic Regularization

Classic regularizer that prevents co-adaptation of features

Concept 52 of 100OptimizationPhase 10
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#52DropoutOptimization
key equation
h~=h⊙m,m∼Bernoulli(1−p)\tilde{h} = h \odot m, \quad m \sim \text{Bernoulli}(1-p)
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Concept 52 of 100DropoutOptimization / Phase 10: Mathematical foundations & information geometry
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Dropout injects noise proportional to activation magnitude—implicitly favors robust features

h~=h⊙m,m∼Bernoulli(1−p)\tilde{h} = h \odot m, \quad m \sim \text{Bernoulli}(1-p)
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Why It Matters for Modern Models

  • Classic regularizer that prevents co-adaptation of features
  • Foundation for understanding stochastic regularization (also: droppath, stochastic depth)
  • Modern LLMs often use minimal dropout—understanding when it helps/hurts is practical knowledge

What Tutorials Skip

What is still poorly explained in textbooks and papers:

  • Dropout injects noise proportional to activation magnitude—implicitly favors robust features
  • Different dropout rates per layer: higher dropout in final layers often helps
  • At large scale with lots of data, dropout can hurt: the ensemble benefit is dominated by data diversity

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Key Equation
h~=h⊙m,m∼Bernoulli(1−p)\tilde{h} = h \odot m, \quad m \sim \text{Bernoulli}(1-p)

Dropout randomly zeros activations during training:

h~=h⊙m,mi∼Bernoulli(1−p)\tilde{h} = h \odot m, \quad m_i \sim \text{Bernoulli}(1-p)

At test time, scale by keep probability:

htest=(1−p)⋅hh_{\text{test}} = (1-p) \cdot h

Or use inverted dropout (scale during training):

h~=h⊙m1−p\tilde{h} = \frac{h \odot m}{1-p}

Dropout approximates ensemble averaging over 2n2^n sub-networks.

Canonical Papers

Dropout: A Simple Way to Prevent Neural Networks from Overfitting

Srivastava et al.2014JMLR
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Prerequisites

ℒML/CE/KL⌇Sharpness

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