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Claude 4 Sonnet via @hdevalence.bsky.social

Looking at Section 2 of the GELU paper, here are the definitions of the three concepts mentioned:

ReLU (Rectified Linear Unit)

ReLU(x)=max⁡(0,x)=x⋅1x>0\text{ReLU}(x) = \max(0, x) = x \cdot \mathbf{1}_{x>0}

Where 1x>0\mathbf{1}_{x>0} is the indicator function that equals 1 when x>0x > 0 and 0 otherwise. ReLU deterministically multiplies the input by zero or one based on the input's sign.

Dropout

A stochastic regularization technique that randomly sets some neuron outputs to zero during training. It stochastically multiplies inputs by zero with some probability pp (the dropout rate). This creates a "pseudoensemble" effect by randomly altering activation decisions through zero multiplication.

Zoneout

A regularization technique for RNNs that stochastically multiplies inputs by one. Unlike dropout which zeros out activations, zoneout preserves the previous hidden state with some probability, effectively keeping the activation unchanged.

The key insight from the GELU paper is that these three techniques all involve multiplying inputs by binary values (0 or 1), but they differ in how they make this decision:

  • ReLU: Deterministic based on input sign
  • Dropout: Stochastic, input-independent
  • Zoneout: Stochastic, input-independent (preserves state)

GELU combines these ideas by using a stochastic mask m∼Bernoulli(Φ(x))m \sim \text{Bernoulli}(\Phi(x)) that depends on the input value xx, where Φ(x)\Phi(x) is the standard normal CDF. The final GELU is the expectation of this stochastic process: GELU(x)=xΦ(x)\text{GELU}(x) = x\Phi(x).

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Claude 4 Sonnet via @hdevalence.bsky.social

Dropout is still widely used today, though its application has evolved:

  • Still common in: Fully connected layers, computer vision models, and many practical deep learning applications
  • Less common in: Modern large language models (LLMs) and transformers, where other regularization techniques are preferred
  • Modern variants: DropPath/Stochastic Depth, DropBlock for CNNs, and attention dropout in transformers

Zoneout is much less common now:

  • It was primarily designed for RNNs (LSTMs/GRUs)
  • Since RNNs have largely been replaced by transformers for most sequence modeling tasks, zoneout usage has declined significantly
  • Most modern sequence models use attention mechanisms rather than recurrent architectures

Current regularization landscape:

  • Layer normalization and batch normalization are more fundamental
  • Weight decay (L2 regularization) remains standard
  • Gradient clipping is common for training stability
  • Early stopping and learning rate scheduling
  • Data augmentation techniques
  • Attention dropout in transformers

The GELU paper (2016) was written during the transition period when RNNs were still dominant but transformers were emerging. Today's models rely more on architectural innovations (like attention) and large-scale training rather than traditional stochastic regularization techniques.

So dropout persists but is less central, while zoneout has largely faded with the decline of RNNs.

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