ReLU is better than sigmoid primarily because it avoids the vanishing gradient problem, allowing deep neural networks to actually learn. The sigmoid function squashes all inputs into a range between 0 and 1, which sounds tidy but creates a serious bottleneck: its maximum derivative is only 0.25, and that small gradient gets multiplied layer after layer during training until it effectively disappears. ReLU, by contrast, has a constant gradient of 1 for all positive inputs, so learning signals pass through deep networks without shrinking into oblivion.
The Vanishing Gradient Problem
To understand why ReLU dominates modern deep learning, you need to understand how neural networks learn. During training, the network calculates how wrong its predictions are, then sends correction signals backward through every layer. This process, called backpropagation, relies on multiplying gradients (essentially slopes) at each layer. If those gradients are small, the correction signal weakens as it travels deeper. If they’re very small, it vanishes entirely.
The sigmoid function’s derivative is calculated as sigmoid(x) × (1 − sigmoid(x)). This peaks at 0.25 when the input is zero and drops toward zero as inputs get larger or smaller. In a 10-layer network, even if every layer has the maximum possible sigmoid gradient, the signal shrinks by a factor of 0.25 at each layer. By the time it reaches the earliest layers, it’s been multiplied by 0.25 ten times, leaving roughly 0.000001 of the original signal. In practice, most neurons aren’t sitting at the exact peak, so the problem is even worse.
ReLU sidesteps this entirely. For any positive input, ReLU outputs the input unchanged, and its derivative is simply 1. A gradient of 1 multiplied through many layers stays intact. This is what “non-saturating” means: ReLU doesn’t flatten out at the extremes the way sigmoid does. In experiments with 101-layer networks, ReLU achieves the highest accuracy and fastest convergence, while sigmoid and tanh show almost no learning progress during the first 20 epochs because their deep layers are completely saturated.
Faster Training and Simpler Math
ReLU is computationally cheap. The function is just max(0, x): if the input is positive, pass it through; if negative, output zero. There’s no exponential to calculate, no division. Sigmoid requires computing 1/(1 + e^(−x)), which involves an exponent at every neuron, every forward pass, every training step. In networks with millions or billions of parameters, that difference in arithmetic adds up quickly.
This simplicity also translates to faster convergence. Because ReLU gradients don’t shrink, weight updates remain meaningful throughout the network, so the model reaches a good solution in fewer passes through the data. Even when the final accuracy gap between ReLU and sigmoid is small, ReLU typically gets there faster. For sigmoid, the first 20 or more training epochs in a deep network can be essentially wasted while the model struggles to push gradients through saturated layers.
Sparsity Makes Networks More Efficient
ReLU zeroes out all negative inputs, which means a large portion of neurons in any given layer output exactly zero. This creates what’s called a sparse representation: only a subset of neurons are active for any particular input. Sparsity is useful for two reasons. First, it makes the network’s internal representations more interpretable and less redundant. Second, it enables significant computational savings because zero-valued neurons can be skipped entirely during inference.
Research on large language models shows that ReLU-based architectures exhibit up to 50% activation sparsity, meaning half the neurons in their feed-forward layers output zero at any given time. This sparsity can be exploited to reduce inference computation by up to three times with minimal performance trade-offs. Newer activation functions like GELU and SiLU, which are popular in modern transformers, produce non-zero outputs even for negative inputs, making it harder to achieve this kind of efficiency. Some researchers have found that converting these models back to ReLU-based activations can match performance while unlocking substantial speed gains.
The Dying ReLU Problem
ReLU isn’t perfect. Its main weakness is the “dying ReLU” problem: if a neuron’s inputs consistently land in the negative range, it always outputs zero. Since the gradient of ReLU is also zero for negative inputs, a dead neuron receives no gradient updates and can’t recover. In the worst case, a large portion of the network becomes permanently inactive, turning the model into something close to a constant function.
This typically happens when learning rates are set too high, causing weights to shift dramatically and push many neurons into the negative zone. Several ReLU variants address this directly. Leaky ReLU adds a small slope (like 0.01) in the negative range, so neurons always pass at least a tiny gradient. Parametric ReLU lets the network learn that slope automatically. Exponential Linear Units (ELU) and Gaussian Error Linear Units (GELU) take different approaches but share the same goal: prevent dead zones while keeping the core benefits of ReLU-style activation.
Where Sigmoid Still Belongs
Sigmoid hasn’t disappeared from neural networks. It remains the standard choice for the output layer of binary classifiers, where you need a probability between 0 and 1. If your network predicts whether an email is spam or not, the final layer uses sigmoid to convert the raw output into a probability score. Logistic regression, one of the most common classification algorithms, is built entirely around the sigmoid function for this reason.
The key distinction is between hidden layers and output layers. In hidden layers, where a network builds up its internal representation across potentially dozens or hundreds of layers, ReLU’s non-saturating gradient is critical. At the output layer, where there’s only one layer to pass through and you need a bounded probability, sigmoid’s 0-to-1 range is exactly what you want. Modern deep learning practice reflects this: ReLU (or a variant) for hidden layers, sigmoid for binary classification outputs, and softmax for multi-class outputs.
Why ReLU Became the Default
ReLU’s rise tracks directly with the rise of deep learning itself. Shallow networks with two or three layers can get by with sigmoid because gradients don’t have far to travel. Once networks grew to tens or hundreds of layers, sigmoid became a practical impossibility for hidden layers. ReLU made depth feasible, and depth is what unlocked the performance gains that define modern AI.
Today, ReLU is considered the default activation function for most neural network architectures. Some state-of-the-art models, particularly large language models, have moved toward GELU and SiLU for nuanced reasons related to smooth gradients. But these are still closer to ReLU in spirit than to sigmoid: they’re designed to avoid saturation and keep gradients flowing. The fundamental insight that made ReLU better than sigmoid, that activation functions shouldn’t crush gradients in deep networks, remains the guiding principle behind every modern alternative.