Why Transformers Train Like Any Neural Network: Backpropagation Explained

Before writing this, I revisited the common stumbling point when students first encounter Transformers and decided to break it down from an engineering perspective, optimization principles, and intuitive analogies.

Everyone talks about QKV but skips the key point

Many have seen the formula many times:

Attention(Q,K,V)=softmax(QKᵀ/√d_k)·V

Most resources stop here and label it a "self‑attention mechanism" that lets each token attend to all others, but the real question is:

Why can a Transformer be trained? How are its W and B updated by back‑propagation?

This is the core that makes it feel like a genuine network.

Fundamentally Transformer is still a neural network, back‑propagation works as usual

We can decompose it: the basic components are:

Input → Embedding → Multi-Head Attention → FFN → Output

All Linear layers contain parameters. For example:

q_linear = nn.Linear(hidden_size, hidden_size)

k_linear = nn.Linear(hidden_size, hidden_size)

v_linear = nn.Linear(hidden_size, hidden_size)

o_linear = nn.Linear(hidden_size, hidden_size)

Both fully‑connected layers inside the FFN are also Linear

These layers each have a weight W and bias b that are automatically updated by gradient back‑propagation.

What about the softmax and dot‑product in attention?

Many think attention only computes coefficients and cannot be back‑propagated, but it can.

attention_scores = torch.matmul(query, key.transpose(-1, -2)) / sqrt(d_k)

This line performs matrix multiplication, division, softmax and weighted sum, all of which support gradient flow in PyTorch.

loss = criterion(outputs, labels)
loss.backward()

Consequently: q_linear, k_linear, v_linear, o_linear parameters are updated;

FFN’s fully‑connected layers are updated;

The entire attention path is a differentiable chain with no break.

Intuitive view: attention is a weighted average with scores

It is like using Q to compute dot‑products with each K to measure relevance, then using those scores to weight‑average the V vectors, producing a new vector.

Q, K, V are obtained from the original input via trainable Linear layers, so they carry their own W and b. The whole process is a complex function that is fully differentiable.

Transformer training is no different from CNN training

CNN extracts features with convolution kernels;

RNN propagates state across time steps;

Transformer integrates information globally with the attention module.

All are neural networks optimized end‑to‑end via loss.backward().

Answering the key questions

Weights come from all Linear layers (Q, K, V, O, FFN);

The training uses the standard back‑propagation mechanism;

Every operator (matrix multiplication, softmax, addition) supports chain‑rule differentiation;

The attention module is not a black box but part of the computational graph.

Final tip

Implement a simplified Multi‑Head Attention to see the gradients in action:

query = self.q_linear(hidden_state)
key = self.k_linear(hidden_state)
value = self.v_linear(hidden_state)
...
attention_scores = torch.matmul(query, key.transpose(-1, -2)) / sqrt(d_k)
attention_probs = F.softmax(attention_scores, dim=-1)
output = torch.matmul(attention_probs, value)

Each Linear has parameters that get updated, confirming the intuition.

In short, a Transformer is just a fully‑connected + softmax + weighted‑average neural network; every parameter is optimized by back‑propagation.