1. Overview
Positional Encoding is a technique used in Transformer architectures to encode the order of tokens in a sequence.
Transformers process tokens in parallel, unlike sequential models such as RNNs. Because of this, the model has no inherent understanding of token order. Positional encoding injects information about token positions into token embeddings before they enter the self-attention layers.
The final representation sent to the transformer is:
Input = TokenEmbedding + PositionalEncoding
This allows the model to learn both:
2. Why This Exists
The Core Problem
Self-attention processes tokens simultaneously, not sequentially.
Example sentence:
"Nitish killed lion"
"Lion killed Nitish"
Both sentences contain the same tokens:
[Nitish, killed, lion]
If sent to self-attention simultaneously, the model cannot distinguish token order, so both sequences appear identical.
This is a fundamental limitation because word order determines meaning in natural language.
Why Previous Models Didn't Have This Problem
| Model |
Order Awareness |
Reason |
| RNN |
Yes |
Tokens processed sequentially |
| LSTM |
Yes |
Hidden state carries time information |
| Transformer |
No |
Tokens processed in parallel |
Transformers sacrifice sequential processing for parallel efficiency, so positional information must be explicitly added.
3. First Principles Explanation
To solve the ordering problem, we must encode position information alongside token embeddings.
Components
Token Embedding
Positional Encoding
Self-Attention Layer
Interaction
Token → Embedding Vector
Position → Positional Encoding Vector
Final Input = Embedding + Positional Encoding
Each token therefore carries:
semantic information + positional information
Design Requirements
A good positional encoding must satisfy:
- Bounded values
Neural networks train best with values in small ranges (e.g. -1 to 1).
- Continuous values
Neural networks prefer smooth functions, not discrete jumps.
- Ability to capture relative positions
The model should infer relationships like:
distance(token_i, token_j)
- Unique representation
Each position must have a distinct encoding.
4. How It Works
Step 1 — Tokenize Sentence
Example:
Sentence: "River Bank"
Tokens: [River, Bank]
Step 2 — Convert Tokens to Embeddings
Example:
River → embedding vector (d_model)
Bank → embedding vector (d_model)
Example dimension:
d_model = 512
Step 3 — Generate Positional Encoding
For position pos and dimension i:
PE(pos,2i) = sin(pos / 10000^(2i/d_model))
PE(pos,2i+1) = cos(pos / 10000^(2i/d_model))
Key ideas:
even dimensions → sine
odd dimensions → cosine
Step 4 — Add Positional Encoding to Embedding
InputVector = Embedding + PositionalEncoding
Step 5 — Send to Self-Attention
The resulting vector contains both:
semantic meaning + position
This vector becomes the input to the transformer encoder.
5. Example
Situation
Sentence:
"The lion runs"
Token positions:
The → position 0
lion → position 1
runs → position 2
Implementation Idea
Compute positional encodings:
PE(0)
PE(1)
PE(2)
Then combine:
Embedding(The) + PE(0)
Embedding(lion) + PE(1)
Embedding(runs) + PE(2)
Expected Outcome
The transformer can now learn relationships such as:
Summary
Transformers process tokens in parallel, losing order information.
Positional encoding injects token position information.
Encodings are generated using sine and cosine functions at multiple frequencies.
Positional vectors have the same dimension as embeddings.
Final input to transformers is:
embedding + positional_encoding
