LLM Safety and Security Stack
I would like to know how the LLM works internally to generate the next token from an input embedding. So after the user inputs a prompt, the prompt gets converted to an embedding, which is then passed to the model to predict the next token. So from there, how is the next token predicted? Does it use the input embedding to solve a math equation to yields the next token?
Excellent question! 🔥 You're thinking about the **core mechanics of autoregressive LLMs** — how they go from an input prompt (turned into embeddings) to predicting the next token. Let’s carefully break this down.
---
## 1. Input stage: prompt → embeddings
1. You type a prompt:
> "The cat sat on the"
2. Tokenizer breaks this into discrete tokens (e.g., `"The"`, `"cat"`, `"sat"`, `"on"`, `"the"`).
3. Each token is mapped to a **vector** using a learned embedding matrix $E \in \mathbb{R}^{V \times d}$, where:
* $V$ = vocabulary size (say, 50k tokens),
* $d$ = embedding dimension (say, 4096).
So now your prompt is represented as a sequence of vectors in $\mathbb{R}^d$.
---
## 2. Transformer stack: contextualizing embeddings
These embeddings are fed into a **transformer network**, which is a stack of blocks containing:
* **Multi-Head Self-Attention**:
Each token embedding is projected into Query, Key, and Value vectors.
Attention computes weighted sums so that each token can "look at" other tokens in the context.
This creates contextualized representations — e.g., the word `"cat"` knows it comes after `"The"` and before `"sat"`.
* **Feedforward layers (MLPs)**:
Nonlinear transformations that enrich each token’s representation.
* **Residual connections & LayerNorm**:
Help stability and gradient flow.
After passing through, each token is now a highly **contextual embedding** that encodes meaning, syntax, and long-range dependencies.
---
## 3. Final hidden state → logits
Take the hidden state for the **last token** in your prompt (say `"the"`).
Call it $h \in \mathbb{R}^d$.
Now apply the **output projection**:
$$
z = W_{\text{out}} h,
$$
where $W_{\text{out}} \in \mathbb{R}^{V \times d}$ is a big matrix (often tied to the embedding matrix $E$).
* $z$ is a vector of length $V$ (vocabulary size).
* Each entry $z_i$ is a **logit**, representing how compatible the hidden state is with token $i$.
---
## 4. From logits → probabilities
Apply **softmax**:
$$
P(\text{token}=i \mid \text{context}) = \frac{\exp(z_i)}{\sum_j \exp(z_j)}.
$$
This gives a probability distribution over all tokens in the vocabulary.
For example:
* `"mat"` → 0.35
* `"dog"` → 0.02
* `"car"` → 0.001
* … etc.
---
## 5. Sampling / decoding
Now the model must **choose the next token**. There are different strategies:
* **Greedy**: pick the highest probability (deterministic, but can be repetitive).
* **Top-k sampling**: pick among the top $k$ tokens at random.
* **Nucleus (top-p) sampling**: pick from the smallest set of tokens whose probabilities sum to $p$ (e.g., 0.9).
* **Temperature scaling**: controls randomness by flattening/sharpening the distribution.
Suppose `"mat"` is chosen — that’s the predicted next token.
---
## 6. Autoregressive loop
Append `"mat"` to the input sequence, re-run the transformer (with cached states for efficiency), predict the next token, and so on … until stopping condition (EOS, max length).
---
## ✅ Summary
To your specific question:
> "Does it use the input embedding to solve a math equation to yield the next token?"
🔹 **Yes — but not a single equation.**
It’s a massive sequence of matrix multiplications, nonlinearities, and attention operations.
* Input embedding → contextualized by transformer layers.
* Final hidden state → projected into logits over vocabulary.
* Softmax → probabilities.
* Sampling → picks next token.
So it’s really **statistical prediction via learned parameters**, not symbolic rule-solving.
---
Would you like me to **draw a diagram of the full pipeline** (prompt → embeddings → transformer → logits → softmax → next token) so you can visually see each step?
.
ok, so in terms of the concrete implementation of these steps that you have outlined to predict the next token, is there a program that performs each of these steps using the learned weights extracted from the LLM model file? If so, can you give a high level step of this program, down to the sampling decoding step
Exactly ✅ — when you run an LLM (say GPT, LLaMA, Falcon, etc.), what’s happening inside is literally a program executing the exact steps I outlined — but instead of “math on paper,” it’s **tensor operations with the learned weights** from the model file.
Let me give you a **high-level algorithmic breakdown** of how the program works, step by step, all the way down to sampling:
---
## 🔹 High-Level Program to Predict the Next Token
**Inputs**:
* `model_weights` (embedding matrix, transformer layers, output projection, etc.)
* `tokenizer` (maps text ↔ tokens)
* `prompt` (user input text)
---
### Step 1. Tokenization
```python
tokens = tokenizer.encode(prompt)
```
* Example: `"The cat sat on the"` → `[1012, 4521, 2941, 1184, 310]`
---
### Step 2. Embedding lookup
```python
embeddings = model_weights["embedding_matrix"][tokens]
```
* Each token ID is mapped to a dense vector of size `d`.
---
### Step 3. Pass through transformer layers
For each layer `l` in `1...L`:
1. **Self-attention**:
* Compute Q, K, V = `Wq * h`, `Wk * h`, `Wv * h`.
* Attention weights = `softmax(QK^T / sqrt(d))`.
* New representation = `weights * V`.
2. **Feedforward network (MLP)**:
* Apply nonlinear transformation: `h = W2 * GELU(W1 * h)`.
3. **Residual & LayerNorm**:
* Add input back in, normalize.
At the end of `L` layers, you have contextualized hidden states for all tokens.
---
### Step 4. Select last token’s hidden state
```python
h_last = hidden_states[-1]
```
* This is the vector that encodes the **entire prompt** context up to the last token.
---
### Step 5. Project to vocabulary (logits)
```python
logits = model_weights["output_projection"] @ h_last
```
* Shape: `[V]` (where `V` = vocab size, e.g. 50k).
* Each entry = unnormalized score for a token.
---
### Step 6. Softmax to get probabilities
```python
probs = softmax(logits)
```
* Converts logits → probability distribution over all tokens.
---
### Step 7. Sampling / decoding
Options:
* **Greedy**:
```python
next_token = argmax(probs)
```
* **Top-k**:
```python
next_token = sample_from_top_k(probs, k=50)
```
* **Nucleus (top-p)**:
```python
next_token = sample_from_top_p(probs, p=0.9)
```
* **Temperature scaling**:
```python
probs = softmax(logits / temperature)
```
---
### Step 8. Append & repeat
```python
tokens.append(next_token)
```
* Feed updated `tokens` back into steps 2–7 (with caching to avoid recomputing all attention from scratch).
* Continue until EOS token or max length.
---
## ✅ Summary of Program Flow
```
Prompt → Tokenize → Embedding lookup
→ Transformer layers (attention + MLP)
→ Last hidden state → Output projection (logits)
→ Softmax → Probabilities
→ Sampling (decode strategy) → Next token
→ Loop
```
So yes — the actual implementation is **just matrix multiplications, nonlinearities, and probability sampling**, applied repeatedly using the learned weights in the model file. Frameworks like **PyTorch, TensorFlow, or specialized inference engines (e.g. vLLM, TensorRT-LLM, GGML)** carry this out.
---
👉 Would you like me to **write a minimal PyTorch-like pseudocode** for a single forward pass + token sampling, so you can see how all these steps look in an actual implementation?
I am very curious about your step 3 above, the pass through transformer layers. Was the embeddings of the prompts used any where in that step. ?. I did not see it. Please elaborate more o n the steps, giving more details on the pseudo code.
Beautiful question 🔥 — you caught the subtlety. Yes, the **embeddings of the prompt are absolutely used** in Step 3: they are the **initial hidden states** that flow through the transformer stack.
Let’s really open up **Step 3 (the transformer block)** in detail and show how the embeddings drive everything. I’ll use pseudocode that looks like PyTorch but simplified for clarity.
---
## 🔹 Transformer Flow in Detail
### Step 0. Input embeddings
When you tokenize the prompt, you map tokens into embeddings:
```python
# Suppose tokens = [1012, 4521, 2941, 1184, 310]
h = embedding_matrix[tokens] # shape: [seq_len, d_model]
```
* This is the **input to the first transformer block**.
* From now on, `h` is the evolving representation (hidden states) at each layer.
---
### Step 1. Add positional information
Since transformers don’t “know” order, we inject position:
```python
h = h + positional_encoding[:seq_len]
```
Now each token embedding carries both **its identity** and **its position** in the sequence.
---
### Step 2. Transformer layer (repeated L times)
Each block refines the hidden states by mixing tokens together via **self-attention** and then transforming them via an MLP.
#### (a) LayerNorm before attention
```python
h_norm = layernorm1(h)
```
#### (b) Compute queries, keys, values
```python
Q = h_norm @ Wq # shape: [seq_len, d_k]
K = h_norm @ Wk # shape: [seq_len, d_k]
V = h_norm @ Wv # shape: [seq_len, d_v]
```
* $Q, K, V$ are learned linear projections of the **input embeddings (or hidden states)**.
#### (c) Scaled dot-product attention
```python
attn_scores = (Q @ K.T) / sqrt(d_k) # shape: [seq_len, seq_len]
attn_scores = mask_future(attn_scores) # causal mask to prevent "peeking ahead"
attn_weights = softmax(attn_scores, dim=-1) # probability distribution
context = attn_weights @ V # weighted sum of values
```
Each token’s new representation is a weighted mixture of other tokens’ values, so it becomes **contextualized**.
#### (d) Residual connection
```python
h = h + context @ Wo # Wo is the output projection of attention
```
#### (e) Feedforward network (MLP)
```python
h_norm = layernorm2(h)
mlp_out = gelu(h_norm @ W1) @ W2
h = h + mlp_out
```
#### (f) End of one transformer block
At this point, `h` has richer contextual information. This repeats across **L layers**.
---
### Step 3. Final hidden state
After L transformer layers:
```python
h_final = h[-1] # take last token’s representation
```
This vector encodes the **entire prompt history** up to the last token.
---
### Step 4. Output projection → logits
```python
logits = h_final @ Wout.T # shape: [vocab_size]
```
---
### Step 5. Softmax & sampling
```python
probs = softmax(logits / temperature)
next_token = sample(probs, strategy="top_p", p=0.9)
```
---
## ✅ Answer to your key question
* The **prompt embeddings are not discarded**; they are the **very first hidden states** fed into the transformer.
* Each transformer layer takes those embeddings, contextualizes them through **attention + MLP**, and outputs refined hidden states.
* At the end, the hidden state of the **last prompt token** is projected to predict the **next token**.
---
Think of it like this:
* **Embeddings** = raw “meaning vectors” of the prompt tokens.
* **Attention layers** = let each token “talk to” the others and blend information.
* **MLPs + normalization** = transform and refine representations.
* **Output head** = turn the final hidden vector into probabilities over the vocabulary.
---
👉 Would you like me to now **write a minimal but runnable PyTorch-like snippet** (say 30–40 lines) that takes a prompt, runs embeddings → 1 transformer block → logits → next token? That way you can see all these steps executed in code.
Perfect 🚀 — let’s build a **minimal PyTorch-like snippet** that shows exactly how embeddings → transformer block → logits → next token works.
This will be **very stripped down**: just 1 block, 1 head of attention, no caching, no batching — but it captures the *essence* of how a real LLM does i
t.-
--## 🔹 Minimal Transformer Next-Token Predictor (Pseudo-PyTorc
h)```pyth
import torch
import torch.nn.functional as F
on# ---- Config --
vocab_size = 10000 # pretend vocabulary size
d_model = 64 # embedding dimension
seq_len = 5 # example prompt length
--# ---- Weights (normally loaded from model file) --
embedding_matrix = torch.randn(vocab_size, d_model)
--Wq = torch.randn(d_model, d_mode
Wk = torch.randn(d_model, d_model)
Wv = torch.randn(d_model, d_model)
Wo = torch.randn(d_model, d_model)
l)W1 = torch.randn(d_model, 4 * d_model) # MLP expansi
W2 = torch.randn(4 * d_model, d_model)
onWout = torch.randn(vocab_size, d_model) # output projecti
on# ---- Example prompt --
tokens = torch.tensor([12, 532, 41, 999, 7]) # token IDs
--# ---- Step 1. Embedding lookup --
h = embedding_matrix[tokens] # shape: [seq_len, d_model]
--# ---- Step 2. Add positional encoding (simplified as identity here) --
# (In a real model, you'd add sinusoidal or rotary position encodings)
# h = h + pos_encoding[:seq_len]
--# ---- Step 3a. Self-attention --
Q = h @ Wq
K = h @ Wk
V = h @ Wv
--# scaled dot-product attenti
attn_scores = (Q @ K.T) / (d_model ** 0.5) # [seq_len, seq_len]
attn_weights = F.softmax(attn_scores, dim=-1) # [seq_len, seq_len]
context = attn_weights @ V # [seq_len, d_model]
on# residual connecti
h = h + context @ Wo
on# ---- Step 3b. Feedforward MLP --
mlp_out = F.gelu(h @ W1) @ W2
h = h + mlp_out
--# ---- Step 4. Take last token's hidden state --
h_last = h[-1] # [d_model]
--# ---- Step 5. Project to logits --
logits = Wout @ h_last # [vocab_size]
--# ---- Step 6. Softmax & sampling --
probs = F.softmax(logits, dim=-1)
--# Greedy decode (pick max pro
next_token = torch.argmax(probs).item()
b)print("Predicted next token ID:", next_toke
```
n)-
--## 🔹 Explanati
on* **`embedding_matrix[tokens]`** → turns prompt tokens into embeddings (your starting point
* **Attention block** (`Q,K,V`) → lets each token mix info with others.
* **Residual + MLP** → refine the representation.
* **Take last token hidden state** → this represents the *entire prompt context*.
* **Project to logits** → scores for every vocab word.
* **Softmax + sample** → pick the next token.
).This is literally what a “real” LLM does, just repeated across **many layers (L \~ 32–100+)** and **many attention heads** (not just 1
).-
--👉 Question for yo
Would you like me to extend this minimal example to show **multi-head attention** (the way real models use multiple Q/K/V projections in parallel), or would you prefer we keep it at this single-head level to stay focused on the overall flow?
So when people use the term LLMs or models, do they refer to the program that runs these steps or the input data containing the weights, or both?
Fantastic question — and it gets at a subtle but important distinction in how people talk about “models” in machine learning, especially LLMs.
Let’s unpack it carefully:
---
## 🔹 Two Sides of a Model
### 1. **The learned parameters (weights)**
* These are the giant arrays of numbers (tensors) produced after training.
* They encode all the statistical knowledge the LLM has learned from data.
* Example: LLaMA-2-7B’s checkpoint file (\~13GB) contains just weights.
* Without these weights, the architecture alone is “an empty brain.”
---
### 2. **The architecture + inference code (the program)**
* This is the *recipe* (transformer architecture) that knows how to use the weights.
* It defines:
* Embedding lookup
* Attention layers
* MLPs
* Output projection
* Sampling loop
* Implemented in frameworks like **PyTorch, TensorFlow, JAX, or C++ inference engines (GGML, vLLM, FasterTransformer, etc.)**.
---
## 🔹 So what does “LLM” mean in practice?
When people say “LLM” or “model,” they could mean either (or both), depending on context:
* **Weights-only sense**:
> “I downloaded the LLaMA-2 model.”
> 👉 Means they got the checkpoint file (the trained parameters).
* **Program-only sense**:
> “I implemented a transformer model from scratch.”
> 👉 Means they wrote the inference/training code (without pretrained weights, it’s untrained).
* **Full system sense (weights + architecture)**:
> “We deployed GPT-4 in production.”
> 👉 Means they have the inference program running with the trained weights — i.e., a *usable LLM*.
---
## 🔹 Analogy
Think of a **video game**:
* The **weights** are like the saved game data file (all the progress, unlocked levels, character stats).
* The **program** is like the game engine (code that knows how to run the rules of the game).
* The **LLM as people actually use it** = the engine + the save file.
Without the save file, the engine runs but is “dumb.” Without the engine, the save file is just numbers.
---
✅ **So in everyday usage, "LLM" usually means the combination of both architecture + weights.**
But if someone says “checkpoint” or “model file,” they’re talking specifically about the weights.
---
Would you like me to also explain how **fine-tuning** and **adapters (LoRA, PEFT)** fit into this “weights vs. architecture” distinction?