# 04 — Training Explained: LoRA, SFT & Hyperparameters

## 🎓 Why This Chapter Matters

This is where we answer: *"How do we actually teach the model to use tools?"*

By the end of this chapter, you'll understand:
- What LoRA is and why it's magical for budget training
- What SFT does step-by-step
- What each hyperparameter controls
- How to read training logs and know if it's working

---

## 🧠 Concept 1: Why Can't We Just Use the Base Model?

**Qwen3-1.7B** is already a great model. It can chat, answer questions, write code. 
But it doesn't know how to use **tools** in a structured way.

### What Base Models Know

Base model Qwen3-1.7B:
- ✅ Understands English, can chat
- ✅ Can write Python code
- ✅ Can answer questions about the world
- ❌ Doesn't know about your specific tool schemas
- ❌ Doesn't output tool calls in correct JSON-RPC format
- ❌ Doesn't plan multi-step tool chains
- ❌ Doesn't ask clarifying questions
- ❌ Doesn't refuse dangerous requests

### What Fine-Tuning Adds

After training on 15,694 tool-calling examples:
- ✅ Understands tool schemas ("Here's what this tool needs")
- ✅ Generates correct JSON-RPC tool calls
- ✅ Plans multi-step sequences ("First A, then B using A's result")
- ✅ Asks when info is missing
- ✅ Refuses harmful operations

**Think of it like this:**
- Base model = A smart person who knows how to talk but doesn't know your tools
- Fine-tuned model = The same person after reading 15,000 instruction manuals

---

## 🧠 Concept 2: LoRA — The Magic of Cheap Fine-Tuning

### The Problem: Full Fine-Tuning Is Expensive

To fine-tune all 2 billion parameters of Qwen3-1.7B:

| Component | Size | Why |
|-----------|------|-----|
| Model weights | 4 GB | 2B params × 2 bytes (fp16) |
| Gradients | 4 GB | Need gradients for every parameter |
| Optimizer states | 16 GB | Adam optimizer keeps 2 copies per param |
| **Total** | **24 GB** | **Doesn't fit on T4 (16GB)!** |

You'd need an **A100 GPU** (80GB) which costs **$3-4/hour**.

### The Solution: LoRA (Low-Rank Adaptation)

Instead of updating ALL parameters, we add tiny matrices to each layer:

```
Original Layer (Frozen — Never Changes)
┌─────────────────────────────┐
│  W (2048 × 2048) = 4.2M    │  ← 4 MILLION parameters
│  parameters                 │     These stay FROZEN
└─────────────────────────────┘
         │
         │ input x
         ▼
    y = W × x
         │
         ▼
    output

LoRA Adapters (Trainable — These Learn)
┌─────────────────────┐    ┌─────────────────────┐
│  A (2048 × 16)      │───▶│  B (16 × 2048)      │
│  = 32K params       │    │  = 32K params       │
│  (initialized       │    │  (initialized to 0) │
│   randomly)         │    │                     │
└─────────────────────┘    └─────────────────────┘
         │                         │
         ▼                         ▼
    h = A × x                  y' = B × h
                                   = B × (A × x)

Final Output:
y = W × x + B × A × x
    ↑           ↑
  frozen     trained
```

**Math:**
- Original: W is 2048×2048 = 4,194,304 parameters
- LoRA: A is 2048×16 = 32,768, B is 16×2048 = 32,768
- Total LoRA: 65,536 parameters (1.6% of original!)
- Memory for training: ~5GB total (fits on T4!)

### Why This Works

The idea: neural network weights often have **low-rank structure**.
Even though W is 2048×2048, the "important directions" of change can be 
captured by much smaller matrices.

Think of it like adjusting a steering wheel:
- Full fine-tuning = Rebuilding the entire car to turn better
- LoRA = Adding a small steering adjustment module (tiny, cheap, effective)

### Our LoRA Configuration

```python
from peft import LoraConfig

peft_config = LoraConfig(
    r=16,                    # Rank: "resolution" of the adapter
    lora_alpha=32,          # Scaling: how strongly LoRA affects output
    target_modules="all-linear",  # Apply to ALL linear layers
    lora_dropout=0.05,      # Dropout: 5% random zeroing (prevents overfitting)
    bias="none",             # Don't train bias terms (saves memory)
    task_type="CAUSAL_LM",   # This is a language model
)
```

**r=16:** Think of this as the "resolution." Higher = more detail but more memory. 
For ~16K training examples, r=16 is the sweet spot. (TinyAgent used r=64 for 80K examples)

**lora_alpha=32:** Scaling factor. Rule of thumb: 2× rank. Controls how much 
the LoRA output contributes to the final result.

**target_modules="all-linear":** The "LoRA Without Regret" paper proved that 
applying LoRA to ALL linear layers (not just attention projections) matches 
full fine-tuning quality. This is our secret sauce.

---

## 🧠 Concept 3: SFT — Supervised Fine-Tuning

### What Is SFT?

SFT = **teaching by example.** We show the model:

```
Input:  "Find all Python files"
Output: {"tool": "shell_exec", "arguments": {"command": "find . -name '*.py'"}}

Input:  "Delete all files"
Output: "I cannot help with that. Deleting all files is dangerous..."

Input:  "Clone the repo and find TODOs"
Output: {"tool": "shell_exec", "arguments": {"command": "git clone https://... && grep -r 'TODO' ."}}
```

The model learns to predict the output given the input.

### How SFT Works Step by Step

#### Step 1: Tokenize

Convert text → numbers:

```
"Find Python files"
↓ Tokenizer
[4921, 12729, 4367, 8921, 1023]
```

Each number is an index in a vocabulary of ~100,000 tokens.

#### Step 2: Forward Pass

The model processes the tokenized input and predicts the next token at EACH position:

```
Input tokens:  [4921, 12729, 4367, 8921]
                                    │
Predictions:   [?,    ?,    ?,    ?  ] ──▶ next token should be 1023
```

The model outputs a probability distribution over all ~100,000 possible tokens.

#### Step 3: Compute Loss (Cross-Entropy)

```
Predicted probabilities:  [0.01, 0.03, 0.001, ..., 0.45, ..., 0.002]
                              ↑                    ↑
                           wrong                 correct (1023)

Loss = -log(probability_of_correct_token)
     = -log(0.45)
     = 0.80
```

**Lower loss = better prediction.**

If the model predicted token 1023 with probability 0.45, loss is 0.80.
If it predicted with probability 0.99, loss is 0.01 (much better!).

#### Step 4: Backward Pass (Backpropagation)

Compute gradients: which direction to adjust weights to reduce loss.

```
For each LoRA parameter:
  gradient = how much changing this parameter would change the loss
```

This is done automatically by PyTorch's autograd.

#### Step 5: Update Weights (Adam Optimizer)

```
new_weight = old_weight - learning_rate × gradient
```

Adam is smarter — it uses momentum and adaptive learning rates per parameter.

#### Step 6: Repeat

Do this for ALL examples in the dataset, then repeat for 3 epochs.

---

## 🧠 Concept 4: Hyperparameters — The Recipe

Think of training as cooking. Hyperparameters are your recipe.

### Learning Rate: 2e-4

**What it controls:** How big each weight update step is.

```
Learning Rate
   │
1e-2│  ╳─── Too high: loss oscillates, model never settles
   │   │
2e-4│    ●── Sweet spot for LoRA (10× higher than full fine-tuning)
   │      ╲
1e-5│       ╲── Too low: barely moves, takes forever
   │         ╲
   └─────────────────
        Steps
```

**Why 2e-4 for LoRA?**
- Full fine-tuning typically uses 2e-5
- LoRA has 100× fewer parameters
- Each parameter update needs 10× more impact
- So: 2e-5 × 10 = **2e-4**

### Batch Size: 4 × 4 = 16 Effective

**What it controls:** How many examples the model sees before updating weights.

**Without Gradient Accumulation:**
  Process 4 examples → Compute gradients → Update weights → Next 4

**With Gradient Accumulation (what we do):**
  Process 4 examples → Compute gradients → SAVE gradients (don't update)
  Process 4 examples → Compute gradients → ADD to saved gradients
  Process 4 examples → Compute gradients → ADD to saved gradients
  Process 4 examples → Compute gradients → ADD to saved gradients
  Now update weights (accumulated from 4 × 4 = 16 examples)

**Why gradient accumulation?**
- GPU can only fit 4 examples at once (memory limit)
- But effective batch of 16 gives more stable gradients
- It's a memory-saving trick

**Trade-off:** Slower (4× more forward passes per update) but better quality.

### Epochs: 3

**What it controls:** How many times the model sees the entire dataset.

**Epoch 1:** Sees all 15,694 examples → learns basic patterns
**Epoch 2:** Sees all again → refines understanding
**Epoch 3:** Sees all again → final tuning

**Why 3?**
- 1 epoch: Underfitting (hasn't seen enough)
- 3 epochs: Sweet spot (learns patterns without memorizing)
- 10 epochs: Overfitting (memorizes training data, fails on new data)

### Warmup Ratio: 0.1 (10%)

**What it controls:** For the first 10% of training, learning rate starts at 0 
and gradually ramps up to the full rate.

**Why warmup?**
- At the start, model knows NOTHING about tool-calling
- Large updates could push weights in random bad directions
- Warmup lets model "get its bearings" first

### Cosine LR Schedule

After warmup, learning rate follows a cosine curve:
```
Learning Rate
   │
2e-4│    ╱──╲
   │   ╱    ╲
   │  ╱      ╲
   │ ╱        ╲
  0 │╱          ╲────
   └─────────────────
     warmup    end
```

**Why cosine?**
- High in the middle: aggressive learning when model has basic understanding
- Low at the end: fine-tuning details, settling into optimal weights
- Prevents overshooting at the end of training

### Max Sequence Length: 2048 tokens

**What it controls:** Maximum number of tokens per training example.

```
Example conversation:
  System prompt:  ~500 tokens
  User message:   ~100 tokens
  Assistant reply: ~300 tokens
  Total:          ~900 tokens  ← Fits in 2048 ✓
```

**Why 2048?**
- Covers all our examples (most are under 1000 tokens)
- Fits in T4 memory (longer sequences = more memory)
- Standard for instruction-tuned models

### Gradient Checkpointing: ON

**What it does:** Saves memory by recomputing some values during backward pass.

```
Without checkpointing:
  Forward pass: Store all intermediate activations → Backward pass uses them
  Memory: 8 GB

With checkpointing:
  Forward pass: Store only SOME activations
  Backward pass: Recompute missing ones on-the-fly
  Memory: 5 GB (saves ~40%)
```

**Trade-off:** Slower (needs extra computation) but fits on T4.

---

## 📊 Reading Training Logs

### What You'll See

```
Step 10/245: loss=2.847, learning_rate=2.0e-05
Step 20/245: loss=2.654, learning_rate=4.0e-05
...
Step 100/245: loss=1.234, learning_rate=1.8e-04
...
Step 245/245: loss=0.876, learning_rate=1.2e-05
```

### How to Interpret

| Observation | Meaning |
|-------------|---------|
| Loss going DOWN | ✅ Model is learning |
| Loss going UP after going down | ⚠️ Overfitting — stop early |
| Loss stuck at ~3.0 | ❌ Not learning — check data/format |
| Loss drops fast then plateaus | ✅ Normal — model learned basics |
| Eval loss ≈ Train loss | ✅ Good generalization |
| Eval loss >> Train loss | ❌ Overfitting — model memorized training data |

### Target Numbers (for reference)

- **Initial loss:** ~2.5-3.5 (random guessing among many tokens)
- **Final loss:** ~0.8-1.2 (decent learning on 16K examples)
- **Eval loss:** Should be within 0.1-0.3 of train loss

---

## 🧮 Training Math

### How Long Does It Take?

```
Dataset: 15,694 examples
Batch size: 4 (per device)
Gradient accumulation: 4 steps
Effective batch: 4 × 4 = 16

Steps per epoch: 15,694 ÷ 16 = ~980 steps
Total steps (3 epochs): 980 × 3 = ~2,940 steps

Time per step (T4): ~2-3 seconds
Total time: 2,940 × 2.5s = ~7,350s = ~2 hours
```

### Cost Calculation

```
T4 GPU on HF Jobs: ~$0.60/hour
Training time: ~2 hours
Total cost: $0.60 × 2 = $1.20
```

Well under $10! ✅

---

## 🎓 Summary: Key Training Concepts

| Concept | What It Is | Why It Matters |
|---------|-----------|----------------|
| **LoRA** | Tiny trainable matrices added to frozen layers | Makes training affordable (5GB vs 24GB) |
| **SFT** | Teaching model with input→output examples | Gives model tool-calling knowledge |
| **Loss** | Measure of how wrong predictions are | Lower = better learning |
| **Learning Rate** | Size of weight updates | Too high = chaos, too low = slow |
| **Batch Size** | Examples per weight update | More = stable gradients, needs more memory |
| **Gradient Accumulation** | Fake larger batch sizes | Memory-saving trick |
| **Epochs** | Times model sees full dataset | 3 is sweet spot |
| **Warmup** | Gradual LR increase at start | Prevents early instability |
| **Cosine Schedule** | LR high→low curve | Aggressive middle, gentle end |
| **Gradient Checkpointing** | Recompute activations | Saves ~40% memory |

---

## 🔜 Next Step

Read `05-dataset.md` to understand our training data — what we have, what's missing, and how to make it better.