[Doc] Reorganize intelligent routing tutorials into focused guides (vllm-project#636)

* [Doc] Reorganize intelligent routing tutorials into focused guides

- Remove overview.md and reasoning.md
- Create 4 new focused routing guides:
  - domain-routing.md: Fine-tuned classification (efficient, specialized)
  - embedding-routing.md: Semantic similarity routing (scalable, fast)
  - keyword-routing.md: Keyword-based routing (transparent, compliant)
  - mcp-routing.md: External service routing (extensible, private)
- Update lora-routing.md to clarify it combines other routing methods
- Update sidebar navigation to reflect new structure
- Add comprehensive use cases and problem-solution context to each guide
- Align all guides with consistent structure and friendly tone

Signed-off-by: bitliu <[email protected]>

* [Doc] Fix MDX compilation and markdown lint errors

- Escape < characters in numeric comparisons (&lt;1%, &lt;1ms, etc.)
- Add blank lines around fenced code blocks
- Remove multiple consecutive blank lines at end of files
- Fix list formatting around code blocks

Signed-off-by: bitliu <[email protected]>

---------

Signed-off-by: bitliu <[email protected]>

Author: Xunzhuo

website/docs/tutorials/intelligent-route/domain-routing.md

@@ -0,0 +1,228 @@
+# Domain Based Routing
+
+This guide shows you how to use fine-tuned classification models for intelligent routing based on academic and professional domains. Domain routing uses specialized models (ModernBERT, Qwen3-Embedding, EmbeddingGemma) with LoRA adapters to classify queries into categories like math, physics, law, business, and more.
+
+## Key Advantages
+
+- **Efficient**: Fine-tuned models with LoRA adapters provide fast inference (5-20ms) with high accuracy
+- **Specialized**: Multiple model options (ModernBERT for English, Qwen3 for multilingual/long-context, Gemma for small footprint)
+- **Multi-task**: LoRA enables running multiple classification tasks (domain + PII + jailbreak) with shared base model
+- **Cost-effective**: Lower latency than LLM-based classification, no API costs
+
+## What Problem Does It Solve?
+
+Generic classification approaches struggle with domain-specific terminology and nuanced differences between academic/professional fields. Domain routing provides:
+
+- **Accurate domain detection**: Fine-tuned models distinguish between math, physics, chemistry, law, business, etc.
+- **Multi-task efficiency**: LoRA adapters enable simultaneous domain classification, PII detection, and jailbreak detection with one base model pass
+- **Long-context support**: Qwen3-Embedding handles up to 32K tokens (vs ModernBERT's 8K limit)
+- **Multilingual routing**: Qwen3 trained on 100+ languages, ModernBERT optimized for English
+- **Resource optimization**: Expensive reasoning only enabled for domains that benefit (math, physics, chemistry)
+
+## When to Use
+
+- **Educational platforms** with diverse subject areas (STEM, humanities, social sciences)
+- **Professional services** requiring domain expertise (legal, medical, financial)
+- **Enterprise knowledge bases** spanning multiple departments
+- **Research assistance** tools needing academic domain awareness
+- **Multi-domain products** where classification accuracy is critical
+
+## Configuration
+
+Configure the domain classifier in your `config.yaml`:
+
+```yaml
+classifier:
+  category_model:
+    model_id: "models/category_classifier_modernbert-base_model"
+    use_modernbert: true
+    threshold: 0.6
+    use_cpu: true
+    category_mapping_path: "models/category_classifier_modernbert-base_model/category_mapping.json"
+  
+  pii_model:
+    model_id: "models/pii_classifier_modernbert-base_presidio_token_model"
+    use_modernbert: true
+    threshold: 0.7
+    use_cpu: true
+    pii_mapping_path: "models/pii_classifier_modernbert-base_presidio_token_model/pii_type_mapping.json"
+
+categories:
+  - name: math
+    system_prompt: "You are a mathematics expert. Provide step-by-step solutions."
+    model_scores:
+      - model: qwen3
+        score: 1.0
+        use_reasoning: true
+  
+  - name: physics
+    system_prompt: "You are a physics expert with deep understanding of physical laws."
+    model_scores:
+      - model: qwen3
+        score: 0.7
+        use_reasoning: true
+  
+  - name: computer science
+    system_prompt: "You are a computer science expert with knowledge of algorithms and data structures."
+    model_scores:
+      - model: qwen3
+        score: 0.6
+        use_reasoning: false
+  
+  - name: business
+    system_prompt: "You are a senior business consultant and strategic advisor."
+    model_scores:
+      - model: qwen3
+        score: 0.7
+        use_reasoning: false
+  
+  - name: health
+    system_prompt: "You are a health and medical information expert."
+    semantic_cache_enabled: true
+    semantic_cache_similarity_threshold: 0.95
+    model_scores:
+      - model: qwen3
+        score: 0.5
+        use_reasoning: false
+  
+  - name: law
+    system_prompt: "You are a knowledgeable legal expert."
+    model_scores:
+      - model: qwen3
+        score: 0.4
+        use_reasoning: false
+
+default_model: qwen3
+```
+
+## Supported Domains
+
+Academic: math, physics, chemistry, biology, computer science, engineering
+
+Professional: business, law, economics, health, psychology
+
+General: philosophy, history, other
+
+## Features
+
+- **PII Detection**: Automatically detects and handles sensitive information
+- **Semantic Caching**: Cache similar queries for faster responses
+- **Reasoning Control**: Enable/disable reasoning per domain
+- **Custom Thresholds**: Adjust cache sensitivity per category
+
+## Example Requests
+
+```bash
+# Math query (reasoning enabled)
+curl -X POST http://localhost:8801/v1/chat/completions \
+  -H "Content-Type: application/json" \
+  -d '{
+    "model": "MoM",
+    "messages": [{"role": "user", "content": "Solve: x^2 + 5x + 6 = 0"}]
+  }'
+
+# Business query (reasoning disabled)
+curl -X POST http://localhost:8801/v1/chat/completions \
+  -H "Content-Type: application/json" \
+  -d '{
+    "model": "MoM",
+    "messages": [{"role": "user", "content": "What is a SWOT analysis?"}]
+  }'
+
+# Health query (high cache threshold)
+curl -X POST http://localhost:8801/v1/chat/completions \
+  -H "Content-Type: application/json" \
+  -d '{
+    "model": "MoM",
+    "messages": [{"role": "user", "content": "What are symptoms of diabetes?"}]
+  }'
+```
+
+## Real-World Use Cases
+
+### 1. Multi-Task Classification with LoRA (Efficient)
+**Problem**: Need domain classification + PII detection + jailbreak detection on every request
+**Solution**: LoRA adapters run all 3 tasks with one base model pass instead of 3 separate models
+**Impact**: 3x faster than running 3 full models, <1% parameter overhead per task
+
+### 2. Long Document Analysis (Specialized - Qwen3)
+**Problem**: Research papers and legal documents exceed 8K token limit of ModernBERT
+**Solution**: Qwen3-Embedding supports up to 32K tokens without truncation
+**Impact**: Accurate classification on full documents, no information loss from truncation
+
+### 3. Multilingual Education Platform (Specialized - Qwen3)
+**Problem**: Students ask questions in 100+ languages, ModernBERT limited to English
+**Solution**: Qwen3-Embedding trained on 100+ languages handles multilingual routing
+**Impact**: Single model serves global users, consistent quality across languages
+
+### 4. Edge Deployment (Specialized - Gemma)
+**Problem**: Mobile/IoT devices can't run large classification models
+**Solution**: EmbeddingGemma-300M with Matryoshka embeddings (128-768 dims)
+**Impact**: 5x smaller model, runs on edge devices with <100MB memory
+
+### 5. STEM Tutoring Platform (Efficient Reasoning Control)
+**Problem**: Math/physics need reasoning, but history/literature don't
+**Solution**: Domain classifier routes STEM → reasoning models, humanities → fast models
+**Impact**: 2x better STEM accuracy, 60% cost savings on non-STEM queries
+
+## Domain-Specific Optimizations
+
+### STEM Domains (Reasoning Enabled)
+
+```yaml
+- name: math
+  use_reasoning: true  # Step-by-step solutions
+  score: 1.0           # Highest priority
+- name: physics
+  use_reasoning: true  # Derivations and proofs
+  score: 0.7
+- name: chemistry
+  use_reasoning: true  # Reaction mechanisms
+  score: 0.6
+```
+
+### Professional Domains (PII + Caching)
+
+```yaml
+- name: health
+  semantic_cache_enabled: true
+  semantic_cache_similarity_threshold: 0.95  # Very strict
+  pii_detection_enabled: true
+- name: law
+  score: 0.4  # Conservative routing
+  pii_detection_enabled: true
+```
+
+### General Domains (Fast + Cached)
+
+```yaml
+- name: business
+  use_reasoning: false  # Fast responses
+  score: 0.7
+- name: other
+  semantic_cache_similarity_threshold: 0.75  # Relaxed
+  score: 0.7
+```
+
+## Performance Characteristics
+
+| Domain | Reasoning | Cache Threshold | Avg Latency | Use Case |
+|--------|-----------|-----------------|-------------|----------|
+| Math | ✅ | 0.85 | 2-5s | Step-by-step solutions |
+| Physics | ✅ | 0.85 | 2-5s | Derivations |
+| Chemistry | ✅ | 0.85 | 2-5s | Mechanisms |
+| Health | ❌ | 0.95 | 500ms | Safety-critical |
+| Law | ❌ | 0.85 | 500ms | Compliance |
+| Business | ❌ | 0.80 | 300ms | Fast insights |
+| Other | ❌ | 0.75 | 200ms | General queries |
+
+## Cost Optimization Strategy
+
+1. **Reasoning Budget**: Enable only for STEM (30% of queries) → 60% cost reduction
+2. **Caching Strategy**: High threshold for sensitive domains → 70% hit rate
+3. **Model Selection**: Lower scores for low-value domains → cheaper models
+4. **PII Detection**: Only for health/law → reduced processing overhead
+
+## Reference
+
+See [bert_classification.yaml](https://github.com/vllm-project/semantic-router/blob/main/config/intelligent-routing/in-tree/bert_classification.yaml) for complete configuration.