feat(ai-memory-engine): Add 8 vector storage backends + hyperbolic geometry

Storage Backends:
- ApifyBinary: 4x smaller binary Float32Array storage
- PostgreSQL/Supabase/Neon: pgvector with IVFFlat indexing
- Qdrant: High-throughput cloud vector DB with filtering
- Pinecone: Serverless managed infrastructure
- Weaviate: GraphQL-based hybrid search
- LanceDB: Local embedded vector database
- Hyperbolic: Poincaré ball model for hierarchical data

Hyperbolic Geometry:
- Poincaré ball projection and distance
- Möbius addition for vector operations
- Exponential/logarithmic maps (tangent ↔ hyperbolic)
- Fréchet mean (hyperbolic centroid)
- Hyperbolic k-means clustering
- Batch distance computation (SIMD-friendly)
- Parallel transport and geodesic interpolation

Input Schema:
- storageBackend selector (8 options)
- Connection strings for Postgres/Qdrant/Pinecone/Weaviate
- Curvature parameter for hyperbolic embeddings
- Hyperbolic clustering toggle

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

examples/apify/ai-memory-engine/.actor/input_schema.json

@@ -762,6 +762,103 @@
       "description": "Set a seed for reproducible results across runs",
       "editor": "textfield",
       "example": "42"
+    },
+
+    "storageBackend": {
+      "title": "Storage Backend",
+      "type": "string",
+      "description": "Choose how and where to persist your memory embeddings. Different backends offer different trade-offs for scalability, persistence, and features.",
+      "editor": "select",
+      "default": "apify-binary",
+      "sectionCaption": "Vector Storage & Persistence",
+      "sectionDescription": "Configure advanced vector storage options. Choose from 8 backends including cloud vector databases, hyperbolic embeddings, and local storage.",
+      "enum": [
+        "apify-binary",
+        "postgres",
+        "supabase",
+        "neon",
+        "qdrant",
+        "pinecone",
+        "weaviate",
+        "lancedb",
+        "hyperbolic"
+      ],
+      "enumTitles": [
+        "Apify Binary - Default, 4x smaller than JSON (recommended)",
+        "PostgreSQL - Self-hosted with pgvector extension",
+        "Supabase - Managed PostgreSQL with pgvector",
+        "Neon - Serverless PostgreSQL with pgvector",
+        "Qdrant - High-performance vector database",
+        "Pinecone - Serverless managed vector DB",
+        "Weaviate - GraphQL-based vector search",
+        "LanceDB - Local embedded vector DB",
+        "Hyperbolic - Poincaré ball for hierarchical data"
+      ]
+    },
+    "postgresUrl": {
+      "title": "PostgreSQL Connection URL",
+      "type": "string",
+      "description": "Connection string for PostgreSQL/Supabase/Neon (e.g., postgres://user:pass@host:5432/db)",
+      "editor": "textfield",
+      "isSecret": true,
+      "example": "postgres://user:password@db.supabase.co:5432/postgres"
+    },
+    "qdrantUrl": {
+      "title": "Qdrant URL",
+      "type": "string",
+      "description": "Qdrant server URL (cloud or self-hosted)",
+      "editor": "textfield",
+      "default": "http://localhost:6333",
+      "example": "https://your-cluster.qdrant.io"
+    },
+    "qdrantApiKey": {
+      "title": "Qdrant API Key",
+      "type": "string",
+      "description": "API key for Qdrant Cloud authentication",
+      "editor": "textfield",
+      "isSecret": true
+    },
+    "pineconeApiKey": {
+      "title": "Pinecone API Key",
+      "type": "string",
+      "description": "API key for Pinecone serverless",
+      "editor": "textfield",
+      "isSecret": true
+    },
+    "pineconeIndex": {
+      "title": "Pinecone Index Name",
+      "type": "string",
+      "description": "Name of your Pinecone index",
+      "editor": "textfield",
+      "default": "ai-memories"
+    },
+    "weaviateHost": {
+      "title": "Weaviate Host",
+      "type": "string",
+      "description": "Weaviate instance host (without https://)",
+      "editor": "textfield",
+      "example": "your-instance.weaviate.network"
+    },
+    "weaviateApiKey": {
+      "title": "Weaviate API Key",
+      "type": "string",
+      "description": "API key for Weaviate Cloud authentication",
+      "editor": "textfield",
+      "isSecret": true
+    },
+    "curvature": {
+      "title": "Hyperbolic Curvature",
+      "type": "number",
+      "description": "Curvature parameter for Poincaré ball model (higher = more curved, better for deep hierarchies)",
+      "default": 1.0,
+      "minimum": 0.1,
+      "maximum": 10.0
+    },
+    "hyperbolicClustering": {
+      "title": "Enable Hyperbolic Clustering",
+      "type": "boolean",
+      "description": "Use hyperbolic k-means for hierarchical data clustering (better for tree-like relationships)",
+      "default": false
     }
   },
   "required": ["action"]

examples/apify/ai-memory-engine/README.md

@@ -2,7 +2,7 @@
 
 **Give your AI persistent memory.** Store conversations, search semantically, build knowledge graphs, and watch your AI get smarter with every interaction. The ultimate memory solution for AI agents, chatbots, and intelligent automation.
 
-🧠 **Self-Learning** · 🔍 **Semantic Search** · 🕸️ **Knowledge Graphs** · ⚡ **Sub-millisecond** · 🔗 **LLM Agnostic** · 🔌 **One-Click Integrations**
+🧠 **Self-Learning** · 🔍 **Semantic Search** · 🕸️ **Knowledge Graphs** · ⚡ **Sub-millisecond** · 🔗 **LLM Agnostic** · 🔌 **One-Click Integrations** · 📊 **8 Vector DB Backends** · 🌀 **Hyperbolic Embeddings**
 
 [![Apify Actor](https://img.shields.io/badge/Apify-Actor-blue)](https://apify.com/ruv/ai-memory-engine)
 [![License: MIT](https://img.shields.io/badge/License-MIT-green.svg)](https://opensource.org/licenses/MIT)
@@ -21,9 +21,10 @@
 |---------|------------------|----------------------|
 | **Setup Time** | 1 minute | Hours to days |
 | **Cost** | Pay per use ($0.001/operation) | $50-500/month subscriptions |
-| **Memory Persistence** | Built-in cross-session | Requires external DB |
+| **Memory Persistence** | 8 storage backends (Supabase, Qdrant, Pinecone, etc.) | Single DB only |
 | **Self-Learning** | SONA neural architecture | Manual tuning |
 | **Apify Integration** | One-click from any actor | Custom code required |
+| **Hyperbolic Geometry** | Poincaré ball for hierarchical data | Euclidean only |
 | **Export Options** | 6 vector DB formats | Limited |
 
 ### Key Capabilities
@@ -35,6 +36,15 @@
 - **Integration**: integrate_actor, integrate_synthetic, integrate_scraper, template
 - **Utilities**: natural language commands, cluster, export_vectordb, feedback
 
+**8 Storage Backends**:
+- **Apify Binary** - Default, 4x smaller than JSON with HNSW re-indexing
+- **PostgreSQL/Supabase/Neon** - pgvector for production deployments
+- **Qdrant** - High-throughput cloud vector DB
+- **Pinecone** - Serverless managed infrastructure
+- **Weaviate** - GraphQL-based hybrid search
+- **LanceDB** - Local embedded database
+- **Hyperbolic** - Poincaré ball for hierarchical data
+
 **One-Click Actor Integration** with 10+ popular scrapers:
 - Google Maps, Instagram, TikTok, YouTube, Twitter, Amazon, TripAdvisor, LinkedIn, and more
 - Automatically memorize any scraper results with semantic search
@@ -503,6 +513,134 @@ Each template includes:
 
 ---
 
+## Vector Storage Backends
+
+**8 storage backends** for different scalability and persistence needs:
+
+```json
+{
+  "action": "store",
+  "memories": [...],
+  "storageBackend": "supabase",
+  "postgresUrl": "postgres://user:pass@db.supabase.co:5432/postgres"
+}
+```
+
+### Available Backends
+
+| Backend | Best For | Features |
+|---------|----------|----------|
+| `apify-binary` | Default, simple persistence | 4x smaller than JSON, automatic HNSW re-indexing |
+| `postgres` / `supabase` / `neon` | Production deployments | pgvector extension, SQL queries, ACID compliance |
+| `qdrant` | High-throughput search | Built-in filtering, clustering, 100M+ vectors |
+| `pinecone` | Serverless, zero ops | Managed infrastructure, auto-scaling |
+| `weaviate` | GraphQL queries | Hybrid search, graph traversal |
+| `lancedb` | Local/embedded | No server needed, ML-pipeline friendly |
+| `hyperbolic` | Hierarchical data | Poincaré ball embeddings, tree structures |
+
+### PostgreSQL / Supabase / Neon
+
+Use pgvector for production-grade vector search:
+
+```json
+{
+  "action": "store",
+  "memories": [{"text": "Product X specs..."}],
+  "storageBackend": "supabase",
+  "postgresUrl": "postgres://user:pass@db.supabase.co:5432/postgres",
+  "sessionId": "my-app"
+}
+```
+
+Features:
+- IVFFlat and HNSW indexing
+- SQL filtering with vector search
+- Automatic schema creation
+- Incremental updates (upsert)
+
+### Qdrant Cloud
+
+High-performance vector search at scale:
+
+```json
+{
+  "action": "store",
+  "storageBackend": "qdrant",
+  "qdrantUrl": "https://your-cluster.qdrant.io",
+  "qdrantApiKey": "your-api-key"
+}
+```
+
+### Pinecone Serverless
+
+Zero-ops managed vector database:
+
+```json
+{
+  "action": "store",
+  "storageBackend": "pinecone",
+  "pineconeApiKey": "your-api-key",
+  "pineconeIndex": "my-memories"
+}
+```
+
+---
+
+## Hyperbolic Embeddings
+
+**NEW: Poincaré ball embeddings** for hierarchical and tree-structured data:
+
+```json
+{
+  "action": "store",
+  "memories": [
+    {"text": "CEO leads the company", "metadata": {"level": 1}},
+    {"text": "VP Engineering reports to CEO", "metadata": {"level": 2}},
+    {"text": "Senior Engineer reports to VP", "metadata": {"level": 3}}
+  ],
+  "storageBackend": "hyperbolic",
+  "curvature": 1.0
+}
+```
+
+### Why Hyperbolic?
+
+Traditional Euclidean embeddings struggle with:
+- **Taxonomies** (products → categories → subcategories)
+- **Organization charts** (CEO → VPs → Managers → Staff)
+- **Knowledge graphs** (concepts → related concepts)
+- **File systems** (directories → subdirectories → files)
+
+Hyperbolic space naturally represents hierarchical relationships because:
+- Distance from origin = depth in hierarchy
+- Points near boundary = leaf nodes
+- Points near center = root nodes
+
+### Hyperbolic Features
+
+| Feature | Description |
+|---------|-------------|
+| `poincareDistance` | True geodesic distance in curved space |
+| `mobiusAdd` | Addition operation preserving geometry |
+| `frechetMean` | Hyperbolic centroid computation |
+| `hyperbolicKMeans` | Clustering respecting hierarchy |
+| `expMap` / `logMap` | Tangent space operations |
+
+### Hyperbolic Clustering
+
+Group hierarchical data naturally:
+
+```json
+{
+  "action": "cluster",
+  "numClusters": 5,
+  "hyperbolicClustering": true,
+  "curvature": 1.0
+}
+```
+
+---
+
 ## Vector DB Export
 
 **Export to any vector database:**