AKA: Claude's word- and code-salad after I gave it some ideas about geometric representations for LLM tokens and corresponding real-world phenomena
A Novel AI Architecture for Understanding and Generating Software from First Principles
Copyright © 2025 Arkadiy Agyeyev. Contact: [email protected]
It's unlikely I'll return to this project, if you somehow find it useful in any way, feel free to do whatever you want with it. Do let me know please.
- Vision & Philosophy
- Core Concepts
- Multi-Space Architecture
- Architecture Overview
- Key Components
- Installation & Setup
- Usage Guide
- API Reference
- Technical Deep Dive
- Future Directions
- Acknowledgments
RegionAI represents a fundamental departure from traditional AI approaches to code generation and understanding. Rather than treating programming as a text generation problem, RegionAI approaches it as a discovery problem - learning the underlying computational transformations that constitute all software.
All computation can be understood as transformations in abstract spaces. RegionAI discovers these transformations from examples, composes them into complex algorithms, and grounds them in executable meaning. This creates an AI that doesn't just generate code - it understands computation at a fundamental level.
- Bottom-Up Discovery: Start with primitive operations and discover complexity through composition
- Grounded Understanding: Every concept has executable meaning - no mere symbol manipulation
- Region-Based Representation: Concepts are regions in space, not points, naturally handling uncertainty
- Unified Framework: The same system handles deterministic logic, probabilistic reasoning, and fuzzy concepts
- Learning Through Failure: Failed attempts guide the discovery of new concepts and strategies
Traditional AI systems represent concepts as points in vector space. RegionAI represents them as regions - geometric volumes that can overlap, contain each other, and have fuzzy boundaries. This provides several advantages:
- Hierarchical Relationships: "Dog" is a sub-region of "Animal"
- Graded Membership: Objects can partially belong to concepts
- Natural Uncertainty: Region size represents confidence
- Compositional Semantics: Complex concepts are intersections/unions of simple ones
RegionAI learns by discovering transformations that map inputs to outputs:
# Example: Discovering the "double" transformation
problems = [
Problem(input=2, output=4),
Problem(input=3, output=6),
Problem(input=5, output=10)
]
# RegionAI discovers: λx. x * 2These transformations are composed to form complex algorithms:
# Discovering filter-map-sum pattern
problems = [
Problem(input=[1,2,3,4], output=6), # sum of evens
Problem(input=[2,4,6,8], output=20) # all even, sum all
]
# RegionAI discovers: λxs. sum(filter(even?, xs))RegionAI includes a complete abstract interpretation framework for program analysis:
- Sign Domain: Track whether values are positive, negative, or zero
- Nullability Domain: Detect potential null pointer exceptions
- Range Domain: Verify array bounds and prevent overflows
- Fixpoint Analysis: Handle loops soundly with widening operators
The symbolic language engine bridges natural language to computational concepts:
- Lazy Evaluation: Constraints remain symbolic until resolution is needed
- Beam Search: Manage ambiguity by keeping top-k interpretations
- Contextual Resolution: Pronouns and references resolved using context
- Learning: Successful resolutions strengthen word-concept mappings
RegionAI implements a clean three-tier architecture that separates universal reasoning capabilities from domain-specific knowledge and situational contexts:
The immutable core that provides universal reasoning capabilities:
- Knowledge Infrastructure: World knowledge graphs, reasoning knowledge graphs, storage/query services
- Discovery Mechanisms: Concept discovery, knowledge linking, action discovery, Bayesian updating
- Region Algebra: N-dimensional regions with containment, overlap, join/meet operations, fuzzy boundaries
- Six-Brain Cognitive Architecture: Bayesian, Logic, Utility, Observer, Temporal, Sensorimotor brains
- Reasoning Engine: Planning, heuristic registry, utility updating, proof systems
- Abstract Interpretation: Sign analysis, nullability domains, range analysis, fixpoint computation
- Configuration System: Comprehensive analysis profiles (FAST, BALANCED, PRECISE, DEBUG)
- Safety Mechanisms: Containment, red-teaming, and security measures
- Versioned and Immutable: Never mutated at runtime, ensuring stability
Hot-swappable modules providing domain-specific knowledge and test cases:
- Mathematics: Arithmetic, algebra, curriculum generation, test problems
- Computer Science: Static analysis, semantic fingerprinting, CFG construction, interprocedural analysis
- Linguistics: Natural language processing, symbolic parsing, grammar extraction, AST processing
- Physics: (Future) Conservation laws, units, physical modeling
- Chemistry: (Future) Molecular structures, reaction patterns, bonding rules
- Biology: (Future) Cellular processes, genetics, evolution principles
- Test Infrastructure: Problem definitions, curriculum factories, test case management
- Each module provides pure domain knowledge without reasoning logic
Lightweight infrastructure for future situational contexts:
- User Contexts: Personal preferences, customizations, user-specific adaptations
- World Contexts: Specific world models, physical parameters, environmental settings
- Situation Management: Context activation, deactivation, forking, and switching
- Overlay Infrastructure: Framework for context-dependent behavior without core modification
- Future Work: Currently contains only infrastructure for future development
- Separation of Concerns: Universal reasoning (Tier 1) separated from domain knowledge (Tier 2) and situational contexts (Tier 3)
- Stability: Immutable reasoning kernel ensures core logic never changes
- Modularity: Domain modules can be updated without affecting reasoning capabilities
- Isolation: Domain-specific knowledge cannot corrupt universal reasoning
- Testability: Each tier can be tested independently with clear interfaces
- Flexibility: Hot-swappable domain modules enable rapid adaptation
from tier1.kernel import UniversalReasoningKernel
from tier1.knowledge import KnowledgeHubV2, WorldKnowledgeGraph
from tier1.reasoning import ReasoningEngine, Planner
from tier2.domain_hub import DomainHub
from tier3.situation_manager import SituationManager
# Initialize the three-tier architecture
kernel = UniversalReasoningKernel(version="1.0.0")
knowledge_hub = KnowledgeHubV2()
reasoning_engine = ReasoningEngine()
# Load domain knowledge (Tier 2)
domain_hub = DomainHub()
domain_hub.load_domain("mathematics")
domain_hub.load_domain("computer_science")
# Create situational context (Tier 3)
situation_manager = SituationManager()
user_context = situation_manager.create_user_context("alice", {
"analysis_depth": "precise",
"risk_tolerance": "low"
})
# Apply universal reasoning with domain knowledge
problem = "Analyze this code for potential bugs"
domain_knowledge = domain_hub.get_domain_knowledge("computer_science")
# Reason with the universal kernel
result = kernel.reason(problem, domain_knowledge, user_context)
print(f"Analysis: {result}")For complete details, see docs/architecture/MAIN.md.
RegionAI uses a clean three-tier architecture that separates concerns for stability, modularity, and maintainability:
RegionAI/
├── tier1/ # Universal Reasoning Engine (Immutable Core)
│ ├── brains/ # Six-Brain Cognitive Architecture
│ │ ├── bayesian.py # Probabilistic reasoning
│ │ ├── logic.py # Formal proof systems
│ │ ├── utility.py # Resource allocation
│ │ ├── observer.py # Meta-cognitive monitoring
│ │ ├── temporal.py # Time-based reasoning
│ │ └── sensorimotor.py # Embodied interaction
│ │
│ ├── discovery/ # Concept and Transformation Discovery
│ │ ├── simple_discovery.py # Basic discovery mechanisms
│ │ ├── concept_discoverer.py # Concept formation
│ │ ├── action_discoverer.py # Action learning
│ │ └── bayesian_updater.py # Evidence integration
│ │
│ ├── knowledge/ # Knowledge Infrastructure
│ │ ├── infrastructure/ # Core graph structures
│ │ │ ├── world_graph.py # World knowledge graph
│ │ │ ├── reasoning_graph.py # Reasoning knowledge graph
│ │ │ └── storage.py # Storage services
│ │ ├── discovery/ # Knowledge discovery services
│ │ │ ├── services/ # Specialized discovery services
│ │ │ └── hub.py # Discovery orchestration
│ │ └── query/ # Query services
│ │
│ ├── reasoning/ # Reasoning Engine
│ │ ├── engine.py # Core reasoning engine
│ │ ├── planner.py # Multi-step planning
│ │ ├── heuristics/ # Reasoning heuristics
│ │ │ ├── registry.py # Heuristic management
│ │ │ ├── math.py # Mathematical heuristics
│ │ │ ├── patterns.py # Pattern-based heuristics
│ │ │ └── security.py # Security heuristics
│ │ └── utilities/ # Utility updating
│ │
│ ├── core/ # Core Abstractions
│ │ ├── region.py # N-dimensional regions
│ │ ├── transformation.py # Transformations
│ │ ├── abstract_domains.py # Analysis domains
│ │ └── primitives.py # Primitive operations
│ │
│ ├── analysis/ # Abstract Interpretation
│ │ ├── cfg.py # Control flow graphs
│ │ ├── fixpoint.py # Fixpoint computation
│ │ ├── interprocedural.py # Cross-function analysis
│ │ └── pointer_analysis.py # Memory analysis
│ │
│ └── kernel.py # Universal Reasoning Kernel
│
├── tier2/ # Domain Knowledge Modules (Hot-swappable)
│ ├── mathematics/ # Mathematical domain
│ │ ├── curriculum/ # Math curriculum generation
│ │ │ └── math_curriculum.py
│ │ ├── arithmetic.py # Basic arithmetic
│ │ └── algebra.py # Algebraic reasoning
│ │
│ ├── computer_science/ # CS domain knowledge
│ │ ├── static_analysis.py # Code analysis knowledge
│ │ ├── semantic_fingerprinting.py # Code patterns
│ │ └── cfg_construction.py # Control flow knowledge
│ │
│ ├── linguistics/ # Language domain
│ │ ├── symbolic_parser.py # NLP structures
│ │ ├── grammar_extraction.py # Grammar patterns
│ │ └── nlp_utils.py # Language utilities
│ │
│ ├── test_infrastructure/ # Test framework
│ │ ├── problem.py # Problem definitions
│ │ ├── curriculum_factory.py # Test generation
│ │ └── validators.py # Solution validation
│ │
│ └── domain_hub.py # Domain management
│
├── tier3/ # Situational Overlays (Future Infrastructure)
│ ├── user_contexts/ # User-specific adaptations
│ ├── world_contexts/ # Environmental parameters
│ └── situation_manager.py # Context management
│
├── src/regionai/ # Legacy Compatibility Layer
│ └── __init__.py # Backward compatibility shim
│
├── tests/ # Comprehensive test suite
└── docs/ # Documentation
- Tier 1 (Universal Reasoning): Immutable, versioned core that provides consistent reasoning capabilities across all domains
- Tier 2 (Domain Knowledge): Modular, hot-swappable domain expertise that can be updated without affecting core reasoning
- Tier 3 (Situational Overlays): Lightweight context management for user preferences and environmental adaptations
The immutable core that provides all universal reasoning capabilities:
from tier1.kernel import UniversalReasoningKernel
from tier1.brains import (
BayesianBrain, # Probabilistic reasoning
UtilityBrain, # Resource allocation
LogicBrain, # Formal proofs
ObserverBrain, # Meta-cognition
TemporalBrain, # Time reasoning
SensorimotorBrain # Embodied interaction
)
# Initialize the universal reasoning kernel
kernel = UniversalReasoningKernel(version="1.0.0")
# Example: Bayesian reasoning
bayesian = BayesianBrain()
bayesian.observe("sky", "cloudy", True, confidence=0.9)
bayesian.observe("rain", "likely", True, confidence=0.7)
belief = bayesian.query_belief("will_rain") # Returns: 0.8
# Example: Logic proving
logic = LogicBrain()
logic.add_axiom("humans_are_mortal", "∀x. Human(x) → Mortal(x)")
logic.add_fact("socrates_human", "Human(Socrates)")
proof = logic.prove("Mortal(Socrates)") # Returns: True with proof steps
# Example: Meta-cognitive monitoring
observer = ObserverBrain()
observer.monitor_confidence("bayesian", "weather_prediction", 0.8)
observer.monitor_confidence("logic", "weather_prediction", 0.3)
alert = observer.detect_disagreement() # Alerts on conflicting assessmentsHot-swappable domain expertise that provides specialized knowledge:
from tier2.domain_hub import DomainHub
from tier2.mathematics.curriculum.math_curriculum import MathCurriculumFactory
from tier2.test_infrastructure.problem import Problem
# Load domain knowledge
domain_hub = DomainHub()
domain_hub.load_domain("mathematics")
domain_hub.load_domain("computer_science")
domain_hub.load_domain("linguistics")
# Generate domain-specific problems
math_curriculum = MathCurriculumFactory()
problems = math_curriculum.generate_arithmetic_problems(difficulty=3, count=10)
# Access domain-specific knowledge
math_knowledge = domain_hub.get_domain_knowledge("mathematics")
cs_knowledge = domain_hub.get_domain_knowledge("computer_science")The discovery engine learns new transformations and concepts from failed problems:
from tier1.discovery.simple_discovery import SimpleDiscoveryEngine
from tier1.discovery.concept_discoverer import ConceptDiscoverer
from tier1.discovery.bayesian_updater import BayesianUpdater
from tier2.test_infrastructure.problem import Problem
# Initialize discovery components
discovery_engine = SimpleDiscoveryEngine()
concept_discoverer = ConceptDiscoverer()
bayesian_updater = BayesianUpdater()
# Failed problems guide discovery
failed_problems = [
Problem(input=[1,2,3], output=6), # sum
Problem(input=[2,4,6], output=12), # sum
]
# Discover the SUM transformation
new_concept = discovery_engine.discover_from_failures(failed_problems)
concept_discoverer.register_concept(new_concept)Transformations are the atomic units of computation in the universal reasoning kernel:
from tier1.core.transformation import Transformation, compose
from tier1.core.primitives import ADD, MULTIPLY, FILTER, SUM
# Primitive transformations from the universal core
add_op = Transformation("ADD", lambda x, y: x + y)
multiply_op = Transformation("MULTIPLY", lambda x, y: x * y)
filter_op = Transformation("FILTER", lambda pred, xs: filter(pred, xs))
# Composed transformations
double = multiply_op.apply(2) # Partial application
sum_evens = compose(SUM, filter_op.apply(lambda x: x % 2 == 0))The abstract interpretation framework in the universal reasoning kernel enables program verification:
from tier1.analysis.fixpoint import analyze_with_fixpoint
from tier1.analysis.cfg import build_control_flow_graph
from tier1.core.abstract_domains import SignDomain, RangeDomain
# Analyze a function for potential bugs
def risky_function(arr, index):
if index >= 0:
return arr[index] # Potential out-of-bounds
return None
# Build control flow graph and analyze
cfg = build_control_flow_graph(risky_function)
analysis = analyze_with_fixpoint(cfg, RangeDomain())
# Detects: Possible array bounds violation when index >= len(arr)Natural language understanding through symbolic constraints:
from regionai.domains.language import SymbolicParser, CandidateGenerator
from regionai.knowledge import WorldKnowledgeGraph
# Initialize components
wkg = WorldKnowledgeGraph()
candidate_gen = CandidateGenerator(wkg)
parser = SymbolicParser(candidate_gen)
# Parse natural language
tree = parser.parse_sentence("The cat that chased the mouse sat on the mat")
# Produces hierarchical structure with resolved referencesThe world knowledge graph maintains discovered concepts and relationships:
from regionai.knowledge import WorldKnowledgeGraph, Concept
wkg = WorldKnowledgeGraph()
# Add concepts
animal = Concept("animal")
cat = Concept("cat")
wkg.add_concept(animal)
wkg.add_concept(cat)
wkg.add_relation(cat, "is_a", animal)
# Query relationships
wkg.query_descendants(animal) # Returns: [cat, ...]- Python 3.9 or higher
- Poetry (for dependency management)
- Optional: spaCy language models for NLP features
# Clone the repository
git clone https://github.com/username/RegionAI.git
cd RegionAI
# Install with Poetry
poetry install
# Download spaCy model (optional, for NLP features)
poetry run python -m spacy download en_core_web_sm# Install development dependencies
poetry install --with dev
# Run tests
poetry run pytest
# Run with coverage
poetry run pytest --cov=regionai
# Format code
poetry run black src/ tests/
poetry run isort src/ tests/
# Type checking
poetry run mypy src/from regionai.discovery import discover_transformations
from regionai.data import Problem
# Define problems that demonstrate a pattern
problems = [
Problem(input=[1, 2, 3], output=[2, 4, 6]), # double each
Problem(input=[5, 10], output=[10, 20])
]
# Discover the transformation
discovered = discover_transformations(problems)
print(discovered) # MAP(λx. x * 2)from regionai.api import AnalysisAPI
api = AnalysisAPI()
code = '''
def process_data(data):
result = []
for item in data:
if item > 0:
result.append(item * 2)
return result
'''
analysis = api.analyze_code(code)
print(analysis.semantic_fingerprint) # Identifies: FILTER + MAP patternfrom regionai.tools import parse_sentence
# Parse with full analysis
result = parse_sentence(
"The algorithm that processes the data should optimize for speed"
)
# Access hierarchical structure
print(result.tree)
print(result.constraints)
print(result.resolved_concepts)from regionai.api import KnowledgeAPI
api = KnowledgeAPI()
# Analyze a codebase and build knowledge graph
kg = api.build_knowledge_graph("/path/to/project")
# Query the graph
concepts = kg.get_concepts()
functions = kg.get_functions()
relationships = kg.get_relations("implements")# Parse natural language
poetry run parse "The cat sat on the mat"
# Analyze a codebase
poetry run analyze-codebase --path ./my_project --output report.txt
# Run demonstrations
poetry run demo all
# Start API server
poetry run parse-api --port 8000# Transformation Discovery
from regionai.discovery import UnifiedDiscoveryEngine
engine = UnifiedDiscoveryEngine()
engine.discover(problems, strategy='sequential')
engine.discover(problems, strategy='conditional')
engine.discover(problems, strategy='iterative')
# Add custom strategy
engine.add_strategy('custom', MyStrategy())# Static Analysis
from regionai.api import (
AnalysisAPI,
TrainingAPI,
KnowledgeAPI
)
# Initialize API
analysis_api = AnalysisAPI()
# Analyze code
result = analysis_api.analyze_code(source_code)
result.bugs # List of potential issues
result.optimizations # Suggested improvements
result.semantic_fingerprint # Behavioral signature
# Check safety
safety_result = analysis_api.check_safety(source_code)# Natural Language Processing
from regionai.domains.language import (
SymbolicParser,
CandidateGenerator,
ContextResolver
)
# Parse with context
parser = SymbolicParser(candidate_generator)
trees = parser.parse_sequence([
"The cat chased the mouse.",
"It hid under the table." # 'It' resolved to 'mouse'
])# Knowledge Management
from regionai.knowledge import (
WorldKnowledgeGraph,
ConceptDiscoverer,
KnowledgeHub
)
# Build and query knowledge
hub = KnowledgeHub()
hub.add_world_concept(concept, metadata)
hub.discover_patterns()
hub.link_concepts()Regions in RegionAI are not simple hyperspheres but complex geometric shapes that can represent:
- Concept Hierarchies: Nested regions represent IS-A relationships
- Fuzzy Boundaries: Soft edges allow graded membership
- Intersections: Overlapping regions create compound concepts
- Transformations: Functions are regions in input×output space
The discovery engine uses several strategies:
- Sequential Discovery: Find sequences of transformations
- Conditional Discovery: Learn branching patterns
- Iterative Discovery: Recognize loops and recursion
- Compositional Discovery: Build complex from simple
The abstract interpretation framework implements:
- Lattice Theory: Proper ordering and join operations
- Widening Operators: Ensure termination on loops
- Transfer Functions: Model statement effects
- Interprocedural Analysis: Track across function calls
The language engine employs:
- Lazy Evaluation: Defer resolution until needed
- Beam Search: Maintain k-best interpretations
- Memoization: Cache expensive resolutions
- Backpropagation: Learn from successful resolutions
-
Mathematics Bootstrap (In Progress)
- Discover arithmetic from examples
- Learn algebraic laws
- Build geometric intuitions
- Connect to theorem proving
-
Enhanced Language Understanding
- Richer grammatical analysis
- Multi-sentence reasoning
- Dialogue understanding
- Technical documentation parsing
-
Code Generation
- Transform specifications to code
- Maintain correctness proofs
- Optimize for performance
- Generate multiple languages
-
Self-Analysis
- Analyze RegionAI's own code
- Discover improvement opportunities
- Generate optimized versions
- Bootstrap enhanced capabilities
-
Distributed Reasoning
- Multi-agent discovery
- Parallel hypothesis testing
- Distributed knowledge graphs
- Federated learning
-
Domain Specialization
- Scientific computing
- Systems programming
- Web development
- Machine learning
-
Artificial General Intelligence
- Universal problem solving
- Creative algorithm discovery
- Scientific theory formation
- Mathematical proof generation
-
Human-AI Collaboration
- Natural programming interfaces
- Collaborative debugging
- Knowledge transfer
- Teaching and tutoring
-
Theoretical Foundations
- Formal correctness proofs
- Complexity guarantees
- Learning bounds
- Philosophical implications
RegionAI builds upon decades of research in:
- Program Synthesis: From examples to code
- Abstract Interpretation: Cousot & Cousot's framework
- Cognitive Science: Conceptual spaces theory
- Machine Learning: Neural-symbolic integration
- Formal Methods: Verification and theorem proving
Special thanks to the open-source community for tools like Python, PyTorch, spaCy, and the countless libraries that make this work possible.
Copyright © 2025 Arkadiy Agyeyev. All rights reserved.
For licensing inquiries, research collaborations, or general questions:
- Email: [email protected]
- Subject: RegionAI Inquiry
"The best way to understand intelligence is to build it from first principles."
RegionAI: Where computation meets comprehension, and discovery drives understanding.