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# EXO-AI 2025: System Architecture
## SPARC Phase 3: Architecture Design
### Executive Summary
This document defines the modular architecture for an experimental cognitive substrate platform, consuming the ruvector ecosystem as an SDK while exploring technologies projected for 2035-2060.
---
## 1. Architectural Principles
### 1.1 Core Design Tenets
| Principle | Description | Implementation |
|-----------|-------------|----------------|
| **SDK Consumer** | No modifications to ruvector crates | Clean dependency boundaries |
| **Backend Agnostic** | Hardware abstraction via traits | PIM, neuromorphic, photonic backends |
| **Substrate-First** | Data and compute unified | In-memory operations where possible |
| **Topology Native** | Hypergraph as primary structure | Edges span arbitrary entity sets |
| **Temporal Coherent** | Causal memory by default | Every operation timestamped |
### 1.2 Layer Architecture
```
┌─────────────────────────────────────────────────────────────────┐
│ APPLICATION LAYER │
│ ┌─────────────┐ ┌──────────────┐ ┌───────────────────────────┐ │
│ │ Agent SDK │ │ Query Engine │ │ Federation Gateway │ │
│ └─────────────┘ └──────────────┘ └───────────────────────────┘ │
├─────────────────────────────────────────────────────────────────┤
│ SUBSTRATE LAYER │
│ ┌─────────────┐ ┌──────────────┐ ┌───────────────────────────┐ │
│ │ Manifold │ │ Hypergraph │ │ Temporal Memory │ │
│ │ Engine │ │ Substrate │ │ Coordinator │ │
│ └─────────────┘ └──────────────┘ └───────────────────────────┘ │
├─────────────────────────────────────────────────────────────────┤
│ BACKEND ABSTRACTION │
│ ┌─────────────┐ ┌──────────────┐ ┌───────────────────────────┐ │
│ │ Classical │ │ Neuromorphic │ │ Photonic │ │
│ │ (ruvector) │ │ (Future) │ │ (Future) │ │
│ └─────────────┘ └──────────────┘ └───────────────────────────┘ │
├─────────────────────────────────────────────────────────────────┤
│ INFRASTRUCTURE │
│ ┌─────────────┐ ┌──────────────┐ ┌───────────────────────────┐ │
│ │ WASM │ │ NAPI-RS │ │ Native │ │
│ │ Runtime │ │ Bindings │ │ Binaries │ │
│ └─────────────┘ └──────────────┘ └───────────────────────────┘ │
└─────────────────────────────────────────────────────────────────┘
```
---
## 2. Module Design
### 2.1 Core Modules
```
exo-ai-2025/
├── crates/
│ ├── exo-core/ # Core traits and types
│ ├── exo-manifold/ # Learned manifold engine
│ ├── exo-hypergraph/ # Hypergraph substrate
│ ├── exo-temporal/ # Temporal memory coordinator
│ ├── exo-federation/ # Federated mesh networking
│ ├── exo-backend-classical/ # Classical backend (ruvector)
│ ├── exo-backend-sim/ # Neuromorphic/photonic simulator
│ ├── exo-wasm/ # WASM bindings
│ └── exo-node/ # NAPI-RS bindings
├── examples/
├── docs/
└── research/
```
### 2.2 exo-core: Foundational Traits
```rust
//! Core trait definitions for backend abstraction
/// Backend trait for substrate compute operations
pub trait SubstrateBackend: Send + Sync {
type Error: std::error::Error;
/// Execute similarity search on substrate
fn similarity_search(
&self,
query: &[f32],
k: usize,
filter: Option<&Filter>,
) -> Result<Vec<SearchResult>, Self::Error>;
/// Deform manifold to incorporate new pattern
fn manifold_deform(
&self,
pattern: &Pattern,
learning_rate: f32,
) -> Result<ManifoldDelta, Self::Error>;
/// Execute hyperedge query
fn hyperedge_query(
&self,
query: &TopologicalQuery,
) -> Result<HyperedgeResult, Self::Error>;
}
/// Temporal context for causal operations
pub trait TemporalContext {
/// Get current substrate time
fn now(&self) -> SubstrateTime;
/// Query with causal cone constraints
fn causal_query(
&self,
query: &Query,
cone: &CausalCone,
) -> Result<Vec<CausalResult>, Error>;
/// Predictive pre-fetch based on anticipated queries
fn anticipate(&self, hints: &[AnticipationHint]) -> Result<(), Error>;
}
/// Pattern representation in substrate
#[derive(Clone, Debug)]
pub struct Pattern {
/// Vector embedding
pub embedding: Vec<f32>,
/// Metadata
pub metadata: Metadata,
/// Temporal origin
pub timestamp: SubstrateTime,
/// Causal antecedents
pub antecedents: Vec<PatternId>,
}
/// Topological query specification
#[derive(Clone, Debug)]
pub enum TopologicalQuery {
/// Find persistent homology features
PersistentHomology {
dimension: usize,
epsilon_range: (f32, f32),
},
/// Find N-dimensional holes in structure
BettiNumbers {
max_dimension: usize,
},
/// Sheaf consistency check
SheafConsistency {
local_sections: Vec<SectionId>,
},
}
```
### 2.3 exo-manifold: Learned Representation Engine
```rust
//! Continuous manifold storage replacing discrete indices
use burn::prelude::*;
use crate::core::{Pattern, SubstrateBackend, ManifoldDelta};
/// Implicit Neural Representation for manifold storage
pub struct ManifoldEngine<B: Backend> {
/// Neural network representing the manifold
network: LearnedManifold<B>,
/// Tensor Train decomposition for compression
tt_decomposition: Option<TensorTrainConfig>,
/// Consolidation scheduler
consolidation: ConsolidationPolicy,
}
impl<B: Backend> ManifoldEngine<B> {
/// Query manifold via gradient descent
pub fn retrieve(
&self,
query: Tensor<B, 1>,
k: usize,
) -> Vec<(Pattern, f32)> {
// Initialize at query position
let mut position = query.clone();
// Gradient descent toward relevant memories
for _ in 0..self.config.max_descent_steps {
let relevance = self.network.forward(position.clone());
let gradient = relevance.backward();
position = position - self.config.learning_rate * gradient;
if gradient.norm() < self.config.convergence_threshold {
break;
}
}
// Extract patterns from converged region
self.extract_patterns_near(position, k)
}
/// Continuous manifold deformation (replaces insert)
pub fn deform(&mut self, pattern: Pattern, salience: f32) {
let embedding = Tensor::from_floats(&pattern.embedding);
// Deformation = gradient update to manifold weights
let loss = self.deformation_loss(embedding, salience);
let gradients = loss.backward();
self.optimizer.step(gradients);
}
/// Strategic forgetting via manifold smoothing
pub fn forget(&mut self, region: &ManifoldRegion, decay_rate: f32) {
// Smooth the manifold in low-salience regions
self.apply_forgetting_kernel(region, decay_rate);
}
}
/// Learned manifold network architecture
#[derive(Module)]
pub struct LearnedManifold<B: Backend> {
/// SIREN-style sinusoidal layers
layers: Vec<SirenLayer<B>>,
/// Fourier feature encoding
fourier_features: FourierEncoding<B>,
}
```
### 2.4 exo-hypergraph: Topological Substrate
```rust
//! Hypergraph substrate for higher-order relations
use petgraph::Graph;
use simplicial_topology::SimplicialComplex;
use ruvector_graph::{GraphDatabase, HyperedgeSupport};
/// Hypergraph substrate extending ruvector-graph
pub struct HypergraphSubstrate {
/// Base graph from ruvector-graph
base: GraphDatabase,
/// Hyperedge index (relations spanning >2 entities)
hyperedges: HyperedgeIndex,
/// Simplicial complex for TDA
topology: SimplicialComplex,
/// Sheaf structure for consistency
sheaf: Option<SheafStructure>,
}
impl HypergraphSubstrate {
/// Create hyperedge spanning multiple entities
pub fn create_hyperedge(
&mut self,
entities: &[EntityId],
relation: &Relation,
) -> Result<HyperedgeId, Error> {
// Validate entity existence
for entity in entities {
self.base.get_node(*entity)?;
}
// Create hyperedge in index
let hyperedge_id = self.hyperedges.insert(entities, relation);
// Update simplicial complex
self.topology.add_simplex(entities);
// Update sheaf sections if enabled
if let Some(ref mut sheaf) = self.sheaf {
sheaf.update_sections(hyperedge_id, entities)?;
}
Ok(hyperedge_id)
}
/// Topological query: find persistent features
pub fn persistent_homology(
&self,
dimension: usize,
epsilon_range: (f32, f32),
) -> PersistenceDiagram {
use teia::persistence::compute_persistence;
let filtration = self.topology.filtration(epsilon_range);
compute_persistence(&filtration, dimension)
}
/// Query Betti numbers (topological invariants)
pub fn betti_numbers(&self, max_dim: usize) -> Vec<usize> {
(0..=max_dim)
.map(|d| self.topology.betti_number(d))
.collect()
}
/// Sheaf consistency: check local-to-global coherence
pub fn check_sheaf_consistency(
&self,
sections: &[SectionId],
) -> SheafConsistencyResult {
match &self.sheaf {
Some(sheaf) => sheaf.check_consistency(sections),
None => SheafConsistencyResult::NotConfigured,
}
}
}
/// Hyperedge index structure
struct HyperedgeIndex {
/// Hyperedge storage
edges: DashMap<HyperedgeId, Hyperedge>,
/// Inverted index: entity -> hyperedges containing it
entity_index: DashMap<EntityId, Vec<HyperedgeId>>,
/// Relation type index
relation_index: DashMap<RelationType, Vec<HyperedgeId>>,
}
```
### 2.5 exo-temporal: Causal Memory Coordinator
```rust
//! Temporal memory with causal structure
use std::collections::BTreeMap;
use ruvector_core::VectorIndex;
/// Temporal memory coordinator
pub struct TemporalMemory {
/// Short-term volatile memory
short_term: ShortTermBuffer,
/// Long-term consolidated memory
long_term: LongTermStore,
/// Causal graph tracking antecedent relationships
causal_graph: CausalGraph,
/// Temporal knowledge graph (Zep-inspired)
tkg: TemporalKnowledgeGraph,
}
impl TemporalMemory {
/// Store with causal context
pub fn store(
&mut self,
pattern: Pattern,
antecedents: &[PatternId],
) -> Result<PatternId, Error> {
// Add to short-term buffer
let id = self.short_term.insert(pattern.clone());
// Record causal relationships
for antecedent in antecedents {
self.causal_graph.add_edge(*antecedent, id);
}
// Update TKG with temporal relations
self.tkg.add_temporal_fact(id, &pattern, antecedents)?;
// Schedule consolidation if buffer full
if self.short_term.should_consolidate() {
self.trigger_consolidation();
}
Ok(id)
}
/// Causal cone query: retrieve within light-cone constraints
pub fn causal_query(
&self,
query: &Query,
reference_time: SubstrateTime,
cone_type: CausalConeType,
) -> Vec<CausalResult> {
// Determine valid time range based on cone
let time_range = match cone_type {
CausalConeType::Past => (SubstrateTime::MIN, reference_time),
CausalConeType::Future => (reference_time, SubstrateTime::MAX),
CausalConeType::LightCone { velocity } => {
self.compute_light_cone(reference_time, velocity)
}
};
// Query with temporal filter
self.long_term
.search_with_time_range(query, time_range)
.into_iter()
.map(|r| CausalResult {
pattern: r.pattern,
causal_distance: self.causal_graph.distance(r.id, query.origin),
temporal_distance: (r.timestamp - reference_time).abs(),
})
.collect()
}
/// Anticipatory pre-fetch for predictive retrieval
pub fn anticipate(&mut self, hints: &[AnticipationHint]) {
for hint in hints {
// Pre-compute likely future queries
let predicted_queries = self.predict_future_queries(hint);
// Warm cache with predicted results
for query in predicted_queries {
self.prefetch_cache.insert(query.hash(),
self.long_term.search(&query));
}
}
}
/// Memory consolidation: short-term -> long-term
fn consolidate(&mut self) {
// Identify salient patterns
let salient = self.short_term
.drain()
.filter(|p| p.salience > self.consolidation_threshold);
// Compress via manifold integration
for pattern in salient {
self.long_term.integrate(pattern);
}
// Strategic forgetting in long-term
self.long_term.decay_low_salience(self.decay_rate);
}
}
/// Causal graph for tracking antecedent relationships
struct CausalGraph {
/// Forward edges: cause -> effects
forward: DashMap<PatternId, Vec<PatternId>>,
/// Backward edges: effect -> causes
backward: DashMap<PatternId, Vec<PatternId>>,
}
```
### 2.6 exo-federation: Distributed Cognitive Mesh
```rust
//! Federated substrate with cryptographic sovereignty
use ruvector_raft::{RaftNode, RaftConfig};
use ruvector_cluster::ClusterManager;
use kyberlib::{keypair, encapsulate, decapsulate};
/// Federated cognitive mesh
pub struct FederatedMesh {
/// Local substrate instance
local: Arc<SubstrateInstance>,
/// Raft consensus for local cluster
consensus: RaftNode,
/// Federation gateway
gateway: FederationGateway,
/// Post-quantum keypair
pq_keys: PostQuantumKeypair,
}
impl FederatedMesh {
/// Join federation with cryptographic handshake
pub async fn join_federation(
&mut self,
peer: &PeerAddress,
) -> Result<FederationToken, Error> {
// Post-quantum key exchange
let (ciphertext, shared_secret) = encapsulate(&peer.public_key)?;
// Establish encrypted channel
let channel = self.gateway.establish_channel(
peer,
ciphertext,
shared_secret,
).await?;
// Exchange federation capabilities
let token = channel.negotiate_federation().await?;
Ok(token)
}
/// Federated query with privacy preservation
pub async fn federated_query(
&self,
query: &Query,
scope: FederationScope,
) -> Vec<FederatedResult> {
// Route through onion network for intent privacy
let onion_query = self.gateway.onion_wrap(query, scope)?;
// Broadcast to federation peers
let responses = self.gateway.broadcast(onion_query).await;
// CRDT reconciliation for eventual consistency
let reconciled = self.reconcile_crdt(responses)?;
reconciled
}
/// Byzantine fault tolerant consensus on shared state
pub async fn byzantine_commit(
&self,
update: &StateUpdate,
) -> Result<CommitProof, Error> {
// Require 2f+1 agreement for n=3f+1 nodes
let threshold = (self.peer_count() * 2 / 3) + 1;
// Propose update
let proposal = self.consensus.propose(update)?;
// Collect votes
let votes = self.gateway.collect_votes(proposal).await;
if votes.len() >= threshold {
Ok(CommitProof::from_votes(votes))
} else {
Err(Error::InsufficientConsensus)
}
}
}
/// Post-quantum cryptographic keypair
struct PostQuantumKeypair {
/// CRYSTALS-Kyber public key
public: [u8; 1184],
/// CRYSTALS-Kyber secret key
secret: [u8; 2400],
}
```
---
## 3. Backend Abstraction Layer
### 3.1 Classical Backend (ruvector SDK)
```rust
//! Classical backend consuming ruvector crates
use ruvector_core::{VectorIndex, HnswConfig};
use ruvector_graph::GraphDatabase;
use ruvector_gnn::GnnLayer;
/// Classical substrate backend using ruvector
pub struct ClassicalBackend {
/// Vector index from ruvector-core
vector_index: VectorIndex,
/// Graph database from ruvector-graph
graph_db: GraphDatabase,
/// GNN layer from ruvector-gnn
gnn: Option<GnnLayer>,
}
impl SubstrateBackend for ClassicalBackend {
type Error = ruvector_core::Error;
fn similarity_search(
&self,
query: &[f32],
k: usize,
filter: Option<&Filter>,
) -> Result<Vec<SearchResult>, Self::Error> {
// Direct delegation to ruvector-core
let results = match filter {
Some(f) => self.vector_index.search_with_filter(query, k, f)?,
None => self.vector_index.search(query, k)?,
};
Ok(results.into_iter().map(SearchResult::from).collect())
}
fn manifold_deform(
&self,
pattern: &Pattern,
_learning_rate: f32,
) -> Result<ManifoldDelta, Self::Error> {
// Classical backend: discrete insert
let id = self.vector_index.insert(&pattern.embedding, &pattern.metadata)?;
Ok(ManifoldDelta::DiscreteInsert { id })
}
fn hyperedge_query(
&self,
query: &TopologicalQuery,
) -> Result<HyperedgeResult, Self::Error> {
// Use ruvector-graph hyperedge support
match query {
TopologicalQuery::PersistentHomology { .. } => {
// Compute via graph traversal
unimplemented!("TDA on classical backend")
}
TopologicalQuery::BettiNumbers { .. } => {
// Approximate via connected components
unimplemented!("Betti numbers on classical backend")
}
TopologicalQuery::SheafConsistency { .. } => {
// Not supported on classical backend
Ok(HyperedgeResult::NotSupported)
}
}
}
}
```
### 3.2 Future Backend Traits
```rust
//! Placeholder traits for future hardware backends
/// Processing-in-Memory backend interface
pub trait PimBackend: SubstrateBackend {
/// Execute operation in memory bank
fn execute_in_memory(&self, op: &MemoryOperation) -> Result<(), Error>;
/// Query memory bank location for data
fn data_location(&self, pattern_id: PatternId) -> MemoryBank;
}
/// Neuromorphic backend interface
pub trait NeuromorphicBackend: SubstrateBackend {
/// Encode vector as spike train
fn encode_spikes(&self, vector: &[f32]) -> SpikeTrain;
/// Decode spike train to vector
fn decode_spikes(&self, spikes: &SpikeTrain) -> Vec<f32>;
/// Submit spike computation
fn submit_spike_compute(&self, input: SpikeTrain) -> Result<SpikeTrain, Error>;
}
/// Photonic backend interface
pub trait PhotonicBackend: SubstrateBackend {
/// Optical matrix-vector multiply
fn optical_matmul(&self, matrix: &OpticalMatrix, vector: &[f32]) -> Vec<f32>;
/// Configure optical interference pattern
fn configure_mzi(&self, config: &MziConfig) -> Result<(), Error>;
}
```
---
## 4. WASM & NAPI-RS Integration
### 4.1 WASM Module Structure
```rust
//! WASM bindings for browser/edge deployment
use wasm_bindgen::prelude::*;
use crate::core::{Pattern, Query};
#[wasm_bindgen]
pub struct ExoSubstrate {
inner: Arc<SubstrateInstance>,
}
#[wasm_bindgen]
impl ExoSubstrate {
#[wasm_bindgen(constructor)]
pub fn new(config: JsValue) -> Result<ExoSubstrate, JsError> {
let config: SubstrateConfig = serde_wasm_bindgen::from_value(config)?;
let inner = SubstrateInstance::new(config)?;
Ok(Self { inner: Arc::new(inner) })
}
#[wasm_bindgen]
pub async fn query(&self, embedding: Float32Array, k: u32) -> Result<JsValue, JsError> {
let query = Query::from_embedding(embedding.to_vec());
let results = self.inner.search(query, k as usize).await?;
Ok(serde_wasm_bindgen::to_value(&results)?)
}
#[wasm_bindgen]
pub fn store(&self, pattern: JsValue) -> Result<String, JsError> {
let pattern: Pattern = serde_wasm_bindgen::from_value(pattern)?;
let id = self.inner.store(pattern)?;
Ok(id.to_string())
}
}
```
### 4.2 NAPI-RS Bindings
```rust
//! Node.js bindings via NAPI-RS
use napi::bindgen_prelude::*;
use napi_derive::napi;
#[napi]
pub struct ExoSubstrateNode {
inner: Arc<RwLock<SubstrateInstance>>,
}
#[napi]
impl ExoSubstrateNode {
#[napi(constructor)]
pub fn new(config: serde_json::Value) -> Result<Self> {
let config: SubstrateConfig = serde_json::from_value(config)?;
let inner = SubstrateInstance::new(config)?;
Ok(Self { inner: Arc::new(RwLock::new(inner)) })
}
#[napi]
pub async fn search(&self, embedding: Float32Array, k: u32) -> Result<Vec<SearchResultJs>> {
let guard = self.inner.read().await;
let results = guard.search(
Query::from_embedding(embedding.to_vec()),
k as usize,
).await?;
Ok(results.into_iter().map(SearchResultJs::from).collect())
}
#[napi]
pub async fn hypergraph_query(&self, query: String) -> Result<serde_json::Value> {
let guard = self.inner.read().await;
let topo_query: TopologicalQuery = serde_json::from_str(&query)?;
let result = guard.hypergraph.query(&topo_query).await?;
Ok(serde_json::to_value(result)?)
}
}
```
---
## 5. Deployment Targets
### 5.1 Build Configurations
```toml
# Cargo.toml feature flags
[features]
default = ["classical-backend"]
# Backends
classical-backend = ["ruvector-core", "ruvector-graph", "ruvector-gnn"]
sim-neuromorphic = []
sim-photonic = []
# Deployment targets
wasm = ["wasm-bindgen", "getrandom/js"]
napi = ["napi", "napi-derive"]
# Experimental features
tensor-train = []
sheaf-consistency = []
post-quantum = ["kyberlib", "pqcrypto"]
```
### 5.2 Platform Matrix
| Target | Backend | Features | Size |
|--------|---------|----------|------|
| `wasm32-unknown-unknown` | Classical (memory-only) | Core substrate | ~2MB |
| `x86_64-unknown-linux-gnu` | Classical (full) | All features | ~15MB |
| `aarch64-apple-darwin` | Classical (full) | All features | ~12MB |
| Node.js (NAPI) | Classical (full) | All features | ~8MB |
---
## 6. Future Architecture Extensions
### 6.1 PIM Integration Path
```
Phase 1: Abstraction (Current)
├── Define PimBackend trait
├── Implement simulation mode
└── Profile classical baseline
Phase 2: Emulation
├── UPMEM SDK integration
├── Performance modeling
└── Hybrid execution strategies
Phase 3: Native Hardware
├── Custom PIM firmware
├── Memory bank allocation
└── Direct execution path
```
### 6.2 Consciousness Metrics (Research)
```rust
//! Experimental: Integrated Information metrics
/// Compute Phi (integrated information) for substrate region
pub fn compute_phi(
substrate: &SubstrateRegion,
partition_strategy: PartitionStrategy,
) -> f64 {
// Compute information generated by whole
let whole_info = substrate.effective_information();
// Compute information generated by parts
let partitions = partition_strategy.partition(substrate);
let parts_info: f64 = partitions
.iter()
.map(|p| p.effective_information())
.sum();
// Phi = whole - parts (simplified IIT measure)
(whole_info - parts_info).max(0.0)
}
```
---
## References
- SPARC Specification: `specs/SPECIFICATION.md`
- Research Papers: `research/PAPERS.md`
- Rust Libraries: `research/RUST_LIBRARIES.md`

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# EXO-AI 2025: Pseudocode Design
## SPARC Phase 2: Algorithm Design
This document presents high-level pseudocode for the core algorithms in the EXO-AI cognitive substrate.
---
## 1. Learned Manifold Engine
### 1.1 Manifold Retrieval via Gradient Descent
```pseudocode
FUNCTION ManifoldRetrieve(query_vector, k, manifold_network):
// Initialize search position at query
position = query_vector
visited_positions = []
// Gradient descent toward high-relevance regions
FOR step IN 1..MAX_DESCENT_STEPS:
// Forward pass through learned manifold
relevance_field = manifold_network.forward(position)
// Compute gradient of relevance
gradient = manifold_network.backward(relevance_field)
// Update position following relevance gradient
position = position - LEARNING_RATE * gradient
visited_positions.append(position)
// Check convergence
IF norm(gradient) < CONVERGENCE_THRESHOLD:
BREAK
// Extract k nearest patterns from converged region
results = []
FOR pos IN visited_positions.last(k):
patterns = ExtractPatternsNear(pos, manifold_network)
results.extend(patterns)
RETURN TopK(results, k)
```
### 1.2 Continuous Manifold Deformation
```pseudocode
FUNCTION ManifoldDeform(pattern, salience, manifold_network, optimizer):
// No discrete insert - continuous deformation instead
// Encode pattern as tensor
embedding = Tensor(pattern.embedding)
// Compute deformation loss
// Loss = how much the manifold needs to change to represent this pattern
current_relevance = manifold_network.forward(embedding)
target_relevance = salience
deformation_loss = (current_relevance - target_relevance)^2
// Add regularization for manifold smoothness
smoothness_loss = ManifoldCurvatureRegularizer(manifold_network)
total_loss = deformation_loss + LAMBDA * smoothness_loss
// Gradient update to manifold weights
gradients = total_loss.backward()
optimizer.step(gradients)
// Return delta for logging
RETURN ManifoldDelta(embedding, salience, total_loss)
```
### 1.3 Strategic Forgetting
```pseudocode
FUNCTION StrategicForget(manifold_network, decay_rate, salience_threshold):
// Identify low-salience regions
low_salience_regions = []
FOR region IN manifold_network.sample_regions():
avg_salience = ComputeAverageSalience(region)
IF avg_salience < salience_threshold:
low_salience_regions.append(region)
// Apply smoothing kernel to low-salience regions
// This effectively "forgets" by reducing specificity
FOR region IN low_salience_regions:
ForgetKernel = GaussianKernel(sigma=decay_rate)
manifold_network.apply_kernel(region, ForgetKernel)
// Optional: prune near-zero weights
manifold_network.prune_weights(threshold=1e-6)
```
---
## 2. Hypergraph Substrate
### 2.1 Hyperedge Creation
```pseudocode
FUNCTION CreateHyperedge(entities, relation, hypergraph):
// Validate all entities exist
FOR entity IN entities:
IF NOT hypergraph.base_graph.contains(entity):
RAISE EntityNotFoundError(entity)
// Generate hyperedge ID
hyperedge_id = GenerateUUID()
// Create hyperedge record
hyperedge = Hyperedge(
id = hyperedge_id,
entities = entities,
relation = relation,
created_at = NOW(),
weight = 1.0
)
// Insert into hyperedge storage
hypergraph.hyperedges.insert(hyperedge_id, hyperedge)
// Update inverted index (entity -> hyperedges)
FOR entity IN entities:
hypergraph.entity_index[entity].append(hyperedge_id)
// Update relation type index
hypergraph.relation_index[relation.type].append(hyperedge_id)
// Update simplicial complex for TDA
simplex = entities.as_simplex()
hypergraph.topology.add_simplex(simplex)
RETURN hyperedge_id
```
### 2.2 Persistent Homology Computation
```pseudocode
FUNCTION ComputePersistentHomology(hypergraph, dimension, epsilon_range):
// Build filtration (nested sequence of simplicial complexes)
filtration = BuildFiltration(hypergraph.topology, epsilon_range)
// Initialize boundary matrix for column reduction
boundary_matrix = BuildBoundaryMatrix(filtration, dimension)
// Column reduction algorithm (standard persistent homology)
reduced_matrix = ColumnReduction(boundary_matrix)
// Extract persistence pairs
pairs = []
FOR col_j IN reduced_matrix.columns:
IF reduced_matrix.low(j) != NULL:
i = reduced_matrix.low(j)
birth = filtration.birth_time(i)
death = filtration.birth_time(j)
pairs.append((birth, death))
ELSE IF col_j is a cycle:
birth = filtration.birth_time(j)
death = INFINITY // Essential feature
pairs.append((birth, death))
// Build persistence diagram
diagram = PersistenceDiagram(
pairs = pairs,
dimension = dimension
)
RETURN diagram
FUNCTION ColumnReduction(matrix):
// Standard algorithm from computational topology
FOR j IN 1..matrix.num_cols:
WHILE EXISTS j' < j WITH low(j') = low(j):
// Add column j' to column j to reduce
matrix.column(j) = matrix.column(j) XOR matrix.column(j')
RETURN matrix
```
### 2.3 Sheaf Consistency Check
```pseudocode
FUNCTION CheckSheafConsistency(sheaf, sections):
// Sheaf consistency: local sections should agree on overlaps
inconsistencies = []
// Check all pairs of overlapping sections
FOR (section_a, section_b) IN Pairs(sections):
overlap = section_a.domain.intersect(section_b.domain)
IF overlap.is_empty():
CONTINUE
// Restriction maps
restricted_a = sheaf.restrict(section_a, overlap)
restricted_b = sheaf.restrict(section_b, overlap)
// Check agreement
IF NOT ApproximatelyEqual(restricted_a, restricted_b, tolerance=EPSILON):
inconsistencies.append(
SheafInconsistency(
sections = (section_a, section_b),
overlap = overlap,
discrepancy = Distance(restricted_a, restricted_b)
)
)
IF inconsistencies.is_empty():
RETURN SheafConsistencyResult.Consistent
ELSE:
RETURN SheafConsistencyResult.Inconsistent(inconsistencies)
```
---
## 3. Temporal Memory Coordinator
### 3.1 Causal Cone Query
```pseudocode
FUNCTION CausalQuery(query, reference_time, cone_type, temporal_memory):
// Determine valid time range based on causal cone
SWITCH cone_type:
CASE Past:
time_range = (MIN_TIME, reference_time)
CASE Future:
time_range = (reference_time, MAX_TIME)
CASE LightCone(velocity):
// Relativistic constraint: |delta_x| <= c * |delta_t|
time_range = ComputeLightCone(reference_time, query.origin, velocity)
// Filter candidates by time range
candidates = temporal_memory.long_term.filter_by_time(time_range)
// Similarity search within temporal constraint
similarities = []
FOR candidate IN candidates:
sim = CosineSimilarity(query.embedding, candidate.embedding)
causal_dist = temporal_memory.causal_graph.shortest_path(
query.origin,
candidate.id
)
similarities.append((candidate, sim, causal_dist))
// Rank by combined temporal and causal relevance
scored = []
FOR (candidate, sim, causal_dist) IN similarities:
temporal_score = 1.0 / (1.0 + abs(candidate.timestamp - reference_time))
causal_score = 1.0 / (1.0 + causal_dist) IF causal_dist != INF ELSE 0.0
combined = ALPHA * sim + BETA * temporal_score + GAMMA * causal_score
scored.append((candidate, combined))
RETURN sorted(scored, by=combined, descending=True)
```
### 3.2 Memory Consolidation
```pseudocode
FUNCTION Consolidate(temporal_memory):
// Biological-inspired memory consolidation
// Short-term -> Long-term with salience filtering
// Compute salience for all short-term items
salience_scores = []
FOR item IN temporal_memory.short_term:
salience = ComputeSalience(item, temporal_memory)
salience_scores.append((item, salience))
// Salience computation factors:
// - Frequency of access
// - Recency of access
// - Causal importance (how many things depend on it)
// - Surprise (deviation from expected)
FUNCTION ComputeSalience(item, memory):
access_freq = memory.access_counts[item.id]
recency = 1.0 / (1.0 + (NOW() - item.last_accessed))
causal_importance = memory.causal_graph.out_degree(item.id)
surprise = ComputeSurprise(item, memory.long_term)
RETURN W1*access_freq + W2*recency + W3*causal_importance + W4*surprise
// Filter by salience threshold
salient_items = [item FOR (item, s) IN salience_scores IF s > THRESHOLD]
// Integrate into long-term (manifold deformation)
FOR item IN salient_items:
temporal_memory.long_term.manifold.deform(item, salience)
// Strategic forgetting for low-salience items
FOR item IN temporal_memory.short_term:
IF item NOT IN salient_items:
// Don't integrate - let it decay
PASS
// Clear short-term buffer
temporal_memory.short_term.clear()
// Decay low-salience regions in long-term
temporal_memory.long_term.strategic_forget(DECAY_RATE)
```
### 3.3 Predictive Anticipation
```pseudocode
FUNCTION Anticipate(hints, temporal_memory):
// Pre-compute likely future queries based on hints
// This enables "predictive retrieval before queries are issued"
predicted_queries = []
FOR hint IN hints:
SWITCH hint.type:
CASE SequentialPattern:
// If A then B pattern detected
recent = temporal_memory.recent_queries()
FOR pattern IN temporal_memory.sequential_patterns:
IF pattern.matches_prefix(recent):
predicted = pattern.next_likely_query()
predicted_queries.append(predicted)
CASE TemporalCycle:
// Time-of-day or periodic patterns
current_phase = GetTemporalPhase(NOW())
historical = temporal_memory.queries_at_phase(current_phase)
predicted_queries.extend(historical.top_k(5))
CASE CausalChain:
// Causal dependencies predict next queries
current_context = hint.current_context
downstream = temporal_memory.causal_graph.downstream(current_context)
FOR node IN downstream:
predicted_queries.append(QueryFor(node))
// Pre-fetch and cache
FOR query IN predicted_queries:
cache_key = Hash(query)
IF cache_key NOT IN temporal_memory.prefetch_cache:
result = temporal_memory.long_term.search(query)
temporal_memory.prefetch_cache[cache_key] = result
```
---
## 4. Federated Cognitive Mesh
### 4.1 Post-Quantum Federation Handshake
```pseudocode
FUNCTION JoinFederation(local_node, peer_address):
// CRYSTALS-Kyber key exchange
// Generate ephemeral keypair
(local_public, local_secret) = Kyber.KeyGen()
// Send public key to peer
SendMessage(peer_address, FederationRequest(local_public))
// Receive peer's encapsulated shared secret
response = ReceiveMessage(peer_address)
ciphertext = response.ciphertext
// Decapsulate to get shared secret
shared_secret = Kyber.Decapsulate(ciphertext, local_secret)
// Derive session keys from shared secret
(encrypt_key, mac_key) = DeriveKeys(shared_secret)
// Establish encrypted channel
channel = EncryptedChannel(peer_address, encrypt_key, mac_key)
// Exchange capabilities and negotiate federation terms
local_caps = local_node.capabilities()
peer_caps = channel.exchange(local_caps)
terms = NegotiateFederationTerms(local_caps, peer_caps)
// Create federation token
token = FederationToken(
peer = peer_address,
channel = channel,
terms = terms,
expires = NOW() + TOKEN_VALIDITY
)
RETURN token
```
### 4.2 Onion-Routed Query
```pseudocode
FUNCTION OnionQuery(query, destination, relay_nodes, local_keys):
// Privacy-preserving query routing through onion network
// Build onion layers (innermost to outermost)
layers = [destination] + relay_nodes // Reverse order for wrapping
// Start with plaintext query
current_payload = SerializeQuery(query)
// Wrap in layers
FOR node IN layers:
// Encrypt with node's public key
encrypted = AsymmetricEncrypt(current_payload, node.public_key)
// Add routing header
header = OnionHeader(
next_hop = node.address,
payload_type = "onion_layer"
)
current_payload = header + encrypted
// Send to first relay
first_relay = relay_nodes.last()
SendMessage(first_relay, current_payload)
// Receive response (also onion-wrapped)
encrypted_response = ReceiveMessage(first_relay)
// Unwrap response layers
current_response = encrypted_response
FOR node IN reverse(relay_nodes):
current_response = AsymmetricDecrypt(current_response, local_keys.secret)
// Final decryption with destination's response
result = DeserializeResponse(current_response)
RETURN result
```
### 4.3 CRDT Reconciliation
```pseudocode
FUNCTION ReconcileCRDT(responses, local_state):
// Conflict-free merge of federated query results
// Use G-Set CRDT for search results (grow-only set)
merged_results = GSet()
FOR response IN responses:
FOR result IN response.results:
// G-Set merge: union operation
merged_results.add(result)
// For rankings, use LWW-Register (last-writer-wins)
ranking_map = LWWMap()
FOR response IN responses:
FOR (result_id, score, timestamp) IN response.rankings:
ranking_map.set(result_id, score, timestamp)
// Combine: results from G-Set, scores from LWW-Map
final_results = []
FOR result IN merged_results:
score = ranking_map.get(result.id)
final_results.append((result, score))
// Sort by reconciled scores
final_results.sort(by=score, descending=True)
RETURN final_results
```
### 4.4 Byzantine Fault Tolerant Commit
```pseudocode
FUNCTION ByzantineCommit(update, federation):
// PBFT-style consensus for state updates
n = federation.node_count()
f = (n - 1) / 3 // Maximum Byzantine faults tolerable
threshold = 2*f + 1 // Required agreement
// Phase 1: Pre-prepare (leader proposes)
IF federation.is_leader():
proposal = SignedProposal(update, sequence_number=NEXT_SEQ)
Broadcast(federation.nodes, PrePrepare(proposal))
// Phase 2: Prepare (nodes acknowledge receipt)
pre_prepare = ReceivePrePrepare()
IF ValidateProposal(pre_prepare):
prepare_msg = Prepare(pre_prepare.digest, federation.local_id)
Broadcast(federation.nodes, prepare_msg)
// Collect prepare messages
prepares = CollectMessages(type=Prepare, count=threshold)
IF len(prepares) < threshold:
RETURN CommitResult.InsufficientPrepares
// Phase 3: Commit (nodes commit to proposal)
commit_msg = Commit(pre_prepare.digest, federation.local_id)
Broadcast(federation.nodes, commit_msg)
// Collect commit messages
commits = CollectMessages(type=Commit, count=threshold)
IF len(commits) >= threshold:
// Execute update
federation.apply_update(update)
proof = CommitProof(commits)
RETURN CommitResult.Success(proof)
ELSE:
RETURN CommitResult.InsufficientCommits
```
---
## 5. Backend Abstraction
### 5.1 Backend Selection
```pseudocode
FUNCTION SelectBackend(requirements, available_backends):
// Automatic backend selection based on requirements
scored_backends = []
FOR backend IN available_backends:
score = 0.0
// Evaluate against requirements
IF requirements.latency_target:
latency_score = 1.0 / backend.expected_latency
score += W_LATENCY * latency_score
IF requirements.energy_target:
energy_score = 1.0 / backend.expected_energy
score += W_ENERGY * energy_score
IF requirements.accuracy_target:
accuracy_score = backend.expected_accuracy
score += W_ACCURACY * accuracy_score
IF requirements.scale_target:
scale_score = backend.max_scale / requirements.scale_target
score += W_SCALE * min(scale_score, 1.0)
// Check hard constraints
IF requirements.wasm_required AND NOT backend.supports_wasm:
CONTINUE
IF requirements.post_quantum_required AND NOT backend.supports_pq:
CONTINUE
scored_backends.append((backend, score))
// Select highest scoring backend
best_backend = max(scored_backends, by=score)
RETURN best_backend
```
### 5.2 Hybrid Execution
```pseudocode
FUNCTION HybridExecute(operation, backends):
// Execute across multiple backends, combine results
// Partition operation if possible
partitions = PartitionOperation(operation)
// Assign partitions to backends based on suitability
assignments = []
FOR partition IN partitions:
best_backend = SelectBackendForPartition(partition, backends)
assignments.append((partition, best_backend))
// Execute in parallel
futures = []
FOR (partition, backend) IN assignments:
future = backend.execute_async(partition)
futures.append(future)
// Await all results
results = AwaitAll(futures)
// Merge partition results
merged = MergePartitionResults(results, operation.type)
RETURN merged
```
---
## 6. Consciousness Metrics (Research)
### 6.1 Phi (Integrated Information) Approximation
```pseudocode
FUNCTION ApproximatePhi(substrate_region):
// Compute integrated information (IIT-inspired)
// Full Phi computation is intractable; this is an approximation
// Step 1: Compute whole-system effective information
whole_state = substrate_region.current_state()
perturbed_states = []
FOR _ IN 1..NUM_PERTURBATIONS:
perturbed = ApplyRandomPerturbation(whole_state)
evolved = substrate_region.evolve(perturbed)
perturbed_states.append(evolved)
whole_EI = MutualInformation(whole_state, perturbed_states)
// Step 2: Find minimum information partition (MIP)
partitions = GeneratePartitions(substrate_region)
min_partition_EI = INFINITY
FOR partition IN partitions:
partition_EI = 0.0
FOR part IN partition:
part_state = part.current_state()
part_perturbed = [ApplyRandomPerturbation(part_state) FOR _ IN 1..NUM_PERTURBATIONS]
part_evolved = [part.evolve(p) FOR p IN part_perturbed]
partition_EI += MutualInformation(part_state, part_evolved)
IF partition_EI < min_partition_EI:
min_partition_EI = partition_EI
mip = partition
// Step 3: Phi = whole - minimum partition
phi = whole_EI - min_partition_EI
RETURN max(phi, 0.0) // Phi cannot be negative
```
---
## Summary
These pseudocode algorithms define the core computational patterns for the EXO-AI cognitive substrate:
| Component | Key Algorithm | Complexity |
|-----------|---------------|------------|
| Manifold Engine | Gradient descent retrieval | O(k × d × steps) |
| Hypergraph | Persistent homology | O(n³) worst case |
| Temporal Memory | Causal cone query | O(n × log n) |
| Federation | Byzantine consensus | O(n²) messages |
| Phi Metric | Partition enumeration | O(B(n)) Bell numbers |
Where:
- k = number of results
- d = embedding dimension
- n = number of entities/nodes
- steps = gradient descent iterations