20 KiB
20 KiB
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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