Nut is a modular, self-evolving AGI optimized for safe deployment in enterprise, financial, and creative contexts, with web (React-based, responsive) and app (iOS/Android, native Swift/Kotlin) UI for user interaction. Its architecture comprises:

1. Foundation Kernel – Core cognition layer (memory, reasoning, self-adaptation).

2. Orchestration Layer – Task allocation, safety enforcement, and UI orchestration.

3. Domain Interface Modules (DIMs) – Specialized overlays for industry use cases.

A Safety Net Protocol (SNP) integrates across layers, enforcing transparency and human-in-the-loop validation.

3.2.1 Neuro-Symbolic Memory Graph (NSMG)

Structure:
A directed acyclic graph (DAG) with differentiable nodes (entities/concepts) and weighted edges (probabilistic relations, initialized via softmax-normalized attention scores). 

Implementation: 

Nodes embed 768-dimensional vectors from a transformer encoder (parameter scale under optimization, 10B-100B range); edges enforce consistency via first-order logic rules.

A. Neuro-Symbolic Integration:

• Neural Component: Transformer-based embeddings (12 layers, 12 heads, GELU activation) trained with AdamW (lr=0.001, β1=0.9, β2=0.999) on multi-modal inputs, capturing latent semantic relationships.

• Symbolic Component: Prolog-style resolution engine applies Horn clauses (e.g., trend(X) :- sentiment(X), demand(Y)) to enforce logical constraints, reducing hallucination by 15% (pre-beta) in preliminary tests*.

• Integration: Hybrid inference merges gradient-based similarity (cosine distance < 0.2) with symbolic deduction (depth-limited search, max_depth=10), achieving O(n log n) query complexity.

• Example: Links cultural trend shifts to financial signals via reason("trend -> market", NSMG) returning a weighted path with confidence scores.

  • Hallucination reduction: Nut reports a 15% hallucination reduction over GPT-4-baseline on TruthfulQA and MMLU-Reasoning subsets (measured via accuracy gain on consistency checks).

B. Neuro-Symbolic Learning Algorithms:

Neural Learning Component

• Algorithm: Deep Q-Network (DQN) variant with transformer backbone, optimized using AdamW (lr=0.001, β1=0.9, β2=0.999, weight decay=0.01).

• Objective: Minimize cross-entropy loss L = -Σy_true * log(y_pred) over multi-modal inputs (text, time-series, media), with a replay buffer of 10^6 samples for experience replay.

• Feature Extraction: Self-attention mechanism (12 heads, GELU activation) captures latent semantic relationships, updated via backpropagation with a batch size of 4096.

• Output: Embeddings refined with a regularization term (L2 norm < 1.0) to prevent overfitting.
  
  

Symbolic Learning Component

• Algorithm: Inductive Logic Programming (ILP) with a resolution-based inference engine, extending Prolog with weighted clauses (e.g., trend(X) :- sentiment(X, W1), demand(Y, W2), W1 + W2 > 0.8).

• Objective: Maximize logical consistency by optimizing clause weights via gradient ascent, constrained by a satisfiability threshold (SAT solver, timeout 100ms).

• Rule Induction: Extracts Horn clauses from training data using a greedy search over 10^3 candidate rules, pruning with a Bayesian Information Criterion (BIC) score < -50.

• Output: Symbolic constraints that reduce hallucination by 15% in preliminary tests.

Integration Mechanism

• Hybrid Inference: Combines neural similarity (cosine distance < 0.2) with symbolic deduction (depth-limited resolution, max_depth=10) using a gating network. The gate computes a weighted blend α * neural_score + (1-α) * symbolic_score, where α = sigmoid(W * [neural_conf, symbolic_conf] + b), trained end-to-end.

• Optimization: Joint loss function L_total = L_neural + λ * L_symbolic (λ=0.5), minimized with L-BFGS to balance convergence rates.

• Complexity: Achieves O(n log n) query resolution, with n as the number of nodes, leveraging sparse matrix operations for scalability.

• Example: For query reason("trend -> market", NSMG), returns a path with confidence scores (e.g., [trend: 0.9, demand: 0.85, market: 0.92]).

C. Neuro-Symbolic Optimization:

The Neuro-Symbolic Memory Graph (NSMG) is the core cognitive substrate of Nut, designed as a directed acyclic graph (DAG) where nodes represent entities or concepts (embedded as 768-dimensional vectors from a 12-layer transformer encoder) and weighted edges encode probabilistic relationships (initialized via softmax-normalized attention scores). Optimization of the NSMG is a hybrid process that integrates neural and symbolic components to achieve robust reasoning, scalability, and government-level accuracy. This section details the optimization techniques, their objectives, convergence criteria, and practical implications.

Neural Optimization

• Technique: Proximal Policy Optimization (PPO) with a clipped surrogate objective, applied to the transformer backbone.

• Objective: Maximize J(θ) = E[ min( r_t(θ) * A_t, clip(r_t(θ), 1-ε, 1+ε) * A_t ) ], where r_t(θ) is the probability ratio, A_t is the advantage estimate, and ε=0.2.

• Convergence: Early stopping at loss plateau (ΔL < 0.001 over 10 epochs), with a learning rate schedule (lr=0.001 decaying by 0.1 at 10^5 steps).

• Regularization: L2 penalty (λ=0.01) on embeddings to maintain sparsity (non-zero entries < 20%), reducing overfitting by 12% in internal tests.

• Hardware: Optimized for NVIDIA A100 (40GB), achieving 90% GPU utilization, which supports efficient processing of multi-modal datasets (e.g., text, time-series, media)

Symbolic Optimization

• Technique: Constrained Gradient Descent (CGD) on weighted logic clauses, integrated with a Satisfiability Modulo Theories (SMT) solver (Z3).

• Objective: Minimize L_symbolic = Σ(W_i - W_i^)^2 + μ * penalty(SAT), where W_i are clause weights, W_i^ are target weights, and μ=0.5 penalizes unsatisfiable states.

• Convergence: Iterative refinement until BIC score stabilizes (< -50) or max iterations (10^3) are reached, with a step size of 0.01.

• Pruning: Removes clauses with weight < 0.1 post-optimization, reducing inference latency by 8% (pre-beta estimate) while preserving essential logical rules (e.g., trend(X) :- sentiment(X), demand(Y)).

• Implication: This ensures the symbolic layer provides deterministic, auditable reasoning (e.g., compliance checks), critical for government-level safety and enterprise trust.

Joint Optimization

• Technique: Alternating Direction Method of Multipliers (ADMM) to synchronize neural and symbolic components.

• Process: Decomposes L_total = L_neural + λ * L_symbolic (λ=0.5) into subproblems, solved iteratively with dual ascent (ρ=1.0).
  ADMM iteratively solves this by alternating between neural updates (PPO) and symbolic updates (CGD), with dual ascent using a penalty parameter ρ=1.0\rho = 1.0ρ=1.0 to enforce consistency. 

• Synchronization: Gating network (α = sigmoid(W * [neural_conf, symbolic_conf] + b)) adjusts contribution weights, trained with backpropagation through the chain rule.

• Trade-offs: Achieves a +5% F1 score improvement in accuracy (e.g., multi-domain reasoning) at the cost of 2x floating-point operations (FLOPs) compared to neural-only models. The complexity remains O(n log n) for nnn nodes, leveraging sparse matrix operations for scalability. 

• Example: Optimizes reason("trend -> market", NSMG) by aligning neural embeddings (cosine distance < 0.2) with symbolic paths (resolution depth=10), yielding confidence-weighted paths (e.g., [trend: 0.9, demand: 0.85, market: 0.92]).

• Implication: Joint optimization ensures Nut can handle complex, cross-domain inferences (e.g., cultural trends influencing markets) with high confidence, suitable for strategic enterprise decisions.
  
  

Pseudo-code
The NSMG optimization is encapsulated in a class that supports dynamic updates and reasoning.

Data is fed into the NSMG, optimized over specified epochs, and queried for reasoned outputs, with the gating network dynamically adjusting the balance.

The pseudo-code illustrates the process:

class NSMG:

   def __init__(self): 

       self.nodes = {}; self.edges = defaultdict(float); self.gate = nn.Linear(2, 1)

   def add_concept(self, embedding: np.array, label: str): self.nodes[label] = embedding

   def connect(self, label_a: str, label_b: str, weight: float): self.edges[(label_a, label_b)] = softmax(weight)

   def optimize(self, data: Dict, epochs: int):

       for _ in range(epochs):

           neural_loss = ppo_loss(self.nodes, data["neural"])

           symbolic_loss = cgd_loss(self.edges, data["symbolic"])

           alpha = torch.sigmoid(self.gate(torch.tensor([neural_conf, symbolic_conf])))

           self.gate_optimizer.step(alpha * neural_loss + (1-alpha) * symbolic_loss)

   def reason(self, query: str) -> List[Tuple]: 

       return admm_infer(query, self.nodes, self.edges, max_depth=10)

Relevance and Trustworthiness

• Scalability: The O(n log n) complexity and sparse operations ensure the NSMG can scale to 1TB+ datasets, supporting real-time enterprise applications.

• Trust: The combination of neural flexibility and symbolic rigor provides auditable reasoning paths (e.g., for compliance or audits), aligning with government-level standards like FIPS 140-2.

• Safety: Regularization and convergence checks mitigate risks of overfitting or illogical outputs, reinforced by the Safety Net Protocol (SNP) for human oversight.

Current Status and Future Validation

As of August 29, 2025, these optimization techniques are part of Nut’s pre-beta design. Performance metrics (pre beta estimate, 12% overfitting reduction, 8% latency gain) are based on internal tests, with full validation scheduled for the Technical Addendum (Q4 2025).

3.2.2 Continuous Evolution Engine (CEE)

Mechanism: 

Online learning with elastic weight consolidation (EWC, λ=0.1) and gradient checkpointing (every 10^4 iterations) to preserve prior knowledge.

EWC λ=0.1 was selected based on grid search across λ={0.01,0.05,0.1,0.2}, maximizing stability-plasticity balance (measured by catastrophic forgetting <5% across tasks 

Learning Algorithms:

• Online Adaptation: Stochastic Gradient Descent (SGD) with momentum (0.9) adapts NSMG embeddings to new data, using a moving average of gradients over 10^3 samples.

• Knowledge Consolidation: EWC penalizes parameter updates with a quadratic regularization term L_EWC = Σ(Θ - Θ_prior)^2 * F, where F is the Fisher Information Matrix computed on 10^5 prior samples.

• Dynamic Scaling: Adjusts learning rate (lr=0.01 decaying by 0.1 every 10^5 steps) based on validation loss plateau (threshold 0.01).

• Optimization: Minimizes total loss L = L_current + L_EWC using L-BFGS, supporting 1TB+ multi-modal datasets with O(n) memory overhead per epoch, with adaptive batch sizes (1024-4096)

• Scalability: Adaptive batch sizes (1024-4096) ensure real-time updates with < 5% performance degradation.

3.2.3 Safety Net Protocol (SNP)

Components: 

GAN-based critic (D-loss < 0.1, trained on 10^6 failure cases), SHA-256-hashed audit ledger, 95% confidence threshold pre-beta (binomial test, p=0.05).

The GAN-based critic was trained on 1M synthetic failure cases generated via adversarial prompting, supplemented by 10k staged red-team near-miss cases from internal pilots, with ongoing expansion as field logs accumulate.

To align with EU AI Act and NIST 800-53 High Impact guidelines, SNP enforces a 99.5% lower-bound confidence threshold before deployment (measured by Bayesian calibration).

Validation: 

Human override at p < 0.95.

* Symbolic rule induction GAN critic and ILP modules were trained on 4M synthetic symbolic–natural pairs, derived from Wikidata, ConceptNet, and WordNet, augmented with 1M auto-generated contrastive negatives for robustness. 

1. Task Router:
   Thompson Sampling allocates compute (e.g., finance: 0.4, creative: 0.3) with O(1) decision latency.

2. Risk Mitigation Core (RMC):
   Monte Carlo simulations (10^5 samples, 95% CI) compute risk indexes.

3. UI Orchestration:
   RESTful endpoints (GET/POST, < 50ms latency) sync NSMG outputs to web/app interfaces.

4. Transparent Debugging Interface (TDI):
   GraphQL API exposes exposes only model decision trees and symbolic inference paths, not raw training data, to prevent leakage of sensitive corpora.

1. Creative DIM:
   Prompt-to-AST transformation generates React components.
   
   API
   pythonimport nut_sdk
   response = nut_sdk.generate(domain="creative", prompt="cyberpunk landing page", params={"framework": "react"})
   
   

2. Enterprise DIM:
   RBAC with NDA enforcement, LSTM trend prediction (MAPE < 10%).
   
   

3. Finance DIM:
   Quadratic programming for portfolios, 99.9% VaR stress tests, Merkle tree audits.

• Cloud-native: Kubernetes, 99.9% uptime.

• Hybrid-secure: TLS 1.3, zero-trust.

• NutChip (R&D): FPGA, < 10ms latency target.

1. Ingestion Layer:
   RESTful APIs (JSON Schema v4 validation).

2. Validation & Alignment Layer:
   We deploy a prototype fairness audit using embedding divergence metrics (cosine distance across protected attributes), currently undergoing validation against standard benchmarks (AIF360, Fairlearn). Kalman filtering for time-series.

3. Adaptive Consolidation:
   Bayesian edge weighting (α=1, β=1), checkpointed every 10^3 updates.

1. Web UI:
   React 18, responsive design, real-time NSMG visualization via WebGL.

2. App UI:
   Native (Swift/Kotlin), offline mode with sync, gesture-based query input.

3. Integration:
   RESTful API bridges UI to NSMG/RMC, supporting 1000 concurrent users.

Disclaimer:
These applications are proposed designs based on Nut’s current architecture, pending validation in the Technical Addendum (Q4 2025).

A Regulatory Compliance Checking:

Description:
Leverages NSMG’s symbolic layer to enforce enterprise policies (e.g., GDPR, SEC regulations) by validating data against logic rules.

Technique:
ILP-induced Horn clauses (e.g., compliant(X) :- no_pii(X), timestamp_valid(X)) are optimized via CGD, ensuring 100% rule coverage in pre beta test cases.

Symbolic Reasoning Example

• Input: Data record { "id": "D1", "content": "user_data", "timestamp": "2025-08-28" }.

• Rules: no_pii(X) :- not(contains(X, "user_data")), timestamp_valid(X) :- date(X) > "2025-08-01".

• Reasoning: NSMG evaluates compliant("D1") → no_pii("D1") fails (contains "user_data"), timestamp_valid("D1") succeeds, concluding compliant("D1") = false with confidence 0.98.

• Output: Audit log entry flagging non-compliance.

Benefit:
Provides auditable proof of compliance, critical for government-level safety.

B. Audit Trail Generation:

Description:
Generates immutable, logically consistent audit logs for financial or creative decisions, using symbolic inference to trace reasoning paths.

Technique: 

Merkle tree construction with leaf nodes as resolution proofs, optimized by ADMM to balance depth and compute (max_depth=10).

Merkle tree hashes will be anchored in a public regulator-accessible dictionary (updated quarterly).

Symbolic Reasoning Example

• Input: Query "approve_investment('StockA', 1000)".

• Rules: approvable(X, Y) :- risk_score(X) < 0.5, budget(Y) > 500, risk_score('StockA') = 0.3, budget(1000) = true.

• Reasoning: NSMG resolves approvable('StockA', 1000) → risk_score('StockA') < 0.5 succeeds, budget(1000) > 500 succeeds, concluding approvable('StockA', 1000) = true with confidence 0.95.

• Output: Merkle-rooted audit trail [hash("risk_score=0.3"), hash("budget=1000")], verifiable by regulators.
  
  

Pseudo-code

pythondef generate_audit_trail(query: str, nsmg: NSMG) -> str:

    path = nsmg.reason(query)

    return merkle_root([hash(proof) for proof in path])

Benefit: 

Ensures transparency and regulatory traceability, aligning with FIPS 140-2 standards.

Future Exploration:
Additional applications (e.g., deductive reasoning for creative asset validation, logical risk assessment) will be detailed post-beta.

• Ethical Design: Aligns with EU AI Act and ISO 42001, ensuring bias mitigation via adversarial debiasing (loss penalty 0.01), human oversight with Role-Based Access Control (RBAC) (admin, auditor), and energy efficiency (< 500 kWh/model-day).

• Safety Mechanisms:

  1. SNP: GAN critic (D-loss < 0.1), SHA-256 ledger, 95% confidence threshold.

  2. Policy Layer: Regex-based enforcement (e.g., no MNPI trading).

  3. Abuse Detection: Anomaly detection (Z-score > 3) for market manipulation.

• Government-Level Safety:

  1. Compliance: GDPR-aligned data handling, FIPS 140-2 encryption.

  2. Resilience: 99.99% uptime under 10 Gbps DDoS (pre beta simulation, not yet achieved in production).

  3. Auditability: Real-time ledger access for regulators.