AI → Machine Learning → Deep Learning — Family Tree (with Mathematical Backbone)

Comprehensive family tree mapping the AI ecosystem with its underlying mathematical foundations, from core concepts to cutting-edge models.

🌿 Branch = domain (NLP, CV, robotics, etc.) 🔷 Family = related model line ✨ Model = concrete checkpoint/version 📐 Math = mathematical foundation 🔥 Hot = trending/breakthrough ⚡ Emerging = cutting-edge research
50+
Model Families
200+
Individual Models
30+
Math Concepts
12
AI Domains
2025
Latest Updates
Artificial Intelligence (AI) umbrella field
Symbolic AI / Expert Systems rule-based
Knowledge representation, logic programming, and rule-based reasoning systems.
Based on formal logic: propositional & predicate calculus, model theory, proof systems
🔷 Knowledge Graphs
  • Neo4j Graph Database
  • Cypher Query Language
  • Google Knowledge Graph
  • Graph traversal algorithms, RDF triples
🔷 Logic Programming
  • Prolog
  • Answer Set Programming (ASP)
  • Horn clauses, unification, resolution theorem proving
Machine Learning (ML) learns from data
Classical Machine Learning traditional algorithms
🔷 Supervised Learning
Optimization of loss functions via gradient methods, closed-form solutions
  • Linear/Logistic Regression
  • Ordinary least squares: β = (X^T X)^(-1) X^T y
  • Support Vector Machines (SVM)
  • Quadratic programming, kernel methods, margin maximization
  • Random Forest
  • Bootstrap aggregating, information gain, Gini impurity
  • XGBoost / LightGBM
  • Gradient boosting, second-order Taylor approximation
  • Naive Bayes
  • Conditional independence assumption, Bayes' theorem
🔷 Unsupervised Learning
Eigenvalue decomposition, clustering metrics, density estimation
  • K-Means Clustering
  • Lloyd's algorithm, within-cluster sum of squares minimization
  • DBSCAN
  • Density-based clustering, ε-neighborhoods
  • Principal Component Analysis (PCA)
  • Eigendecomposition of covariance matrix, dimensionality reduction
  • t-SNE / UMAP
  • Non-linear manifold learning, probabilistic embeddings
🔷 Ensemble Methods
Bias-variance tradeoff, weighted combination of weak learners
  • AdaBoost
  • Exponential loss minimization, weighted voting
  • Gradient Boosting
  • Functional gradient descent in function space
  • Voting Classifiers
  • Majority voting, weighted averaging
Deep Learning (DL) neural networks
Universal function approximation, backpropagation, stochastic gradient descent
🌿 Natural Language Processing (NLP) text & language
Sequence modeling, attention mechanisms, transformer architectures
🔷 Large Language Models (LLMs)
Foundation models trained on massive text corpora for general language understanding and generation.
Autoregressive modeling: P(x₁,...,xₙ) = ∏P(xᵢ|x₁,...,xᵢ₋₁), self-attention, layer normalization
GPT Family (OpenAI)
  • GPT‑1 2018
  • GPT‑2 1.5B params
  • DistilGPT‑2 compressed
  • GPT‑3 175B params
  • GPT‑3.5‑turbo
  • GPT‑4 / GPT‑4‑turbo
  • GPT‑4o multimodal
  • GPT‑4.1 latest
  • o1 / o1‑mini reasoning
  • Decoder-only transformer, causal attention masking
Claude Family (Anthropic)
  • Claude 1.0
  • Claude 2.0 / 2.1
  • Claude 3 Haiku fast
  • Claude 3 Sonnet balanced
  • Claude 3 Opus most capable
  • Claude 3.5 Sonnet enhanced
  • Claude 4 Sonnet latest
  • Constitutional AI, RLHF training, safety objectives
Gemini Family (Google)
  • LaMDA conversation
  • PaLM / PaLM 2
  • Gemini Pro
  • Gemini Ultra
  • Gemini 1.5 long context
  • Gemini 2.0 multimodal
  • Mixture of experts (MoE), Pathways architecture
Meta LLaMA Family
  • LLaMA 1 7B-65B
  • LLaMA 2 chat variants
  • Code Llama programming
  • LLaMA 3 / 3.1 405B
  • LLaMA 3.2 multimodal
  • RMSNorm, SwiGLU activation, rotary positional embeddings
Open Source Alternatives
  • Mistral 7B / 8x7B (Mixtral)
  • Falcon 7B / 40B / 180B
  • Alpaca (Stanford)
  • Vicuna (LMSYS)
  • MPT (MosaicML)
  • Qwen (Alibaba)
  • Yi (01.AI)
  • Various architectural optimizations, efficiency improvements
🔷 Specialized NLP Models
Understanding Models (Encoders)
Bidirectional attention, masked language modeling objective
  • BERT / RoBERTa
  • Masked LM: P(xᵢ|x₋ᵢ), bidirectional transformer
  • DeBERTa
  • Disentangled attention, enhanced mask decoder
  • ELECTRA
  • Replaced token detection, generator-discriminator training
  • DistilBERT compressed
  • Knowledge distillation from teacher to student model
Text-to-Text Models
Encoder-decoder architecture, span denoising objectives
  • T5 / UL2
  • Text-to-text unified framework, span corruption
  • BART
  • Denoising autoencoder, various noise functions
  • Pegasus summarization
  • Gap sentence generation pre-training
Embedding Models
Contrastive learning, cosine similarity, semantic vector spaces
  • Sentence-BERT
  • Siamese networks, triplet loss
  • OpenAI text-embedding-ada-002
  • E5 / BGE
  • Instructor task-specific
  • Task-aware embeddings, instruction following
🔷 Code Generation Models
Programming language modeling, syntax-aware attention
  • GitHub Copilot (OpenAI Codex)
  • CodeT5 / CodeGen
  • StarCoder / Code Llama
  • Replit Code v1.5
  • Amazon CodeWhisperer
  • Tabnine
  • Abstract syntax tree (AST) modeling, code completion probability
🌿 Computer Vision (CV) images & video
Convolutional operations, spatial hierarchies, visual feature learning
🔷 Object Detection & Segmentation
Non-maximum suppression, intersection over union (IoU), anchor-based/anchor-free methods
YOLO Family
  • YOLOv1 → v3 early versions
  • YOLOv4 / YOLOv5
  • YOLOX / YOLOv6
  • YOLOv8 ultralytics
  • YOLO11 latest
  • Grid-based detection, confidence × class probability
R-CNN Family
  • R-CNN
  • Fast R-CNN
  • Faster R-CNN
  • Mask R-CNN segmentation
  • Region proposal networks, ROI pooling/align
Modern Detection
  • SSD (Single Shot Detector)
  • RetinaNet
  • Focal loss for class imbalance
  • DETR (Detection Transformer)
  • Set prediction, Hungarian matching algorithm
  • EfficientDet
  • Compound scaling, BiFPN architecture
🔷 Image Classification & Backbones
Hierarchical feature extraction, skip connections, batch normalization
Convolutional Networks
  • LeNet / AlexNet historical
  • Convolution: (f*g)[n] = Σf[m]g[n-m]
  • VGG-16 / VGG-19
  • Small 3×3 filters, depth over width
  • ResNet (18/34/50/101/152)
  • Residual connections: F(x) + x, gradient highway
  • ResNeXt / Wide ResNet
  • DenseNet
  • Dense connections, feature reuse
  • EfficientNet v1/v2
  • Neural architecture search, compound scaling
  • RegNet
Vision Transformers
Patch embeddings, positional encoding, self-attention for vision
  • Vision Transformer (ViT)
  • Image patches as tokens, position embeddings
  • DeiT (Data-efficient ViT)
  • Distillation token, teacher-student training
  • Swin Transformer
  • Shifted windows, hierarchical feature maps
  • ConvNeXt modernized ConvNet
  • ConvNet with transformer design principles
  • MaxViT
🔷 Image Generation
Diffusion Models
Forward/reverse diffusion processes, denoising score matching
  • DDPM / DDIM
  • q(x_t|x₀) = N(√α̅_t x₀, (1-α̅_t)I), reverse process
  • Stable Diffusion 1.5 / 2.0
  • Stable Diffusion XL (SDXL)
  • Stable Diffusion 3 latest
  • DALL·E 2 / DALL·E 3
  • Midjourney v5 / v6
  • Imagen (Google)
  • Adobe Firefly
  • Latent space diffusion, CLIP guidance, classifier-free guidance
GANs & Other Generative
Minimax game theory, adversarial training, Nash equilibrium
  • StyleGAN 2/3
  • Style injection, AdaIN normalization
  • BigGAN
  • VQ-VAE / VQ-GAN
  • Vector quantization, codebook learning
  • Parti (Google)
🔷 Video Understanding
Spatio-temporal convolutions, temporal modeling, motion estimation
  • Video Swin Transformer
  • TimeSformer
  • Divided space-time attention
  • SlowFast Networks
  • Dual pathway: slow (spatial) + fast (temporal)
  • I3D (Inflated 3D ConvNet)
  • OpenAI Sora video generation
  • Runway Gen-2
  • Stable Video Diffusion
🌿 Speech & Audio AI sound processing
Signal processing, spectrograms, mel-frequency cepstral coefficients (MFCC)
🔷 Speech Recognition (ASR)
Hidden Markov models, connectionist temporal classification (CTC)
  • Whisper (OpenAI) multilingual
  • Sequence-to-sequence with attention
  • Wav2Vec 2.0 (Meta)
  • Contrastive learning on raw audio waveforms
  • DeepSpeech (Mozilla)
  • CTC loss, RNN-based architecture
  • Conformer
  • Convolution + transformer hybrid
  • Google Speech-to-Text
  • Amazon Transcribe
🔷 Text-to-Speech (TTS)
Vocoder design, mel-spectrogram prediction, neural audio synthesis
  • Tacotron 2
  • Encoder-decoder with attention, mel-spectrogram prediction
  • WaveNet / WaveGlow
  • Dilated causal convolutions, autoregressive generation
  • VITS (End-to-end TTS)
  • Variational inference, normalizing flows
  • Bark (Suno AI) expressive
  • ElevenLabs commercial
  • Tortoise TTS
🔷 Music & Audio Generation
Audio synthesis, harmonic analysis, rhythm modeling
  • MusicLM (Google)
  • Suno AI commercial
  • Udio commercial
  • Jukebox (OpenAI)
  • VQ-VAE hierarchical modeling
  • AudioCraft (Meta)
  • MusiCNN
🔷 Audio Processing
  • PANNs (Audio Tagging)
  • YAMNet (Audio Event Detection)
  • AudioMAE
  • Masked autoencoding for audio spectrograms
🌿 Multimodal AI text + image + audio + video
Cross-modal attention, contrastive learning, unified embedding spaces
🔷 Vision-Language Models
Cross-attention between visual and textual features
  • GPT‑4o / GPT‑4‑vision OpenAI
  • Claude 3 Opus/Sonnet (vision)
  • Gemini Pro Vision / Ultra
  • LLaVA (Large Language and Vision)
  • Visual instruction tuning, cross-modal alignment
  • BLIP / BLIP-2
  • Bootstrap vision-language pre-training
  • Flamingo (DeepMind)
  • Few-shot learning with frozen language models
  • Kosmos‑1/2 (Microsoft)
  • Qwen-VL
🔷 CLIP & Embedding Models
Contrastive learning: maximize similarity of correct pairs, minimize incorrect pairs
  • CLIP (OpenAI)
  • Contrastive loss: L = -log(exp(sim(x,y)/τ) / Σexp(sim(x,y')/τ))
  • ALIGN (Google)
  • CoCa (Contrastive Captioners)
  • SigLIP
  • Sigmoid loss instead of softmax for efficiency
🔷 Multimodal Generation
  • GPT-4o text→image→text
  • Gemini 2.0 comprehensive
  • Any-to-Any (Meta) research
  • Unified tokenization across modalities
🌿 Robotics & Embodied AI physical world
Control theory, kinematics, dynamics, trajectory optimization
🔷 Manipulation & Control
Inverse kinematics, PID control, Model Predictive Control (MPC)
  • RT-1 / RT-2 (Google)
  • Transformer for robotics, vision-language-action
  • PaLM-E language + robotics
  • RoboCat (DeepMind)
  • OpenVLA vision-language-action
  • SARA (Stanford)
  • Spatial action representations
🔷 Simulation & Training
Physics simulation, contact dynamics, domain randomization
  • Isaac Gym (NVIDIA)
  • MuJoCo
  • Multi-joint dynamics with contact
  • PyBullet
  • Habitat (Meta)
🔷 Navigation & SLAM
Simultaneous Localization and Mapping, particle filters, graph optimization
  • Neural SLAM
  • PointNet++
  • Hierarchical point set feature learning
  • DD-PPO (Distributed RL)
🌿 Reinforcement Learning (RL) decision making
Markov Decision Processes, Bellman equations, policy gradients, temporal difference learning
🔷 Game Playing
Monte Carlo Tree Search, value/policy networks, self-play
  • AlphaGo / AlphaZero
  • MCTS + neural networks, UCB1 selection
  • MuZero
  • Model-based planning with learned dynamics
  • OpenAI Five (Dota 2)
  • AlphaStar (StarCraft II)
  • Agent57 (Atari)
  • Meta-controller for exploration vs exploitation
🔷 RLHF & Alignment
Human feedback training for AI alignment and safety.
Preference modeling, reward learning from comparisons, KL regularization
  • InstructGPT (OpenAI)
  • PPO with KL penalty: J = E[r(x,y)] - β KL(π,π_ref)
  • Constitutional AI (Anthropic)
  • Sparrow (DeepMind)
  • LaMDA Safety Training
🔷 Policy Learning
Policy gradient methods, actor-critic algorithms, experience replay
  • PPO (Proximal Policy Optimization)
  • Clipped surrogate objective, trust region
  • SAC (Soft Actor-Critic)
  • Maximum entropy RL, entropy regularization
  • Rainbow DQN
  • Combines 6 DQN improvements
  • IMPALA
🌿 Recommendation Systems personalization
Collaborative filtering, matrix factorization, embedding learning
🔷 Deep Recommenders
Neural collaborative filtering, factorization machines, deep CTR prediction
  • Neural Collaborative Filtering
  • Replace inner product with neural networks
  • Wide & Deep (Google)
  • Memorization (wide) + generalization (deep)
  • DeepFM
  • Factorization machines + deep neural networks
  • DIN / DIEN (Alibaba)
  • Attention-based user interest modeling
  • PinSage (Pinterest)
  • Graph convolutional networks for recommendations
🔷 Sequential Recommendations
Sequence modeling, temporal dynamics, session-based recommendations
  • SASRec (Self-Attention)
  • Self-attention for sequential patterns
  • BERT4Rec
  • Bidirectional encoder for user sequences
  • GRU4Rec
  • RNN for session-based recommendations
🌿 AI for Science & Drug Discovery scientific AI
Molecular dynamics, protein folding energy landscapes, sequence-structure relationships
🔷 Protein Folding & Structure
Energy minimization, Ramachandran plots, contact prediction, attention over residue pairs
  • AlphaFold 2/3 (DeepMind) breakthrough
  • MSA processing, attention over residue pairs, distance/angle prediction
  • ESMFold (Meta)
  • Language model embeddings for folding
  • ChimeraX AlphaFold
  • ColabFold
🔷 Drug Discovery
Molecular representations, SMILES encoding, molecular property prediction
  • AlphaFold DB
  • MolGAN
  • GANs for molecular generation
  • Junction Tree VAE
  • Tree-structured molecular representations
  • ChemBERTa
  • MegaMolBART
🔷 Materials Science
  • Crystal Graph Neural Networks
  • Crystal structure as graphs, material property prediction
  • SchNet
  • Continuous-filter convolutional networks
  • Materials Project ML
🌿 Autonomous Systems self-driving
Sensor fusion, localization, path planning, control theory
🔷 Self-Driving Cars
SLAM, Kalman filtering, trajectory optimization, behavioral planning
  • Tesla FSD (Full Self-Driving)
  • Neural network end-to-end driving
  • Waymo Driver
  • Cruise AV
  • Mobileye EyeQ
  • NVIDIA DRIVE
🔷 Perception Systems
3D object detection, bird's eye view representations, multi-sensor fusion
  • BEVFormer (Bird's Eye View)
  • Spatial cross-attention, temporal self-attention
  • DETR3D
  • PointPillars
  • Point cloud to pseudo-image conversion
  • CenterPoint
🔷 Drones & UAVs
  • DJI AI Flight Control
  • AirSim (Microsoft)
  • FlightGoggles
  • Real-time trajectory optimization, collision avoidance
🌿 Time Series & Forecasting temporal data
Autoregressive models, state space models, spectral analysis, trend decomposition
🔷 Deep Time Series Models
Recurrent architectures, temporal convolutions, attention over time
  • LSTM / GRU
  • Gating mechanisms, forget gates, cell state updates
  • Temporal Convolutional Networks
  • Dilated convolutions, causal convolutions
  • Transformer for Time Series
  • Positional encoding for temporal patterns
  • N-BEATS
  • Neural basis expansion analysis, interpretable forecasting
  • DeepAR (Amazon)
  • Autoregressive RNN with probabilistic forecasting
🔷 Foundation Models for Forecasting
Pre-trained models on diverse time series, zero-shot forecasting
  • TimeGPT Nixtla
  • Transformer pre-trained on 100B+ time series points
  • Chronos (Amazon) zero-shot
  • Tokenized time series, language model scaling laws
  • ForecastPFN
  • Prior-data fitted networks, in-context learning
🌿 Graph Neural Networks structured data
Message passing, graph convolutions, spectral graph theory, adjacency matrices
🔷 Core GNN Architectures
Neighborhood aggregation, permutation invariance, graph isomorphism
  • Graph Convolutional Networks (GCN)
  • H^(l+1) = σ(D^(-1/2)AD^(-1/2)H^(l)W^(l)), spectral approach
  • GraphSAGE
  • Inductive learning, sampling and aggregating
  • Graph Attention Networks (GAT)
  • Self-attention over graph neighborhoods
  • Graph Transformer
  • Global attention with positional encodings
  • Message Passing Neural Networks
  • m_ij = M(h_i, h_j, e_ij), h_i' = U(h_i, Σ m_ij)
🔷 Applications
  • Social Network Analysis
  • Knowledge Graph Reasoning
  • Molecular Property Prediction
  • Traffic Flow Prediction
  • Spatio-temporal graph modeling
🌿 AI Agents & Planning autonomous agents
Planning algorithms, state space search, multi-agent coordination, game theory
🔷 LLM-based Agents
Reasoning chains, tool usage, action space modeling
  • AutoGPT autonomous
  • LangChain Agents
  • ReAct (Reasoning + Acting)
  • Thought-action-observation loops
  • Toolformer
  • Self-supervised tool use learning
  • WebGPT
  • Code Interpreter (OpenAI)
🔷 Multi-Agent Systems
Cooperative game theory, Nash equilibrium, mechanism design
  • AutoGen (Microsoft) multi-agent
  • CrewAI
  • MetaGPT
  • ChatDev
  • Role assignment, communication protocols
🔷 AI Workflow & Automation Platforms
No-code/low-code platforms for building AI-powered workflows and automations.
Directed acyclic graphs (DAGs), workflow orchestration, event-driven systems
AI-First Platforms
  • Dify LLM app builder
  • Flowise drag-and-drop LLM
  • LangFlow visual LangChain
  • Botpress conversational AI
  • Rasa open source chatbot
  • Voiceflow voice/chat apps
General Automation + AI
  • Make (formerly Integromat) visual automation
  • n8n open source workflow
  • Zapier app integration
  • Microsoft Power Automate
  • IFTTT simple triggers
  • Activepieces open source
  • Windmill developer-first
Agent Orchestration
  • MCP (Model Context Protocol) Anthropic standard
  • OpenAI Assistants API
  • LangGraph stateful agents
  • State machines, graph-based agent workflows
  • Semantic Kernel (Microsoft)
  • Haystack deepset
  • Crew AI Studio
Enterprise AI Orchestration
  • Databricks MLflow
  • Kubeflow Pipelines
  • Azure ML Pipelines
  • AWS Step Functions
  • Google Cloud Workflows
  • Prefect data workflows
  • Airflow Apache
  • DAG scheduling, dependency management
🔷 Planning & Reasoning
Search algorithms, constraint satisfaction, logical inference
  • Tree of Thoughts
  • Breadth-first search over reasoning trees
  • Chain-of-Thought Prompting
  • Step-by-step reasoning decomposition
  • Self-Consistency Decoding
  • Sample multiple reasoning paths, majority vote
  • Program-aided Language Models
  • Code generation for numerical reasoning
🌿 Generative AI Architectures creation
Probabilistic modeling, likelihood maximization, latent variable models
🔷 Transformer Architectures
Self-attention: Attention(Q,K,V) = softmax(QK^T/√d_k)V, positional encoding
  • Vanilla Transformer
  • Multi-head attention, feed-forward networks
  • GPT (Decoder-only)
  • Causal masking, autoregressive generation
  • BERT (Encoder-only)
  • Bidirectional attention, masked language modeling
  • T5 (Encoder-Decoder)
  • Text-to-text unified framework
  • PaLM (Pathways)
  • Switch Transformer
  • Mixture of experts routing
  • Mamba state space
  • Selective state spaces, linear attention alternative
🔷 Diffusion Models
Forward process: q(x_t|x_{t-1}) = N(√(1-β_t)x_{t-1}, β_t I), reverse denoising
  • DDPM (Denoising Diffusion)
  • Markov chain diffusion, score matching
  • Stable Diffusion
  • DALL·E 2/3
  • Imagen / Parti
  • ControlNet controllable generation
  • Conditional generation with spatial controls
🔷 Variational Models
Evidence Lower BOund (ELBO), KL divergence regularization
  • VAE (Variational Autoencoder)
  • ELBO = E[log p(x|z)] - KL(q(z|x)||p(z))
  • β-VAE
  • β-weighted KL term for disentanglement
  • VQ-VAE / VQ-VAE-2
  • Vector quantization, discrete latent space
🌿 AI Safety & Alignment responsible AI
Robustness optimization, distributional shift, adversarial examples, reward modeling
🔷 Alignment Techniques
Human preference modeling, reward learning, value alignment
  • RLHF (Reinforcement Learning from Human Feedback)
  • Bradley-Terry preference model, reward model training
  • Constitutional AI (Anthropic)
  • Self-supervised harmfulness reduction
  • AI Safety via Debate
  • Two-player zero-sum game for truthfulness
  • Iterated Amplification
  • Red Teaming Methods
  • Adversarial testing, failure mode discovery
🔷 Interpretability & Explainability
Attribution methods, gradient-based explanations, feature importance
  • LIME / SHAP
  • Local linear approximations, Shapley values
  • Attention Visualization
  • Concept Activation Vectors
  • TCAV: directional derivatives in concept space
  • Mechanistic Interpretability
  • Anthropic's Circuit Analysis
  • Reverse engineering neural network computations
🔷 Robustness & Security
Adversarial perturbations, certified defenses, distributional robustness
  • Adversarial Training
  • Minimax optimization, PGD attacks
  • Certified Defenses
  • Lipschitz constraints, interval bound propagation
  • Differential Privacy
  • ε-differential privacy, noise injection
  • Federated Learning
  • Distributed learning, privacy preservation
🌿 Edge AI & Model Optimization efficiency
Model compression, quantization, pruning, efficient architectures
🔷 Model Compression
Singular value decomposition, weight magnitude pruning, entropy-based quantization
  • Knowledge Distillation
  • Student mimics teacher: L = αL_CE + (1-α)L_KD
  • Pruning (Magnitude/Structured)
  • Weight magnitude thresholding, lottery ticket hypothesis
  • Quantization (INT8/INT4)
  • Uniform/non-uniform quantization, calibration datasets
  • Low-Rank Factorization
  • Matrix decomposition: W ≈ UV^T
  • LoRA (Low-Rank Adaptation)
  • W = W₀ + BA, where B∈R^(d×r), A∈R^(r×k)
🔷 Mobile & Edge Models
Depthwise separable convolutions, neural architecture search
  • MobileNet v1/v2/v3
  • Depthwise separable convolutions, inverted residuals
  • EfficientNet
  • Compound scaling: depth/width/resolution
  • TinyBERT
  • DistilBERT
  • TensorFlow Lite
  • ONNX Runtime
  • Apple Core ML
🌿 Domain-Specific AI specialized applications
Domain adaptation, transfer learning, specialized loss functions
🔷 Healthcare & Medical AI
Medical image analysis, diagnostic classification, survival analysis
  • Med-PaLM (Google)
  • GPT-4 Medical
  • CheXNet (Chest X-ray)
  • DenseNet for radiological diagnosis
  • DeepMind AlphaFold
  • IBM Watson Health
  • Radiology AI (Various)
🔷 Finance & Trading
Time series forecasting, risk modeling, portfolio optimization
  • BloombergGPT
  • FinBERT
  • Algorithmic Trading AI
  • Market microstructure modeling, order flow prediction
  • Risk Management Models
  • Value at Risk (VaR), Monte Carlo simulations
  • Fraud Detection Systems
  • Anomaly detection, graph-based fraud networks
🔷 Legal AI
  • Legal BERT variants
  • Contract Analysis AI
  • Case Law Search
  • Patent Analysis
  • Legal document similarity, citation networks
🔷 Education & Learning
Adaptive learning, knowledge tracing, educational data mining
  • Khan Academy AI Tutor
  • Duolingo AI
  • Spaced repetition algorithms, forgetting curves
  • Adaptive Learning Systems
  • Bayesian knowledge tracing, item response theory
  • Academic Writing Assistants
🌿 Quantum AI & Computing quantum advantage
Quantum superposition, entanglement, quantum circuit learning, variational quantum algorithms
🔷 Quantum Machine Learning (QML)
Quantum feature maps, parameterized quantum circuits, quantum kernels
  • Variational Quantum Circuits (VQC)
  • U(θ) = ∏U_i(θ_i), parameterized quantum gates
  • Quantum Neural Networks
  • Quantum perceptrons, quantum backpropagation
  • Quantum Support Vector Machines
  • Quantum feature maps, exponential kernel spaces
  • Quantum Generative Models
  • Born machine, quantum GANs
  • IBM Qiskit Machine Learning
  • Google Cirq TensorFlow Quantum
  • PennyLane (Xanadu)
🔷 Quantum Algorithms
Grover's algorithm, quantum Fourier transform, amplitude amplification
  • Variational Quantum Eigensolver (VQE)
  • ⟨ψ(θ)|H|ψ(θ)⟩ minimization, NISQ algorithms
  • Quantum Approximate Optimization (QAOA)
  • Alternating ansatz: e^(-iγH_C)e^(-iβH_M)
  • Quantum Principal Component Analysis
  • Quantum matrix exponentiation, HHL algorithm
  • D-Wave Quantum Annealing
  • Ising model optimization, quantum tunneling
🔷 Hybrid Quantum-Classical
Variational hybrid algorithms, classical optimization of quantum circuits
  • Quantum-Classical Neural Networks
  • Quantum Transfer Learning
  • Pre-trained quantum feature extractors
  • Quantum Reinforcement Learning
  • Quantum policy gradients, quantum Q-learning
  • Quantum Federated Learning
🌿 Federated & Distributed Learning privacy-preserving
Distributed optimization, privacy preservation, secure aggregation, communication efficiency
🔷 Federated Learning Algorithms
Federated averaging, non-IID data challenges, client sampling strategies
  • FedAvg (Federated Averaging)
  • w^{t+1} = w^t - η∇F(w^t), F = Σp_kF_k(w)
  • FedProx (Federated Proximal)
  • Proximal term: μ/2||w-w^t||², heterogeneity handling
  • FedNova (Federated Nova)
  • Normalized averaging, varying local steps
  • SCAFFOLD
  • Control variates for client drift correction
  • FedOpt (Adam/AdaGrad variants)
  • Server-side adaptive optimization
🔷 Split & Vertical Learning
Model splitting, gradient compression, vertical data partitioning
  • Split Learning
  • Forward pass splitting, smashed data transmission
  • Vertical Federated Learning
  • Feature space partitioning, secure computation
  • SplitFed (Split + Federated)
  • Gradient Compression
  • Sparsification, quantization, error feedback
🔷 Privacy & Security
Differential privacy, secure aggregation, homomorphic encryption
  • Differential Privacy in FL
  • DP-SGD: noise σ = C√(2ln(1.25/δ))/ε
  • Secure Multiparty Computation
  • Secret sharing, garbled circuits
  • Byzantine-Robust Aggregation
  • Krum, trimmed mean, geometric median
  • Homomorphic Encryption
  • Computing on encrypted data, CKKS scheme
🌿 AI Infrastructure & MLOps production systems
Continuous integration/deployment, model monitoring, A/B testing, drift detection
🔷 Model Deployment & Serving
Load balancing, auto-scaling, latency optimization, resource allocation
  • Hugging Face Inference Endpoints
  • Replicate Cloud Platform
  • AWS SageMaker Endpoints
  • Google Vertex AI
  • Azure ML Endpoints
  • Seldon Core
  • KServe (Kubernetes)
  • TensorFlow Serving
  • TorchServe
  • ONNX Runtime Server
  • Request batching, model caching, GPU utilization
🔷 Monitoring & Observability
Statistical drift detection, performance monitoring, alert systems
  • Weights & Biases
  • MLflow Tracking
  • Neptune AI
  • ClearML
  • Evidently AI drift detection
  • KL divergence drift: D_KL(P_ref||P_curr)
  • Arize AI
  • Fiddler AI
  • WhyLabs
  • Population stability index, data quality metrics
🔷 Feature Engineering & Storage
Feature pipelines, versioning, real-time serving, consistency
  • Feast (Feature Store)
  • Tecton
  • Hopsworks
  • AWS Feature Store
  • Databricks Feature Store
  • DVC (Data Version Control)
  • Great Expectations
  • Feature consistency, point-in-time correctness
🔷 A/B Testing & Experimentation
Statistical significance, power analysis, multi-armed bandits
  • Optimizely
  • LaunchDarkly
  • Split.io
  • Google Optimize
  • Facebook Planout
  • Welch's t-test, sequential testing, false discovery rate
  • Multi-Armed Bandits
  • Thompson sampling, upper confidence bounds
🌿 Retrieval-Augmented Generation (RAG) knowledge integration
Dense retrieval, vector similarity, knowledge fusion, query decomposition
🔷 Dense Retrieval Systems
Bi-encoder architecture, contrastive learning, hard negative mining
  • DPR (Dense Passage Retrieval)
  • Similarity: sim(q,p) = E_Q(q)^T E_P(p)
  • ColBERT
  • Late interaction: Σ max_j E_q_i^T E_p_j
  • ANCE (Approximate Nearest Neighbor)
  • RetroMAE
  • Masked autoencoding for retrieval
  • E5 / BGE Embeddings
  • Instructor Embeddings
  • Task-aware dense retrieval
🔷 Advanced RAG Architectures
Multi-hop reasoning, fusion-in-decoder, retrieval refinement
  • FiD (Fusion-in-Decoder)
  • Independent encoding, joint decoding
  • REALM (Retrieval-Enhanced LM)
  • End-to-end retrieval learning
  • RAG-Token / RAG-Sequence
  • Self-RAG reflection
  • Retrieval necessity prediction, self-critique
  • Modular RAG
  • Graph RAG
  • Knowledge graph enhanced retrieval
🔷 Vector Databases & Search
Approximate nearest neighbor search, indexing algorithms, sharding
  • Pinecone
  • Weaviate
  • Qdrant
  • Chroma
  • Milvus / Zilliz
  • FAISS (Meta)
  • HNSW: Hierarchical Navigable Small World
  • Annoy (Spotify)
  • ScaNN (Google)
  • Product quantization, inverted file index
🌿 Causal AI & World Models reasoning & simulation
Causal inference, structural equations, counterfactual reasoning, physics simulation
🔷 Causal Inference & Discovery
Directed acyclic graphs, do-calculus, structural causal models
  • PC Algorithm
  • Constraint-based causal discovery
  • GES (Greedy Equivalence Search)
  • CausalML (Uber)
  • DoWhy (Microsoft)
  • do(X=x): P(Y|do(X=x)) causal intervention
  • Neural Causal Models
  • Structural equation models with neural networks
  • CausalNex
  • pgmpy (Probabilistic Graphical Models)
🔷 World Models & Simulation
Model-based reinforcement learning, physics simulation, predictive modeling
  • DreamerV3 (DeepMind)
  • Latent world model: p(s_{t+1}|s_t,a_t)
  • MuJoCo (Multi-Joint dynamics)
  • Contact dynamics, constraint solving
  • Isaac Gym (NVIDIA)
  • PyBullet
  • Habitat (Meta)
  • AI Habitat 2.0
  • ThreeDWorld (MIT)
  • Physics-informed neural networks (PINNs)
🔷 Digital Twins & Simulation
Real-time synchronization, digital-physical coupling, predictive maintenance
  • NVIDIA Omniverse
  • Unity ML-Agents
  • Unreal Engine AI
  • AnyLogic Simulation
  • CARLA (Autonomous Driving)
  • Sensor simulation, traffic modeling
  • Gazebo (Robotics)
  • CoppeliaSim
🌿 Creative AI artistic generation
Style transfer, generative adversarial training, artistic style optimization
🔷 Art & Visual Generation
Neural style transfer, GANs for art, aesthetic loss functions
  • DALL·E 2/3 text-to-image
  • Midjourney v6
  • Stable Diffusion Art
  • Adobe Firefly
  • RunwayML Gen-2
  • StyleGAN for Art
  • Style loss: L_style = Σ||G(F) - G(S)||²
  • Neural Style Transfer
  • Gram matrices, content + style loss
  • ArtBreeder
  • NightCafe Studio
🔷 Music & Audio Generation
Harmonic analysis, rhythm modeling, spectral synthesis
  • Suno AI commercial music
  • Udio AI music
  • MusicLM (Google)
  • Jukebox (OpenAI)
  • VQ-VAE hierarchical audio modeling
  • AIVA (AI Composer)
  • Amper Music
  • Soundraw
  • MuseNet (OpenAI)
  • Transformer for symbolic music
🔷 Creative Writing & Content
Language modeling for creativity, style control, narrative generation
  • GPT-4 Creative Writing
  • Claude Creative Assistant
  • Jasper AI
  • Copy.ai
  • Writesonic
  • NovelAI
  • Sudowrite
  • Controllable generation, style conditioning
🔷 Interactive & Procedural AI
Real-time generation, user interaction modeling, procedural algorithms
  • AI Dungeon
  • Character.AI
  • Replika
  • Procedural Content Generation
  • L-systems, cellular automata, noise functions
  • Unity ML-Agents Creative
  • Unreal Engine MetaHuman
🌿 Emerging AI Research cutting-edge
Scaling laws: L(N) = aN^(-α), compute-optimal training, emergent capabilities
🔷 Foundation Model Research
Scaling laws: L(N) = aN^(-α), compute-optimal training
  • GPT-5 rumored
  • Claude 4+ future
  • Gemini Advanced
  • Meta LLaMA 4 development
  • Mixture of Experts (MoE) scaling
  • Sparse expert routing, load balancing
🔷 Novel Architectures
Alternative attention mechanisms, efficient transformers
  • Mamba (State Space Models) efficiency
  • Selective state spaces, linear complexity
  • RetNet (Alternative to Transformers)
  • Retention mechanism, parallel/recurrent duality
  • Hyena (Subquadratic Attention)
  • Convolutional operators, implicit attention
  • Kolmogorov-Arnold Networks
  • KAN: learnable activation functions on edges
  • Liquid Neural Networks
  • Time-aware neurons, causal interactions
🔷 AGI Research
Multi-task learning, meta-learning, unified architectures
  • OpenAI Q* rumored reasoning
  • DeepMind Gato generalist agent
  • Multi-modal tokenization, unified architecture
  • AdA (Adaptive Agent)
  • Artificial General Intelligence projects
🔷 Neuromorphic Computing
Spiking neural networks, event-driven computation, brain-inspired architectures
  • Intel Loihi 2
  • Spiking neural networks, asynchronous computation
  • IBM TrueNorth
  • SpiNNaker (Manchester)
  • BrainChip Akida
  • Integrate-and-fire neurons, spike-timing dependent plasticity
  • Memristor Networks
  • Resistive memory, in-memory computation
Alternative ML Paradigms non-deep learning
Population-based algorithms, probabilistic inference, continual adaptation
🔷 Evolutionary & Genetic Algorithms
Population dynamics, fitness functions, genetic operators
  • NEAT (NeuroEvolution)
  • Topology evolution, complexification
  • Genetic Programming
  • Tree-based program evolution
  • Differential Evolution
  • DE: x' = x_a + F(x_b - x_c)
  • Particle Swarm Optimization
  • Swarm intelligence, velocity updates
🔷 Probabilistic & Bayesian ML
Prior distributions, posterior inference, uncertainty quantification
  • Gaussian Processes
  • Kernel methods, posterior predictive distribution
  • Bayesian Neural Networks
  • Weight uncertainty, variational inference
  • Variational Inference
  • KL divergence minimization, ELBO optimization
  • Hidden Markov Models
  • Forward-backward algorithm, Viterbi decoding
🔷 Online & Continual Learning
Catastrophic forgetting, memory replay, elastic weight consolidation
  • Online Gradient Descent
  • Regret bounds, convergence rates
  • Elastic Weight Consolidation
  • Fisher information matrix, importance weights
  • Progressive Neural Networks
  • Lateral connections, task-specific columns
  • Meta-Learning (MAML)
  • Gradient-based meta-learning, few-shot adaptation
📐 Mathematical Foundations & Backbone core theory
The mathematical bedrock that underlies all AI systems - from classical statistics to modern deep learning theory.
Linear Algebra vectors & matrices
Foundation of all neural network computations, transformations, and data representations.
  • Vector Spaces & Linear Transformations
  • Matrix Multiplication & Decomposition (SVD, LU, QR)
  • Eigenvalues & Eigenvectors
  • Principal Component Analysis (PCA)
  • Tensor Operations (multi-dimensional arrays)
Matrix multiplication: C = AB where C[i,j] = Σ(k) A[i,k] * B[k,j]
Neural layer: y = σ(Wx + b) where W=weights, x=input, b=bias, σ=activation
Calculus & Optimization learning algorithms
Drives gradient-based learning, backpropagation, and parameter optimization in neural networks.
  • Partial Derivatives & Gradients
  • Chain Rule (backpropagation foundation)
  • Gradient Descent & Variants (SGD, Adam, AdaGrad)
  • Lagrange Multipliers (constrained optimization)
  • Convex Optimization
  • Automatic Differentiation
Gradient Descent: θ(t+1) = θ(t) - α∇J(θ)
Backprop: ∂L/∂w = ∂L/∂y * ∂y/∂w (chain rule)
Adam: m(t) = β₁m(t-1) + (1-β₁)g(t), v(t) = β₂v(t-1) + (1-β₂)g(t)²
Probability & Statistics uncertainty & learning
Handles uncertainty, enables Bayesian learning, and provides theoretical foundations for many ML algorithms.
  • Bayes' Theorem & Bayesian Inference
  • Probability Distributions (Gaussian, Bernoulli, Categorical)
  • Maximum Likelihood Estimation (MLE)
  • Maximum A Posteriori (MAP) Estimation
  • Central Limit Theorem
  • Monte Carlo Methods
  • Markov Chains & Stochastic Processes
Bayes: P(A|B) = P(B|A)P(A) / P(B)
MLE: θ* = argmax Π P(x_i|θ)
Cross-entropy loss: L = -Σ y_i log(ŷ_i)
Information Theory entropy & compression
Quantifies information content, drives attention mechanisms, and enables efficient model architectures.
  • Entropy & Mutual Information
  • Kullback-Leibler (KL) Divergence
  • Cross-Entropy & Log-Likelihood
  • Data Compression & Coding Theory
  • Channel Capacity
Entropy: H(X) = -Σ P(x)log P(x)
KL Divergence: D_KL(P||Q) = Σ P(x)log(P(x)/Q(x))
Attention: Attention(Q,K,V) = softmax(QK^T/√d_k)V
Graph Theory & Discrete Math structure & logic
Powers graph neural networks, combinatorial optimization, and symbolic AI reasoning systems.
  • Graph Algorithms (BFS, DFS, Shortest Path)
  • Adjacency Matrices & Laplacian
  • Spectral Graph Theory
  • Boolean Logic & Satisfiability
  • Combinatorial Optimization
  • Message Passing Algorithms
GCN Layer: H^(l+1) = σ(D^(-1/2)AD^(-1/2)H^(l)W^(l))
Message Passing: h_v^(t+1) = UPDATE(h_v^(t), AGGREGATE({h_u^(t): u ∈ N(v)}))
Functional Analysis & Kernel Methods infinite dimensions
Provides theoretical foundations for SVMs, Gaussian processes, and function approximation theory.
  • Reproducing Kernel Hilbert Spaces (RKHS)
  • Kernel Trick & Kernel Functions
  • Universal Approximation Theorem
  • Fourier Analysis & Transforms
  • Wavelets & Multi-resolution Analysis
Kernel SVM: f(x) = Σ α_i y_i K(x_i, x) + b
RBF Kernel: K(x,x') = exp(-||x-x'||²/2σ²)
Neural Tangent Kernel: K_NTK(x,x') = E[∇f(x;θ)·∇f(x';θ)]
Numerical Methods & Computational Math efficient computation
Enables fast, stable computation in high-dimensional spaces with finite precision arithmetic.
  • Numerical Stability & Conditioning
  • Fast Fourier Transform (FFT)
  • Iterative Methods (Conjugate Gradient)
  • Approximation Theory
  • Finite Difference & Finite Element Methods
  • Parallel & Distributed Algorithms
Numerical stability: condition number κ(A) = ||A|| ||A^(-1)||
FFT: O(n log n) instead of O(n²) for DFT
BatchNorm: y = γ(x-μ)/σ + β (normalize then scale/shift)
Topology & Manifold Learning shape of data
Understanding the geometric structure of high-dimensional data and latent spaces in deep learning.
  • Manifold Theory & Embeddings
  • Riemannian Geometry
  • Persistent Homology
  • Dimensionality Reduction (t-SNE, UMAP)
  • Geometric Deep Learning
t-SNE: P(j|i) = exp(-||x_i-x_j||²/2σ_i²) / Σ exp(-||x_i-x_k||²/2σ_i²)
Manifold assumption: high-dim data lies on low-dim manifold
Game Theory & Decision Theory strategic learning
Foundation for multi-agent systems, GANs, reinforcement learning, and AI safety research.
  • Nash Equilibrium & Game Solutions
  • Minimax & Zero-sum Games
  • Mechanism Design
  • Auction Theory
  • Markov Decision Processes (MDPs)
  • Multi-Agent Reinforcement Learning
Minimax: min_θ max_φ V(θ,φ) (GANs)
Bellman: V(s) = max_a Σ P(s'|s,a)[R(s,a,s') + γV(s')]
Nash: strategies where no player benefits from unilateral change
Measure Theory & Advanced Probability rigorous foundations
Provides rigorous mathematical foundations for probability theory, stochastic processes, and learning theory.
  • σ-algebras & Measure Spaces
  • Lebesgue Integration
  • Martingales & Stopping Times
  • Concentration Inequalities
  • PAC Learning Theory
  • VC Dimension & Generalization Bounds
Hoeffding: P(|S_n - E[S_n]| ≥ t) ≤ 2exp(-2t²/n)
PAC: P(error ≤ ε) ≥ 1-δ with sufficient samples
VC bound: generalization error ≤ empirical error + complexity term
🔧 Metaheuristics & Optimization Paradigms algorithmic strategies
Applied optimization strategies and search algorithms that leverage mathematical foundations to solve complex problems across domains.
Classical Optimization Algorithms deterministic methods
Direct application of calculus and linear algebra for systematic optimization.
🔷 Gradient-Based Methods
  • Steepest Descent
  • θ(t+1) = θ(t) - α∇f(θ(t))
  • Newton's Method
  • θ(t+1) = θ(t) - [∇²f(θ(t))]⁻¹∇f(θ(t))
  • Quasi-Newton (BFGS, L-BFGS)
  • Hessian approximation, limited memory variants
  • Conjugate Gradient
  • Orthogonal search directions, quadratic convergence
🔷 Constrained Optimization
  • Sequential Quadratic Programming (SQP)
  • Quadratic subproblems, KKT conditions
  • Interior Point Methods
  • Barrier functions, primal-dual algorithms
  • Active Set Methods
  • Working set strategy, constraint identification
  • Penalty & Augmented Lagrangian
  • ℓ(x,λ,μ) = f(x) + λᵀh(x) + μ/2||h(x)||²
Metaheuristic Methods nature-inspired
Bio-inspired and physics-inspired algorithms for global optimization and search.
🔷 Evolutionary Algorithms
  • Genetic Algorithm (GA)
  • Selection, crossover, mutation operators
  • Evolution Strategy (ES)
  • (μ,λ)-ES: μ parents, λ offspring, selection
  • Differential Evolution (DE)
  • v = x_r1 + F(x_r2 - x_r3), mutation factor F
  • Genetic Programming (GP)
  • Tree-based program evolution, parse trees
  • NSGA-II/III
  • Multi-objective optimization, Pareto dominance
🔷 Swarm Intelligence
  • Particle Swarm Optimization (PSO)
  • v(t+1) = w·v(t) + c₁r₁(p_best - x) + c₂r₂(g_best - x)
  • Ant Colony Optimization (ACO)
  • Pheromone trails, probabilistic path construction
  • Artificial Bee Colony (ABC)
  • Employed/onlooker/scout bees, waggle dance
  • Firefly Algorithm
  • Attractiveness β₀e^(-γr²), distance-based movement
  • Grey Wolf Optimizer (GWO)
  • α, β, δ wolves hierarchy, encircling prey
🔷 Physics-Based Algorithms
  • Simulated Annealing (SA)
  • P(accept) = exp(-ΔE/kT), cooling schedule
  • Gravitational Search Algorithm
  • F = G·M₁M₂/R², gravitational force
  • Big Bang-Big Crunch
  • Expansion and contraction phases
  • Harmony Search
  • HMCR, PAR parameters, pitch adjustment
  • Water Cycle Algorithm
  • Evaporation, condensation, precipitation
🔷 Human-Based Algorithms
  • Teaching-Learning Based Optimization
  • Teacher phase, learner phase interactions
  • Imperialist Competitive Algorithm
  • Empires, colonies, assimilation policy
  • Social Spider Optimization
  • Vibrations on web, mating behavior
  • Brain Storm Optimization
  • Brainstorming process, idea generation
Specialized Search Algorithms domain-specific
Tailored algorithms for specific problem structures and constraints.
🔷 Tree & Graph Search
  • A* Search
  • f(n) = g(n) + h(n), admissible heuristic
  • Branch and Bound
  • Lower bounds, pruning strategies
  • Monte Carlo Tree Search (MCTS)
  • UCB1: x̄ᵢ + √(2lnn/nᵢ), exploration-exploitation
  • Minimax with Alpha-Beta
  • Game tree pruning, α-β cutoffs
🔷 Local Search Methods
  • Hill Climbing
  • Greedy local improvement, local optima
  • Tabu Search
  • Tabu list, aspiration criteria, memory structures
  • Variable Neighborhood Search
  • Systematic neighborhood changes
  • Iterated Local Search
  • Perturbation and local search cycles
  • GRASP (Greedy Randomized)
  • Construction + local search phases
🔷 Hybrid & Multi-Objective
  • Memetic Algorithms
  • Evolution + local search combination
  • MOEA/D (Multi-Objective EA)
  • Decomposition approach, weight vectors
  • SPEA2 (Strength Pareto)
  • Strength calculation, archive maintenance
  • Scatter Search
  • Reference set, diversification generation
Optimization Test Functions & Benchmarks evaluation
Standard benchmark problems for algorithm testing and comparison.
🔷 Classical Test Functions
  • Sphere Function
  • f(x) = Σxᵢ², unimodal, separable
  • Rosenbrock Function
  • f(x) = Σ[100(xᵢ₊₁-xᵢ²)² + (1-xᵢ)²], banana-shaped
  • Rastrigin Function
  • f(x) = An + Σ[xᵢ² - A cos(2πxᵢ)], multimodal
  • Ackley Function
  • Exponential and cosine terms, many local optima
  • Griewank Function
  • f(x) = 1 + (1/4000)Σxᵢ² - Π cos(xᵢ/√i)
🔷 CEC Competition Functions
  • CEC 2013/2017/2020 Suites
  • Shifted, rotated, composed functions
  • Large-Scale Optimization
  • High-dimensional problems, scalability testing
  • Multi-Modal Optimization
  • Multiple global optima, niching methods
  • Expensive Optimization
  • Limited function evaluations, surrogate models
🔷 Real-World Inspired Problems
  • Traveling Salesman Problem (TSP)
  • Combinatorial optimization, Hamiltonian cycle
  • Knapsack Problems
  • 0-1, bounded, unbounded variants
  • Vehicle Routing Problem
  • Capacity constraints, time windows
  • Job Shop Scheduling
  • Makespan minimization, precedence constraints
  • Portfolio Optimization
  • Risk-return tradeoff, correlation matrices
Modern Optimization Paradigms contemporary approaches
Recent developments combining traditional methods with machine learning.
🔷 Learning-Augmented Optimization
  • Neural Evolution Strategies
  • ES with neural networks, policy gradients
  • Differentiable Evolution
  • Gradient-based evolution, relaxed operations
  • Meta-Learning for Optimization
  • Learning to optimize, algorithm configuration
  • Bayesian Optimization
  • Gaussian process surrogates, acquisition functions
🔷 Quantum-Inspired Algorithms
  • Quantum Evolutionary Algorithm
  • Quantum bit representation, rotation gates
  • Quantum Particle Swarm
  • Quantum mechanics principles in PSO
  • Quantum Annealing
  • Adiabatic quantum computation, Ising models
🔷 Distributed & Parallel Optimization
  • Island Model GA
  • Population islands, migration strategies
  • Asynchronous Evolution
  • Non-blocking parallel evaluation
  • MapReduce Optimization
  • Distributed fitness evaluation, reduce operations
  • GPU-Accelerated Algorithms
  • Massive parallelization, CUDA implementations