Complete AI & Machine Learning Ecosystem (2025)

graph TD ROOT["Artificial Intelligence & Machine Learning"]:::main %% Supervised - Split into Classification & Regression ROOT --> SUP["Supervised Learning"]:::main SUP --> CLS["Classification
• Logistic Regression: $P(y=1|x) = \frac{1}{1 + e^{-(\beta_0 + \beta_1 x)}}$
• SVM: Maximize margin $2 / ||w||$
• Decision Trees: Entropy = $-\sum p_i \log p_i$
• Random Forest: Bagging + Trees
• KNN: Euclidean Distance $\sqrt{\sum (x_i - y_i)^2}$
• Naive Bayes: $P(y|x) = \frac{P(x|y)P(y)}{P(x)}$
• XGBoost: Gradient Boosting + Trees
• LightGBM: Leaf-wise Trees
• CatBoost: Categorical Handling
• Neural Networks: Softmax Output"]:::sub SUP --> REG["Regression
• Linear: $y = \beta_0 + \beta_1 x + \epsilon$
• Polynomial: $y = \beta_0 + \beta_1 x + \beta_2 x^2 + ...$
• Ridge: L2 Reg. $\lambda \sum \beta_i^2$
• Lasso: L1 Reg. $\lambda \sum |\beta_i|$
• ElasticNet: L1 + L2 Combo
• SVR: Epsilon-Tube Margin
• Gradient Boosting: Sequential Trees"]:::sub %% Unsupervised - Split into Clustering & Dim Reduction ROOT --> UNS["Unsupervised Learning"]:::main UNS --> CLU["Clustering
• K-Means: Minimize $\sum ||x_i - \mu_j||^2$
• Hierarchical: Dendrogram Distance
• DBSCAN: Density-Based $\epsilon$-Neighborhood
• OPTICS: Variable Density
• Gaussian Mixture: EM Algo $P(x) = \sum \pi_k N(x|\mu_k, \Sigma_k)$
• Mean Shift: Kernel Bandwidth"]:::sub UNS --> DIM["Dimensionality Reduction
• PCA: Eigen Decomposition $\Sigma = U \Lambda U^T$
• Kernel PCA: Non-Linear Mapping
• t-SNE: KL Divergence Min.
• UMAP: Manifold Approximation
• Autoencoders: Reconstruction Loss
• LDA: Class Separation
• ICA: Independent Components"]:::sub %% Semi & RL - Split Subtopics ROOT --> SEMI["Semi-Supervised Learning
• Self-Training: Iterative Labeling
• Label Propagation: Graph Diffusion
• Co-Training: Multi-View Features"]:::sub ROOT --> RL["Reinforcement Learning
• Q-Learning: $Q(s,a) = r + \gamma \max Q(s',a')$
• SARSA: On-Policy Update
• DQN / DDQN: Neural Q-Approx.
• PPO: Clipped Surrogate
• A2C / A3C: Advantage Actor-Critic
• SAC: Entropy Regularized"]:::sub %% Deep Learning - Split Architectures ROOT --> DL["Deep Learning"]:::main DL --> ANN["ANN / MLP
• Feedforward: $h = \sigma(Wx + b)$
• Backpropagation: Chain Rule $\frac{\partial L}{\partial w}$"]:::sub DL --> CNN["CNN
• Convolution: $ (f * g)(i,j) = \sum f(m,n) g(i-m,j-n) $
• Pooling: Max/Avg
• ResNet: Skip Connections
• YOLO: Bounding Boxes
• U-Net: Encoder-Decoder
• EfficientNet: Compound Scaling
• MobileNet: Depthwise Conv."]:::sub DL --> RNN["RNN
• Vanilla: $h_t = \tanh(W h_{t-1} + U x_t)$
• LSTM: Gates (Forget/Input/Output)
• GRU: Update/Reset Gates
• Bi-directional: Forward + Backward
• Seq2Seq: Encoder-Decoder"]:::sub DL --> TRANS["Transformers
• Attention: $ \text{Attn} = \text{softmax}(QK^T / \sqrt{d}) V $
• BERT: Masked LM
• GPT: Autoregressive
• LLaMA: Efficient Training
• Mistral: Sliding Window
• Grok: xAI Model
• ViT: Patch Embeddings
• Mamba: State Space"]:::sub DL --> LLM["Large Language Models
• Gemini: Multimodal
• Claude: Constitutional AI
• PaLM: Pathways
• Qwen: Chinese Focus
• Mixtral: MoE"]:::sub DL --> GEN["Generative Models
• GANs: Min-Max $V(G,D)$
• Diffusion: Denoising $p(x_{t-1}|x_t)$
• Stable Diffusion: Latent Space
• DALL·E: CLIP Guided
• Sora: Video Diffusion"]:::sub %% Domains - Split ROOT --> DOM["Domains"]:::main DOM --> CV["Computer Vision
• Object Detection: IoU
• Segmentation: Dice Coeff.
• Pose Estimation: Keypoints
• OCR: CTC Loss"]:::sub DOM --> NLP["Natural Language Processing
• NER: Entity F1
• Sentiment: Polarity Scores
• Translation: BLEU
• Summarization: ROUGE"]:::sub DOM --> AUDIO["Audio & Speech
• ASR: WER Metric
• TTS: MOS Score
• Whisper: CTC
• Wav2Vec: Self-Supervised
• HuBERT: Clustering
• VALL-E: Codec
• AudioLM: Tokenization"]:::sub DOM --> MULTI["Multimodal
• CLIP: Contrastive Loss
• LLaVA: Vision-Language
• Flamingo: Few-Shot
• ImageBind: Bind Modalities
• Kosmos: Unified"]:::sub %% Core - Split ROOT --> CORE["Core Components"]:::main CORE --> OPT["Optimizers
• SGD: $\theta = \theta - \eta \nabla L$
• Adam: Bias-Corrected Moments
• AdamW: Decoupled Decay
• RMSprop: Adaptive LR
• Lion: Sign Momentum
• LAMB: Layer-Wise"]:::sub CORE --> LOSS["Loss Functions
• Cross-Entropy: $-\sum y \log \hat{y}$
• MSE: $\frac{1}{n} \sum (y - \hat{y})^2$
• Focal: Modulated CE
• Contrastive: NT-Xent
• CTC: Alignment"]:::sub CORE --> REG["Regularization
• Dropout: Random Mask
• BatchNorm: $\hat{x} = \gamma (x - \mu)/\sigma + \beta$
• LayerNorm: Per-Feature
• Weight Decay: L2 on Weights
• Augmentation: Random Transforms"]:::sub %% Advanced - Split ROOT --> ADV["Advanced Techniques"]:::main ADV --> ENS["Ensemble Methods
• Bagging: Bootstrap Agg.
• Boosting: Weighted Errors
• XGBoost: 2nd-Order Grad.
• LightGBM: GOSS
• CatBoost: Ordered Boost."]:::sub ADV --> TRANSF["Transfer Learning
• Fine-Tuning: Last Layers
• Prompt Tuning: Soft Prompts
• Few-Shot: In-Context
• Zero-Shot: Pre-Trained"]:::sub %% Foundations - Split ROOT --> FOUND["Foundations"]:::main FOUND --> MATH["Mathematics"]:::main MATH --> LA["Linear Algebra
• Vectors: Dot Product $u \cdot v$
• Matrices: Det(A)
• SVD: $A = U \Sigma V^T$
• Eigen: $A v = \lambda v$"]:::sub MATH --> CALC["Calculus
• Derivatives: $f'(x)$
• Gradients: $\nabla f$
• Chain Rule: $(f \circ g)' = f' g'$"]:::sub MATH --> PROB["Probability & Stats
• Distributions: PDF/PMF
• Bayes: $P(A|B) = P(B|A)P(A)/P(B)$
• MLE: Argmax Log-Lik."]:::sub FOUND --> EVAL["Evaluation
• Accuracy / F1: $2PR/(P+R)$
• ROC-AUC: TPR vs FPR
• BLEU / ROUGE: N-Gram
• FID / IS: Generative
• Cross-Val: K-Fold"]:::sub %% Frameworks - Split ROOT --> FRAME["Frameworks & Tools"]:::main FRAME --> SK["Scikit-learn
• Pipelines
• Grid Search"]:::sub FRAME --> TORCH["PyTorch
• Dynamic Graphs
• Lightning: Trainer
• TorchVision: Datasets"]:::sub FRAME --> TF["TensorFlow
• Static Graphs
• Keras: Sequential
• TF Hub: Pre-Trained"]:::sub FRAME --> HF["Hugging Face
• Transformers Lib.
• Datasets Hub"]:::sub FRAME --> TOOLS["Others
• JAX: Autodiff
• Gradio: UI
• Streamlit: Apps
• OpenCV: CV
• W&B: Logging"]:::sub classDef main fill:#15803d,stroke:#166534,stroke-width:3px,color:white,font-weight:bold classDef sub fill:#fffbeb,stroke:#d97706,stroke-width:2px,color:black,font-weight:500