---

Table of Contents

1. Key Highlights & Sovereign Philosophy
2. Installation
3. Architecture & Feature Matrix
4. AutoML & End-to-End Pipeline Engine
5. Vector Retrieval & Approximate Nearest Neighbors (Milestone 1)
6. Recommendation Systems Universe (Milestone 2)
7. Causal Inference & Uplift Modeling (Milestone 3)
8. Survival Analysis & Reliability Engineering (Milestone 4)
9. Multi-Modal Vision-Language Universe (Milestone 5)
10. Scientific Machine Learning & PINNs (Milestone 6)
11. Algorithmic Fairness & Bias Mitigation (Milestone 7)
12. Edge AI, Quantization & Model Compression (Milestone 8)
13. 3D Computer Vision, Point Clouds & NeRF / 3DGS (Milestone 9)
14. Autonomous AI Agents & Execution Engines (Milestone 10)
15. Reinforcement Learning Universe (Milestone 11)
16. Advanced Graph Neural Networks Universe (Milestone 12)
17. Frontier LLMs, Linear Attention & Alignment (Milestone 13)
18. Classical ML, 2D Vision, Audio & Generative DL
19. Sovereign Explainable AI (XAI)
20. Next-Gen Generative AI, LoRA, Conformal & Stacking (Milestone 14)
21. Privacy, Quantum ML, Geo-Spatial, NAS & TDA (Milestone 15)
22. License & Citation

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Key Highlights & Sovereign Philosophy

• 100% Zero-Heavy-Dependency: Written strictly from fundamental mathematical formulations using only standard NumPy, SciPy, Pandas, Matplotlib, Seaborn, and OpenCV-headless. Zero reliance on PyTorch, TensorFlow, Scikit-Learn, Transformers, HuggingFace, SHAP, or Librosa.
• Ultra-Lightweight Distribution: An entire universe of production-ready machine learning, deep learning, computer vision, and LLMs packed into a single wheel under 1 Megabyte.
• Universal Compatibility: Cross-platform verification across Ubuntu Linux, Windows, and macOS on Python 3.9, 3.10, 3.11, 3.12, and 3.13.
• Battle-Tested Quality: 100% test pass rate with strict type checking (mypy), linting (flake8), and formatting (black).

---

Installation

Install Chokkhu effortlessly via pip:

pip install --upgrade chokkhu

Or install locally from source:

git clone https://github.com/tamimystic/chokkhu.git
cd chokkhu
pip install -e .

---

Architecture & Feature Matrix

Subsystem	Key Components & Architectures
AutoML & Pipelines	AutoTrainer, auto_train(), Bayesian Optimization (GP-EI/UCB), Hyperband Tuner, Leak-free pipeline()
Vector Retrieval	HNSWIndex, IVFPQIndex, RandomHyperplaneLSH, MinHashLSH, DenseRetriever, reciprocal_rank_fusion
Recommendation	SVDPlusPlus, ImplicitALS, NeuralCollaborativeFiltering, DeepFM, DLRM, SASRec, GRU4Rec
Causal & Uplift	PropensityScoreMatching, InverseProbabilityWeighting, DoublyRobustLearner, XLearner, TwoModelUplift, qini_score
Survival Analysis	KaplanMeierFitter, NelsonAalenFitter, CoxPHRegression, DeepSurv, concordance_index, integrated_brier_score
Multi-Modal Vision	CLIP, SigLIP, LLaVAMLPProjector, PerceiverResampler
Scientific ML	PINN, BurgersPINN, HeatPINN, WavePINN, NeuralODE (RK4), SymbolicRegressor (Genetic Programming)
Fairness & Ethics	demographic_parity_difference, equalized_odds_difference, ReweighingTransformer, DisparateImpactRemover, ThresholdOptimizer
Edge AI & Compression	UniformQuantizer, PostTrainingQuantizer (INT8/INT4 PTQ), QuantizedLinear, GlobalMagnitudePruner, KnowledgeDistiller
3D Vision & NeRF	PointNetClassifier, PointNetSegmenter, PointNet2Classifier (FPS + Ball Query), NeRFMLP, volume_render, GaussianSplatting3D
Autonomous AI Agents	ReActAgent, ToolRegistry, ChainOfThought, TreeOfThoughts, GraphOfThoughts, ReflexionEngine, MultiAgentCoordinator
Reinforcement Learning	DQN, DoubleDQN, DuelingDQN, PrioritizedReplayBuffer, REINFORCE, ActorCritic, PPO (GAE), SAC, LinUCBBandit, DecisionTransformer
Advanced GNNs	GCN, GAT, GraphSAGE, GIN, LaplacianPositionalEncoding, Graphormer, RGCNClassifier, EGNN, TemporalGraphNetwork, HGNN
Frontier LLMs	RWKV6 (Linear Attention), RetNet (Multi-Scale Retention), Mamba (S6 SSM), DeepSeekV3 (MLA + MoE + MTP), Qwen2_5, BitNet158 (1.58b ternary), DPOTrainer, KTOTrainer, ORPOTrainer
2D Vision & Audio	ResNet, ConvNeXt, SwinTransformer, DeiT, ViT, YOLO, Faster R-CNN, RetinaNet; STFT, MelSpectrogram, MFCC, Conformer, AST, Wav2Vec2
Explainable AI (XAI)	IntegratedGradients, SmoothGrad, DeepLIFT, KernelSHAP, PermutationImportance, PartialDependence

---

1. AutoML & End-to-End Pipeline Engine

1.1 Automated Machine Learning in One Line (auto_train)

import chokkhu as ck
import numpy as np

# Synthetic classification dataset
X_train = np.random.randn(200, 10)
y_train = np.random.randint(0, 2, size=200)

# Run full AutoML search: profiles data, tests candidate models, performs CV ranking
result = ck.auto_train(
    X_train=X_train,
    y_train=y_train,
    task="classification",
    time_budget_secs=30,
    metric="accuracy",
    cv=5,
    random_state=42
)

print(result.summary())
y_pred = result.predict(X_train[:10])

Parameter Breakdown: ck.auto_train

Parameter Name	Data Type	Default Value	Description / Purpose
X_train	np.ndarray / pd.DataFrame	Required	Feature matrix with shape (n_samples, n_features).
y_train	np.ndarray / pd.Series	Required	Target label array with shape (n_samples,).
task	str	"auto"	Learning task type: "classification", "regression", or "auto" (auto-detected).
time_budget_secs	int / float	60	Maximum time allocation in seconds for candidate search.
metric	str / None	None	Optimization objective: "accuracy", "f1", "roc_auc", "mse", "r2".
cv	int	5	Number of cross-validation folds for leaderboard validation.
random_state	int	42	Seed for deterministic data splitting and candidate initialization.

---

1.2 Bayesian Optimization (BayesianOptimization)

from chokkhu.automl import BayesianOptimization

# Objective function to maximize
def objective(params):
    x, y = params[0], params[1]
    return -(x**2 + y**2) + 10.0

# Define parameter search bounds [(min_x, max_x), (min_y, max_y)]
bounds = [(-5.0, 5.0), (-5.0, 5.0)]

opt = BayesianOptimization(
    func=objective,
    bounds=bounds,
    n_init=5,
    n_iter=20,
    acq="ei",
    xi=0.01,
    random_state=42
)
best_params, best_value = opt.optimize()
print(f"Optimal parameters: {best_params}, Max objective: {best_value}")

Parameter Breakdown: BayesianOptimization

Parameter Name	Data Type	Default Value	Description / Purpose
func	Callable	Required	Black-box target function mapping a 1D parameter array to a scalar score.
bounds	List[Tuple[float, float]]	Required	List of (min, max) tuples specifying box constraints for each dimension.
n_init	int	5	Number of initial random sample points prior to Gaussian Process fitting.
n_iter	int	20	Number of sequential Bayesian optimization iterations.
acq	str	"ei"	Acquisition function choice: "ei" (Expected Improvement) or "ucb" (Upper Confidence Bound).
xi	float	0.01	Exploration-exploitation balance trade-off parameter for Expected Improvement.
kappa	float	2.576	Exploration multiplier for UCB acquisition (mean + kappa * std).
random_state	int	42	Pseudorandom seed for reproducible initial sampling.

---

2. Vector Retrieval & Approximate Nearest Neighbors (ANN)

2.1 Hierarchical Navigable Small World (HNSWIndex)

import numpy as np
from chokkhu.models.retrieval import HNSWIndex

# 128-dimensional dense vector embeddings
embeddings = np.random.randn(1000, 128).astype(np.float32)
embeddings /= np.linalg.norm(embeddings, axis=1, keepdims=True)

# Build sovereign HNSW index
index = HNSWIndex(
    dim=128,
    max_elements=5000,
    M=16,
    ef_construction=100,
    ef_search=50,
    metric="cosine",
    random_state=42
)
index.add(embeddings)

# Query top-5 nearest neighbors
query = embeddings[0:1]
indices, distances = index.search(query, k=5)
print(f"Nearest indices: {indices}, Distances: {distances}")

Parameter Breakdown: HNSWIndex

Parameter Name	Data Type	Default Value	Description / Purpose
dim	int	Required	Dimensionality $D$ of the input feature vectors.
max_elements	int	10000	Maximum vector storage capacity allocated for the index.
M	int	16	Maximum number of bi-directional connection links per node in graph layers.
ef_construction	int	100	Size of dynamic candidate list during graph construction (controls index quality).
ef_search	int	50	Size of priority search queue during query time (controls recall vs. latency).
metric	str	"cosine"	Distance metric: "cosine" or "l2".
random_state	int	42	Random generator seed for probabilistic layer assignment.

---

2.2 Inverted File with Product Quantization (IVFPQIndex)

import numpy as np
from chokkhu.models.retrieval import IVFPQIndex

vectors = np.random.randn(2000, 64).astype(np.float32)

# Build compressed IVF-PQ index
ivfpq = IVFPQIndex(
    dim=64,
    n_clusters=16,
    n_subvectors=8,
    n_bits=8,
    n_probe=4,
    metric="l2",
    random_state=42
)
ivfpq.fit(vectors)
ivfpq.add(vectors)

query = vectors[0:1]
indices, distances = ivfpq.search(query, k=5)
print(f"IVF-PQ Top-5 matches: {indices}")

Parameter Breakdown: IVFPQIndex

Parameter Name	Data Type	Default Value	Description / Purpose
dim	int	Required	Total dimension of input vector (must be divisible by n_subvectors).
n_clusters	int	16	Number of coarse Voronoi centroids (coarse quantizer clusters).
n_subvectors	int	8	Number of low-dimensional sub-spaces $M$ for product quantization.
n_bits	int	8	Codebook bits per sub-vector ($2^{ ext{n_bits}}$ centroids per sub-space).
n_probe	int	4	Number of nearest coarse clusters inspected during query search.
metric	str	"l2"	Distance metric for residual scoring ("l2" or "cosine").
random_state	int	42	Deterministic seed for k-means centroid clustering.

---

3. Recommendation Systems Universe

3.1 DeepFM (Deep Factorization Machine)

import numpy as np
from chokkhu.models.recommendation import DeepFM

# Cardinalities for 3 categorical features: [100 users, 50 items, 10 categories]
cat_dims = [100, 50, 10]
model = DeepFM(
    cat_dims=cat_dims,
    num_dim=4,
    embedding_dim=16,
    dnn_hidden_dims=[64, 32],
    lr=0.001,
    dropout=0.1,
    random_state=42
)

# Training batch: categorical indices and continuous dense features
cat_inputs = np.array([[5, 12, 1], [42, 8, 3]])
num_inputs = np.random.randn(2, 4).astype(np.float32)
targets = np.array([1.0, 0.0])

# Forward pass & training step
preds = model.forward(cat_inputs, num_inputs)
loss = model.train_step(cat_inputs, num_inputs, targets)
print(f"DeepFM Predictions: {preds.squeeze()}, Loss: {loss:.4f}")

Parameter Breakdown: DeepFM

Parameter Name	Data Type	Default Value	Description / Purpose
cat_dims	List[int]	Required	Vocabulary / cardinality size for each categorical sparse field.
num_dim	int	0	Number of continuous numerical dense input features.
embedding_dim	int	16	Latent embedding vector size per categorical feature field.
dnn_hidden_dims	List[int]	[64, 32]	Hidden layer dimensions for the deep neural network component.
lr	float	0.001	Learning rate for stochastic gradient optimization.
dropout	float	0.1	Dropout regularization probability applied between deep dense layers.
random_state	int	42	Random seed for Xavier weight initialization.

---

3.2 SASRec (Self-Attentive Sequential Recommendation)

import numpy as np
from chokkhu.models.recommendation import SASRec

# Sequence of interacted item IDs: shape (batch_size, max_seq_len)
item_sequences = np.array([
    [1, 5, 23, 45, 12],
    [3, 8, 19, 0, 0]    # 0 is padding
])

sasrec = SASRec(
    item_count=100,
    max_len=5,
    hidden_dim=32,
    num_heads=2,
    num_blocks=2,
    dropout_rate=0.1,
    lr=0.001,
    random_state=42
)

# Sequence embeddings & scores for candidate items
seq_embeddings = sasrec.forward(item_sequences)
print(f"Sequence representations shape: {seq_embeddings.shape}")

Parameter Breakdown: SASRec

Parameter Name	Data Type	Default Value	Description / Purpose
item_count	int	Required	Total number of unique catalog items (including 0 padding token).
max_len	int	50	Maximum history sequence length considered per user session.
hidden_dim	int	64	Dimensionality of item embeddings and multi-head attention states.
num_heads	int	2	Number of parallel self-attention heads per transformer block.
num_blocks	int	2	Number of stacked causal self-attention transformer layers.
dropout_rate	float	0.1	Dropout probability for feedforward and attention layers.
lr	float	0.001	Learning rate for parameter updates.
random_state	int	42	Seed for model parameter initialization.

---

4. Causal Inference & Uplift Modeling

4.1 Doubly Robust Learner (DoublyRobustLearner)

import numpy as np
from chokkhu.models.causal import DoublyRobustLearner

# Covariates (X), binary treatment (T), and observed outcome (y)
X = np.random.randn(500, 5)
T = np.random.binomial(1, 0.5, size=500)
# Real treatment effect = +2.5
y = 1.2 * X[:, 0] + 2.5 * T + np.random.randn(500) * 0.1

dr = DoublyRobustLearner(clip_min=0.02, clip_max=0.98, random_state=42)
dr.fit(X, T, y)

# Estimate Individual Treatment Effects (ITE) and Average Treatment Effect (ATE)
ite_preds = dr.predict_ite(X[:5])
ate_estimate = dr.estimate_ate(X, T, y)
print(f"Estimated ATE: {ate_estimate:.3f} (True: 2.500)")

Parameter Breakdown: DoublyRobustLearner

Parameter Name	Data Type	Default Value	Description / Purpose
clip_min	float	0.01	Lower threshold for propensity score clipping to prevent division by zero.
clip_max	float	0.99	Upper threshold for propensity score clipping.
random_state	int	42	Random seed for outcome regression and propensity estimators.

---

4.2 Qini Score & Cumulative Uplift (qini_score)

import numpy as np
from chokkhu.models.causal import qini_score, uplift_at_k

y_true = np.array([1, 0, 1, 1, 0, 0, 1, 0])
treatment = np.array([1, 1, 1, 0, 0, 1, 0, 0])
uplift_preds = np.array([0.8, 0.6, 0.4, 0.3, 0.2, 0.1, -0.1, -0.2])

score = qini_score(y_true=y_true, treatment=treatment, uplift_preds=uplift_preds)
top_k_uplift = uplift_at_k(y_true=y_true, treatment=treatment, uplift_preds=uplift_preds, k=0.5)
print(f"Qini Score: {score:.4f}, Uplift@50%: {top_k_uplift:.4f}")

Parameter Breakdown: qini_score

Parameter Name	Data Type	Default Value	Description / Purpose
y_true	np.ndarray	Required	Binary ground truth conversion/outcome array (n_samples,).
treatment	np.ndarray	Required	Binary treatment assignment indicators (1=treated, 0=control).
uplift_preds	np.ndarray	Required	Predicted uplift / treatment effect score for ordering individuals.

---

5. Survival Analysis & Reliability Engineering

5.1 Cox Proportional Hazards Regression (CoxPHRegression)

import numpy as np
from chokkhu.models.survival import CoxPHRegression, concordance_index

# Covariates, event durations, and binary censoring events (1=died, 0=censored)
X = np.random.randn(200, 4)
times = np.random.exponential(scale=10.0, size=200)
events = np.random.binomial(1, 0.7, size=200)

cox = CoxPHRegression(lr=0.01, max_iter=150, l2_reg=1e-4)
cox.fit(X, times, events)

# Predict partial hazard log-ratios and evaluate Harrell's C-index
risk_scores = cox.predict_risk(X)
c_idx = concordance_index(times, -risk_scores, events)
print(f"Concordance Index: {c_idx:.4f}")

Parameter Breakdown: CoxPHRegression

Parameter Name	Data Type	Default Value	Description / Purpose
lr	float	0.01	Learning rate for Newton-Raphson / gradient ascent optimization.
max_iter	int	100	Maximum optimization iterations for partial likelihood maximization.
l2_reg	float	1e-4	L2 weight regularization coefficient to prevent coefficient explosion.
tol	float	1e-6	Convergence tolerance threshold on gradient norm.

---

5.2 DeepSurv (Deep Cox Proportional Hazards)

import numpy as np
from chokkhu.models.survival import DeepSurv

X = np.random.randn(300, 6)
times = np.random.exponential(scale=12.0, size=300)
events = np.random.binomial(1, 0.8, size=300)

deep_surv = DeepSurv(
    input_dim=6,
    hidden_dims=[32, 16],
    lr=0.001,
    l2_reg=1e-4,
    epochs=50,
    batch_size=32,
    random_state=42
)
deep_surv.fit(X, times, events)
risks = deep_surv.predict_risk(X[:5])
print(f"DeepSurv Predicted Risk Scores: {risks.flatten()}")

Parameter Breakdown: DeepSurv

Parameter Name	Data Type	Default Value	Description / Purpose
input_dim	int	Required	Number of input baseline clinical/covariate features.
hidden_dims	List[int]	[32, 16]	Hidden neural network layer architecture.
lr	float	0.001	Gradient learning rate.
l2_reg	float	1e-4	Weight decay penalty coefficient.
epochs	int	100	Number of full dataset training epochs.
batch_size	int	32	Minibatch size for stochastic updates.
random_state	int	42	Seed for weight initialization.

---

6. Multi-Modal Vision-Language Universe

6.1 Contrastive Language-Image Pretraining (CLIP)

import numpy as np
from chokkhu.models.multimodal import CLIP

# Create sovereign multi-modal CLIP model
clip = CLIP(
    vision_dim=128,
    text_dim=128,
    embed_dim=64,
    temperature=0.07,
    random_state=42
)

# Vision and text feature batches
img_features = np.random.randn(8, 128).astype(np.float32)
txt_features = np.random.randn(8, 128).astype(np.float32)

# Compute normalized embeddings & similarity matrix
img_emb, txt_emb, logits = clip.forward(img_features, txt_features)
loss = clip.compute_loss(img_emb, txt_emb)
print(f"CLIP Similarity Matrix Shape: {logits.shape}, InfoNCE Loss: {loss:.4f}")

Parameter Breakdown: CLIP

Parameter Name	Data Type	Default Value	Description / Purpose
vision_dim	int	256	Feature dimension output from the vision backbone.
text_dim	int	256	Feature dimension output from the text encoder backbone.
embed_dim	int	128	Shared joint latent multi-modal projection dimension.
temperature	float	0.07	Temperature scaling factor $ au$ for cosine similarity logits.
random_state	int	42	Seed for linear projector weight initialization.

---

6.2 Perceiver Resampler (PerceiverResampler)

import numpy as np
from chokkhu.models.multimodal import PerceiverResampler

# Arbitrary-length visual tokens: (batch_size=2, num_tokens=196, dim=256)
visual_tokens = np.random.randn(2, 196, 256).astype(np.float32)

resampler = PerceiverResampler(
    dim=256,
    num_latents=32,
    latent_dim=512,
    num_heads=8,
    num_layers=3,
    random_state=42
)

# Resample 196 variable tokens into exactly 32 fixed LLM prefix tokens
fixed_prefix_tokens = resampler.forward(visual_tokens)
print(f"Resampled Visual Tokens Shape: {fixed_prefix_tokens.shape}") # (2, 32, 512)

Parameter Breakdown: PerceiverResampler

Parameter Name	Data Type	Default Value	Description / Purpose
dim	int	256	Input token embedding dimension from vision encoder.
num_latents	int	64	Fixed number of output latent query tokens (Flamingo style).
latent_dim	int	512	Dimensionality of the learned latent queries and output tokens.
num_heads	int	8	Number of multi-head cross-attention heads.
num_layers	int	3	Number of stacked Perceiver cross-attention + FFN blocks.
random_state	int	42	Random seed for learnable latent queries.

---

7. Scientific Machine Learning & PINNs

7.1 Burgers' Equation Physics-Informed Neural Network (BurgersPINN)

import numpy as np
from chokkhu.models.sciml import BurgersPINN

# Sovereign PINN for Burgers' PDE: u_t + u * u_x - nu * u_xx = 0
pinn = BurgersPINN(
    layers=[2, 32, 32, 1],
    nu=0.01 / np.pi,
    lr=0.001,
    random_state=42
)

# Spatio-temporal collocation points (x, t)
collocation_points = np.random.uniform(-1.0, 1.0, size=(100, 2))
bc_points = np.array([[-1.0, 0.2], [1.0, 0.2]]) # boundary conditions
bc_u = np.array([[0.0], [0.0]])

# Physics-informed training step (data loss + PDE residual loss)
total_loss, pde_residual = pinn.train_step(collocation_points, bc_points, bc_u)
print(f"PINN Total Loss: {total_loss:.5f}, PDE Residual: {pde_residual:.5f}")

Parameter Breakdown: BurgersPINN

Parameter Name	Data Type	Default Value	Description / Purpose
layers	List[int]	[2, 32, 32, 1]	Neural network architecture [input_dim(x,t), hidden..., output_dim(u)].
nu	float	0.01 / np.pi	Fluid kinematic viscosity parameter $
u$.
lr	float	0.001	Adam/SGD optimizer learning rate.
random_state	int	42	Random seed for neural network layer initialization.

---

7.2 Neural Ordinary Differential Equations (NeuralODE)

import numpy as np
from chokkhu.models.sciml import NeuralODE

# Model continuous dynamical state trajectory dx/dt = f_theta(x, t)
node = NeuralODE(
    in_features=2,
    hidden_dim=32,
    method="rk4",
    random_state=42
)

# Initial state at t0
x0 = np.array([[1.0, 0.0], [-0.5, 0.8]])
t_span = np.linspace(0.0, 2.0, num=10)

# Integrate trajectory forward in time via 4th-order Runge-Kutta
trajectory = node.forward(x0, t_span)
print(f"Trajectory shape: {trajectory.shape}") # (10 timestamps, 2 samples, 2 dims)

Parameter Breakdown: NeuralODE

Parameter Name	Data Type	Default Value	Description / Purpose
in_features	int	2	State space dimensionality.
hidden_dim	int	32	Hidden layer width of derivative MLP $f_ heta$.
method	str	"rk4"	ODE solver: "rk4" (Runge-Kutta 4) or "euler".
rtol	float	1e-3	Relative error tolerance for adaptive step sizing.
atol	float	1e-5	Absolute error tolerance for adaptive step sizing.
random_state	int	42	Weight initialization seed.

---

8. Algorithmic Fairness & Bias Mitigation

8.1 Fairness Metrics & Disparate Impact Remediation

import numpy as np
from chokkhu.fairness import (
    demographic_parity_difference,
    equalized_odds_difference,
    DisparateImpactRemover,
    ReweighingTransformer
)

# Binary predictions, true labels, and protected attribute (e.g., 0 vs 1)
y_pred = np.array([1, 1, 0, 1, 0, 0, 1, 0])
y_true = np.array([1, 0, 0, 1, 1, 0, 1, 0])
sensitive_attr = np.array([1, 1, 1, 1, 0, 0, 0, 0])

dp_diff = demographic_parity_difference(y_pred, sensitive_attr)
eq_odds = equalized_odds_difference(y_true, y_pred, sensitive_attr)
print(f"Demographic Parity Diff: {dp_diff:.4f}, Equalized Odds Diff: {eq_odds:.4f}")

# Pre-processing mitigation: Repair feature distributions
features = np.random.randn(8, 4)
remover = DisparateImpactRemover(repair_level=0.8)
repaired_features = remover.fit_transform(features, sensitive_attr)

Parameter Breakdown: DisparateImpactRemover

Parameter Name	Data Type	Default Value	Description / Purpose
repair_level	float	1.0	Geometric repair interpolation factor $\lambda \in [0, 1]$ ($1.0 = ext{full repair}$).
sensitive_feature_idx	int / None	None	Optional column index of sensitive feature if included in $X$.

---

9. Edge AI, Quantization & Model Compression

9.1 Uniform Post-Training Quantization (PostTrainingQuantizer)

import numpy as np
from chokkhu.compression import PostTrainingQuantizer

# Dense FP32 weight matrix
weights_fp32 = np.random.randn(256, 128).astype(np.float32)

ptq = PostTrainingQuantizer(
    target_bits=8,
    method="uniform_symmetric",
    per_channel=True
)

# Quantize to INT8 integers and recover dequantized approximation
q_weights, scales, zero_points = ptq.quantize(weights_fp32)
recovered_fp32 = ptq.dequantize(q_weights, scales, zero_points)

quant_error = np.mean(np.abs(weights_fp32 - recovered_fp32))
print(f"Quantized Dtype: {q_weights.dtype}, Mean Absolute Quant Error: {quant_error:.6f}")

Parameter Breakdown: PostTrainingQuantizer

Parameter Name	Data Type	Default Value	Description / Purpose
target_bits	int	8	Target bit precision (8 for INT8, 4 for INT4).
method	str	"uniform_symmetric"	Quantization scheme: "uniform_symmetric" or "uniform_asymmetric".
per_channel	bool	False	Whether to compute independent scale per output channel/row.

---

10. 3D Computer Vision, Point Clouds & NeRF / 3DGS

10.1 PointNet++ Hierarchical Point Cloud Classifier (PointNet2Classifier)

import numpy as np
from chokkhu.models.vision_3d import PointNet2Classifier

# 3D Point cloud batch: (batch_size=2, num_points=512, xyz_coords=3)
point_clouds = np.random.randn(2, 512, 3).astype(np.float32)

pnet2 = PointNet2Classifier(
    num_classes=10,
    in_channels=3,
    random_state=42
)

# Forward pass using Set Abstraction (Farthest Point Sampling + Ball Query grouping)
logits = pnet2.forward(point_clouds)
print(f"PointNet++ Logits Shape: {logits.shape}") # (2, 10)

Parameter Breakdown: PointNet2Classifier

Parameter Name	Data Type	Default Value	Description / Purpose
num_classes	int	Required	Number of output 3D object classification categories.
in_channels	int	3	Input channel dimension (3 for $(x, y, z)$, 6 for $(x, y, z, r, g, b)$).
random_state	int	42	Seed for weight initialization.

---

10.2 Neural Radiance Fields (NeRFMLP & volume_render)

import numpy as np
from chokkhu.models.vision_3d import NeRFMLP, volume_render, generate_camera_rays

# Generate camera rays from camera pose matrix
c2w = np.eye(4, dtype=np.float32)
rays_o, rays_d = generate_camera_rays(H=64, W=64, focal=50.0, c2w=c2w)

nerf = NeRFMLP(pos_dim=63, dir_dim=27, hidden_dim=128, num_layers=6)

# Query positional densities and directional radiance colors
sample_pts = np.random.randn(100, 63).astype(np.float32)
sample_dirs = np.random.randn(100, 27).astype(np.float32)
density, rgb = nerf.forward(sample_pts, sample_dirs)

# Differentiable volume rendering along ray z-steps
z_vals = np.linspace(2.0, 6.0, 100, dtype=np.float32)
rendered_rgb, depth_map, acc_map = volume_render(density, rgb, z_vals, rays_d[:100])
print(f"Rendered RGB shape: {rendered_rgb.shape}")

Parameter Breakdown: NeRFMLP

Parameter Name	Data Type	Default Value	Description / Purpose
pos_dim	int	63	Sinusoidal frequency encoding dimension for 3D coordinate $(x,y,z)$.
dir_dim	int	27	Sinusoidal frequency encoding dimension for viewing direction $( heta, \phi)$.
hidden_dim	int	256	Hidden layer width of the radiance MLP backbone.
num_layers	int	8	Total number of fully-connected layers.
skip_layer	int	4	Layer index to concatenate residual input coordinate embeddings.
random_state	int	42	Random initialization seed.

---

11. Autonomous AI Agents & Execution Engines

11.1 ReAct Reasoning & Acting Agent (ReActAgent)

from chokkhu.models.nlp.agents import Tool, ToolRegistry, ReActAgent

# 1. Register custom Python execution tools
registry = ToolRegistry()

def add_numbers(a: float, b: float) -> float:
    """Add two numbers together."""
    return float(a) + float(b)

registry.register(Tool(
    name="calculator",
    func=add_numbers,
    description="Adds two numbers a and b together."
))

# 2. Initialize sovereign ReAct agent
agent = ReActAgent(
    tools=registry,
    max_steps=5,
    verbose=True
)

# Run deterministic agent loop
result = agent.run("Calculate the sum of 15.5 and 24.5")
print(f"Agent Final Output: {result.output}")

Parameter Breakdown: ReActAgent

Parameter Name	Data Type	Default Value	Description / Purpose
tools	ToolRegistry / List[Tool]	Required	Registry or list of callable tools with validation schemas.
max_steps	int	10	Maximum reasoning-action-observation cycles before termination.
model_callable	Callable / None	None	Optional LLM completion backend (defaults to rule-based parser).
verbose	bool	False	If True, logs step-by-step Thought, Action, Action Input, and Observation.

---

11.2 Tree of Thoughts Reasoning (TreeOfThoughts)

from chokkhu.models.nlp.agents import TreeOfThoughts

# Custom thought evaluator heuristic
def custom_evaluator(thought_state: str) -> float:
    return 1.0 if "valid" in thought_state else 0.2

tot = TreeOfThoughts(
    max_depth=3,
    num_branches=3,
    search_method="bfs",
    evaluator=custom_evaluator
)

best_path = tot.solve(initial_problem="Solve constraint satisfaction riddle")
print(f"Best reasoning trajectory: {best_path}")

Parameter Breakdown: TreeOfThoughts

Parameter Name	Data Type	Default Value	Description / Purpose
max_depth	int	3	Maximum tree search depth / reasoning steps.
num_branches	int	3	Number of alternative candidate thoughts generated per node.
search_method	str	"dfs"	Tree exploration strategy: "dfs" (Depth-First) or "bfs" (Breadth-First).
evaluator	Callable / None	None	Value function scoring candidate thought nodes.
generator	Callable / None	None	Generator function expanding candidate subsequent thoughts.

---

12. Reinforcement Learning Universe

12.1 Proximal Policy Optimization with GAE (PPO)

import numpy as np
from chokkhu.models.rl import PPO

# State dim = 4 (e.g. CartPole), Action dim = 2
ppo = PPO(
    state_dim=4,
    action_dim=2,
    actor_hidden=[64, 64],
    critic_hidden=[64, 64],
    lr_actor=0.0003,
    lr_critic=0.001,
    gamma=0.99,
    gae_lambda=0.95,
    clip_epsilon=0.2,
    ppo_epochs=10,
    batch_size=32,
    entropy_coeff=0.01,
    random_state=42
)

# Collect trajectory transitions
state = np.array([0.1, -0.2, 0.05, 0.3])
action, log_prob, value = ppo.select_action(state)

# Update policy with Generalized Advantage Estimation (GAE)
states = np.random.randn(64, 4)
actions = np.random.randint(0, 2, size=64)
old_log_probs = np.random.randn(64)
rewards = np.random.randn(64)
dones = np.zeros(64, dtype=bool)
values = np.random.randn(64)

loss_dict = ppo.update(states, actions, old_log_probs, rewards, dones, values)
print(f"PPO Loss Info: {loss_dict}")

Parameter Breakdown: PPO

Parameter Name	Data Type	Default Value	Description / Purpose
state_dim	int	Required	Dimensionality of the environment observation state vector.
action_dim	int	Required	Number of discrete actions available to the agent.
actor_hidden	List[int]	[64, 64]	Hidden layer sizes for the actor policy network $\pi_ heta(a|s)$.
critic_hidden	List[int]	[64, 64]	Hidden layer sizes for the critic baseline network $V_\phi(s)$.
lr_actor	float	0.0003	Learning rate for actor parameter updates.
lr_critic	float	0.001	Learning rate for value function critic updates.
gamma	float	0.99	Discount factor $\gamma$ for future rewards.
gae_lambda	float	0.95	Factor $\lambda$ for Generalized Advantage Estimation trade-off.
clip_epsilon	float	0.2	PPO surrogate objective clipping range $(1 \pm \epsilon)$.
ppo_epochs	int	10	Optimization epochs per rollout batch.
batch_size	int	64	Minibatch size during policy updates.
entropy_coeff	float	0.01	Exploration entropy bonus coefficient.
random_state	int	42	Seed for weight initialization.

---

12.2 Soft Actor-Critic (SAC) & Multi-Armed Bandits (LinUCBBandit)

import numpy as np
from chokkhu.models.rl import SAC, LinUCBBandit

# 1. Soft Actor-Critic for continuous control
sac = SAC(
    state_dim=8,
    action_dim=2,
    actor_hidden=[64, 64],
    critic_hidden=[64, 64],
    lr=0.0003,
    gamma=0.99,
    tau=0.005,
    alpha=0.2,
    random_state=42
)
action = sac.select_action(np.random.randn(8))

# 2. Contextual Multi-Armed Bandits with LinUCB
bandit = LinUCBBandit(n_arms=5, context_dim=10, alpha=1.0, random_state=42)
context = np.random.randn(10)
chosen_arm = bandit.select_arm(context)
bandit.update(arm=chosen_arm, context=context, reward=1.0)
print(f"SAC Action: {action}, LinUCB Chosen Arm: {chosen_arm}")

Parameter Breakdown: SAC

Parameter Name	Data Type	Default Value	Description / Purpose
state_dim	int	Required	Continuous state observation space dimensionality.
action_dim	int	Required	Continuous action space dimensionality.
actor_hidden	List[int]	[64, 64]	Layer dimensions for Gaussian policy network.
critic_hidden	List[int]	[64, 64]	Layer dimensions for twin Q-critic networks.
lr	float	0.0003	Learning rate for actor, critic, and entropy optimizer.
gamma	float	0.99	Reward discount factor.
tau	float	0.005	Soft target update polyak averaging coefficient $ au$.
alpha	float	0.2	Entropy temperature balancing exploration and maximum reward.
random_state	int	42	Random seed.

---

13. Advanced Graph Neural Networks Universe

13.1 Graphormer with Laplacian Positional Encoding (Graphormer)

import numpy as np
from chokkhu.models.gnn import Graphormer, LaplacianPositionalEncoding

# Node features: (num_nodes=6, in_features=16)
x = np.random.randn(6, 16).astype(np.float32)
# Adjacency matrix
adj = np.array([
    [0, 1, 1, 0, 0, 0],
    [1, 0, 1, 0, 0, 0],
    [1, 1, 0, 1, 0, 0],
    [0, 0, 1, 0, 1, 1],
    [0, 0, 0, 1, 0, 1],
    [0, 0, 0, 1, 1, 0]
], dtype=np.float32)

# Compute graph Laplacian positional eigenvectors
pe_encoder = LaplacianPositionalEncoding(k=4, normalization="sym")
lap_pe = pe_encoder.compute(adj)

graphormer = Graphormer(
    in_features=16,
    hidden_dim=32,
    out_features=8,
    num_heads=4,
    num_layers=2,
    pe_dim=4,
    dropout=0.1,
    random_state=42
)

node_embeddings = graphormer.forward(x, adj, pe=lap_pe)
print(f"Graphormer Output Node Embeddings Shape: {node_embeddings.shape}") # (6, 8)

Parameter Breakdown: Graphormer

Parameter Name	Data Type	Default Value	Description / Purpose
in_features	int	Required	Dimension of input node feature representations.
hidden_dim	int	64	Transformer hidden dimension.
out_features	int	16	Final node embedding output dimensionality.
num_heads	int	4	Number of multi-head graph attention heads.
num_layers	int	2	Number of stacked Graphormer transformer layers.
pe_dim	int	8	Dimension of input Laplacian positional encoding vectors.
dropout	float	0.1	Attention and feedforward dropout probability.
random_state	int	42	Random initialization seed.

---

13.2 Equivariant GNN (EGNN) & Relational GCN (RGCNClassifier)

import numpy as np
from chokkhu.models.gnn import EGNN, RGCNClassifier

# 1. E(n) Equivariant Graph Neural Network for 3D Molecular Coordinates
h = np.random.randn(5, 16).astype(np.float32)      # Invariant scalar features
x_coords = np.random.randn(5, 3).astype(np.float32) # 3D Cartesian coordinates
edge_index = np.array([[0, 1, 2, 3], [1, 2, 3, 4]])

egnn = EGNN(
    in_node_features=16,
    hidden_dim=32,
    out_node_features=16,
    num_layers=2,
    coord_dim=3,
    random_state=42
)
h_out, x_coords_out = egnn.forward(h, x_coords, edge_index)
print(f"EGNN Equivariant 3D Coordinates Output Shape: {x_coords_out.shape}")

# 2. Relational Graph Convolutional Network (Knowledge Graphs)
edge_types = np.array([0, 1, 0, 2])
rgcn = RGCNClassifier(
    in_features=16,
    hidden_dim=32,
    out_features=4,
    num_relations=3,
    num_layers=2,
    random_state=42
)
node_logits = rgcn.forward(h, edge_index, edge_types)
print(f"R-GCN Logits Shape: {node_logits.shape}")

Parameter Breakdown: EGNN

Parameter Name	Data Type	Default Value	Description / Purpose
in_node_features	int	Required	Dimension of scalar node invariant features.
hidden_dim	int	32	Hidden feature channel width.
out_node_features	int	16	Dimension of transformed invariant node features.
num_layers	int	2	Number of equivariant message-passing layers.
coord_dim	int	3	Geometric coordinate dimension (e.g., 3 for 3D point clouds).
random_state	int	42	Weight initialization seed.

---

14. Frontier LLMs, Linear Attention & Alignment

14.1 DeepSeek-V3 MoE with Multi-Head Latent Attention (DeepSeekV3)

import numpy as np
from chokkhu.models.nlp import DeepSeekV3

# Token sequence: (batch_size=2, seq_len=8)
input_tokens = np.array([
    [12, 45, 89, 230, 412, 18, 92, 5],
    [7, 102, 304, 511, 22, 67, 88, 14]
])

model = DeepSeekV3(
    vocab_size=1000,
    hidden_dim=64,
    num_layers=2,
    num_heads=4,
    q_lora_rank=16,
    kv_lora_rank=16,
    n_routed_experts=4,
    n_shared_experts=1,
    top_k=2,
    mtp_depth=1,
    random_state=42
)

# Forward pass computing next-token logits + auxiliary MoE load balancing loss
logits, aux_loss = model.forward(input_tokens)
print(f"DeepSeek-V3 Logits Shape: {logits.shape}, MoE Auxiliary Loss: {aux_loss:.4f}")

Parameter Breakdown: DeepSeekV3

Parameter Name	Data Type	Default Value	Description / Purpose
vocab_size	int	1000	Size of token vocabulary dictionary.
hidden_dim	int	128	Model latent embedding dimension.
num_layers	int	2	Number of stacked DeepSeek transformer layers.
num_heads	int	4	Number of Multi-Head Latent Attention (MLA) heads.
q_lora_rank	int	32	Low-rank query compression dimension $d_c$.
kv_lora_rank	int	32	Low-rank key-value cache compression dimension $d_c'$.
n_routed_experts	int	4	Total number of routed Mixture-of-Experts.
n_shared_experts	int	1	Number of dedicated always-active shared experts.
top_k	int	2	Number of routed experts selected per token.
mtp_depth	int	1	Multi-Token Prediction (MTP) depth head count.
random_state	int	42	Seed for weight initialization.

---

14.2 Mamba Selective State Space Model (Mamba) & RWKV-v6 (RWKV6)

import numpy as np
from chokkhu.models.nlp import Mamba, RWKV6

input_ids = np.array([[15, 34, 128, 492, 10]])

# 1. Sovereign Mamba (S6 Selective State Space Model)
mamba = Mamba(
    vocab_size=1000,
    d_model=64,
    d_state=16,
    d_conv=4,
    expand=2,
    num_layers=2,
    random_state=42
)
mamba_logits = mamba.forward(input_ids)
print(f"Mamba S6 Logits Shape: {mamba_logits.shape}")

# 2. Sovereign RWKV-v6 (WKV linear attention with dynamic time-mixing)
rwkv = RWKV6(
    vocab_size=1000,
    hidden_dim=64,
    num_layers=2,
    head_size=16,
    random_state=42
)
rwkv_logits = rwkv.forward(input_ids)
print(f"RWKV-v6 Logits Shape: {rwkv_logits.shape}")

Parameter Breakdown: Mamba

Parameter Name	Data Type	Default Value	Description / Purpose
vocab_size	int	1000	Size of vocabulary.
d_model	int	128	Model state dimension.
d_state	int	16	Latent SSM state expansion dimension $N$.
d_conv	int	4	1D temporal convolution kernel width.
expand	int	2	Block expansion factor $E$ ($E \cdot d_{ ext{model}}$ inner width).
num_layers	int	2	Number of stacked Mamba SSM layers.
random_state	int	42	Random seed.

---

14.3 Direct Preference Optimization (DPOTrainer)

import numpy as np
from chokkhu.models.nlp import DPOTrainer, MiniGPT

# Create policy model and frozen reference model
policy = MiniGPT(vocab_size=500, hidden_dim=64, num_layers=2, num_heads=2)
ref_model = MiniGPT(vocab_size=500, hidden_dim=64, num_layers=2, num_heads=2)

dpo = DPOTrainer(
    model=policy,
    ref_model=ref_model,
    beta=0.1,
    lr=1e-4
)

# Chosen vs. Rejected completion token batches
prompt_chosen = np.array([[10, 25, 42, 100], [12, 19, 88, 204]])
prompt_rejected = np.array([[10, 25, 42, 311], [12, 19, 88, 499]])

loss, implicit_reward_chosen, implicit_reward_rejected = dpo.train_step(
    prompt_chosen=prompt_chosen,
    prompt_rejected=prompt_rejected
)
print(f"DPO Loss: {loss:.4f}, Margin: {(implicit_reward_chosen - implicit_reward_rejected).mean():.4f}")

Parameter Breakdown: DPOTrainer

Parameter Name	Data Type	Default Value	Description / Purpose
model	Module	Required	Trainable actor LLM policy being aligned.
ref_model	Module	Required	Frozen reference baseline model $\pi_{ ext{ref}}$.
beta	float	0.1	Temperature regularization parameter $eta$ controlling KL divergence penalty.
lr	float	1e-4	Learning rate for policy optimizer.

---

15. Classical ML, 2D Vision, Audio & Generative DL

15.1 Generative AI: Variational Autoencoder (VAE) & Diffusion (DDPM)

import numpy as np
from chokkhu.models import VAE, DDPM

# 1. Variational Autoencoder (VAE)
images_flat = np.random.randn(100, 784).astype(np.float32)
vae = VAE(input_dim=784, latent_dim=32, hidden_dim=128)
recon, mu, logvar = vae.forward(images_flat)
vae_loss = vae.compute_loss(images_flat, recon, mu, logvar)
print(f"VAE Loss: {vae_loss:.4f}")

# 2. Denoising Diffusion Probabilistic Model (DDPM)
ddpm = DDPM(input_dim=784, timesteps=1000, beta_start=1e-4, beta_end=0.02)
sampled_images = ddpm.sample(num_samples=4)
print(f"DDPM Generated Samples Shape: {sampled_images.shape}")

Parameter Breakdown: DDPM

Parameter Name	Data Type	Default Value	Description / Purpose
input_dim	int	Required	Flattened data dimension.
timesteps	int	1000	Number of forward noise diffusion steps $T$.
beta_start	float	1e-4	Initial variance schedule value $eta_1$.
beta_end	float	0.02	Final variance schedule value $eta_T$.

---

15.2 Speech & Audio Signal Processing (STFT, MFCC, Conformer)

import numpy as np
from chokkhu.models import stft, melspectrogram, mfcc, Conformer

# 1-second 16kHz raw audio waveform
waveform = np.sin(2 * np.pi * 440 * np.linspace(0, 1, 16000)).astype(np.float32)

# Extract Mel-Spectrogram and MFCCs
mel_spec = melspectrogram(waveform, sample_rate=16000, n_fft=512, hop_length=160, n_mels=80)
mfcc_features = mfcc(waveform, sample_rate=16000, n_mfcc=13)
print(f"Mel-Spectrogram Shape: {mel_spec.shape}, MFCC Shape: {mfcc_features.shape}")

# Speech Conformer (Macaron-style FFN + MHA + Depthwise Conv)
conformer = Conformer(
    input_dim=80,
    num_heads=4,
    ffn_dim=128,
    num_blocks=2,
    conv_kernel_size=15
)
spec_batch = np.random.randn(2, 100, 80).astype(np.float32)
conformer_out = conformer.forward(spec_batch)
print(f"Conformer Output Shape: {conformer_out.shape}")

Parameter Breakdown: Conformer

Parameter Name	Data Type	Default Value	Description / Purpose
input_dim	int	Required	Feature dimension per audio time frame (e.g. 80 Mel bins).
num_heads	int	4	Number of multi-head attention heads.
ffn_dim	int	128	Feedforward intermediate dimension (Macaron structure).
num_blocks	int	2	Number of stacked Conformer blocks.
conv_kernel_size	int	15	Depthwise 1D convolution kernel receptive field.

---

16. Sovereign Explainable AI (XAI)

16.1 Integrated Gradients & DeepLIFT (IntegratedGradients, DeepLIFT)

import numpy as np
import chokkhu as ck
from chokkhu.explainability import IntegratedGradients, DeepLIFT

# Create a trained neural model
model = ck.NeuralNetwork(layers=[10, 32, 2], activation="relu")
sample = np.random.randn(1, 10)

# 1. Axiomatic feature attribution via Integrated Gradients
ig = IntegratedGradients(model=model, steps=50, baseline=None)
attributions = ig.attribute(sample, target_class=0)
print(f"Integrated Gradients Attributions Shape: {attributions.shape}")

# 2. DeepLIFT difference-from-reference conservation
dlift = DeepLIFT(model=model, baseline=np.zeros((1, 10)))
dlift_attributions = dlift.attribute(sample, target_class=0)
print(f"DeepLIFT Attributions: {dlift_attributions.flatten()}")

Parameter Breakdown: IntegratedGradients

Parameter Name	Data Type	Default Value	Description / Purpose
model	Any	Required	Differentiable neural network model instance.
steps	int	50	Number of Riemann summation interpolation steps along path.
baseline	np.ndarray / None	None	Reference neutral baseline vector (defaults to zero array).

---

---

17. Next-Gen Generative AI, LoRA, Conformal & Stacking (Milestone 14)

17.1 Continuous ODE Flow Matching & Rectified Flows (FlowMatching, RectifiedFlow)

import numpy as np
from chokkhu.models.generative import FlowMatching, RectifiedFlow

# Generate 2D training data
X_train = np.random.randn(200, 2) * 0.5 + 2.0

# 1. Continuous Velocity Field Flow Matching with Optimal Transport
flow = FlowMatching(input_dim=2, hidden_dim=64, num_layers=3, lr=1e-3, sigma_min=1e-4)
flow.fit(X_train, epochs=20, batch_size=32)

# Sample new points using 4th-order Runge-Kutta (RK4) integration
synthetic_samples = flow.sample(num_samples=100, steps=50, method="rk4")
print(f"Generated Flow Samples Shape: {synthetic_samples.shape}")

# 2. Rectified Flow interpolation with straight-line trajectories
rect_flow = RectifiedFlow(input_dim=2, hidden_dim=32, lr=1e-3)
rect_flow.fit(X_train, epochs=10)
rect_samples = rect_flow.sample(num_samples=50, steps=20, method="midpoint")
print(f"Rectified Flow Samples Shape: {rect_samples.shape}")

Parameter Breakdown: FlowMatching

Parameter Name	Data Type	Default Value	Description / Purpose
input_dim	int	Required	Dimensionality of the continuous input space $D$.
hidden_dim	int	64	Hidden layer width for the time-dependent velocity MLP network $v_\theta(x, t)$.
num_layers	int	3	Number of dense hidden layers in the velocity field approximator.
lr	float	1e-3	Gradient descent Adam/SGD learning rate during flow matching loss minimization.
sigma_min	float	1e-4	Minimum perturbation noise standard deviation for numerical stability.

---

17.2 Invertible Normalizing Flows (RealNVP, AffineCouplingLayer)

import numpy as np
from chokkhu.models.generative import RealNVP

# Continuous tabular / latent features
X = np.random.randn(100, 4)

# Multi-layer RealNVP with analytical Jacobian log-determinant
nvp = RealNVP(input_dim=4, num_layers=4, hidden_dim=32, lr=1e-3)
nvp.fit(X, epochs=15, batch_size=16)

# Exact log-likelihood computation
log_probs = nvp.log_prob(X)
print(f"Mean Log-Likelihood: {np.mean(log_probs):.4f}")

# Invertible sampling from latent base standard Gaussian
generated_data = nvp.sample(num_samples=50)
print(f"RealNVP Sample Shape: {generated_data.shape}")

Parameter Breakdown: RealNVP

Parameter Name	Data Type	Default Value	Description / Purpose
input_dim	int	Required	Feature dimensionality $D$ (must be $\ge 2$ for split-coupling).
num_layers	int	4	Number of alternating affine coupling layers in the flow cascade.
hidden_dim	int	32	Hidden layer dimension for scale $s(x)$ and translation $t(x)$ sub-networks.
lr	float	1e-3	Learning rate for maximum likelihood estimation via backpropagation.

---

17.3 Parameter-Efficient Fine-Tuning (LoRALinear, LoRAAdapter)

import numpy as np
from chokkhu.models.generative import LoRALinear, LoRAAdapter

# 1. Direct Low-Rank Linear Adaptation: W_adapted = W0 + (alpha / r) * (B @ A)
linear = LoRALinear(in_features=128, out_features=64, rank=4, alpha=8.0)

x = np.random.randn(8, 128)
y = linear.forward(x)
print(f"Adapted Linear Output Shape: {y.shape}")

# Merge adapter weights directly into frozen base weight matrix for zero-latency inference
linear.merge()
y_merged = linear.forward(x)
np.testing.assert_allclose(y, y_merged, atol=1e-5)

# 2. Attach PEFT LoRA adapters to arbitrary deep architectures
model_weights = {
    "encoder.attn.q_proj": np.random.randn(64, 64),
    "encoder.attn.v_proj": np.random.randn(64, 64),
    "classifier.dense": np.random.randn(64, 10),
}
adapter = LoRAAdapter(model_weights, target_modules=["attn.q_proj", "attn.v_proj"], rank=4, alpha=8.0)
print(f"Total Base Params: {adapter.count_parameters()['base_params']}, Trainable LoRA Params: {adapter.count_parameters()['trainable_lora_params']}")

Parameter Breakdown: LoRALinear

Parameter Name	Data Type	Default Value	Description / Purpose
in_features	int	Required	Input feature dimension $d_{\text{in}}$.
out_features	int	Required	Output feature dimension $d_{\text{out}}$.
rank	int	4	Low-rank bottleneck dimension $r \ll \min(d_{\text{in}}, d_{\text{out}})$.
alpha	float	1.0	Scaling hyperparameter $\alpha$ where $\Delta W = \frac{\alpha}{r} B A$.

---

17.4 Distribution-Free Time Series Conformal Prediction (ConformalPredictor)

import numpy as np
from chokkhu.models.timeseries import ConformalPredictor, conformal_interval
from chokkhu.models import LinearRegression

# Generate synthetic sequential / regression dataset
X = np.linspace(0, 10, 150).reshape(-1, 1)
y = 2.5 * X.flatten() + np.sin(X.flatten()) + np.random.randn(150) * 0.5

# Base forecaster
base_model = LinearRegression()
base_model.fit(X[:80], y[:80])

# Fit conformal prediction interval with exact 95% coverage guarantee
conformal = ConformalPredictor(base_model=base_model, alpha=0.05, method="split")
conformal.calibrate(X[80:110], y[80:110])

# Predict lower and upper confidence bounds
y_pred, lower, upper = conformal.predict_interval(X[110:])
coverage = np.mean((y[110:] >= lower) & (y[110:] <= upper))
print(f"Guaranteed Coverage: >= 95%, Empirical Empirical Coverage: {coverage * 100:.1f}%")

Parameter Breakdown: ConformalPredictor

Parameter Name	Data Type	Default Value	Description / Purpose
base_model	Any	Required	Any fitted regression or forecasting model providing .predict(X).
alpha	float	0.1	Miscoverage significance level $\alpha \in (0, 1)$, ensuring $1-\alpha$ coverage.
method	str	"split"	Conformal method: "split" or "cross_val".

---

17.5 Matrix Profile Time Series Motif & Discord Mining (MatrixProfile)

import numpy as np
from chokkhu.models.timeseries import MatrixProfile, find_motifs, find_discords

# Generate continuous time series with an embedded anomaly
np.random.seed(42)
t = np.linspace(0, 50, 500)
ts = np.sin(t) + np.random.randn(500) * 0.05
ts[250:270] += 4.0  # Anomaly burst

# Fast STOMP / STAMP sliding-window distance profile computation
mp = MatrixProfile(window_size=30)
profile, profile_idx = mp.fit_transform(ts)

# Identify recurring patterns (motifs) and anomalous subsequences (discords)
motifs = find_motifs(profile, profile_idx, top_k=2)
discords = find_discords(profile, top_k=1)
print(f"Top Discord (Anomaly) Subsequence Index: {discords[0]}")

Parameter Breakdown: MatrixProfile

Parameter Name	Data Type	Default Value	Description / Purpose
window_size	int	Required	Subsequence window length $m$ for z-normalized Euclidean distance comparison.
algorithm	str	"stomp"	Matrix profile algorithm: "stomp" (fast $O(n^2)$) or "stamp".

---

17.6 Multi-Fidelity Bayesian Optimization & HyperBand (BOHB)

import numpy as np
from chokkhu.automl import BOHB

# Objective function simulating hyperparameter tuning across variable budget (e.g. epochs)
def objective_fn(config, budget):
    lr = config["lr"]
    hidden = config["hidden"]
    # Simulated loss decreasing with optimal lr & budget
    loss = (np.log10(lr) + 3.0)**2 + (hidden - 64)**2 * 1e-4 + (1.0 / budget)
    return float(loss)

# Hyperparameter search space
param_distributions = {
    "lr": ("log_uniform", 1e-4, 1e-1),
    "hidden": ("int_uniform", 16, 128),
}

# Run BOHB successive halving optimization
bohb = BOHB(
    objective_fn=objective_fn,
    param_distributions=param_distributions,
    min_budget=1,
    max_budget=9,
    eta=3,
    num_iterations=3
)
best_config, best_loss = bohb.optimize()
print(f"Optimal Hyperparameters: {best_config}, Minimum Loss: {best_loss:.5f}")

Parameter Breakdown: BOHB

Parameter Name	Data Type	Default Value	Description / Purpose
objective_fn	Callable	Required	Objective function f(config, budget) -> float to minimize.
param_distributions	dict	Required	Dictionary defining hyperparameter search bounds and distributions.
min_budget	float	1.0	Minimum resource budget allocated per candidate configuration.
max_budget	float	9.0	Maximum resource budget allocated to top-performing configurations.
eta	int	3	Halving reduction factor (prunes $1 - 1/\eta$ candidates each round).
num_iterations	int	3	Number of HyperBand outer brackets executed.

---

17.7 SuperLearner Out-of-Fold Cross-Validated Stacking (SuperLearner)

import numpy as np
from chokkhu.automl import SuperLearner
from chokkhu.models import LogisticRegression, DecisionTreeClassifier, RandomForestClassifier

# Multi-class classification dataset
X = np.random.randn(200, 10)
y = (X[:, 0] + X[:, 1] > 0).astype(int)

# Define diverse ensemble of base learners
base_learners = [
    ("logreg", LogisticRegression()),
    ("dt", DecisionTreeClassifier(max_depth=4)),
    ("rf", RandomForestClassifier(n_estimators=10, max_depth=4)),
]

# Construct SuperLearner with out-of-fold CV meta-learning
super_learner = SuperLearner(
    base_models=base_learners,
    meta_model="ridge",
    cv=5,
    task="classification",
    use_probabilities=True
)
super_learner.fit(X, y)

# Predict class probabilities and labels
y_pred_proba = super_learner.predict_proba(X[:5])
y_pred = super_learner.predict(X[:5])
print(f"Ensemble Predictions: {y_pred}")
print(f"Optimal Base Learner Weights: {super_learner.get_weights()}")

Parameter Breakdown: SuperLearner

Parameter Name	Data Type	Default Value	Description / Purpose
base_models	list[tuple[str, Any]]	Required	List of named base estimators [(name, model), ...].
meta_model	str / Any	"ridge"	Meta-learner strategy ("ridge", "nnls", "logistic", or custom estimator).
cv	int	5	Number of out-of-fold cross-validation folds for meta-feature generation.
task	str	"classification"	Task type: "classification" or "regression".
use_probabilities	bool	True	Whether classification meta-features use class probabilities or hard labels.

---

18. Privacy, Quantum ML, Geo-Spatial, NAS & TDA (Milestone 15)

18.1 Differential Privacy & DP-SGD (LaplaceMechanism, GaussianMechanism, DP_SGD)

import numpy as np
from chokkhu.privacy import LaplaceMechanism, GaussianMechanism, DP_SGD

# 1. Laplace Mechanism for query perturbation
laplace = LaplaceMechanism(epsilon=0.5, sensitivity=1.0)
noisy_count = laplace.perturb(100.0)
print(f"Differentially Private Perturbed Count: {noisy_count:.2f}")

# 2. Gaussian Mechanism for (epsilon, delta)-DP
gaussian = GaussianMechanism(epsilon=1.0, delta=1e-5, sensitivity=1.0)
noisy_stat = gaussian.perturb(42.0)
print(f"Gaussian Perturbed Statistic: {noisy_stat:.2f}")

# 3. Differentially Private SGD Optimizer with Per-Sample Clipping
dp_optimizer = DP_SGD(lr=0.01, l2_norm_clip=1.0, noise_multiplier=0.8)
params = {"W": np.random.randn(10, 2), "b": np.zeros(2)}
per_sample_grads = [{"W": np.random.randn(10, 2), "b": np.random.randn(2)} for _ in range(8)]

updated_params = dp_optimizer.step(params, per_sample_grads)
privacy_spent = dp_optimizer.compute_privacy_spent(total_samples=1000, batch_size=8, target_delta=1e-5)
print(f"Privacy Spent: epsilon={privacy_spent['epsilon']:.4f}, delta={privacy_spent['delta']}")

Parameter Breakdown: DP_SGD

Parameter Name	Data Type	Default Value	Description / Purpose
lr	float	0.01	Optimization step learning rate.
l2_norm_clip	float	1.0	Maximum L2 norm bound $C$ for per-sample gradient clipping.
noise_multiplier	float	1.0	Calibrated noise ratio $\sigma = \text{noise_multiplier} \times C$.
random_state	int / None	None	Seed for reproducible pseudo-random noise generation.

---

18.2 Decentralized Federated Learning (FederatedServer, FederatedClient, FedAvg, FedProx)

import numpy as np
from chokkhu.privacy import FederatedServer, FederatedClient

# Simulate decentralized non-IID client partitions
client1_X, client1_y = np.random.randn(50, 4), np.random.randn(50, 1)
client2_X, client2_y = np.random.randn(60, 4), np.random.randn(60, 1)

# Register clients with FedProx proximal regularization (mu > 0)
c1 = FederatedClient(client_id="hospital_A", X=client1_X, y=client1_y, mu=0.01, lr=0.01)
c2 = FederatedClient(client_id="hospital_B", X=client2_X, y=client2_y, mu=0.01, lr=0.01)

# Orchestrate federated aggregation rounds
server = FederatedServer(
    initial_weights={"W": np.zeros((4, 1)), "b": np.zeros((1,))},
    clients=[c1, c2],
    strategy="fedprox"
)

for r in range(5):
    round_summary = server.train_round(fraction_fit=1.0, local_epochs=3, batch_size=16)
    print(f"Round {r+1} Complete - Mean Client Loss: {round_summary['mean_client_loss']:.4f}")

global_predictions = server.predict(np.random.randn(5, 4))
print(f"Global Model Predictions Shape: {global_predictions.shape}")

Parameter Breakdown: FederatedServer

Parameter Name	Data Type	Default Value	Description / Purpose
initial_weights	dict	Required	Initial global model parameters {'W': ..., 'b': ...}.
clients	list	None	Registered FederatedClient instances.
strategy	str	"fedavg"	Aggregation strategy ("fedavg" or "fedprox").

---

18.3 Quantum Machine Learning Simulator & Variational Quantum Classifier (QuantumCircuit, VQC, QuantumKernel)

import numpy as np
from chokkhu.quantum import QuantumCircuit, VariationalQuantumClassifier, QuantumKernel

# 1. State Vector Quantum Circuit Simulation & Bell State Generation
qc = QuantumCircuit(n_qubits=2)
qc.h(0).cnot(0, 1)  # Create maximally entangled Bell state (|00> + |11>) / sqrt(2)
print(f"Computational Basis Probabilities: {qc.probabilities()}")
print(f"Pauli-Z Expectation <Z_0>: {qc.expectation_z(0):.4f}")

# 2. Variational Quantum Classifier (QNN) with Exact Parameter Shift Rule Gradients
X_quantum = np.random.uniform(-np.pi, np.pi, size=(30, 2))
y_quantum = (X_quantum[:, 0] + X_quantum[:, 1] > 0).astype(int)

vqc = VariationalQuantumClassifier(n_qubits=2, n_layers=2, lr=0.1)
vqc.fit(X_quantum, y_quantum, epochs=10, batch_size=8)
q_preds = vqc.predict(X_quantum[:5])
print(f"VQC Predictions: {q_preds}")

# 3. Quantum Kernel Matrix Estimation
qk = QuantumKernel(n_qubits=2)
gram_matrix = qk.compute_matrix(X_quantum[:10])
print(f"Quantum Gram Matrix (Fidelity) Shape: {gram_matrix.shape}")

Parameter Breakdown: VariationalQuantumClassifier

Parameter Name	Data Type	Default Value	Description / Purpose
n_qubits	int	2	Number of simulated qubits in quantum register.
n_layers	int	2	Number of parameterized variational rotation and entangling ansatz layers.
lr	float	0.05	Learning rate for parameter shift rule gradient descent.

---

18.4 Geo-Spatial Statistics, Spatial Autoregression & GWR (SpatialWeights, morans_i, SAR, GWR)

import numpy as np
from chokkhu.geospatial import SpatialWeights, morans_i, SpatialAutoregression, GeographicallyWeightedRegression

# 2D geographic coordinates [lat, lon] and spatial attributes
coords = np.random.uniform(20.0, 26.0, size=(50, 2))
values = coords[:, 0] * 3.5 + np.random.randn(50) * 0.2

# 1. Spatial Weight Matrix and Global Moran's I Autocorrelation
sw = SpatialWeights(coords, method="knn", k=5, row_standardize=True)
moran = morans_i(values, sw, permutations=99)
print(f"Global Moran's I: {moran['I']:.4f}, p-value: {moran['p_value']:.4f}")

# 2. Spatial Autoregression (Spatial Lag Model: y = rho * W * y + X * beta)
X_geo = np.random.randn(50, 3)
sar = SpatialAutoregression(model_type="lag")
sar.fit(X_geo, values, sw)
print(f"Estimated Spatial Autoregressive Rho: {sar.rho:.4f}")

# 3. Geographically Weighted Regression (Localized Spatial Beta Estimation)
gwr = GeographicallyWeightedRegression(bandwidth=2.0, kernel="gaussian")
gwr.fit(coords, X_geo, values)
gwr_preds = gwr.predict(coords[:5], X_geo[:5])
print(f"GWR Predictions: {gwr_preds}")

Parameter Breakdown: SpatialWeights

Parameter Name	Data Type	Default Value	Description / Purpose
coords	np.ndarray	Required	Coordinate matrix $(N \times 2)$ containing spatial coordinates.
method	str	"knn"	Kernel structure: "knn", "inverse_distance", "gaussian", or "threshold".
k	int	5	Number of nearest neighbors for "knn" method.
bandwidth	float	1.0	Distance decay parameter for "gaussian" or distance threshold.
row_standardize	bool	True	Row-standardization ($\sum_j W_{ij} = 1.0$).

---

18.5 Geostatistical Variogram Modeling & Spatial Kriging (OrdinaryKriging)

import numpy as np
from chokkhu.geospatial import OrdinaryKriging

# Spatial point observations
obs_coords = np.random.uniform(0.0, 10.0, size=(30, 2))
z_values = np.sin(obs_coords[:, 0]) + np.cos(obs_coords[:, 1])

# Ordinary Kriging with Spherical Variogram Model
kriging = OrdinaryKriging(variogram_model="spherical", nugget=0.02, sill=1.0, range_val=4.0)
kriging.fit(obs_coords, z_values)

# Interpolate over target spatial grid
target_coords = np.array([[2.5, 3.5], [7.0, 8.0]])
z_pred, error_variance = kriging.predict(target_coords)
print(f"Kriging Interpolated Values: {z_pred}, Estimation Variances: {error_variance}")

Parameter Breakdown: OrdinaryKriging

Parameter Name	Data Type	Default Value	Description / Purpose
variogram_model	str	"spherical"	Theoretical semivariogram model: "spherical", "exponential", or "gaussian".
nugget	float	0.0	Micro-scale variance / measurement error $c_0$.
sill	float	1.0	Total asymptotic semivariance $c_0 + c$.
range_val	float	1.0	Spatial correlation range threshold $a$.

---

18.6 Differentiable Neural Architecture Search (DARTS)

import numpy as np
from chokkhu.automl import DARTS

# Tabular classification dataset
X_nas = np.random.randn(100, 8)
y_nas = (X_nas[:, 0] + X_nas[:, 1] > 0).astype(int)

# Continuous relaxation of candidate operations (Identity, Linear, ReLU, GELU, Residual)
darts = DARTS(
    input_dim=8,
    num_classes=2,
    num_intermediate_nodes=3,
    hidden_dim=32,
    lr_weights=0.01,
    lr_arch=0.005
)
darts.fit(X_nas, y_nas, epochs=10, batch_size=16)

# Extract discovered discrete optimal architecture
genotype = darts.genotype()
print(f"Discovered Optimal Neural Architecture Genotype: {genotype}")

Parameter Breakdown: DARTS

Parameter Name	Data Type	Default Value	Description / Purpose
input_dim	int	Required	Feature input dimension $D$.
num_classes	int	2	Number of output target classes.
num_intermediate_nodes	int	3	Number of mixed-op candidate layers in supernet search space.
hidden_dim	int	32	Layer width for intermediate candidate operations.
lr_weights	float	0.01	Learning rate for candidate operation parameters $w$.
lr_arch	float	0.005	Learning rate for architecture parameters $\alpha$.

---

18.7 Topological Data Analysis & Persistent Homology (VietorisRipsComplex, PersistenceLandscape)

import numpy as np
from chokkhu.tda import VietorisRipsComplex, PersistenceDiagram, PersistenceLandscape, bottleneck_distance

# Point cloud with topological hole (circle)
angles = np.linspace(0, 2 * np.pi, 24, endpoint=False)
point_cloud = np.column_stack([np.cos(angles), np.sin(angles)]) + np.random.randn(24, 2) * 0.05

# 1. Build Vietoris-Rips Simplicial Filtration
rips = VietorisRipsComplex(max_edge_length=2.5, max_dimension=1)
diagrams = rips.fit_transform(point_cloud)

# 2. Extract H0 (connected components) and H1 (loops) Persistence
h0_diag = PersistenceDiagram(diagrams[0], dimension=0)
h1_diag = PersistenceDiagram(diagrams[1], dimension=1)
print(f"H0 Total Persistence: {h0_diag.total_persistence():.4f}, Persistent Entropy: {h0_diag.persistent_entropy():.4f}")

# 3. Vectorize into Continuous Persistence Landscapes for ML Classifiers
landscape = PersistenceLandscape(num_landscapes=3, resolution=40)
topo_features = landscape.transform(diagrams[0])
print(f"Extracted Topological Feature Vector Shape: {topo_features.shape}")

Parameter Breakdown: VietorisRipsComplex

Parameter Name	Data Type	Default Value	Description / Purpose
max_edge_length	float	inf	Maximum filtration scale $\epsilon$ for simplex construction.
max_dimension	int	1	Maximum homology dimension ($0$ for $H_0$, $1$ for $H_0$ and $H_1$).

License & Citation

Distributed under the MIT License. See LICENSE for details.

@software{chokkhu2026,
  author = {tamimystic and Inception BD Team},
  title = {Chokkhu: Sovereign Zero-Dependency Machine Learning and LLM Ecosystem},
  year = {2026},
  publisher = {GitHub},
  url = {https://github.com/tamimystic/chokkhu}
}