PolyMath AI Workshop Series: From Data Manifolds to Causal Inference

To bridge the gap between advanced mathematical concepts and practical AI modeling, empowering participants to understand, design, and evaluate intelligent systems grounded in geometrical reasoning, probabilistic logic, and causal inference.

• Make participants mathematically literate in core AI concepts

• Enable AI practitioners to go beyond empirical performance to model robustness

• Promote a science-first approach to ethical, interpretable AI

• Bridge the divide between academia and application through modular labs

• Foster a new generation of thinkers who can reason with and about intelligent systems

Day 1: Data Foundations & Statistical Learning

• AM Session

• Kolmogorov-Smirnov tests for data quality in spam datasets

• Bayesian inference for real-time data stream prioritization

• Hands-On

• Compare Poisson vs Gaussian distributions in email arrival patterns

• Calculate p-values for spam feature significance

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Day 2: Model Optimization & Validation

• AM Session:

• Deriving Fβ-score thresholds for medical vs commercial spam filters

• Wolfe conditions analysis for optimal learning rates in PySpark ML

• Hands-On:

• Plot ROC curves with confidence intervals using bootstrapping

• Implement line search optimization for decision tree pruning

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Day 3: RAG Architecture & Vector Math

• AM Session:

• Manifold learning for document embedding visualization

• Proof of convergence for iterative re-ranking algorithms

• Hands-On:

• Calculate MMR (Maximal Marginal Relevance) balance using Lagrange multipliers

• Persistent homology analysis of knowledge graph connections

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Day 4: Multi-Modal Systems & Metrics

• AM Session:

• Hausdorff distance for cross-modal (text/sensor) alignment

• σ-algebra construction for academic knowledge bases

• Hands-On:

• Compute BLEU-4 scores with statistical significance testing

• Optimal transport theory for PDF-to-database alignment

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Day 5: Embedded AI & Optimization

• AM Session:

• Karush-Kuhn-Tucker conditions for edge device power constraints

• Semidefinite programming for model quantization

• Hands-On:

• Solve sensor deployment as traveling salesman problem (TSP)

• FPGA resource allocation using integer linear programming

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Day 6: Integrated Capstone & Validation

• AM Session:

• Do-calculus for evaluating AI system impact on research outcomes

• Shapley value analysis of multi-component systems

• Hands-On:

• Build counterfactual scenarios for edge AI failure modes

• Perform sensitivity analysis on full pipeline (Big Data → RAG → Edge)

• Master the math behind how AI models learn and generalize

• Visualize and analyze high-dimensional data using geometrical tools

• Develop robust probabilistic models with uncertainty estimation

• Apply causal inference to make AI systems more transparent and decision-ready

• Receive a series certificate documenting your advanced AI methodology training

• PhD students and researchers in AI, Data Science, Mathematics, or Physics

• AI/ML engineers interested in model interpretability and causality

• Applied statisticians and economists using predictive or decision models

• Academicians teaching or developing theory-backed AI systems