PolyMath AI Workshop Series: From Data Manifolds to Causal Inference

PolyMath AI is an international, modular workshop series designed for those who seek to dive deep into the mathematical underpinnings of Artificial Intelligence. This unique workshop spans a conceptual journey from the geometry of data manifolds, through probabilistic and statistical learning, to causality in AI systems.

Built for researchers, developers, and academic professionals, the series offers an immersive blend of theoretical foundations and hands-on demonstrations using tools such as Python, PyTorch, and DoWhy. Participants will emerge with a stronger ability to reason about AI beyond black-box approximations, enabling them to build interpretable, robust, and causally aware systems.

• 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

Analytical Focus: Hypothesis Testing & Distributions

• 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

Analytical Focus: ROC Analysis & Gradient Descent

• 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

Analytical Focus: Topological Data Analysis

• 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

Analytical Focus: Measure Theory for AI

• 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

Analytical Focus: Convex Relaxation

• 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

Analytical Focus: Causal Inference

• 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)

• 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