Data Science & ML Claude 技能

SplitMix Ternary Streams

Extends splittable random number generation with GF(3) balanced ternary streams for parallel triadic systems.

CRN Topology & Reaction Networks

Generates and analyzes chemical reaction network (CRN) topologies to predict dynamical behaviors through graph theory and linear algebra.

Infinity Topoi Framework

Implements higher topos theory and ∞-sheaf logic to provide a rigorous mathematical framework for complex systems and BCI data modeling.

Rubato Composer Integration

Implements Guerino Mazzola’s mathematical music theory using categorical structures, Scheme integration, and the Topos of Music framework.

Curiosity-Driven Learning

Implements Schmidhuber's curiosity-driven framework to provide AI agents with intrinsic motivation based on compression progress.

Active Inference Self-Validation Loop

Validates triadic color system predictions using active inference and error minimization loops.

Information Geometry

Implements Fisher-Rao metrics and natural gradient optimization on statistical manifolds for advanced probabilistic modeling.

Unworlding Involution Dynamics

Extracts frame-invariant patterns and self-inverse derivation structures from interaction dynamics using GF(3) conservation.

LLM Application Development

Builds sophisticated AI-powered applications using advanced prompt engineering, RAG patterns, and multi-provider LLM integrations.

Causal Inference & World Models

Implements advanced causal reasoning, counterfactual analysis, and System 2 deep learning architectures to build robust, intervention-aware AI models.

Agent-o-rama Learning & Pattern Extraction

Trains cognitive agents to extract behavioral, temporal, and network patterns from complex interaction sequences.

OSM Topology Analysis

Analyzes OpenStreetMap road networks and geographic data using topological graph structures and GF(3) validation.

Three-Match Algorithm Gadget

Facilitates 3-SAT reductions to colored subgraph isomorphism using non-backtracking geodesic gadgets and Möbius filtering.

Self-Evolving AI Agent Patterns

Implements Darwin Gödel Machine patterns to enable autonomous code evolution and self-improvement for AI agents.

Emergent Role Assignment

Orchestrates spontaneous role assignment and hierarchical self-organization in multi-agent systems using topological and chemical organization principles.

Derived Categories & Homological Algebra

Implements advanced homological algebra frameworks including chain complexes, derived functors, and triangulated categories for BCI signal processing.

Agent-o-Rama Learning Engine

Extracts complex behavioral patterns and trains predictive learning agents from interaction sequences using multi-interpreter analysis.

JaxLife Open-Ended Simulation

Implements high-performance agentic simulators using JAX for researching emergent behaviors and open-ended evolution.

Local Feedforward Learning

Implements the Forward-Forward algorithm and local contrastive learning paradigms to train neural networks without backpropagation.

Categorical Composition Architecture

Implements mathematical category theory abstractions to enable compositional learning and structured parameter transfer in AI models.

JaxLife Open-Ended Simulator

Simulates agentic artificial life and emergent behaviors within Turing-complete programmable environments using JAX.

Sheaf-Theoretic Coordination

Implements advanced topological coordination and distributed reasoning using sheaf theory for multi-agent systems.

Replicate API Expert

Integrates over 600 specialized AI models for image, video, and audio generation into your development workflow using the unified Replicate API.

Senior Data Scientist

Empowers Claude with expert-level statistical modeling, causal inference, and production-grade machine learning capabilities for enterprise data systems.

Oriented Simplicial Networks

Implements directional simplicial neural networks with E(n)-equivariance and persistent homology for advanced topological data analysis.

Kolmogorov Compression

Measures and optimizes data complexity by finding the shortest algorithmic representation to evaluate intelligence and information density.

Curiosity-Driven Learning

Implements intrinsic motivation for AI agents using Schmidhuber's formal theory of creativity and compression progress.

Kolmogorov Complexity & Compression

Measures and optimizes data complexity by finding the shortest program representation to evaluate intelligence and algorithmic efficiency.

Rezk Types & Local Univalence

Implements and reasons about complete Segal spaces and local univalence within synthetic ∞-category theory.

Molecular Assembly Index

Computes molecular complexity using Lee Cronin's Assembly Theory to identify biosignatures and calculate minimal construction pathways.