GoF Simons Collaboration Retreat

Explainability in ML Multi-Agent Inference Blackboard Format

2–6 March 2026
Laboratorio Subterráneo de Canfranc (Spain)

The Geometry of Flows is a focused retreat of the Simons Collaboration dedicated to advancing the foundations of explainability in Machine Learning and multi-agent inference.

Over five days in the unique underground environment of the Laboratorio Subterráneo de Canfranc, a small group of experts from cosmology, artificial intelligence, applied mathematics, and industry research will gather for intensive, collaborative blackboard-driven discussions.

Can we build a unified geometric and analytic framework that makes multi-agent and machine-learning systems interpretable, reducible, and scientifically transparent?

Retreat details

Format: Invitation-only · Blackboard · Discussion-based · no formal slide sessions · minimal preparation burden.
Focus: Explainability · Geometry · Dimensional reduction
Keywords: PDEs · Game theory · Neural nets · Compression
Reference: Analytic compression tool MOPED: astro-ph/9911102.

Core themes

The retreat is structured around three complementary research directions, with the aim of consolidating ongoing progress from weekly collaboration meetings and accelerating toward implementable frameworks.

1) Explainability through geometry

• Understanding ML systems as geometric flows in high-dimensional spaces
• PDE-inspired formulations to clarify neural network behavior
• Geometric structure underlying multi-agent optimization and inference
• Formalizing information flow between agents as dynamical systems

2) Dimensional reduction as interpretability

• Reframing “multi-agent” systems via effective dimensionality reduction
• Reduction to lower-dimensional sufficient statistics
• Efficient information retrieval structures and discovery-oriented inference engines
• Compression schemes that preserve scientific interpretability

3) Analytic compression meets neural networks

• Marrying analytic tools (e.g., MOPED) with neural representations
• Hybrid analytic–neural compression and physically motivated latent spaces
• Interpretable embeddings for multi-agent systems
• Identifying sufficient statistics within deep architectures

Shared language: PDEs, game theory, and inference

• Explainability for processes described by PDEs and the language of game theory
• A common conceptual substrate for physical, cognitive, and linguistic systems
• Cross-domain transfer between cosmology, NLP, and industrial AI

Format

This retreat is intentionally designed for maximum scientific exchange:

Blackboard-first

No formal slide sessions. The emphasis is on derivations, shared notation, and real-time collaboration.

Low preparation burden

Participants are not expected to prepare talks; instead, we prioritize open problems, synthesis, and joint work.

Small-group focus

A compact set of attendees enables depth, continuity, and strong cross-disciplinary engagement.

Goal-oriented discussions

Each day centers on a small number of high-leverage questions, aiming for concrete next steps and prototypes.

Participants

The retreat brings together researchers from academia, foundations, and industry, spanning cosmology, AI research, language systems, and pharmaceutical AI.