Overview
Analytical Connectionism is a 2-week summer course on analytical tools, including methods from statistical physics and probability theory, for probing neural network models of higher-level cognition. The course brings together neuroscience, psychology and machine-learning communities, and introduces attendees to analytical methods for neural network analysis and connectionist theories of higher-level cognition and psychology.
Connectionism, a theoretical approach in cognitive science, uses neural network models to simulate a wide range of phenomena, including perception, memory, decision-making, language, and cognitive control. However, most connectionist models remain, to a certain extent, black boxes, and we lack a mathematical understanding of their behaviors. Recent progress in machine learning theory has provided novel analytical tools that have advanced our mathematical understanding of deep neural networks, and have the potential to help make these “black boxes” more transparent.
During the School, teams of students work closely to develop research projects on topics related to analytical connectionism, presenting initial proposals during week one and interim results at the School’s conclusion.
Additionally, students are grouped based on their expertise and preferences and assigned to take notes for a specific lecturer. These notes are peer-reviewed and collected into a special issue, creating a permanent resource for the community and giving note-takers the opportunity to contribute to a formal publication.
This course will introduce:
- mathematical methods for neural network analysis, providing a solid overview of the analytical tools available to understand neural network models;
- key connectionist models with links to experimental observations, which provide targets for analytical results.
During the course, you will:
- attend lectures given by leading researchers on theoretical methods and applications, key connectionist models, and experimental observations;
- participate in tutorials, poster sessions, and contributed talks;
- present to and engage with lecturers, organizers, and other participants during a poster session;
- collaborate in a group with other participants on a novel research project, mentored by the course organizers and lecturers;
- work together and co-author lecture notes for publication in a special issue.
Interpretability in reasoning and mathematical cognition
Mathematical cognition explores how children (or artificial systems) use and acquire mathematical concepts, how mathematical intuition and mathematical expertise develop and interact, and how these aspects are represented in neural activity. With neural network models, connectionists have studied how number concepts, spatial and geometric thinking, and algebraic manipulation can be implemented and can emerge from experience. Mathematical reasoning has also become a major testbed for modern AI, especially autoformalization and theorem proving, and a growing target of interpretability research.
Among these traditions, the 2027 School on Analytical Connectionism focuses on analytical approaches mathematical cognition and reasoning. Knowing how people learn and understand mathematics may help us guide AI systems to produce more intelligible mathematics, and at the same time, studying what heuristics and abstractions these systems develop may deepen our understanding of human mathematical cognition. The School brings together psychologists studying mathematical cognition, researchers modeling it with neural networks, and those building and interpreting frontier AI systems for mathematics, to share methods and findings to advance these dual goals.
Dates
| Applications open | 1 Feb 2027 |
| Application deadline | 1 Apr 2027 |
| Outcome communicated (round 1) | 17 May 2027 |
| Acceptance admission deadline (round 1) | 30 May 2027 |
| Outcome communicated (round 2) | 31 May 2027 |
| Acceptance admission deadline (round 2) | 13 Jun 2027 |
| School begins | 2 Aug 2027 |
Schedule
| Time | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|
| 08:30 | Registration | ||||
| 09:00–10:30 |
Opening remarks
Core lecture
Break
Core lecture
Break
Core lecture
|
Core lecture | Core lecture | Core lecture | Core lecture |
| 10:30–11:00 | Break | ||||
| 11:00–12:30 | Core lecture | Core lecture | Core lecture | Core lecture | |
|
12:30–14:00
lunch
|
|||||
| 14:00–15:30 | Spotlight talks | Core lecture | Core lecture | Core lecture | Core lecture |
|
15:30–16:00
break
|
|||||
| 16:00–17:30 | Poster session | Project brainstorms | Project brainstorms | Project pitches | Project organization |
| 18:00– | Speaker dinner | School dinner | |||
| Time | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|
| 09:00–10:30 | Frontiers lecture | Frontiers lecture | Frontiers lecture | Frontiers lecture | Project work |
|
10:30–11:00
break
|
|||||
| 11:00–12:30 | Frontiers lecture | Frontiers lecture | Frontiers lecture | Frontiers lecture | Project work |
|
12:30–14:00
lunch
|
|||||
| 14:00–15:30 | Project work | Project work | Project work | Project work | Project presentations |
|
15:30–16:00
break
|
|||||
| 16:00–17:30 | Project work | Project work | Project work | Project work | Project presentations |
| 18:00– | Speaker dinner | Speaker dinner | |||



