Postdoctoral Research Fellowship: Network Thermodynamics of Distributed Computation

Santa Fe Institute • Santa Fe, NM

3d • Onsite

About The Position

The Santa Fe Institute is seeking a highly motivated scholar with expertise in physics (or in special cases in computer science) for a two-year full-time postdoctoral fellowship. This role will focus on understanding the thermodynamic cost of distributed computation across various systems, including digital circuits, neural networks, and human brains. The candidate will work with PI David Wolpert on a project investigating how network coupling influences the trade-offs between thermodynamic cost, speed, robustness against error, and computational precision. A key aspect will be examining how hierarchical and/or modular network structures impact these trade-offs. The primary tool used will be 'mismatch cost' (MMC), a recent extension of the second law applicable to all physical systems performing computation. The project's central challenge is scaling MMC calculations to systems with large state spaces and complex dynamics, employing techniques like coarse-graining, uncertainty quantification, backward differential equations, tensor networks, and Monte Carlo approximations. These methods will be applied to trained feedforward neural networks, restricted Boltzmann machines, and lightweight LLMs, correlating their network topology with thermodynamic cost and computational difficulty, including problems like KSAT.

Requirements

• Ph.D. in Physics, Computer Science, or a related field (by start date).
• Background in stochastic thermodynamics, statistical physics, or theoretical computer science (computational complexity).
• Familiarity with Monte Carlo methods, uncertainty quantification, backward differential equations, and/or tensor network approximations.
• Strong programming skills and interest in interdisciplinary collaboration spanning physics and computer science theory.
• Must be legally able to work in the US.

Responsibilities

• Collaborate with PI and other team members to advance this project through research, publication, workshop organization, etc.
• Develop and apply mismatch-cost theory and large-state-space approximation techniques (e.g., coarse-graining, uncertainty quantification, backward differential equations tensor networks, Monte Carlo) to distributed computational systems
• Design, train, and analyze distributed computational systems — such as feedforward neural networks, restricted Boltzmann machines, and lightweight LLMs — to relate their network topology to thermodynamic cost, robustness, and speed, and computational power.
• Investigate how the "hardness" of computational problems (e.g., KSAT) relates to the thermodynamic cost of solving them.

What This Job Offers

• Job Type: Full-time
• Career Level: Principal
• Education Level: Ph.D. or professional degree