Towards Neuromorphic Complexity Analysis Johan Kwisthout

1. Towards Neuromorphic Complexity Analysis Johan Kwisthout

2. Towards neuromorphic complexity analysis • Where do we fit? • What sort of problems are efficiently solvable on a neuromorphic computer? • Are these problems different / the same as the problems efficiently solvable on a Von Neumann architecture? • Are we asking the right questions? • What do we mean with “efficiently solvable” in this context? Time-efficient, space-efficient, or energy-efficient? • Do our current models of computation (Turing machines) suffice to answer these questions?

3. Rationale Non-van Neumann architecture Energy as bounded resource Analog / spiking behavior Noise/randomness as resource

4. Rationale Non-van Neumann architecture Energy as bounded resource Analog / spiking behavior Noise/randomness as resource

5. Rationale Non-van Neumann architecture Energy as bounded resource Analog / spiking behavior Noise/randomness as resource

6. Rationale Non-van Neumann architecture Energy as bounded resource Analog / spiking behavior Noise/randomness as resource

7. Proposed computational framework • Key aspects are there: • Co-located memory & computation • Learning and adaptation • Noise used as resource for sampling • Spiking behavior • Fruitful  firmly rooted in large body of theory

8. Open issues and research questions • Relationship with traditional models • Probabilistic Turing machines • Thresholds circuits with energy complexity • Complexity classes, hardness criteria • Existence of energy-hard problems? • Structural complexity theory • Reductions between classes • Inclusions, proving hardness • Notions of acceptance criteria • Stability of distribution • Time to convergence • Energy limitations

9. Conclusion • DoE 2016 workshop report, p. 29: “…likely that an entirely new computational theory paradigm will need to be defined in order to encompass the computational abilities of neuromorphic systems” • Application: • Describe what sort of problems can and cannot be solved tractably on neuromorphic hardware • Describe fundamental limits of the brain’s (cognitive) capacity given the available resources • Open for feedback/suggestions – work in progress!