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. Open for feedback/suggestions – work in progress!
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!