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On the nonlearnability of a single spiking neuron
1Institute of Computer Science, Academy of Sciences of the Czech Republic, P.O. Box 5, 18207 Prague 8, Czech Republic. sima@cs.cas.cz
Neural Computation
|October 11, 2005
Summary
Training spiking neurons with adjustable synaptic delays is computationally complex. This study proves their non-learnability and coNP-hard representation problems, impacting artificial intelligence and computational neuroscience.
Area of Science:
- Computational Neuroscience
- Machine Learning Theory
- Artificial Intelligence
Background:
- Spiking neurons are crucial for brain-inspired computing.
- Understanding their learning capabilities is essential for AI development.
- Previous research indicated learning challenges with binary delays.
Purpose of the Study:
- To analyze the computational complexity of training single spiking neurons with adaptive weights, thresholds, and adjustable synaptic delays.
- To generalize findings from binary delays to arbitrary real-valued delays.
- To investigate the learnability and representation capabilities of these complex neuron models.
Main Methods:
- Introduced a synchronization technique to extend results to real-valued delays.
- Proved the NP-completeness of the consistency and approximation problems for spiking neurons with programmable weights, thresholds, and delays.
- Established the coNP-hardness of the representation problem for spiking neurons.
Main Results:
- The consistency and approximation problems for training spiking neurons with programmable weights, thresholds, and delays are NP-complete.
- Spiking neurons with arbitrary synaptic delays are not properly Probably Approximately Learnable (PAC) learnable.
- Robust learning for these neurons is not possible unless RP = NP.
- The problem of determining if a spiking neuron can compute a given Boolean function is coNP-hard.
Conclusions:
- Training spiking neurons with adjustable synaptic delays presents significant computational challenges.
- The findings imply fundamental limitations in the efficient learnability and representational power of such models.
- This research has implications for the design and capabilities of neuromorphic computing systems.
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