Computing Generalized Matrix Inverse on Spiking Neural Substrate

Area of Science:

• Neuromorphic Engineering
• Computational Neuroscience
• Applied Mathematics

Background:

• Emerging neural hardware offers low-energy platforms for numerical algorithms.
• Deploying algorithms on hardware with limited numerical range and precision presents significant challenges.
• Recurrent Hopfield networks can solve linear optimizations by computing matrix inverses.

Purpose of the Study:

• To address the challenges of deploying numerical algorithms on hardware-constrained neural substrates.
• To propose a rigorous mathematical framework for managing range and precision limitations.
• To enable provably correct implementation of linear equation solvers on neuromorphic hardware.

Main Methods:

• Developed techniques for normalizing inputs and quantizing synaptic weights for linear systems.
• Derived a mathematical framework to reason about numerical range and precision on neural substrates.
• Empirically validated the analytical model on the IBM TrueNorth platform.

Main Results:

• The proposed framework provides guarantees for range and precision that hold under experimental conditions.
• Demonstrated energy benefits of deploying a generalized matrix inverse engine on IBM TrueNorth.
• Achieved 10x to 100x energy efficiency improvement compared to FPGA and ARM baselines for optical flow computations.

Conclusions:

• The mathematical framework successfully enables the deployment of numerical algorithms on hardware-constrained neural substrates.
• Provably correct and energy-efficient solutions for linear optimizations can be achieved on neuromorphic hardware.
• This work paves the way for efficient, low-power deployment of complex numerical tasks in real-world applications.