Physics Overview

Paper Read

Physics for Neuromorphic Computing 2020

Human brain:

• large inter-connectivity - high dimension (higher factorial dimension for white matter).
  • memory and computation are not separated. synchronous communication is avoided.
  • large fan-in/fan-out & low energy consumption.
• Compared to neuron networks :
  • neurons are more than non-linear functions : spike, leaky, stochastic, oscillate, synchronize, etc.
  • synapses are more than analog weights : leaky, time scale, parameter pattern, stochastic, etc.

Map AI to physical system:

1. Neuromorphic chips - using memristor (memory-resistor).
   • hard for learning.
2. Photonic Neural networks.
   • neurons - optical resonators; synapses - interferometers & optically active phase change materials.
   • large size; energy cost of lasers.

Materials and physics used - oxide (氧化物) electronics.

• Conductive bridge devices can emulate long short term memory.
• Materials exhibit phase transitions (e.g. Mott insulators) can emulate spiking neurons.
• Chaicogenide-based phase change memories.
• Organic materials.
• Flux quantization in superconductive Josephson junctions.

Unsupervised learning with Spike Timing Dependent Plasticity (STDP) - weight updated depending on the the timing of spikes occurring on both sides of a synapse.

	CMOS synapses and neurons	Resistive switching synapses with CMOS neurons	Photonic synapses and neurons	Spintronic synapses and neurons	Superconductive synapses and neurons
Connections	wires	wires	light	microwaves	wires or microwaves
Min neuron lateral size	10 µm	10 µm	100 µm	10nm	20 nm
Min synapse lateral size	10 µm	10 nm	1 µm	10nm	20 nm
Advantages	commercial	Nanoscale synapse, technology-ready	Wavelength multiplexing, can be totally passive (zero energy consumption)	Nanoscale synapses and neurons, almost commercial technology	Low energy consumption beside cryogenic requirements, all identical spikes
Disadvantages	Size of neurons and synapses, no in-memory computing	Size of neurons, complex wiring	Size of neurons and synapses, dissipation due to lasers	Scalability to be demonstrated	Scalability to be demonstrated
Chips	Inference	Inference coming soon	no	no	no

Spiking-Neural-Network

Paper Read

Spiking Neural Networks and Their Applications: A Review 2022

• Introduction of : biological neurons (dendrites, soma, axon, synapse, neurotransmitters), artificial neural networks (\(r = f(Wu + b)\)), spiking neural networks (spike times).
• Spiking Neuron Models (see wiki - Biological neuron model for more):
  1. Hodgkin-Huxley Model. (efficiency-, plausibility+) include K Na channels.
  2. Leaky Integrate and Fire Model. (efficiency+, plausibility-) ignore iron channels.
  3. Izhikevich Model. (efficiency+, plausibility+) use 2d system (potential & ionic current).
  4. Adaptive Exponential Integrate-and-Fire Model. (efficiency+, plausibility=) 2d system (potential & adaption slow variable).
• Synaptic Models: decay and rise of the PSC (post-synaptic current).
• SNN Learning:
  1. Spike-Based Backpropagation.
  2. Spike Timing Dependent Plasticity (STDP).
  3. ANN-to-SNN Conversion. convert RELU to IF neurons.
• Spike Encoding : decode/encode spikes into/from information - rate encoding & pulse encoding.

Spike-FlowNet: Event-based Optical Flow Estimation with Energy-Efficient Hybrid Neural Networks 2020, github. ANN+SNN optical flow for event camera.

• ANN for pixel-based images rely on photo-consistency constraints; SNN fits Event camera (bio-inspired silicon retinas).
• SNN problem : The number of spikes drastically vanish at deeper layers.
• Make an simple implementation of IF (integrate-and-fire) SNN in python.

Intel Loihi (wikichip) based works:

• Reinforcement co-Learning of Deep and Spiking Neural Networks for Energy-Efficient Mapless Navigation with Neuromorphic Hardware 2020 hybrid SNN + DNN framework.
  • SNN (LIF leaky-integrate-and-fire) : state-to-action network. (trained by backpropagation using pseudo-gradient function)
    • transform to an end-to-end SNN compared to their previous work.
  • DNN : action-value (critic ) network.
• Spiking Neural Network on Neuromorphic Hardware for Energy-Efficient Unidimensional SLAM 2019,
  • mammalian brains space representation.
  • head direction network, reference frame transformation network, distance mapping network, observation likelihood network, bayesian inference network.

python implementation 2018, SpykeTorch 2021, Brian2 2008.

First-Spike-Based Visual Categorization Using Reward-Modulated STDP 2017 : supervised learingin - Reward-Modulated STDP (using RL). R-STDP can change the behavior of a neuron. implementation using SpykeTorch.

• Layer 1 : convert image to spike latencies based on the saliency of its oriented edges.
• Layer 2 : local pooling.
• Layer 3 : integrate-and-fire neurons. (trainable)
• Layer 4 : decision making.
• RL supervised update github :

\[\Delta W_{ij}= \begin{cases} a_{LTP}\times \left(W_{ij}-W_{LB}\right)\times \left(W_{UP}-W_{ij}\right) & \ \ \ t_j - t_i \leq 0,\\ a_{LTD}\times \left(W_{ij}-W_{LB}\right)\times \left(W_{UP}-W_{ij}\right) & \ \ \ t_j - t_i > 0,\\ \end{cases}\]

• My test playground - SNN Heading Estimation.

Bioinspired Programming of Memory Devices for Implementing an Inference Engine 2015.

• problem : von Neumann bottleneck - requirement of large energy budget from the separation of memory and computing. (a neuron only performs basis operations, which depend on a high number of memory access)
• long term memory <- synaptic plasticity. synapse tend to reinforce causal links. -> Spike-timing-dependent plasticity - local, unsupervised.
  • Any synapse that contribute to the firing of a post-synaptic neuron should be made strong i.e it’s value should be increased.
  • Synapses that don’t contribute to the firing of a post-synaptic neuron should be dimished i.e it’s value should be decreased.
• Memory devices:
  1. Multilevel Memory : (a) cumulative memristive device; (b) phase change memory.
  2. Stochastic Synapse : (c) conductive bridge memory; (d) STT-MTJ (basic cell of STT-MARAM).