# US 2020/0401876 A1 · Method for designing scalable and energy-efficient analog neuromorphic processors > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2020/0401876 A1 - Document ID: US20200401876A1 - Status: Published application - Kind: A1 - Application number: 16/910,971 - Filed: 2020-06-24 - Published: 2020-12-24 - Earliest claimed: 2019-06-24 - Assignees: Washington University - Inventors: Shantanu CHAKRABARTTY; Ahana GANGOPADHYAY - Web page: https://patentgrep.com/patent/US20200401876A1 ## CPC - G06N 3/065: Analogue means - G06N 3/0442: characterised by memory or gating, e.g. long short-term memory [LSTM] or gated recurrent units [GRU] - G06N 3/0455: Auto-encoder networks; Encoder-decoder networks - G06N 3/049: Temporal neural networks, e.g. delay elements, oscillating neurons or pulsed inputs - G06N 3/0495: Quantised networks; Sparse networks; Compressed networks - G06N 3/08: Learning methods - G06N 3/082: modifying the architecture, e.g. adding, deleting or silencing nodes or connections - G06N 3/086: using evolutionary algorithms, e.g. genetic algorithms or genetic programming - G06N 3/09: Supervised learning - G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS ## Abstract A spiking neural network includes a plurality of neurons implemented in respective circuits. Each neuron produces a continuous-valued membrane potential according to a Growth Transform bounded by an extrinsic energy constraint. The continuous-valued membrane potential is defined as a function of spiking current received from another neuron in the plurality of neurons, and a received electrical current stimulus. The spiking neural network includes a network energy function representing network energy consumed by the plurality of neurons and a neuromorphic framework. The neuromorphic framework minimizes network energy consumed by the plurality of neurons to determine the extrinsic energy constraint, models synaptic connections among the plurality of neurons as respective transconductances that regulate magnitude of spiking currents received from each of the plurality of neurons by each other of the plurality of neurons, and encodes the received electrical current stimulus in corresponding continuous-valued membrane potentials of the plurality of neurons. ## Claims ### Claim 1 A spiking neural network comprising: a plurality of neurons implemented in respective circuits, each neuron configured to: produce a continuous-valued membrane potential according to a Growth Transform bounded by an extrinsic energy constraint, the continuous-valued membrane potential defined as a function of spiking current received from another neuron in the plurality of neurons, and a received electrical current stimulus; and a network energy function representing network energy consumed by the plurality of neurons; and a neuromorphic framework configured to: minimize network energy consumed by the plurality of neurons to determine the extrinsic energy constraint; model synaptic connections among the plurality of neurons as respective transconductances that regulate magnitude of spiking currents received from each of the plurality of neurons by each other of the plurality of neurons; and encode the received electrical current stimulus in corresponding continuous-valued membrane potentials of the plurality of neurons. ### Claim 2 (depends on 1) The spiking neural network of claim 1, wherein the Growth Transform ensures that the membrane potentials are always bounded. ### Claim 3 (depends on 1) The spiking neural network of claim 1, wherein the extrinsic energy constraint includes power dissipation due to coupling between neurons, power injected to or extracted from the plurality of neurons as a result of external stimulation, and power dissipated due to neural responses. ### Claim 4 (depends on 1) The spiking neural network of claim 1, wherein each neuron of the plurality of neurons includes a modulation function that modulates response trajectories of the plurality of neurons without affecting the minimum network energy and the steady-state solution. ### Claim 5 (depends on 4) The spiking neural network of claim 4, wherein the modulation function is varied to tune transient firing statistics to model cell excitability of the plurality of neurons. ### Claim 6 (depends on 1) The spiking neural network of claim 1, wherein a barrier or penalty function to enable finer control over spiking responses of the plurality of neurons. ### Claim 7 (depends on 1) The spiking neural network of claim 1, wherein the spiking neural network is an associative memory network that uses the Growth Transform to store and recall memory patterns for the plurality of neurons. ### Claim 8 (depends on 1) The spiking neural network of claim 1, wherein the spiking neural network is implemented on fully continuous-time analog architecture. ### Claim 9 A method of operating a neural network, the method comprising: implementing a plurality of neurons in respective circuits; producing a continuous-valued membrane potential according to a Growth Transform bounded by an extrinsic energy constraint; defining a function of spiking current received from another neuron in the plurality of neurons, and a received electrical current stimulus, as a continuous-valued membrane potential; representing network energy consumed by the plurality of neurons as a network energy function; minimizing network energy consumed by the plurality of neurons to determine the extrinsic energy constraint; modeling synaptic connections among the plurality of neurons as respective transconductances that regulate magnitude of spiking currents received from each of the plurality of neurons by each other of the plurality of neurons; and encoding the received electrical current stimulus in corresponding continuous-valued membrane potentials of the plurality of neurons. ### Claim 10 (depends on 9) The method of claim 9, further comprising bounding the membrane potentials by the Growth Transform always. ### Claim 11 (depends on 10) The method of claim 10, further comprising including power dissipation due to coupling between neurons, injecting power to or extracted from the plurality of neurons as a result of external stimulation, and dissipating power due to neural responses in the extrinsic energy constraint. ### Claim 12 (depends on 10) The method of claim 10, further comprising including a modulation function for each neuron of the plurality of neurons that modulates response trajectories of the plurality of neurons without affecting the minimum network energy and the steady-state solution, wherein varying the modulation function tunes transient firing statistics to model cell excitability of the plurality of neurons. ### Claim 13 (depends on 10) The method of claim 10, further comprising enabling finer control over spiking response of the plurality of neurons with a barrier or penalty function. ### Claim 14 (depends on 10) The method of claim 10, further comprising using the Growth Transform to store and recall memory patterns for the plurality of neurons to enable the neural network to be an associative memory network. ### Claim 15 (depends on 10) The method of claim 10, further comprising implementing the neural network on fully continuous-time analog architecture. ### Claim 16 At least one non-transitory computer-readable storage medium having computer-executable instructions embodied thereon for operating a neural network, wherein when executed by at least one processor, the computer-executable instructions cause the processor to: implement a plurality of neurons in respective circuits; produce a continuous-valued membrane potential according to a Growth Transform bounded by an extrinsic energy constraint, define a function of spiking current received from another neuron in the plurality of neurons, and a received electrical current stimulus, as a continuous-valued membrane potential; represent network energy consumed by the plurality of neurons as a network energy function; minimize network energy consumed by the plurality of neurons to determine the extrinsic energy constraint; model synaptic connections among the plurality of neurons as respective transconductances that regulate magnitude of spiking currents received from each of the plurality of neurons by each other of the plurality of neurons; and encode the received electrical current stimulus in corresponding continuous-valued membrane potentials of the plurality of neurons. ### Claim 17 (depends on 16) The computer-readable storage medium of claim 16, wherein the computer-executable instructions cause the processor to always bound the membrane potentials by the Growth Transform. ### Claim 18 (depends on 16) The computer-readable storage medium of claim 16, wherein the computer-executable instructions cause the processor to include power dissipation due to coupling between neurons, inject power to or extracted from the plurality of neurons as a result of external stimulation, and dissipate power due to neural responses in the extrinsic energy constraint. ### Claim 19 (depends on 16) The computer-readable storage medium of claim 16, wherein the computer-executable instructions cause the processor to include a modulation function for each neuron of the plurality of neurons that modulates response trajectories of the plurality of neurons without affecting the minimum network energy and the steady-state solution, wherein varying the modulation function tunes transient firing statistics to model cell excitability of the plurality of neurons. ### Claim 20 (depends on 16) The computer-readable storage medium of claim 16, wherein the computer-executable instructions cause the processor to enable finer control over spiking response of the plurality of neurons with a barrier or penalty function, using the Growth Transform to store and recall memory patterns for the plurality of neurons to enable the neural network to be an associative memory network, and implementing the neural network on fully continuous-time analog architecture.