摘要：
相关源代码：bindsnet/bidsnet/network/nodes。py1，NodesclassNodes（torch.nn.Module）：#language=rst“”“Abstractbaseclassforgroupsofservers.”“”def__init__（self，n:Optional[int]=无，shape:Optional[Iterable[int]]=无
相关源码：bindsnet/bindsnet/network/nodes.py
1、Nodes
class Nodes(torch.nn.Module): # language=rst """ Abstract base class for groups of neurons. """ def __init__( self, n: Optional[int] = None, shape: Optional[Iterable[int]] = None, traces: bool = False, traces_additive: bool = False, tc_trace: Union[float, torch.Tensor] = 20.0, trace_scale: Union[float, torch.Tensor] = 1.0, sum_input: bool = False, learning: bool = True, **kwargs, ) -> None: # language=rst """ Abstract base class constructor. :param n: The number of neurons in the layer. :param shape: The dimensionality of the layer. :param traces: Whether to record decaying spike traces. :param traces_additive: Whether to record spike traces additively. :param tc_trace: Time constant of spike trace decay. :param trace_scale: Scaling factor for spike trace. :param sum_input: Whether to sum all inputs. :param learning: Whether to be in learning or testing. """ super().__init__() assert ( n is not None or shape is not None ), "Must provide either no. of neurons or shape of layer" if n is None: self.n = reduce(mul, shape) # No. of neurons product of shape. else: self.n = n # No. of neurons provided. if shape is None: self.shape = [self.n] # Shape is equal to the size of the layer. else: self.shape = shape # Shape is passed in as an argument. assert self.n == reduce( mul, self.shape ), "No. of neurons and shape do not match" self.traces = traces # Whether to record synaptic traces. self.traces_additive = ( traces_additive # Whether to record spike traces additively. ) self.register_buffer("s", torch.ByteTensor()) # Spike occurrences. self.sum_input = sum_input # Whether to sum all inputs. if self.traces: self.register_buffer("x", torch.Tensor()) # Firing traces. self.register_buffer( "tc_trace", torch.tensor(tc_trace) ) # Time constant of spike trace decay. if self.traces_additive: self.register_buffer( "trace_scale", torch.tensor(trace_scale) ) # Scaling factor for spike trace. self.register_buffer( "trace_decay", torch.empty_like(self.tc_trace) ) # Set in compute_decays, e.g. math.exp(-1/20)=0.9512 if self.sum_input: self.register_buffer("summed", torch.FloatTensor()) # Summed inputs. self.dt = None self.batch_size = None self.trace_decay = None self.learning = learning @abstractmethod def forward(self, x: torch.Tensor) -> None: # language=rst """ Abstract base class method for a single simulation step. :param x: Inputs to the layer. """ if self.traces: # Decay and set spike traces. self.x *= self.trace_decay if self.traces_additive: self.x += self.trace_scale * self.s.float() else: self.x.masked_fill_(self.s, 1) if self.sum_input: # Add current input to running sum. self.summed += x.float() def reset_state_variables(self) -> None: # language=rst """ Abstract base class method for resetting state variables. """ self.s.zero_() if self.traces: self.x.zero_() # Spike traces. if self.sum_input: self.summed.zero_() # Summed inputs. def compute_decays(self, dt) -> None: # language=rst """ Abstract base class method for setting decays. """ self.dt = torch.tensor(dt) if self.traces: self.trace_decay = torch.exp( -self.dt / self.tc_trace ) # Spike trace decay (per timestep). def set_batch_size(self, batch_size) -> None: # language=rst """ Sets mini-batch size. Called when layer is added to a network. :param batch_size: Mini-batch size. """ self.batch_size = batch_size self.s = torch.zeros( batch_size, *self.shape, device=self.s.device, dtype=torch.bool ) if self.traces: self.x = torch.zeros(batch_size, *self.shape, device=self.x.device) if self.sum_input: self.summed = torch.zeros( batch_size, *self.shape, device=self.summed.device ) def train(self, mode: bool = True) -> "Nodes": # language=rst """ Sets the layer in training mode. :param bool mode: Turn training on or off :return: self as specified in `torch.nn.Module` """ self.learning = mode return super().train(mode)
神经元群的抽象基类。当self.traces = True时，先对发放迹进行衰减，然后基于脉冲信号对原本发放迹进行1填充(即发放脉冲的神经元，其发放率为1)。
2、Input
class AbstractInput(ABC): # language=rst """ Abstract base class for groups of input neurons. """ class Input(Nodes, AbstractInput): # language=rst """ Layer of nodes with user-specified spiking behavior. """ def __init__( self, n: Optional[int] = None, shape: Optional[Iterable[int]] = None, traces: bool = False, traces_additive: bool = False, tc_trace: Union[float, torch.Tensor] = 20.0, trace_scale: Union[float, torch.Tensor] = 1.0, sum_input: bool = False, **kwargs, ) -> None: # language=rst """ Instantiates a layer of input neurons. :param n: The number of neurons in the layer. :param shape: The dimensionality of the layer. :param traces: Whether to record decaying spike traces. :param traces_additive: Whether to record spike traces additively. :param tc_trace: Time constant of spike trace decay. :param trace_scale: Scaling factor for spike trace. :param sum_input: Whether to sum all inputs. """ super().__init__( n=n, shape=shape, traces=traces, traces_additive=traces_additive, tc_trace=tc_trace, trace_scale=trace_scale, sum_input=sum_input, ) def forward(self, x: torch.Tensor) -> None: # language=rst """ On each simulation step, set the spikes of the population equal to the inputs. :param x: Inputs to the layer. """ # Set spike occurrences to input values. self.s = x super().forward(x) def reset_state_variables(self) -> None: # language=rst """ Resets relevant state variables. """ super().reset_state_variables()
具有用户指定的脉冲行为的节点层。先将前向输入赋值给脉冲信号，然后执行基类函数。
3、McCullochPitts
class McCullochPitts(Nodes): # language=rst """ Layer of `McCulloch-Pitts neurons <http://wwwold.ece.utep.edu/research/webfuzzy/docs/kk-thesis/kk-thesis-html/node12.html>`_. """ def __init__( self, n: Optional[int] = None, shape: Optional[Iterable[int]] = None, traces: bool = False, traces_additive: bool = False, tc_trace: Union[float, torch.Tensor] = 20.0, trace_scale: Union[float, torch.Tensor] = 1.0, sum_input: bool = False, thresh: Union[float, torch.Tensor] = 1.0, **kwargs, ) -> None: # language=rst """ Instantiates a McCulloch-Pitts layer of neurons. :param n: The number of neurons in the layer. :param shape: The dimensionality of the layer. :param traces: Whether to record spike traces. :param traces_additive: Whether to record spike traces additively. :param tc_trace: Time constant of spike trace decay. :param trace_scale: Scaling factor for spike trace. :param sum_input: Whether to sum all inputs. :param thresh: Spike threshold voltage. """ super().__init__( n=n, shape=shape, traces=traces, traces_additive=traces_additive, tc_trace=tc_trace, trace_scale=trace_scale, sum_input=sum_input, ) self.register_buffer( "thresh", torch.tensor(thresh, dtype=torch.float) ) # Spike threshold voltage. self.register_buffer("v", torch.FloatTensor()) # Neuron voltages. def forward(self, x: torch.Tensor) -> None: # language=rst """ Runs a single simulation step. :param x: Inputs to the layer. """ self.v = x # Voltages are equal to the inputs. self.s = self.v >= self.thresh # Check for spiking neurons. super().forward(x) def reset_state_variables(self) -> None: # language=rst """ Resets relevant state variables. """ super().reset_state_variables() def set_batch_size(self, batch_size) -> None: # language=rst """ Sets mini-batch size. Called when layer is added to a network. :param batch_size: Mini-batch size. """ super().set_batch_size(batch_size=batch_size) self.v = torch.zeros(batch_size, *self.shape, device=self.v.device)
McCulloch-Pitts神经元层。先将前向输入赋值给电压信号；然后将电压与阈值作比较，得到脉冲信号；最后执行基类函数。
4、IFNodes
class IFNodes(Nodes): # language=rst """ Layer of `integrate-and-fire (IF) neurons <http://neuronaldynamics.epfl.ch/online/Ch1.S3.html>`_. """ def __init__( self, n: Optional[int] = None, shape: Optional[Iterable[int]] = None, traces: bool = False, traces_additive: bool = False, tc_trace: Union[float, torch.Tensor] = 20.0, trace_scale: Union[float, torch.Tensor] = 1.0, sum_input: bool = False, thresh: Union[float, torch.Tensor] = -52.0, reset: Union[float, torch.Tensor] = -65.0, refrac: Union[int, torch.Tensor] = 5, lbound: float = None, **kwargs, ) -> None: # language=rst """ Instantiates a layer of IF neurons. :param n: The number of neurons in the layer. :param shape: The dimensionality of the layer. :param traces: Whether to record spike traces. :param traces_additive: Whether to record spike traces additively. :param tc_trace: Time constant of spike trace decay. :param trace_scale: Scaling factor for spike trace. :param sum_input: Whether to sum all inputs. :param thresh: Spike threshold voltage. :param reset: Post-spike reset voltage. :param refrac: Refractory (non-firing) period of the neuron. :param lbound: Lower bound of the voltage. """ super().__init__( n=n, shape=shape, traces=traces, traces_additive=traces_additive, tc_trace=tc_trace, trace_scale=trace_scale, sum_input=sum_input, ) self.register_buffer( "reset", torch.tensor(reset, dtype=torch.float) ) # Post-spike reset voltage. self.register_buffer( "thresh", torch.tensor(thresh, dtype=torch.float) ) # Spike threshold voltage. self.register_buffer( "refrac", torch.tensor(refrac) ) # Post-spike refractory period. self.register_buffer("v", torch.FloatTensor()) # Neuron voltages. self.register_buffer( "refrac_count", torch.FloatTensor() ) # Refractory period counters. self.lbound = lbound # Lower bound of voltage. def forward(self, x: torch.Tensor) -> None: # language=rst """ Runs a single simulation step. :param x: Inputs to the layer. """ # Integrate input voltages. self.v += (self.refrac_count <= 0).float() * x # Decrement refractory counters. self.refrac_count -= self.dt # Check for spiking neurons. self.s = self.v >= self.thresh # Refractoriness and voltage reset. self.refrac_count.masked_fill_(self.s, self.refrac) self.v.masked_fill_(self.s, self.reset) # Voltage clipping to lower bound. if self.lbound is not None: self.v.masked_fill_(self.v < self.lbound, self.lbound) super().forward(x) def reset_state_variables(self) -> None: # language=rst """ Resets relevant state variables. """ super().reset_state_variables() self.v.fill_(self.reset) # Neuron voltages. self.refrac_count.zero_() # Refractory period counters. def set_batch_size(self, batch_size) -> None: # language=rst """ Sets mini-batch size. Called when layer is added to a network. :param batch_size: Mini-batch size. """ super().set_batch_size(batch_size=batch_size) self.v = self.reset * torch.ones(batch_size, *self.shape, device=self.v.device) self.refrac_count = torch.zeros_like(self.v, device=self.refrac_count.device)
IF神经元层。先整合输入电压(同时考虑不应期计数)；然后降低不应期计数；接着将电压与阈值作比较，得到脉冲信号；之后基于脉冲信号对不应期计数器和电压进行修改；电压截断至下限；最后执行基类函数。
5、LIFNodes
class LIFNodes(Nodes): # language=rst """ Layer of `leaky integrate-and-fire (LIF) neurons <http://web.archive.org/web/20190318204706/http://icwww.epfl.ch/~gerstner/SPNM/node26.html#SECTION02311000000000000000>`_. """ def __init__( self, n: Optional[int] = None, shape: Optional[Iterable[int]] = None, traces: bool = False, traces_additive: bool = False, tc_trace: Union[float, torch.Tensor] = 20.0, trace_scale: Union[float, torch.Tensor] = 1.0, sum_input: bool = False, thresh: Union[float, torch.Tensor] = -52.0, rest: Union[float, torch.Tensor] = -65.0, reset: Union[float, torch.Tensor] = -65.0, refrac: Union[int, torch.Tensor] = 5, tc_decay: Union[float, torch.Tensor] = 100.0, lbound: float = None, **kwargs, ) -> None: # language=rst """ Instantiates a layer of LIF neurons. :param n: The number of neurons in the layer. :param shape: The dimensionality of the layer. :param traces: Whether to record spike traces. :param traces_additive: Whether to record spike traces additively. :param tc_trace: Time constant of spike trace decay. :param trace_scale: Scaling factor for spike trace. :param sum_input: Whether to sum all inputs. :param thresh: Spike threshold voltage. :param rest: Resting membrane voltage. :param reset: Post-spike reset voltage. :param refrac: Refractory (non-firing) period of the neuron. :param tc_decay: Time constant of neuron voltage decay. :param lbound: Lower bound of the voltage. """ super().__init__( n=n, shape=shape, traces=traces, traces_additive=traces_additive, tc_trace=tc_trace, trace_scale=trace_scale, sum_input=sum_input, ) self.register_buffer( "rest", torch.tensor(rest, dtype=torch.float) ) # Rest voltage. self.register_buffer( "reset", torch.tensor(reset, dtype=torch.float) ) # Post-spike reset voltage. self.register_buffer( "thresh", torch.tensor(thresh, dtype=torch.float) ) # Spike threshold voltage. self.register_buffer( "refrac", torch.tensor(refrac) ) # Post-spike refractory period. self.register_buffer( "tc_decay", torch.tensor(tc_decay, dtype=torch.float) ) # Time constant of neuron voltage decay. self.register_buffer( "decay", torch.zeros(*self.shape) ) # Set in compute_decays. self.register_buffer("v", torch.FloatTensor()) # Neuron voltages. self.register_buffer( "refrac_count", torch.FloatTensor() ) # Refractory period counters. if lbound is None: self.lbound = None # Lower bound of voltage. else: self.lbound = torch.tensor( lbound, dtype=torch.float ) # Lower bound of voltage. def forward(self, x: torch.Tensor) -> None: # language=rst """ Runs a single simulation step. :param x: Inputs to the layer. """ # Decay voltages. self.v = self.decay * (self.v - self.rest) + self.rest # Integrate inputs. x.masked_fill_(self.refrac_count > 0, 0.0) # Decrement refractory counters. self.refrac_count -= self.dt self.v += x # interlaced # Check for spiking neurons. self.s = self.v >= self.thresh # Refractoriness and voltage reset. self.refrac_count.masked_fill_(self.s, self.refrac) self.v.masked_fill_(self.s, self.reset) # Voltage clipping to lower bound. if self.lbound is not None: self.v.masked_fill_(self.v < self.lbound, self.lbound) super().forward(x) def reset_state_variables(self) -> None: # language=rst """ Resets relevant state variables. """ super().reset_state_variables() self.v.fill_(self.rest) # Neuron voltages. self.refrac_count.zero_() # Refractory period counters. def compute_decays(self, dt) -> None: # language=rst """ Sets the relevant decays. """ super().compute_decays(dt=dt) self.decay = torch.exp( -self.dt / self.tc_decay ) # Neuron voltage decay (per timestep). def set_batch_size(self, batch_size) -> None: # language=rst """ Sets mini-batch size. Called when layer is added to a network. :param batch_size: Mini-batch size. """ super().set_batch_size(batch_size=batch_size) self.v = self.rest * torch.ones(batch_size, *self.shape, device=self.v.device) self.refrac_count = torch.zeros_like(self.v, device=self.refrac_count.device)
LIF神经元层。先整合输入电压(同时考虑不应期计数和电压衰减)；然后降低不应期计数器；接着将电压与阈值作比较，得到脉冲信号；之后基于脉冲信号对不应期计数器以及电压进行修改；电压截断至下限；最后执行基类函数。
6、BoostedLIFNodes
class BoostedLIFNodes(Nodes): # Same as LIFNodes, faster: no rest, no reset, no lbound def __init__( self, n: Optional[int] = None, shape: Optional[Iterable[int]] = None, traces: bool = False, traces_additive: bool = False, tc_trace: Union[float, torch.Tensor] = 20.0, trace_scale: Union[float, torch.Tensor] = 1.0, sum_input: bool = False, thresh: Union[float, torch.Tensor] = 13.0, refrac: Union[int, torch.Tensor] = 5, tc_decay: Union[float, torch.Tensor] = 100.0, **kwargs, ) -> None: # language=rst """ Instantiates a layer of LIF neurons. :param n: The number of neurons in the layer. :param shape: The dimensionality of the layer. :param traces: Whether to record spike traces. :param traces_additive: Whether to record spike traces additively. :param tc_trace: Time constant of spike trace decay. :param trace_scale: Scaling factor for spike trace. :param sum_input: Whether to sum all inputs. :param thresh: Spike threshold voltage. :param reset: Post-spike reset voltage. :param refrac: Refractory (non-firing) period of the neuron. :param tc_decay: Time constant of neuron voltage decay. """ super().__init__( n=n, shape=shape, traces=traces, traces_additive=traces_additive, tc_trace=tc_trace, trace_scale=trace_scale, sum_input=sum_input, ) self.register_buffer( "thresh", torch.tensor(thresh, dtype=torch.float) ) # Spike threshold voltage. self.register_buffer( "refrac", torch.tensor(refrac) ) # Post-spike refractory period. self.register_buffer( "tc_decay", torch.tensor(tc_decay, dtype=torch.float) ) # Time constant of neuron voltage decay. self.register_buffer( "decay", torch.zeros(*self.shape) ) # Set in compute_decays. self.register_buffer("v", torch.FloatTensor()) # Neuron voltages. self.register_buffer( "refrac_count", torch.tensor(0) ) # Refractory period counters. def forward(self, x: torch.Tensor) -> None: # language=rst """ Runs a single simulation step. :param x: Inputs to the layer. """ # Decay voltages. self.v *= self.decay # Integrate inputs. if x is not None: x.masked_fill_(self.refrac_count > 0, 0.0) # Decrement refractory counters. self.refrac_count -= self.dt if x is not None: self.v += x # Check for spiking neurons. self.s = self.v >= self.thresh # Refractoriness and voltage reset. self.refrac_count.masked_fill_(self.s, self.refrac) self.v.masked_fill_(self.s, 0) super().forward(x) def reset_state_variables(self) -> None: # language=rst """ Resets relevant state variables. """ super().reset_state_variables() self.v.fill_(0) # Neuron voltages. self.refrac_count.zero_() # Refractory period counters. def compute_decays(self, dt) -> None: # language=rst """ Sets the relevant decays. """ super().compute_decays(dt=dt) self.decay = torch.exp( -self.dt / self.tc_decay ) # Neuron voltage decay (per timestep). def set_batch_size(self, batch_size) -> None: # language=rst """ Sets mini-batch size. Called when layer is added to a network. :param batch_size: Mini-batch size. """ super().set_batch_size(batch_size=batch_size) self.v = torch.zeros(batch_size, *self.shape, device=self.v.device) self.refrac_count = torch.zeros_like(self.v, device=self.refrac_count.device)
与LIFNodes相同，但更快——无需不应期，没有重置(直接归零)，并且没有下界。
7、CurrentLIFNodes
class CurrentLIFNodes(Nodes): # language=rst """ Layer of `current-based leaky integrate-and-fire (LIF) neurons <http://web.archive.org/web/20190318204706/http://icwww.epfl.ch/~gerstner/SPNM/node26.html#SECTION02313000000000000000>`_. Total synaptic input current is modeled as a decaying memory of input spikes multiplied by synaptic strengths. """ def __init__( self, n: Optional[int] = None, shape: Optional[Iterable[int]] = None, traces: bool = False, traces_additive: bool = False, tc_trace: Union[float, torch.Tensor] = 20.0, trace_scale: Union[float, torch.Tensor] = 1.0, sum_input: bool = False, thresh: Union[float, torch.Tensor] = -52.0, rest: Union[float, torch.Tensor] = -65.0, reset: Union[float, torch.Tensor] = -65.0, refrac: Union[int, torch.Tensor] = 5, tc_decay: Union[float, torch.Tensor] = 100.0, tc_i_decay: Union[float, torch.Tensor] = 2.0, lbound: float = None, **kwargs, ) -> None: # language=rst """ Instantiates a layer of synaptic input current-based LIF neurons. :param n: The number of neurons in the layer. :param shape: The dimensionality of the layer. :param traces: Whether to record spike traces. :param traces_additive: Whether to record spike traces additively. :param tc_trace: Time constant of spike trace decay. :param trace_scale: Scaling factor for spike trace. :param sum_input: Whether to sum all inputs. :param thresh: Spike threshold voltage. :param rest: Resting membrane voltage. :param reset: Post-spike reset voltage. :param refrac: Refractory (non-firing) period of the neuron. :param tc_decay: Time constant of neuron voltage decay. :param tc_i_decay: Time constant of synaptic input current decay. :param lbound: Lower bound of the voltage. """ super().__init__( n=n, shape=shape, traces=traces, traces_additive=traces_additive, tc_trace=tc_trace, trace_scale=trace_scale, sum_input=sum_input, ) self.register_buffer("rest", torch.tensor(rest)) # Rest voltage. self.register_buffer("reset", torch.tensor(reset)) # Post-spike reset voltage. self.register_buffer("thresh", torch.tensor(thresh)) # Spike threshold voltage. self.register_buffer( "refrac", torch.tensor(refrac) ) # Post-spike refractory period. self.register_buffer( "tc_decay", torch.tensor(tc_decay) ) # Time constant of neuron voltage decay. self.register_buffer( "decay", torch.empty_like(self.tc_decay) ) # Set in compute_decays. self.register_buffer( "tc_i_decay", torch.tensor(tc_i_decay) ) # Time constant of synaptic input current decay. self.register_buffer( "i_decay", torch.empty_like(self.tc_i_decay) ) # Set in compute_decays. self.register_buffer("v", torch.FloatTensor()) # Neuron voltages. self.register_buffer("i", torch.FloatTensor()) # Synaptic input currents. self.register_buffer( "refrac_count", torch.FloatTensor() ) # Refractory period counters. self.lbound = lbound # Lower bound of voltage. def forward(self, x: torch.Tensor) -> None: # language=rst """ Runs a single simulation step. :param x: Inputs to the layer. """ # Decay voltages and current. self.v = self.decay * (self.v - self.rest) + self.rest self.i *= self.i_decay # Decrement refractory counters. self.refrac_count -= self.dt # Integrate inputs. self.i += x self.v += (self.refrac_count <= 0).float() * self.i # Check for spiking neurons. self.s = self.v >= self.thresh # Refractoriness and voltage reset. self.refrac_count.masked_fill_(self.s, self.refrac) self.v.masked_fill_(self.s, self.reset) # Voltage clipping to lower bound. if self.lbound is not None: self.v.masked_fill_(self.v < self.lbound, self.lbound) super().forward(x) def reset_state_variables(self) -> None: # language=rst """ Resets relevant state variables. """ super().reset_state_variables() self.v.fill_(self.rest) # Neuron voltages. self.i.zero_() # Synaptic input currents. self.refrac_count.zero_() # Refractory period counters. def compute_decays(self, dt) -> None: # language=rst """ Sets the relevant decays. """ super().compute_decays(dt=dt) self.decay = torch.exp( -self.dt / self.tc_decay ) # Neuron voltage decay (per timestep). self.i_decay = torch.exp( -self.dt / self.tc_i_decay ) # Synaptic input current decay (per timestep). def set_batch_size(self, batch_size) -> None: # language=rst """ Sets mini-batch size. Called when layer is added to a network. :param batch_size: Mini-batch size. """ super().set_batch_size(batch_size=batch_size) self.v = self.rest * torch.ones(batch_size, *self.shape, device=self.v.device) self.i = torch.zeros_like(self.v, device=self.i.device) self.refrac_count = torch.zeros_like(self.v, device=self.refrac_count.device)
基于电流的LIF神经元层，具体神经元过程如下：
- 电压/电流衰减；
不应期计数器自减；
- 整合输入(电流自增输入项，电压自增不应期计数器小于等于零的电流项)；
- 检查脉冲神经元(当电压>阈值时，发放脉冲)；
- 不应性/电压复位；
- 电压截断至下限；
- Nodes基类前向传播(迹/累积和)。
8、AdaptiveLIFNodes
class AdaptiveLIFNodes(Nodes): # language=rst """ Layer of leaky integrate-and-fire (LIF) neurons with adaptive thresholds. A neuron's voltage threshold is increased by some constant each time it spikes; otherwise, it is decaying back to its default value. """ def __init__( self, n: Optional[int] = None, shape: Optional[Iterable[int]] = None, traces: bool = False, traces_additive: bool = False, tc_trace: Union[float, torch.Tensor] = 20.0, trace_scale: Union[float, torch.Tensor] = 1.0, sum_input: bool = False, rest: Union[float, torch.Tensor] = -65.0, reset: Union[float, torch.Tensor] = -65.0, thresh: Union[float, torch.Tensor] = -52.0, refrac: Union[int, torch.Tensor] = 5, tc_decay: Union[float, torch.Tensor] = 100.0, theta_plus: Union[float, torch.Tensor] = 0.05, tc_theta_decay: Union[float, torch.Tensor] = 1e7, lbound: float = None, **kwargs, ) -> None: # language=rst """ Instantiates a layer of LIF neurons with adaptive firing thresholds. :param n: The number of neurons in the layer. :param shape: The dimensionality of the layer. :param traces: Whether to record spike traces. :param traces_additive: Whether to record spike traces additively. :param tc_trace: Time constant of spike trace decay. :param trace_scale: Scaling factor for spike trace. :param sum_input: Whether to sum all inputs. :param rest: Resting membrane voltage. :param reset: Post-spike reset voltage. :param thresh: Spike threshold voltage. :param refrac: Refractory (non-firing) period of the neuron. :param tc_decay: Time constant of neuron voltage decay. :param theta_plus: Voltage increase of threshold after spiking. :param tc_theta_decay: Time constant of adaptive threshold decay. :param lbound: Lower bound of the voltage. """ super().__init__( n=n, shape=shape, traces=traces, traces_additive=traces_additive, tc_trace=tc_trace, trace_scale=trace_scale, sum_input=sum_input, ) self.register_buffer("rest", torch.tensor(rest)) # Rest voltage. self.register_buffer("reset", torch.tensor(reset)) # Post-spike reset voltage. self.register_buffer("thresh", torch.tensor(thresh)) # Spike threshold voltage. self.register_buffer( "refrac", torch.tensor(refrac) ) # Post-spike refractory period. self.register_buffer( "tc_decay", torch.tensor(tc_decay) ) # Time constant of neuron voltage decay. self.register_buffer( "decay", torch.empty_like(self.tc_decay, dtype=torch.float32) ) # Set in compute_decays. self.register_buffer( "theta_plus", torch.tensor(theta_plus) ) # Constant threshold increase on spike. self.register_buffer( "tc_theta_decay", torch.tensor(tc_theta_decay) ) # Time constant of adaptive threshold decay. self.register_buffer( "theta_decay", torch.empty_like(self.tc_theta_decay) ) # Set in compute_decays. self.register_buffer("v", torch.FloatTensor()) # Neuron voltages. self.register_buffer("theta", torch.zeros(*self.shape)) # Adaptive thresholds. self.register_buffer( "refrac_count", torch.FloatTensor() ) # Refractory period counters. self.lbound = lbound # Lower bound of voltage. def forward(self, x: torch.Tensor) -> None: # language=rst """ Runs a single simulation step. :param x: Inputs to the layer. """ # Decay voltages and adaptive thresholds. self.v = self.decay * (self.v - self.rest) + self.rest if self.learning: self.theta *= self.theta_decay # Integrate inputs. self.v += (self.refrac_count <= 0).float() * x # Decrement refractory counters. self.refrac_count -= self.dt # Check for spiking neurons. self.s = self.v >= self.thresh + self.theta # Refractoriness, voltage reset, and adaptive thresholds. self.refrac_count.masked_fill_(self.s, self.refrac) self.v.masked_fill_(self.s, self.reset) if self.learning: self.theta += self.theta_plus * self.s.float().sum(0) # voltage clipping to lowerbound if self.lbound is not None: self.v.masked_fill_(self.v < self.lbound, self.lbound) super().forward(x) def reset_state_variables(self) -> None: # language=rst """ Resets relevant state variables. """ super().reset_state_variables() self.v.fill_(self.rest) # Neuron voltages. self.refrac_count.zero_() # Refractory period counters. def compute_decays(self, dt) -> None: # language=rst """ Sets the relevant decays. """ super().compute_decays(dt=dt) self.decay = torch.exp( -self.dt / self.tc_decay ) # Neuron voltage decay (per timestep). self.theta_decay = torch.exp( -self.dt / self.tc_theta_decay ) # Adaptive threshold decay (per timestep). def set_batch_size(self, batch_size) -> None: # language=rst """ Sets mini-batch size. Called when layer is added to a network. :param batch_size: Mini-batch size. """ super().set_batch_size(batch_size=batch_size) self.v = self.rest * torch.ones(batch_size, *self.shape, device=self.v.device) self.refrac_count = torch.zeros_like(self.v, device=self.refrac_count.device)
具有自适应阈值的LIF神经元层。神经元的电压阈值在每次脉冲时都会增加一个常数；否则，它就会衰减回默认值。
9、DiehlAndCookNodes
class DiehlAndCookNodes(Nodes): # language=rst """ Layer of leaky integrate-and-fire (LIF) neurons with adaptive thresholds (modified for Diehl & Cook 2015 replication). """ def __init__( self, n: Optional[int] = None, shape: Optional[Iterable[int]] = None, traces: bool = False, traces_additive: bool = False, tc_trace: Union[float, torch.Tensor] = 20.0, trace_scale: Union[float, torch.Tensor] = 1.0, sum_input: bool = False, thresh: Union[float, torch.Tensor] = -52.0, rest: Union[float, torch.Tensor] = -65.0, reset: Union[float, torch.Tensor] = -65.0, refrac: Union[int, torch.Tensor] = 5, tc_decay: Union[float, torch.Tensor] = 100.0, theta_plus: Union[float, torch.Tensor] = 0.05, tc_theta_decay: Union[float, torch.Tensor] = 1e7, lbound: float = None, one_spike: bool = True, **kwargs, ) -> None: # language=rst """ Instantiates a layer of Diehl & Cook 2015 neurons. :param n: The number of neurons in the layer. :param shape: The dimensionality of the layer. :param traces: Whether to record spike traces. :param traces_additive: Whether to record spike traces additively. :param tc_trace: Time constant of spike trace decay. :param trace_scale: Scaling factor for spike trace. :param sum_input: Whether to sum all inputs. :param thresh: Spike threshold voltage. :param rest: Resting membrane voltage. :param reset: Post-spike reset voltage. :param refrac: Refractory (non-firing) period of the neuron. :param tc_decay: Time constant of neuron voltage decay. :param theta_plus: Voltage increase of threshold after spiking. :param tc_theta_decay: Time constant of adaptive threshold decay. :param lbound: Lower bound of the voltage. :param one_spike: Whether to allow only one spike per timestep. """ super().__init__( n=n, shape=shape, traces=traces, traces_additive=traces_additive, tc_trace=tc_trace, trace_scale=trace_scale, sum_input=sum_input, ) self.register_buffer("rest", torch.tensor(rest)) # Rest voltage. self.register_buffer("reset", torch.tensor(reset)) # Post-spike reset voltage. self.register_buffer("thresh", torch.tensor(thresh)) # Spike threshold voltage. self.register_buffer( "refrac", torch.tensor(refrac) ) # Post-spike refractory period. self.register_buffer( "tc_decay", torch.tensor(tc_decay) ) # Time constant of neuron voltage decay. self.register_buffer( "decay", torch.empty_like(self.tc_decay) ) # Set in compute_decays. self.register_buffer( "theta_plus", torch.tensor(theta_plus) ) # Constant threshold increase on spike. self.register_buffer( "tc_theta_decay", torch.tensor(tc_theta_decay) ) # Time constant of adaptive threshold decay. self.register_buffer( "theta_decay", torch.empty_like(self.tc_theta_decay) ) # Set in compute_decays. self.register_buffer("v", torch.FloatTensor()) # Neuron voltages. self.register_buffer("theta", torch.zeros(*self.shape)) # Adaptive thresholds. self.register_buffer( "refrac_count", torch.FloatTensor() ) # Refractory period counters. self.lbound = lbound # Lower bound of voltage. self.one_spike = one_spike # One spike per timestep. def forward(self, x: torch.Tensor) -> None: # language=rst """ Runs a single simulation step. :param x: Inputs to the layer. """ # Decay voltages and adaptive thresholds. self.v = self.decay * (self.v - self.rest) + self.rest if self.learning: self.theta *= self.theta_decay # Integrate inputs. self.v += (self.refrac_count <= 0).float() * x # Decrement refractory counters. self.refrac_count -= self.dt # Check for spiking neurons. self.s = self.v >= self.thresh + self.theta # Refractoriness, voltage reset, and adaptive thresholds. self.refrac_count.masked_fill_(self.s, self.refrac) self.v.masked_fill_(self.s, self.reset) if self.learning: self.theta += self.theta_plus * self.s.float().sum(0) # Choose only a single neuron to spike. if self.one_spike: if self.s.any(): _any = self.s.view(self.batch_size, -1).any(1) ind = torch.multinomial( self.s.float().view(self.batch_size, -1)[_any], 1 ) _any = _any.nonzero() self.s.zero_() self.s.view(self.batch_size, -1)[_any, ind] = 1 # Voltage clipping to lower bound. if self.lbound is not None: self.v.masked_fill_(self.v < self.lbound, self.lbound) super().forward(x) def reset_state_variables(self) -> None: # language=rst """ Resets relevant state variables. """ super().reset_state_variables() self.v.fill_(self.rest) # Neuron voltages. self.refrac_count.zero_() # Refractory period counters. def compute_decays(self, dt) -> None: # language=rst """ Sets the relevant decays. """ super().compute_decays(dt=dt) self.decay = torch.exp( -self.dt / self.tc_decay ) # Neuron voltage decay (per timestep). self.theta_decay = torch.exp( -self.dt / self.tc_theta_decay ) # Adaptive threshold decay (per timestep). def set_batch_size(self, batch_size) -> None: # language=rst """ Sets mini-batch size. Called when layer is added to a network. :param batch_size: Mini-batch size. """ super().set_batch_size(batch_size=batch_size) self.v = self.rest * torch.ones(batch_size, *self.shape, device=self.v.device) self.refrac_count = torch.zeros_like(self.v, device=self.refrac_count.device)
具有自适应阈值的LIF神经元层(针对Diehl & Cook 2015复现进行了修改)，每个时间步骤只发放一个脉冲。
10、IzhikevichNodes
class IzhikevichNodes(Nodes): # language=rst """ Layer of `Izhikevich neurons<https://www.izhikevich.org/publications/spikes.htm>`_. """ def __init__( self, n: Optional[int] = None, shape: Optional[Iterable[int]] = None, traces: bool = False, traces_additive: bool = False, tc_trace: Union[float, torch.Tensor] = 20.0, trace_scale: Union[float, torch.Tensor] = 1.0, sum_input: bool = False, excitatory: float = 1, thresh: Union[float, torch.Tensor] = 45.0, rest: Union[float, torch.Tensor] = -65.0, lbound: float = None, **kwargs, ) -> None: # language=rst """ Instantiates a layer of Izhikevich neurons. :param n: The number of neurons in the layer. :param shape: The dimensionality of the layer. :param traces: Whether to record spike traces. :param traces_additive: Whether to record spike traces additively. :param tc_trace: Time constant of spike trace decay. :param trace_scale: Scaling factor for spike trace. :param sum_input: Whether to sum all inputs. :param excitatory: Percent of excitatory (vs. inhibitory) neurons in the layer; in range ``[0, 1]``. :param thresh: Spike threshold voltage. :param rest: Resting membrane voltage. :param lbound: Lower bound of the voltage. """ super().__init__( n=n, shape=shape, traces=traces, traces_additive=traces_additive, tc_trace=tc_trace, trace_scale=trace_scale, sum_input=sum_input, ) self.register_buffer("rest", torch.tensor(rest)) # Rest voltage. self.register_buffer("thresh", torch.tensor(thresh)) # Spike threshold voltage. self.lbound = lbound self.register_buffer("r", None) self.register_buffer("a", None) self.register_buffer("b", None) self.register_buffer("c", None) self.register_buffer("d", None) self.register_buffer("S", None) self.register_buffer("excitatory", None) if excitatory > 1: excitatory = 1 elif excitatory < 0: excitatory = 0 if excitatory == 1: self.r = torch.rand(n) self.a = 0.02 * torch.ones(n) self.b = 0.2 * torch.ones(n) self.c = -65.0 + 15 * (self.r ** 2) self.d = 8 - 6 * (self.r ** 2) self.S = 0.5 * torch.rand(n, n) self.excitatory = torch.ones(n).byte() elif excitatory == 0: self.r = torch.rand(n) self.a = 0.02 + 0.08 * self.r self.b = 0.25 - 0.05 * self.r self.c = -65.0 * torch.ones(n) self.d = 2 * torch.ones(n) self.S = -torch.rand(n, n) self.excitatory = torch.zeros(n).byte() else: self.excitatory = torch.zeros(n).byte() ex = int(n * excitatory) inh = n - ex # init self.r = torch.zeros(n) self.a = torch.zeros(n) self.b = torch.zeros(n) self.c = torch.zeros(n) self.d = torch.zeros(n) self.S = torch.zeros(n, n) # excitatory self.r[:ex] = torch.rand(ex) self.a[:ex] = 0.02 * torch.ones(ex) self.b[:ex] = 0.2 * torch.ones(ex) self.c[:ex] = -65.0 + 15 * self.r[:ex] ** 2 self.d[:ex] = 8 - 6 * self.r[:ex] ** 2 self.S[:, :ex] = 0.5 * torch.rand(n, ex) self.excitatory[:ex] = 1 # inhibitory self.r[ex:] = torch.rand(inh) self.a[ex:] = 0.02 + 0.08 * self.r[ex:] self.b[ex:] = 0.25 - 0.05 * self.r[ex:] self.c[ex:] = -65.0 * torch.ones(inh) self.d[ex:] = 2 * torch.ones(inh) self.S[:, ex:] = -torch.rand(n, inh) self.excitatory[ex:] = 0 self.register_buffer("v", self.rest * torch.ones(n)) # Neuron voltages. self.register_buffer("u", self.b * self.v) # Neuron recovery. def forward(self, x: torch.Tensor) -> None: # language=rst """ Runs a single simulation step. :param x: Inputs to the layer. """ # Check for spiking neurons. self.s = self.v >= self.thresh # Voltage and recovery reset. self.v = torch.where(self.s, self.c, self.v) self.u = torch.where(self.s, self.u + self.d, self.u) # Add inter-columnar input. if self.s.any(): x += torch.cat( [self.S[:, self.s[i]].sum(dim=1)[None] for i in range(self.s.shape[0])], dim=0, ) # Apply v and u updates. self.v += self.dt * 0.5 * (0.04 * self.v ** 2 + 5 * self.v + 140 - self.u + x) self.v += self.dt * 0.5 * (0.04 * self.v ** 2 + 5 * self.v + 140 - self.u + x) self.u += self.dt * self.a * (self.b * self.v - self.u) # Voltage clipping to lower bound. if self.lbound is not None: self.v.masked_fill_(self.v < self.lbound, self.lbound) super().forward(x) def reset_state_variables(self) -> None: # language=rst """ Resets relevant state variables. """ super().reset_state_variables() self.v.fill_(self.rest) # Neuron voltages. self.u = self.b * self.v # Neuron recovery. def set_batch_size(self, batch_size) -> None: # language=rst """ Sets mini-batch size. Called when layer is added to a network. :param batch_size: Mini-batch size. """ super().set_batch_size(batch_size=batch_size) self.v = self.rest * torch.ones(batch_size, *self.shape, device=self.v.device) self.u = self.b * self.v
Izhikevich神经元层。r：神经元异质性变量，原则上，可以使用RS细胞来模拟所有兴奋性神经元，而使用FS细胞来模拟所有抑制性神经元，因此，ri = 0对应于常规脉冲(RS)细胞，ri = 1对应于抖振(CH)细胞；a：恢复变量u的时间常数，a越小，恢复的越慢；b：恢复变量u依赖膜电位v的阈值下随机波动的敏感程度；c：发放脉冲后，v的复位值；d：发放脉冲后，u的复位值；S：神经元之间的突触连接权重；excitatory：该层中兴奋性神经元的比例(范围为0-1)；v：膜电位；u：恢复变量，用来代替生理模型中激活的K离子电流和失活的Na离子电流，实现对膜电位V的负反馈；
- 理论公式：
- 实际实现：
11、CSRMNodes
class CSRMNodes(Nodes): """ A layer of Cumulative Spike Response Model (Gerstner and van Hemmen 1992, Gerstner et al. 1996) nodes. It accounts for a model where refractoriness and adaptation were modeled by the combined effects of the spike after potentials of several previous spikes, rather than only the most recent spike. """ def __init__( self, n: Optional[int] = None, shape: Optional[Iterable[int]] = None, traces: bool = False, traces_additive: bool = False, tc_trace: Union[float, torch.Tensor] = 20.0, trace_scale: Union[float, torch.Tensor] = 1.0, sum_input: bool = False, rest: Union[float, torch.Tensor] = -65.0, thresh: Union[float, torch.Tensor] = -52.0, responseKernel: str = "ExponentialKernel", refractoryKernel: str = "EtaKernel", tau: Union[float, torch.Tensor] = 1, res_window_size: Union[float, torch.Tensor] = 20, ref_window_size: Union[float, torch.Tensor] = 10, reset_const: Union[float, torch.Tensor] = 50, tc_decay: Union[float, torch.Tensor] = 100.0, theta_plus: Union[float, torch.Tensor] = 0.05, tc_theta_decay: Union[float, torch.Tensor] = 1e7, lbound: float = None, **kwargs, ) -> None: # language=rst """ Instantiates a layer of Cumulative Spike Response Model nodes. :param n: The number of neurons in the layer. :param shape: The dimensionality of the layer. :param traces: Whether to record spike traces. :param traces_additive: Whether to record spike traces additively. :param tc_trace: Time constant of spike trace decay. :param trace_scale: Scaling factor for spike trace. :param sum_input: Whether to sum all inputs. :param rest: Resting membrane voltage. :param thresh: Spike threshold voltage. :param refrac: Refractory (non-firing) period of the neuron. :param tc_decay: Time constant of neuron voltage decay. :param theta_plus: Voltage increase of threshold after spiking. :param tc_theta_decay: Time constant of adaptive threshold decay. :param lbound: Lower bound of the voltage. """ super().__init__( n=n, shape=shape, traces=traces, traces_additive=traces_additive, tc_trace=tc_trace, trace_scale=trace_scale, sum_input=sum_input, ) self.register_buffer("rest", torch.tensor(rest)) # Rest voltage. self.register_buffer("thresh", torch.tensor(thresh)) # Spike threshold voltage. self.register_buffer( "tau", torch.tensor(tau) ) # Time constant of Spike Response Kernel self.register_buffer( "reset_const", torch.tensor(reset_const) ) # Reset constant of refractory kernel self.register_buffer( "res_window_size", torch.tensor(res_window_size) ) # Window size for sampling incoming input current self.register_buffer( "ref_window_size", torch.tensor(ref_window_size) ) # Window size for sampling previous spikes self.register_buffer( "tc_decay", torch.tensor(tc_decay) ) # Time constant of neuron voltage decay. self.register_buffer( "decay", torch.empty_like(self.tc_decay, dtype=torch.float32) ) # Set in compute_decays. self.register_buffer( "theta_plus", torch.tensor(theta_plus) ) # Constant threshold increase on spike. self.register_buffer( "tc_theta_decay", torch.tensor(tc_theta_decay) ) # Time constant of adaptive threshold decay. self.register_buffer( "theta_decay", torch.empty_like(self.tc_theta_decay) ) # Set in compute_decays. self.register_buffer("v", torch.FloatTensor()) # Neuron voltages. self.register_buffer( "last_spikes", torch.ByteTensor() ) # Previous spikes occurrences in time window self.register_buffer("theta", torch.zeros(*self.shape)) # Adaptive thresholds. self.lbound = lbound # Lower bound of voltage. self.responseKernel = responseKernel # Type of spike response kernel used self.refractoryKernel = refractoryKernel # Type of refractory kernel used self.register_buffer( "resKernel", torch.FloatTensor() ) # Vector of synaptic response kernel values over a window of time self.register_buffer( "refKernel", torch.FloatTensor() ) # Vector of refractory kernel values over a window of time def forward(self, x: torch.Tensor) -> None: # language=rst """ Runs a single simulation step. :param x: Inputs to the layer. """ # Decay voltages. self.v *= self.decay if self.learning: self.theta *= self.theta_decay # Integrate inputs. v = torch.einsum( "i,kij->kj", self.resKernel, x ) # Response due to incoming current v += torch.einsum( "i,kij->kj", self.refKernel, self.last_spikes ) # Refractoriness due to previous spikes self.v += v.view(x.size(0), *self.shape) # Check for spiking neurons. self.s = self.v >= self.thresh + self.theta if self.learning: self.theta += self.theta_plus * self.s.float().sum(0) # Add the spike vector into the first in first out matrix of windowed (ref) spike trains self.last_spikes = torch.cat( (self.last_spikes[:, 1:, :], self.s[:, None, :]), 1 ) # Voltage clipping to lower bound. if self.lbound is not None: self.v.masked_fill_(self.v < self.lbound, self.lbound) super().forward(x) def reset_state_variables(self) -> None: # language=rst """ Resets relevant state variables. """ super().reset_state_variables() self.v.fill_(self.rest) # Neuron voltages. def compute_decays(self, dt) -> None: # language=rst """ Sets the relevant decays. """ super().compute_decays(dt=dt) self.decay = torch.exp( -self.dt / self.tc_decay ) # Neuron voltage decay (per timestep). self.theta_decay = torch.exp( -self.dt / self.tc_theta_decay ) # Adaptive threshold decay (per timestep). def set_batch_size(self, batch_size) -> None: # language=rst """ Sets mini-batch size. Called when layer is added to a network. :param batch_size: Mini-batch size. """ super().set_batch_size(batch_size=batch_size) self.v = self.rest * torch.ones(batch_size, *self.shape, device=self.v.device) self.last_spikes = torch.zeros(batch_size, self.ref_window_size, *self.shape) resKernels = { "AlphaKernel": self.AlphaKernel, "AlphaKernelSLAYER": self.AlphaKernelSLAYER, "LaplacianKernel": self.LaplacianKernel, "ExponentialKernel": self.ExponentialKernel, "RectangularKernel": self.RectangularKernel, "TriangularKernel": self.TriangularKernel, } if self.responseKernel not in resKernels.keys(): raise Exception(" The given response Kernel is not implemented") self.resKernel = resKernels[self.responseKernel](self.dt) refKernels = {"EtaKernel": self.EtaKernel} if self.refractoryKernel not in refKernels.keys(): raise Exception(" The given refractory Kernel is not implemented") self.refKernel = refKernels[self.refractoryKernel](self.dt) def AlphaKernel(self, dt): t = torch.arange(0, self.res_window_size, dt) kernelVec = (1 / (self.tau ** 2)) * t * torch.exp(-t / self.tau) return torch.flip(kernelVec, [0]) def AlphaKernelSLAYER(self, dt): t = torch.arange(0, self.res_window_size, dt) kernelVec = (1 / self.tau) * t * torch.exp(1 - t / self.tau) return torch.flip(kernelVec, [0]) def LaplacianKernel(self, dt): t = torch.arange(0, self.res_window_size, dt) kernelVec = (1 / (self.tau * 2)) * torch.exp(-1 * torch.abs(t / self.tau)) return torch.flip(kernelVec, [0]) def ExponentialKernel(self, dt): t = torch.arange(0, self.res_window_size, dt) kernelVec = (1 / self.tau) * torch.exp(-t / self.tau) return torch.flip(kernelVec, [0]) def RectangularKernel(self, dt): t = torch.arange(0, self.res_window_size, dt) kernelVec = 1 / (selftau * 2) return torch.flip(kernelVec, [0]) def TriangularKernel(self, dt): t = torch.arange(0, self.res_window_size, dt) kernelVec = (1 / self.tau) * (1 - (t / self.tau)) return torch.flip(kernelVec, [0]) def EtaKernel(self, dt): t = torch.arange(0, self.ref_window_size, dt) kernelVec = -self.reset_const * torch.exp(-t / self.tau) return torch.flip(kernelVec, [0])
累积脉冲响应模型(Gerstner and van Hemmen 1992, Gerstner et al. 1996)节点层。它解释了一个模型，在这个模型中，不应期和适应性是由前几次脉冲的电压之后的脉冲(而不仅仅是最近的脉冲)的综合效应来建模的。
12、SRM0Nodes
class SRM0Nodes(Nodes): # language=rst """ Layer of simplified spike response model (SRM0) neurons with stochastic threshold (escape noise). Adapted from `(Vasilaki et al., 2009) <https://intranet.physio.unibe.ch/Publikationen/Dokumente/Vasilaki2009PloSComputBio_1.pdf>`_. """ def __init__( self, n: Optional[int] = None, shape: Optional[Iterable[int]] = None, traces: bool = False, traces_additive: bool = False, tc_trace: Union[float, torch.Tensor] = 20.0, trace_scale: Union[float, torch.Tensor] = 1.0, sum_input: bool = False, thresh: Union[float, torch.Tensor] = -50.0, rest: Union[float, torch.Tensor] = -70.0, reset: Union[float, torch.Tensor] = -70.0, refrac: Union[int, torch.Tensor] = 5, tc_decay: Union[float, torch.Tensor] = 10.0, lbound: float = None, eps_0: Union[float, torch.Tensor] = 1.0, rho_0: Union[float, torch.Tensor] = 1.0, d_thresh: Union[float, torch.Tensor] = 5.0, **kwargs, ) -> None: # language=rst """ Instantiates a layer of SRM0 neurons. :param n: The number of neurons in the layer. :param shape: The dimensionality of the layer. :param traces: Whether to record spike traces. :param traces_additive: Whether to record spike traces additively. :param tc_trace: Time constant of spike trace decay. :param trace_scale: Scaling factor for spike trace. :param sum_input: Whether to sum all inputs. :param thresh: Spike threshold voltage. :param rest: Resting membrane voltage. :param reset: Post-spike reset voltage. :param refrac: Refractory (non-firing) period of the neuron. :param tc_decay: Time constant of neuron voltage decay. :param lbound: Lower bound of the voltage. :param eps_0: Scaling factor for pre-synaptic spike contributions. :param rho_0: Stochastic intensity at threshold. :param d_thresh: Width of the threshold region. """ super().__init__( n=n, shape=shape, traces=traces, traces_additive=traces_additive, tc_trace=tc_trace, trace_scale=trace_scale, sum_input=sum_input, ) self.register_buffer("rest", torch.tensor(rest)) # Rest voltage. self.register_buffer("reset", torch.tensor(reset)) # Post-spike reset voltage. self.register_buffer("thresh", torch.tensor(thresh)) # Spike threshold voltage. self.register_buffer( "refrac", torch.tensor(refrac) ) # Post-spike refractory period. self.register_buffer( "tc_decay", torch.tensor(tc_decay) ) # Time constant of neuron voltage decay. self.register_buffer("decay", torch.tensor(tc_decay)) # Set in compute_decays. self.register_buffer( "eps_0", torch.tensor(eps_0) ) # Scaling factor for pre-synaptic spike contributions. self.register_buffer( "rho_0", torch.tensor(rho_0) ) # Stochastic intensity at threshold. self.register_buffer( "d_thresh", torch.tensor(d_thresh) ) # Width of the threshold region. self.register_buffer("v", torch.FloatTensor()) # Neuron voltages. self.register_buffer( "refrac_count", torch.FloatTensor() ) # Refractory period counters. self.lbound = lbound # Lower bound of voltage. def forward(self, x: torch.Tensor) -> None: # language=rst """ Runs a single simulation step. :param x: Inputs to the layer. """ # Decay voltages. self.v = self.decay * (self.v - self.rest) + self.rest # Integrate inputs. self.v += (self.refrac_count <= 0).float() * self.eps_0 * x # Compute (instantaneous) probabilities of spiking, clamp between 0 and 1 using exponentials. # Also known as 'escape noise', this simulates nearby neurons. self.rho = self.rho_0 * torch.exp((self.v - self.thresh) / self.d_thresh) self.s_prob = 1.0 - torch.exp(-self.rho * self.dt) # Decrement refractory counters. self.refrac_count -= self.dt # Check for spiking neurons (spike when probability > some random number). self.s = torch.rand_like(self.s_prob) < self.s_prob # Refractoriness and voltage reset. self.refrac_count.masked_fill_(self.s, self.refrac) self.v.masked_fill_(self.s, self.reset) # Voltage clipping to lower bound. if self.lbound is not None: self.v.masked_fill_(self.v < self.lbound, self.lbound) super().forward(x) def reset_state_variables(self) -> None: # language=rst """ Resets relevant state variables. """ super().reset_state_variables() self.v.fill_(self.rest) # Neuron voltages. self.refrac_count.zero_() # Refractory period counters. def compute_decays(self, dt) -> None: # language=rst """ Sets the relevant decays. """ super().compute_decays(dt=dt) self.decay = torch.exp( -self.dt / self.tc_decay ) # Neuron voltage decay (per timestep). def set_batch_size(self, batch_size) -> None: # language=rst """ Sets mini-batch size. Called when layer is added to a network. :param batch_size: Mini-batch size. """ super().set_batch_size(batch_size=batch_size) self.v = self.rest * torch.ones(batch_size, *self.shape, device=self.v.device) self.refrac_count = torch.zeros_like(self.v, device=self.refrac_count.device)
具有随机阈值(逃逸噪声)的简化脉冲响应模型(SRM0)神经元层。改编自(Vasilaki et al., 2009)。关于论文与具体实现的关系，开发者回答如下：
“首先，论文有点不清楚。在第13页，等式(23)规定了SRM模型的使用。然而，第15页的图9突然将这些神经元称为"带有逃逸噪声的LIF"。那么，是哪一个？因为文章对等式(23)中的epsilon(t)和eta(t)使用了单指数核，所以SRM模型实际上只是一个具有随机阈值的LIF，我们可以用迭代的方式来计算，而不必在所有的时间步骤上进行卷积。现在让我们继续使用图9的定义。图9中的神经元和BindsNET中的SRM0节点之间的区别纯粹是架构上的：如果我没记错的话，文章中的神经元有前馈连接(一层到下一层)和横向连接(一层神经元之间)。这将解释图9中的亚阈动态方程中的两个输入项：xi(或其对应的希腊字母)的前馈权重，W的横向权重。其他一切都应该是一样的：随机发放与逃逸噪声已经实现，核衰减是相同的。我和其中一位作者谈过一次，她告诉我他们仅用了一个计数器来计算不应期，就像SRM0Nodes一样。”
该神经元具体过程如下：
- 电压衰减；
- 整合输入(不应期计数器小于等于零的输入项)；
- 计算(瞬时)脉冲概率，使用指数在0和1之间截断(也被称为“逃逸噪音”，它模拟附近的神经元)；
- 不应期计数器自减；
- 检查脉冲神经元(当概率>某个随机数时，发放脉冲)；
- 不应性/电压复位；
- 电压截断至下限；
- Nodes基类前向传播(迹/累积和)。