simple_neural_fields
SimpleNeuralField(input_size, output_size, potentials_dyn_fcn, input_embedding=None, output_embedding=None, activation_nonlin=torch.sigmoid, tau_init=10.0, tau_learnable=True, kappa_init=0.001, kappa_learnable=True, capacity_learnable=True, potentials_init=None, init_param_kwargs=None, device='cpu')
¶
Bases: PotentialBased
A simplified version of Amari's potential-based recurrent neural network, without the convolution over time.
See Also
[Luksch et al., 2012] T. Luksch, M. Gineger, M. Mühlig, T. Yoshiike, "Adaptive Movement Sequences and Predictive Decisions based on Hierarchical Dynamical Systems", International Conference on Intelligent Robots and Systems, 2012.
output_size: Number of output dimensions. For this simplified neural fields model, the number of outputs
is equal to the number of neurons in the (single) hidden layer.
input_embedding: Optional (custom) [Module][torch.nn.Module] to extract features from the inputs.
This module must transform the inputs such that the dimensionality matches the number of
neurons of the neural field, i.e., `hidden_size`. By default, a [linear layer][torch.nn.Linear]
without biases is used.
output_embedding: Optional (custom) [Module][torch.nn.Module] to compute the outputs from the activations.
This module must map the activations of shape (`hidden_size`,) to the outputs of shape (`output_size`,)
By default, a [linear layer][torch.nn.Linear] without biases is used.
activation_nonlin: Nonlinearity used to compute the activations from the potential levels.
tau_init: Initial value for the shared time constant of the potentials.
tau_learnable: Whether the time constant is a learnable parameter or fixed.
kappa_init: Initial value for the cubic decay, pass 0 to disable the cubic decay.
kappa_learnable: Whether the cubic decay is a learnable parameter or fixed.
capacity_learnable: Whether the capacity is a learnable parameter or fixed.
potentials_init: Initial for the potentials, i.e., the network's hidden state.
init_param_kwargs: Additional keyword arguments for the policy parameter initialization. For example,
`self_centric_init=True` to initialize the interaction between neurons such that they inhibit the
others and excite themselves.
device: Device to move this module to (after initialization).
Source code in neuralfields/simple_neural_fields.py
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capacity: Union[torch.Tensor, nn.Parameter]
property
¶
Get the capacity parameter (only used for capacity-based dynamics functions).
device: torch.device
property
¶
Get the device this model is located on. This assumes that all parts are located on the same device.
hidden_size: int
property
¶
Get the number of neurons in the neural field layer, i.e., the ones with the in-/exhibition dynamics.
kappa: Union[torch.Tensor, nn.Parameter]
property
¶
Get the cubic decay parameter \(\kappa\).
param_values: torch.Tensor
property
writable
¶
Get the module's parameters as a 1-dimensional array. The values are copied, thus modifying the return value does not propagate back to the module parameters.
stimuli_external: torch.Tensor
property
¶
Get the neurons' external stimuli, resulting from the current inputs. This property is useful for recording during a simulation / rollout.
stimuli_internal: torch.Tensor
property
¶
Get the neurons' internal stimuli, resulting from the previous activations of the neurons. This property is useful for recording during a simulation / rollout.
tau: Union[torch.Tensor, nn.Parameter]
property
¶
Get the timescale parameter, called \(\tau\) in the original paper [Amari_77].
transform_to_img_space: Callable[[torch.Tensor], torch.Tensor] = torch.exp
class-attribute
instance-attribute
¶
Function to map parameters to the image space of the original problem.
transform_to_opt_space: Callable[[torch.Tensor], torch.Tensor] = torch.log
class-attribute
instance-attribute
¶
Function to map parameters to the optimization space.
forward(inputs, hidden=None)
¶
Compute the external and internal stimuli, advance the potential dynamics for one time step, and return the model's output for several time steps in a row.
This method essentially calls forward_one_step several times in a row.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
inputs | Tensor | Inputs of shape | required |
hidden | Optional[Tensor] | Initial values of the hidden states, i.e., the potentials. By default, the network initialized the hidden state to be all zeros. However, via this argument one can set a specific initial value for the potentials. Depending on the shape of | None |
Returns:
Type | Description |
---|---|
Tensor | The outputs, i.e., the (linearly combined) activations, and all intermediate potential values, both of |
Tensor | shape |
Source code in neuralfields/potential_based.py
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init_hidden(batch_size=None, potentials_init=None)
¶
Provide initial values for the hidden parameters. This usually is a zero tensor.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
batch_size | Optional[int] | Number of batches, i.e., states to track in parallel. | None |
potentials_init | Optional[Tensor] | Initial values for the potentials to override the networks default values with. | None |
Returns:
Type | Description |
---|---|
Union[Tensor, Parameter] | Tensor of shape |
Source code in neuralfields/potential_based.py
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potentials_dot(potentials, stimuli)
¶
Compute the derivative of the neurons' potentials per time step.
\(/tau /dot{u} = f(u, s, h)\) with the potentials \(u\), the combined stimuli \(s\), and the resting level \(h\).
Parameters:
Name | Type | Description | Default |
---|---|---|---|
potentials | Tensor | Potential values at the current point in time, of shape | required |
stimuli | Tensor | Sum of external and internal stimuli at the current point in time, of shape | required |
Returns:
Type | Description |
---|---|
Tensor | Time derivative of the potentials \(\frac{dp}{dt}\), of shape |
Source code in neuralfields/simple_neural_fields.py
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pd_capacity_21(p, s, h, tau, kappa, capacity)
¶
Capacity-based dynamics with 2 stable (\(p=-C\), \(p=C\)) and 1 unstable fix points (\(p=0\)) for \(s=0\)
\(\tau \dot{p} = s - (h - p) (1 - \frac{(h - p)^2}{C^2})\)
Notes
This potential dynamics function is strongly recommended to be used with a tanh activation function.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
p | Tensor | Potential, higher values lead to higher activations. | required |
s | Tensor | Stimulus, higher values lead to larger changes of the potentials (depends on the dynamics function). | required |
h | Tensor | Resting level, a.k.a. constant offset. | required |
tau | Tensor | Time scaling factor, higher values lead to slower changes of the potentials (linear dependency). | required |
kappa | Optional[Tensor] | Cubic decay factor for a neuron's potential, ignored for this dynamics function. | required |
capacity | Optional[Tensor] | Capacity value of a neuron's potential. | required |
Returns:
Type | Description |
---|---|
Tensor | Time derivative of the potentials \(\frac{dp}{dt}\). |
Source code in neuralfields/simple_neural_fields.py
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pd_capacity_21_abs(p, s, h, tau, kappa, capacity)
¶
Capacity-based dynamics with 2 stable (\(p=-C\), \(p=C\)) and 1 unstable fix points (\(p=0\)) for \(s=0\)
\(\tau \dot{p} = s - (h - p) (1 - \frac{\left| h - p \right|}{C})\)
The "absolute version" of pd_capacity_21
has a lower magnitude and a lower oder of the resulting polynomial.
Notes
This potential dynamics function is strongly recommended to be used with a tanh activation function.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
p | Tensor | Potential, higher values lead to higher activations. | required |
s | Tensor | Stimulus, higher values lead to larger changes of the potentials (depends on the dynamics function). | required |
h | Tensor | Resting level, a.k.a. constant offset. | required |
tau | Tensor | Time scaling factor, higher values lead to slower changes of the potentials (linear dependency). | required |
kappa | Optional[Tensor] | Cubic decay factor for a neuron's potential, ignored for this dynamics function. | required |
capacity | Optional[Tensor] | Capacity value of a neuron's potential. | required |
Returns:
Type | Description |
---|---|
Tensor | Time derivative of the potentials \(\frac{dp}{dt}\). |
Source code in neuralfields/simple_neural_fields.py
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pd_capacity_32(p, s, h, tau, kappa, capacity)
¶
Capacity-based dynamics with 3 stable (\(p=-C\), \(p=0\), \(p=C\)) and 2 unstable fix points (\(p=-C/2\), \(p=C/2\)) for \(s=0\)
\(\tau \dot{p} = s - (h - p) (1 - \frac{(h - p)^2}{C^2}) (1 - \frac{(2(h - p))^2}{C^2})\)
Notes
This potential dynamics function is strongly recommended to be used with a tanh activation function.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
p | Tensor | Potential, higher values lead to higher activations. | required |
s | Tensor | Stimulus, higher values lead to larger changes of the potentials (depends on the dynamics function). | required |
h | Tensor | Resting level, a.k.a. constant offset. | required |
tau | Tensor | Time scaling factor, higher values lead to slower changes of the potentials (linear dependency). | required |
kappa | Optional[Tensor] | Cubic decay factor for a neuron's potential, ignored for this dynamics function. | required |
capacity | Optional[Tensor] | Capacity value of a neuron's potential. | required |
Returns:
Type | Description |
---|---|
Tensor | Time derivative of the potentials \(\frac{dp}{dt}\). |
Source code in neuralfields/simple_neural_fields.py
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pd_capacity_32_abs(p, s, h, tau, kappa, capacity)
¶
Capacity-based dynamics with 3 stable (\(p=-C\), \(p=0\), \(p=C\)) and 2 unstable fix points (\(p=-C/2\), \(p=C/2\)) for \(s=0\).
\(\tau \dot{p} = \left( s + (h - p) (1 - \frac{\left| (h - p) \right|}{C}) (1 - \frac{2 \left| (h - p) \right|}{C}) \right)\)
The "absolute version" of pd_capacity_32
is less skewed due to a lower oder of the resulting polynomial.
Notes
This potential dynamics function is strongly recommended to be used with a tanh activation function.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
p | Tensor | Potential, higher values lead to higher activations. | required |
s | Tensor | Stimulus, higher values lead to larger changes of the potentials (depends on the dynamics function). | required |
h | Tensor | Resting level, a.k.a. constant offset. | required |
tau | Tensor | Time scaling factor, higher values lead to slower changes of the potentials (linear dependency). | required |
kappa | Optional[Tensor] | Cubic decay factor for a neuron's potential, ignored for this dynamics function. | required |
capacity | Optional[Tensor] | Capacity value of a neuron's potential. | required |
Returns:
Type | Description |
---|---|
Tensor | Time derivative of the potentials \(\frac{dp}{dt}\). |
Source code in neuralfields/simple_neural_fields.py
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pd_cubic(p, s, h, tau, kappa, capacity)
¶
Basic proportional dynamics with additional cubic decay.
\(\tau \dot{p} = s + h - p + \kappa (h - p)^3\)
Notes
This potential dynamics function is strongly recommended to be used with a sigmoid activation function.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
p | Tensor | Potential, higher values lead to higher activations. | required |
s | Tensor | Stimulus, higher values lead to larger changes of the potentials (depends on the dynamics function). | required |
h | Tensor | Resting level, a.k.a. constant offset. | required |
tau | Tensor | Time scaling factor, higher values lead to slower changes of the potentials (linear dependency). | required |
kappa | Optional[Tensor] | Cubic decay factor for a neuron's potential. | required |
capacity | Optional[Tensor] | Capacity value of a neuron's potential, ignored for this dynamics function. | required |
Returns:
Type | Description |
---|---|
Tensor | Time derivative of the potentials \(\frac{dp}{dt}\). |
Source code in neuralfields/simple_neural_fields.py
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pd_linear(p, s, h, tau, kappa, capacity)
¶
Basic proportional dynamics.
\(\tau \dot{p} = s - p\)
Notes
This potential dynamics function is strongly recommended to be used with a sigmoid activation function.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
p | Tensor | Potential, higher values lead to higher activations. | required |
s | Tensor | Stimulus, higher values lead to larger changes of the potentials (depends on the dynamics function). | required |
h | Tensor | Resting level, a.k.a. constant offset. | required |
tau | Tensor | Time scaling factor, higher values lead to slower changes of the potentials (linear dependency). | required |
kappa | Optional[Tensor] | Cubic decay factor for a neuron's potential, ignored for this dynamics function. | required |
capacity | Optional[Tensor] | Capacity value of a neuron's potential, ignored for this dynamics function. | required |
Returns:
Type | Description |
---|---|
Tensor | Time derivative of the potentials \(\frac{dp}{dt}\). |
Source code in neuralfields/simple_neural_fields.py
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