neural_fields
NeuralField(input_size, hidden_size, output_size=None, input_embedding=None, output_embedding=None, activation_nonlin=torch.sigmoid, mirrored_conv_weights=True, conv_kernel_size=None, conv_padding_mode='circular', conv_out_channels=1, conv_pooling_norm=1, tau_init=10, tau_learnable=True, kappa_init=1e-05, kappa_learnable=True, potentials_init=None, init_param_kwargs=None, device='cpu', dtype=None)
¶
Bases: PotentialBased
A potential-based recurrent neural network according to [Amari, 1977].
See Also
[Amari, 1977] S.-I. Amari, "Dynamics of Pattern Formation in Lateral-Inhibition Type Neural Fields", Biological Cybernetics, 1977.
hidden_size: Number of neurons with potential in the (single) hidden layer.
output_size: Number of output dimensions. By default, the number of outputs is equal to the number of
hidden neurons.
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.
mirrored_conv_weights: If `True`, re-use weights for the second half of the kernel to create a
symmetric convolution kernel.
conv_kernel_size: Size of the kernel for the 1-dim convolution along the potential-based neurons.
conv_padding_mode: Padding mode forwarded to [Conv1d][torch.nn.Conv1d], options are "circular",
"reflect", or "zeros".
conv_out_channels: Number of filter for the 1-dim convolution along the potential-based neurons.
conv_pooling_norm: Norm type of the [torch.nn.LPPool1d][] pooling layer applied after the convolution.
Unlike in typical scenarios, here the pooling is performed over the channel dimension. Thus, varying
`conv_pooling_norm` only has an effect if `conv_out_channels > 1`.
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.
potentials_init: Initial for the potentials, i.e., the network's hidden state.
init_param_kwargs: Additional keyword arguments for the policy parameter initialization.
device: Device to move this module to (after initialization).
dtype: Data type forwarded to the initializer of [Conv1d][torch.nn.Conv1d].
Source code in neuralfields/neural_fields.py
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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 w.r.t. time.
\(/tau /dot{u} = s + h - u + /kappa (h - u)^3, /quad /text{with} s = s_{int} + s_{ext} = W*o + /int{w(u, v) f(u) dv}\) with the potentials \(u\), the combined stimuli \(s\), the resting level \(h\), and the cubic decay \(\kappa\).
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/neural_fields.py
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