Exploring advanced configurations¶
Overview¶
In addition to the essential capabilities exposed in the first tutorial, we can exercise fine-grained control in how we wire up biologically-plausible networks. These are some of the functionality we will explore in this section:
- Synapse vs neuron nonlinearities
- Microcircuit archetypes
- Parameter sharing capabilities
- Hierarchically constructed neural areas
- Inter-areal feedback connectivity
import torch
import numpy as np
from bioplnn.models import SpatiallyEmbeddedRNN, SpatiallyEmbeddedAreaConfig
Synapse vs neuron nonlinearities¶
What do we mean by this? In an attempt to distinguish synaptic transfer functions from post-aggregation neuronal transfer functions, we give users the ability to specify pre- and post-integration nonlinearities.
Let us consider the same example model from the previous tutorial: A simple one-area network with two neural classes with the following inter_neuron_type_connectivity: \(\big(\begin{smallmatrix}1&1&0\cr1&1&1\cr1&1&0\end{smallmatrix}\big)\). Following the same convention as the connectivity matrix, you can specify the transfer function for each of those synapse groups by setting the inter_neuron_type_nonlinearity parameter. Similarly, neuron_type_nonlinearity can be used to control the post-aggregation transfer function for each neuron type.
If you were to construe a scenario where synapses have unbounded transfer functions while the neuron as whole is bounded from above (and for the sake of argument: bounded differently for the E and I subpopulations), then you'd do something like this:
# writing a custom activation function that works similarly to a ReLU but is bounded from above!
from torch.nn.modules.activation import Hardtanh
class ModRelu(Hardtanh):
def __init__(self, _ub: float, _lb: float = 0., inplace: bool = False):
super().__init__(_lb, _ub, inplace)
def extra_repr(self) -> str:
inplace_str = 'inplace=True' if self.inplace else ''
return inplace_str
upper_bounded_relu = ModRelu(_ub = 5.)
area_configs = [
SpatiallyEmbeddedAreaConfig(
num_neuron_types = 2,
num_neuron_subtypes = np.array([16, 16]),
neuron_type_class = np.array(['excitatory', 'inhibitory']),
neuron_type_nonlinearity = ['sigmoid', upper_bounded_relu],
inter_neuron_type_connectivity = np.array([[1, 1, 0], [1, 1, 1], [1, 1, 0]]),
inter_neuron_type_nonlinearity = np.array([['relu', 'relu', ''], ['relu', 'relu', 'relu'], ['relu', 'relu', '']]),
in_size = [28, 28],
in_channels = 1,
out_channels = 32,
)
]
model = SpatiallyEmbeddedRNN(num_areas=1, area_configs=area_configs, batch_first=False)
Microcircuit archetypes¶
It must be evident that inter_neuron_type_connectivity is a powerful option that can be used to dictate a wide variety of microcircuit motifs. We provide some examples below for inspiration.
Feedback inhibition¶
Parvalbumin-positive inhibitory cells in Layer ⅔ of the cortex are known to interact with Pyramidal cells through some form of divisive inhibition Jonke et al. (2017). To instantiate this microcircuit, you'd set inter_neuron_type_connectivity = \(\big(\begin{smallmatrix}1&0&0\cr0&1&1\cr1&1&0\end{smallmatrix}\big)\) (conventions same as in the original example).
Feedforward inhibition¶
Feedforward inhibition is another essential mechanism within the brain, to regulate neuronal firing and prevent runaway excitation (Panthi and Leitch (2019), Large et al. (2016)). To implement the microcircuit presented in these (and related) papers, you can set inter_neuron_type_connectivity = \(\big(\begin{smallmatrix}1&1&0\cr1&0&1\cr1&1&1\end{smallmatrix}\big)\) (conventions same as in the original example).
Pyr-PV-SST-VIP motif¶
Interneuron subtypes play a critical role in several aspects of cortical function (Guo and Kumar (2023), Condylis et al. (2022), etc.). Of particular interest is a motif that involves one excitatory and three inhibitory interneuron populations (PV, SST, VIP). Please refer to these papers for pictorial depictions of the microcircuits. To realise this in torch-biopl, we would do the following:
area_configs = [
SpatiallyEmbeddedAreaConfig(
num_neuron_types = 4,
num_neuron_subtypes = np.array([16, 8, 8, 8]),
neuron_type_class = np.array(['excitatory', 'inhibitory', 'inhibitory', 'inhibitory']),
inter_neuron_type_connectivity = np.array([[1, 0, 0, 0, 0], [1, 1, 1, 1, 1], [1, 1, 0, 0, 0], [1, 1, 0, 1, 0], [0, 0, 1, 0, 0]]),
in_size = [28, 28],
in_channels = 1,
out_channels = 32,
)
]
model = SpatiallyEmbeddedRNN(num_areas=1, area_configs=area_configs, batch_first=False)
We remark that this is not an exhaustive list, but merely a window into endless possibilities :)
Parameter sharing capabilities for \(\tau_{mem}\)¶
We provide the user the option to tie neural time constants:
- Across space, but unique for each cell subtype (tau_mode = 'subtype')
- Across cell subtype, but unique for each spatial location (tau_mode = 'spatial')
- Each neuron learns its own time constant (tau_mode = 'subtype_spatial')
- Across types (tau_mode = 'type')
To go hand in hand with this, we also allow the user to provide an initialization for these time constants. This can be done via tau_init_fn. As with the nonlinearities, users can either provide torch initializers or custom functions to accomplish this.
Hierarchically constructed neural areas¶
Intuitive and expressive. For reasons more than one, you may want to wire up brain areas that are connected to each other via long-range synapses. This is quite easy to accomplish in torch-biopl. Note that each area can be configured independently!
area_configs = [
SpatiallyEmbeddedAreaConfig(
num_neuron_types = 2,
num_neuron_subtypes = np.array([16, 16]),
neuron_type_class = np.array(['excitatory', 'inhibitory']),
inter_neuron_type_connectivity = np.array([[1, 1, 0], [1, 1, 1], [1, 1, 0]]),
in_size = [28, 28],
in_channels = 1,
out_channels = 32,
),
SpatiallyEmbeddedAreaConfig(
num_neuron_types = 2,
num_neuron_subtypes = np.array([32, 32]),
neuron_type_class = np.array(['excitatory', 'inhibitory']),
inter_neuron_type_connectivity = np.array([[1, 1, 0], [1, 1, 1], [1, 1, 0]]),
in_size = [14, 14],
in_channels = 32,
out_channels = 32,
)
]
model = SpatiallyEmbeddedRNN(num_areas=2, area_configs=area_configs, batch_first=False)
Inter-areal feedback connectivity¶
Finally, when you have multiple interacting areas, you'd want to ability to feedback information from downstream areas back up to early areas. torch-biopl provides an easy way to configure the flow of information. In simple terms, users can provide an adjacency matrix where rows are presynaptic areas and columns are postsynaptic areas.
conn = SpatiallyEmbeddedAreaConfig.inter_neuron_type_connectivity_template_df(use_feedback=True, num_neuron_types=2)
# this prints out the format of the connectivity adjacency matrix that you can follow
print(conn)
neuron_0 neuron_1 output
input False False False
feedback False False False
neuron_0 False False False
neuron_1 False False False
area_configs_feedback_model = [
SpatiallyEmbeddedAreaConfig(
num_neuron_types = 2,
num_neuron_subtypes = np.array([16, 16]),
neuron_type_class = np.array(['excitatory', 'inhibitory']),
inter_neuron_type_connectivity = np.array([[1, 1, 0], [1, 0, 0], [1, 1, 1], [1, 1, 0]]),
feedback_channels = 16,
in_size = [28, 28],
in_channels = 1,
out_channels = 32,
),
SpatiallyEmbeddedAreaConfig(
num_neuron_types = 2,
num_neuron_subtypes = np.array([32, 32]),
neuron_type_class = np.array(['excitatory', 'inhibitory']),
inter_neuron_type_connectivity = np.array([[1, 1, 0], [1, 1, 1], [1, 1, 0]]),
in_size = [14, 14],
in_channels = 32,
out_channels = 32,
)
]
model_wFeedback = SpatiallyEmbeddedRNN(
num_areas = 2,
area_configs = area_configs_feedback_model,
batch_first = False,
inter_area_feedback_connectivity = np.array([[0, 0],[1, 0]])
)