Nonlinear fusion

Code for the paper Ghosh et al., 2024 Nonlinear fusion is optimal for a wide class of multisensory tasks:

• Paper
• Preprint

If you have any questions regarding the code please contact either Marcus Ghosh or Dan Goodman.

Note some code uses AtF and FtA to refer to linear and nonlinear fusion.

Dependencies

A minimal dependency file is provided in environment.yml.

Our Matplotlib style sheet can be found in style_sheet.mplstyle.

Tasks

Sample Python code for each task can be found in the paper's supporting information.

Otherwise, functions to generate trials for each task can be found in multisensory.py.

To use the latter, install the necessary dependencies, add multisensory.py to your working directory then:

# Import the task(s) you wish to use.
from multisensory import DetectionTask

# Set task parameters - note that these differ per task. 
task = DetectionTask(pm=2 / 3, pe=0.057, pc=0.95, pn=1 / 3, pi=0.01) 

# Generate n_trials, each of length n_steps.
trials = task.generate_trials(n_trials, n_steps) 

trials will be a class object containing the following:

• Repeats: an integar denoting the number of trials.
• time_steps: an integar denoting the number of time steps per trial.
• task: the task and parameters used to generate the trials.
• M: a numpy array with a label per trial (-1: left, 0:neutral, 1:right).
• A: a (repeats x time_steps) numpy array with the stimulus directions for one sensory channel (-1: left, 0:neutral, 1:right).
• V: a (repeats x time_steps) numpy array with the stimulus directions for the other sensory channel (-1: left, 0:neutral, 1:right).

Models

MAP estimators

Our Bayesian observer functions can be found in multisensory.py.

For example, to determine the accuracy of linear and nonlinear fusion on the task above:

# Import the classifier you wish to use. 
from multisensory import MAPClassifier
classifier_type = MAPClassifier

# Calculate accuracy
accuracy = [] 
for pairs in [False, True]: # this flag determines linear (False) vs nonlinear (True) fusion.
	classifier = classifier_type(task, pairs=pairs)
	res = classifier.test(trials)
	accuracy.append(res.accuracy)
print("Linear fusion accuracy: " + str(accuracy[0]))
print("Nonlinear fusion accuracy: " + str(accuracy[1]))

ANNs

Our code for training artificial neural networks, with different activation functions, on our tasks can be found in Task_Space_AF_Comparisons.ipynb.

Note:

• This notebook will run much faster if you reduce the number of: tasks, trials per task (nb_trials) and tested activation functions (multisensory_activations).
• The ideal_data loaded at the start of the notebook can be downloaded from here or regenerated from Ideal_data.ipynb.

SNNs

To train our spiking neural networks we created a pip installable package (m2snn).

A minimal example of using this to train an SNN can be found in minimaL_training.py.

Paper figures

The code for generating each figure can be found in the following files. For all SNN results we used our m2snn package - so simply point to that.

1C - m2snn.

2C - detection_params.ipynb.
2D - detection_params.ipynb.
2E:

• ideal_data_detection_task_family.json can be downloaded from here or
• Regenerated by figure_cns.py and,
• Plotted with detection-family-figure.ipynb.

2F - m2snn.
2G - m2snn.

3 - detection_task_multidim.ipynb.

4A - Task_Space_AF_Comparisons.ipynb.
4B - Single_Unit.ipynb.
4C - m2snn.
4D - m2snn.

5:

• snn_boundaries_data_3651b83e can be downloaded from here or
• Regenerated by m2snn and,
• Plotted with Task_Space_Optimal.ipynb.

S1 - m2snn.
S2 - m2snn.
S3 - continuous_valued_version.ipynb.
S4 - Task_Space_AF_Comparisons.ipynb.
S5 - m2snn.
S6 - m2snn.