simrun ❭ modular_reduced_model_inference ❭ strategy ❭ RaisedCosineBasis

RaisedCosineBasis

class simrun.modular_reduced_model_inference.strategy.RaisedCosineBasis(a=2, c=1, phis=None, width=80, reversed_=False, backend=np)

Set of raised cosine basis functions to use as a kernel for weighing synaptic activation patterns.

A raised cosine is defined as:

\[f_i(x) = \frac{1}{2} cos(a \cdot log(\tau + c) - \phi_i) + \frac{1}{2}\]

where \(\tau\) is the input dimension (space or time e.g.), \(a\) is the steepness, \(c\) is the offset, and \(\phi\) is the phase. These basis functions can be superimposed using learnable weights \(x_i\) to form a single filter \(\mathbf{w}(\tau)\) over the domain \(\tau\):

\[\mathbf{w}(\tau) = \sum_{i} x_i \cdot f_i(\tau)\]

And this filter can then be used to weigh the input data \(\mathbf{D}\):

\[WI(t) = \int_{t-width}^{t} \mathbf{w}(\tau) \cdot \mathbf{D}(\tau)\]

Note

The notation here heavily implies that the cosine functions are defined over the time domain. However, they can equally well be used for spatial or spatiotemporal data.

Parameters:

  • a (int) – The steepness of the raised cosine. Default is \(2\).

  • c (int) – The offset of the raised cosine. Default is \(1\).

  • phis (array) – The phases of the raised cosine. Default is np.arange(1, 11, 0.5).

  • width (int) – The width of the basis functions. Default is \(80\).

  • reversed_ (bool) – Whether to reverse the basis functions. Default is False.

  • backend (module) – The backend to use (cupy or numpy). Default is numpy.

Attributes:

a

The steepness of the raised cosine. Default is \(2\).

Type:

int

c

The offset of the raised cosine. Default is \(1\).

Type:

int

phis

The phases of the raised cosine. Default is np.arange(1, 11, 0.5).

Type:

array

width

The width of the basis functions. Default is \(80\).

Type:

int

basis

The list of basis functions.

Type:

list

reversed_

Whether to reverse the basis functions. Default is False.

Type:

bool

backend

The backend to use (cupy or numpy). Default is numpy.

Type:

module

Methods:

compute(width)

Compute the vector of raised cosine basis functions \(\mathbf{f}\).

get()

Get the basis functions \(\mathbf{f}\).

get_superposition(x)

Get the weighed sum \(\mathbf{w}(\tau)\) of the basis functions \(f\).

visualize(ax, plot_kwargs)

Visualize the basis functions \(\mathbf{f}\).

visualize_w(x, ax, plot_kwargs)

Visualize the superposition \(\mathbf{w}(\tau)\) of the basis functions \(\mathbf{f}\).

get_raised_cosine(a, c, phi, t, backend)

static Calculate a single raised cosine basis function \(f_i\) over the domain \(t\).