# Keywords¶

This module provides the string keywords used throughout psyneulink

Loss function used for learning.

Each keyword specifies a loss function used for learning in a Composition or AutodiffComposition, and the comparable loss functions used by PyTorch when an AutodiffComposition is executed in ExecutionMode.PyTorch mode.

L0

sum of errors: $$\sum\limits^{len}_i|target_i - output_i|$$

SSE

sum of squared errors: $$\sum\limits^{len}_i(target_i - output_i)^2$$

MSE

mean of squared errors: $$\frac{\sum\limits^{len}_i(target_i - output_i)^2}{len}$$

CROSS_ENTROPY

cross entropy: $$\sum\limits^{len}_ioutput_i\log(target_i)$$

KL_DIV

Kullback-Leibler (KL) divergence: $$\sum\limits^{len}_itarget_i\log{(\frac{target_i}{output_i})}$$

NLL

Negative log likelihood loss: $$-{\log(target_i)}$$

POISSON_NLL

Poisson negative log likelihood loss

IDENTITY_MATRIX

a square matrix of 1’s along the diagonal, 0’s elsewhere; this requires that the length of the sender and receiver values are the same.

HOLLOW_MATRIX

a square matrix of 0’s along the diagonal, 1’s elsewhere; this requires that the length of the sender and receiver values are the same.

FULL_CONNECTIVITY_MATRIX

a matrix that has a number of rows equal to the length of the sender’s value, and a number of columns equal to the length of the receiver’s value, all the elements of which are 1’s.

RANDOM_CONNECTIVITY_MATRIX

a matrix that has a number of rows equal to the length of the sender’s value, and a number of columns equal to the length of the receiver’s value, all the elements of which are filled with random values uniformly distributed between 0 and 1.

AUTO_ASSIGN_MATRIX

if the sender and receiver are of equal length, an IDENTITY_MATRIX is assigned; otherwise, a FULL_CONNECTIVITY_MATRIX is assigned.

DEFAULT_MATRIX

used if no matrix specification is provided in the constructor; it presently assigns an IDENTITY_MATRIX.

Distance between two arrays.

Each keyword specifies a metric for the distance between two arrays, $$a_1$$ and $$a_2$$, of equal length for which len is their length, $$\bar{a}$$ is the mean of an array, $$\sigma_{a}$$ the standard deviation of an array, and $$w_{a_1a_2}$$ a coupling coefficient (“weight”) between a pair of elements, one from each array:

MAX_ABS_DIFF

$$d = \max(|a_1-a_2|)$$

DIFFERENCE

(can also be referenced as L0)

$$d = \sum\limits^{len}(|a_1-a_2|)$$

EUCLIDEAN

(can also be referenced as L1)

$$d = \sum\limits^{len}\sqrt{(a_1-a_2)^2}$$

COSINE

$$d = 1 - \frac{\sum\limits^{len}a_1a_2}{\sqrt{\sum\limits^{len}a_1^2}\sqrt{\sum\limits^{len}a_2^2}}$$

CORRELATION

$$d = 1 - \left|\frac{\sum\limits^{len}(a_1-\bar{a}_1)(a_2-\bar{a}_2)}{(len-1)\sigma_{a_1}\sigma_{ a_2}}\right|$$

CROSS_ENTROPY

(can also be referenced as ENTROPY)

$$d = \sum\limits^{len}a_1log(a_2)$$

ENERGY

$$d = -\frac{1}{2}\sum\limits_{i,j}a_{1_i}a_{2_j}w_{ij}$$