modeci_mdf.functions.onnx.lstm

modeci_mdf.functions.onnx.lstm(*args, **kwargs)

Computes an one-layer LSTM. This operator is usually supported via some custom implementation such as CuDNN.

Notations:

X - input tensor

i - input gate

o - output gate

f - forget gate

c - cell gate

t - time step (t-1 means previous time step)

W[iofc] - W parameter weight matrix for input, output, forget, and cell gates

R[iofc] - R recurrence weight matrix for input, output, forget, and cell gates

Wb[iofc] - W bias vectors for input, output, forget, and cell gates

Rb[iofc] - R bias vectors for input, output, forget, and cell gates

P[iof] - P peephole weight vector for input, output, and forget gates

WB[iofc] - W parameter weight matrix for backward input, output, forget, and cell gates

RB[iofc] - R recurrence weight matrix for backward input, output, forget, and cell gates

WBb[iofc] - W bias vectors for backward input, output, forget, and cell gates

RBb[iofc] - R bias vectors for backward input, output, forget, and cell gates

PB[iof] - P peephole weight vector for backward input, output, and forget gates

H - Hidden state

num_directions - 2 if direction == bidirectional else 1

Activation functions:

Relu(x) - max(0, x)

Tanh(x) - (1 - e^{-2x})/(1 + e^{-2x})

Sigmoid(x) - 1/(1 + e^{-x})

(NOTE: Below are optional)

Affine(x) - alpha*x + beta

LeakyRelu(x) - x if x >= 0 else alpha * x

ThresholdedRelu(x) - x if x >= alpha else 0

ScaledTanh(x) - alpha*Tanh(beta*x)

HardSigmoid(x) - min(max(alpha*x + beta, 0), 1)

Elu(x) - x if x >= 0 else alpha*(e^x - 1)

Softsign(x) - x/(1 + |x|)

Softplus(x) - log(1 + e^x)

Equations (Default: f=Sigmoid, g=Tanh, h=Tanh):

• it = f(Xt*(Wi^T) + Ht-1*(Ri^T) + Pi (.) Ct-1 + Wbi + Rbi)

• ft = f(Xt*(Wf^T) + Ht-1*(Rf^T) + Pf (.) Ct-1 + Wbf + Rbf)

• ct = g(Xt*(Wc^T) + Ht-1*(Rc^T) + Wbc + Rbc)

• Ct = ft (.) Ct-1 + it (.) ct

• ot = f(Xt*(Wo^T) + Ht-1*(Ro^T) + Po (.) Ct + Wbo + Rbo)

• Ht = ot (.) h(Ct)

This operator has optional inputs/outputs. See [the doc](IR.md) for more details about the representation of optional arguments. An empty string may be used in the place of an actual argument’s name to indicate a missing argument. Trailing optional arguments (those not followed by an argument that is present) may also be simply omitted.