aihwkit.simulator.tiles.analog module

High level analog tiles (analog).

class aihwkit.simulator.tiles.analog.AnalogTile(*args, **kwds)

Bases: aihwkit.simulator.tiles.base.BaseTile

Analog tile.

This analog tile implements an abstract analog tile where many cycle-tp-cycle non-idealities and systematic parameter-spreads that can be user-defined.

In general stochastic bit pulse trains are generate during update and device materials (or unit cells) at each cross-point are only updated if a coincidence of rows and columns pulses.

Here, a resistive device material is assumed that response with a finite step change of its conductance value that is independent of its own conductance value.

In its basic parameter settings it implements the analog RPU tile model described in Gokmen & Vlasov (2016), but with a number of enhancements that are adjustable by parameter settings.

All tile parameters are given in AnalogTileParameters.

Forward pass:

In general, the following analog forward pass is computed:

\[\mathbf{y} = f_\text{ADC}((W + \sigma_\text{w}\Xi) \otimes (f_\text{DAC}( x/\alpha ) + \sigma_\text{inp}\,\boldsymbol{\xi}_1 ) + \sigma_\text{out}\,\boldsymbol{\xi}_2)\,s_\alpha\, s_\text{out}\,\alpha\]

where \(W\) is the weight matrix, \(\mathbf{x}\) the input vector and the \(\Xi,\boldsymbol{\xi}_1,\boldsymbol{\xi}_2\) Gaussian noise variables (with corresponding matrix and vector sizes). The \(\alpha\) is a scale from the noise management (see rpu_types.NoiseManagementTypeMap). The symbol \(\otimes\) refers to the ‘analog’ matrix-vector multiplication, that might have additional non-linearities.

\(f_\text{Z}\) (with Z either ADC or DAC) indicates the discretization to a number of equidistant steps between a bound value \(-b_\text{Z},\ldots,b_\text{Z}\) potentially with stochastic rounding (SR):

\[f_\text{Z}(x) = \text{round}(x\, \frac{r_\text{Z}}{2\,b_\text{Z}} + \zeta)\frac{2b_\text{Z}}{r_\text{Z}}\]

If SR is enabled \(\zeta\) is an uniform random \(\in [-0.5,0.5)\). Otherwise \(\zeta=0\). Inputs are clipped below \(-b_\text{Z}\) and above \(b_\text{Z}\)

\(r_Z\) is the resolution of the ADC or DAC. E.g. for 8 bit, it would be \(1/256\)


Typically the resolution is reduced by 2 level, eg. in case of 8 bits it is set to \(1/254\) to account for a discretization mirror symmetric around zero, including the zero and discarding one value.

The scalar scale \(s_\text{out}\) can be set by out_scale. The scalar scale \(s_\alpha\) is an additional scale that might be use to map weight better to conductance ranges.

For parameters regarding the forward pass behavior, see AnalogTileInputOutputParameters.

Backward pass:

Identical to the forward direction except that the transposed weight matrix is used. Same parameters as during the forward pass except that bound management is not supported.

For parameters regarding the backward pass behavior, see AnalogTileInputOutputParameters.

General weight update:

The weight update that theoretically needs to be computed is

\[w_{ij} = w_{ij} + \lambda d_i\,x_j\]

thus the outer product of error vector and input vector.

Although the update depends on the ResistiveDevice used, in general, stochastic pulse trains of a given length are drawn, where the probability of occurrence of an pulse is proportional to \(\sqrt{\lambda}d_i\) and \(\sqrt{\lambda}x_j\) respectively. Then for each cross-point, in case a coincidence of column and row pulses occur, the weight is updated one step. For details, see Gokmen & Vlasov (2016).

The amount of how the weight changes per single step might be different for the different resistive devices.

In pseudo code:

# generate prob number
p_i  = quantize(A * d_i, res, sto_round)
q_j  = quantize(B * x_j, res, sto_round)
sign = sign(d_i)*sign(x_j)

# generate pulse trains of length BL
pulse_train_d = gen_pulse_train(p_i, BL) # e.g 101001001
pulse_train_x = gen_pulse_train(q_j, BL) # e.g 001010010

for t in range(BL):
    if (pulse_train_x[t]==1) and (pulse_train_d[t]==1)
        update_once(w_ij, direction = sign)

The probabilities are generated using scaling factors A and B that are determined by the learning rate and pulse train length BL (see below). quantize is an optional discretization of the resulting probability, to account for limited resolution number in the stochastic pulse train generation process on the chip .

The update_once functionality is in general dependent on the analog tile class. For ConstantStep the step width is independent of the actual weight, but has cycle-to-cycle variation, device-to-device variation or systematic bias for up versus down direction (see below).

For parameters regarding the update behaviour, see AnalogTileUpdateParameters.

  • out_size – output vector size of the tile, ie. the dimension of \(\mathbf{y}\) in case of \(\mathbf{y} = W\mathbf{x}\) (or equivalently the dimension of the \(\boldsymbol{\delta}\) of the backward pass).

  • in_size – input vector size, ie. the dimension of the vector \(\mathbf{x}\) in case of \(\mathbf{y} = W\mathbf{x}\)).

  • rpu_config – resistive processing unit configuration.

  • bias – whether to add a bias column to the tile, ie. \(W\) has an extra column to code the biases. Internally, the input \(\mathbf{x}\) will be automatically expanded by an extra dimension which will be set to 1 always.


Return a copy of this tile in CUDA memory.


device (Optional[Union[torch.device, str, int]]) – CUDA device

Return type


class aihwkit.simulator.tiles.analog.CudaAnalogTile(*args, **kwds)

Bases: aihwkit.simulator.tiles.analog.AnalogTile

Analog tile (CUDA).

Analog tile that uses GPU for its operation. The instantiation is based on an existing non-cuda tile: all the source attributes are copied except for the simulator tile, which is recreated using a GPU tile.


source_tile – tile to be used as the source of this tile


Return a copy of this tile in CUDA memory.


device (Optional[Union[torch.device, str, int]]) – CUDA device

Return type


is_cuda = True