# -*- coding: utf-8 -*-
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# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
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"""High level analog tiles (analog)."""
from copy import deepcopy
from typing import Optional, Union, TYPE_CHECKING
from torch import device as torch_device
from torch.cuda import current_device
from torch.cuda import device as cuda_device
from aihwkit.exceptions import CudaError
from aihwkit.simulator.rpu_base import cuda, tiles
from aihwkit.simulator.tiles.base import BaseTile
if TYPE_CHECKING:
from aihwkit.simulator.configs import (
InferenceRPUConfig, SingleRPUConfig, UnitCellRPUConfig
)
[docs]class AnalogTile(BaseTile):
r"""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
:class:`~aihwkit.simulator.parameters.AnalogTileParameters`.
**Forward pass**:
In general, the following analog forward pass is computed:
.. math::
\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 :math:`W` is the weight matrix, :math:`\mathbf{x}` the input
vector and the :math:`\Xi,\boldsymbol{\xi}_1,\boldsymbol{\xi}_2`
Gaussian noise variables (with corresponding matrix and vector
sizes). The :math:`\alpha` is a scale from the noise management
(see :data:`rpu_types.NoiseManagementTypeMap`). The symbol
:math:`\otimes` refers to the 'analog' matrix-vector
multiplication, that might have additional non-linearities.
:math:`f_\text{Z}` (with `Z` either `ADC` or `DAC`) indicates the
discretization to a number of equidistant steps between a bound
value :math:`-b_\text{Z},\ldots,b_\text{Z}` potentially with
stochastic rounding (SR):
.. math::
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 :math:`\zeta` is an uniform random :math:`\in
[-0.5,0.5)`. Otherwise :math:`\zeta=0`. Inputs are clipped below
:math:`-b_\text{Z}` and above :math:`b_\text{Z}`
:math:`r_Z` is the resolution of the `ADC` or `DAC`. E.g. for 8
bit, it would be :math:`1/256`
Note:
Typically the resolution is reduced by 2 level, eg. in case of
8 bits it is set to :math:`1/254` to account for a
discretization mirror symmetric around zero, including the zero
and discarding one value.
The scalar scale :math:`s_\text{out}` can be set by
``out_scale``. The scalar scale :math:`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
:class:`~aihwkit.simulator.parameters.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
:class:`~aihwkit.simulator.parameters.AnalogTileInputOutputParameters`.
**General weight update**:
The weight update that theoretically needs to be computed is
.. math:: 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
:math:`\sqrt{\lambda}d_i` and :math:`\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
:class:`~aihwkit.simulator.parameters.AnalogTileUpdateParameters`.
Args:
out_size: output vector size of the tile, ie. the dimension of
:math:`\mathbf{y}` in case of :math:`\mathbf{y} =
W\mathbf{x}` (or equivalently the dimension of the
:math:`\boldsymbol{\delta}` of the backward pass).
in_size: input vector size, ie. the dimension of the vector
:math:`\mathbf{x}` in case of :math:`\mathbf{y} =
W\mathbf{x}`).
rpu_config: resistive processing unit configuration.
bias: whether to add a bias column to the tile, ie. :math:`W`
has an extra column to code the biases. Internally, the
input :math:`\mathbf{x}` will be automatically expanded by
an extra dimension which will be set to 1 always.
in_trans: Whether to assume an transposed input (batch first).
out_trans: Whether to assume an transposed output (batch first).
.. _Gokmen & Vlasov (2016): https://www.frontiersin.org/articles/10.3389/fnins.2016.00333/full
"""
def __init__(
self,
out_size: int,
in_size: int,
rpu_config: Optional[Union['SingleRPUConfig', 'UnitCellRPUConfig',
'InferenceRPUConfig']] = None,
bias: bool = False,
in_trans: bool = False,
out_trans: bool = False,
):
if not rpu_config:
# Import `SingleRPUConfig` dynamically to avoid import cycles.
# pylint: disable=import-outside-toplevel
from aihwkit.simulator.configs import SingleRPUConfig
rpu_config = SingleRPUConfig()
super().__init__(out_size, in_size, rpu_config, bias, in_trans, out_trans)
[docs] def cpu(self) -> 'BaseTile':
"""Return a copy of this tile in CPU memory.
Note:
CUDA tiles weight can be accessed by `get_weights` etc
methods, there is no need to move them to CPU and it is
currently not supported.
Returns:
self in case of CPU
Raises:
CudaError: if a CUDA tile is moved to CPU
"""
if self.is_cuda:
raise CudaError('Currently it is not possible to move CUDA tile to cpu.')
return self
[docs] def cuda(
self,
device: Optional[Union[torch_device, str, int]] = None
) -> 'BaseTile':
"""Return a copy of this tile in CUDA memory.
Args:
device: CUDA device
Returns:
Self with the underlying C++ tile moved to CUDA memory.
Raises:
CudaError: if the library has not been compiled with CUDA.
"""
if not cuda.is_compiled():
raise CudaError('aihwkit has not been compiled with CUDA support')
device = torch_device('cuda', cuda_device(device).idx)
if self.is_cuda and device != self.device:
raise CudaError('Cannot switch CUDA devices of existing Cuda tiles')
if isinstance(self.tile, tiles.AnalogTile):
with cuda_device(device):
self.tile = tiles.CudaAnalogTile(self.tile)
self.is_cuda = True
self.device = device
self.analog_ctx.cuda(device)
if self.out_scaling_alpha is not None:
self.out_scaling_alpha.data = self.out_scaling_alpha.data.cuda(device)
return self
def _create_simulator_tile(
self,
x_size: int,
d_size: int,
rpu_config: Union['SingleRPUConfig', 'UnitCellRPUConfig', 'InferenceRPUConfig']
) -> tiles.AnalogTile:
"""Create a simulator tile.
Args:
x_size: input size
d_size: output size
rpu_config: resistive processing unit configuration
Returns:
a simulator tile based on the specified configuration.
"""
meta_parameter = rpu_config.as_bindings()
device_parameter = rpu_config.device.as_bindings()
return meta_parameter.create_array(x_size, d_size, device_parameter)
[docs]class CudaAnalogTile(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.
Caution:
Deprecated. Use `AnalogTile(..).cuda()` instead.
Args:
source_tile: tile to be used as the source of this tile
"""
def __init__(self, source_tile: AnalogTile):
if not cuda.is_compiled():
raise CudaError('aihwkit has not been compiled with CUDA support')
# Create a new instance of the rpu config.
new_rpu_config = deepcopy(source_tile.rpu_config)
# Create the tile, replacing the simulator tile.
super().__init__(source_tile.out_size, source_tile.in_size, new_rpu_config,
source_tile.bias, source_tile.in_trans, source_tile.out_trans)
self.cuda(current_device())