Source code for aihwkit.simulator.tiles.analog

# -*- coding: utf-8 -*-

# (C) Copyright 2020, 2021, 2022, 2023, 2024 IBM. All Rights Reserved.
#
# Licensed under the MIT license. See LICENSE file in the project root for details.

# pylint: disable=abstract-method

"""High level analog tiles (analog)."""

from typing import Optional, Tuple, Any

from torch import Tensor

from aihwkit.simulator.tiles.rpucuda import RPUCudaSimulatorTileWrapper
from aihwkit.simulator.tiles.module import TileModule
from aihwkit.simulator.tiles.base import BaseTile
from aihwkit.simulator.tiles.periphery import TileWithPeriphery
from aihwkit.simulator.tiles.functions import AnalogFunction
from aihwkit.simulator.parameters.base import RPUConfigGeneric
from aihwkit.simulator.rpu_base import tiles


[docs]class AnalogTile(TileModule, TileWithPeriphery, RPUCudaSimulatorTileWrapper): 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 """ supports_ddp: bool = False def __init__( self, out_size: int, in_size: int, rpu_config: RPUConfigGeneric, bias: bool = False, in_trans: bool = False, out_trans: bool = False, ): TileModule.__init__(self) RPUCudaSimulatorTileWrapper.__init__( self, out_size, in_size, rpu_config, bias, in_trans, out_trans ) TileWithPeriphery.__init__(self) def _create_simulator_tile( self, x_size: int, d_size: int, rpu_config: RPUConfigGeneric ) -> 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(self.get_data_type()) return meta_parameter.create_array(x_size, d_size, device_parameter)
[docs] def forward( self, x_input: Tensor, tensor_view: Optional[Tuple] = None # type: ignore ) -> Tensor: """Torch forward function that calls the analog forward""" # pylint: disable=arguments-differ out = AnalogFunction.apply( self.get_analog_ctx(), self, x_input, self.shared_weights, not self.training ) if tensor_view is None: tensor_view = self.get_tensor_view(out.dim()) out = self.apply_out_scaling(out, tensor_view) if self.digital_bias: return out + self.bias.view(*tensor_view) return out
[docs]class AnalogTileWithoutPeriphery(TileModule, BaseTile, RPUCudaSimulatorTileWrapper): """Analog tile without the periphery. Same basic functionality as class:`AnalogTile`, however, without the digital periphery, such as weight scaling and bias. """ supports_indexed: bool = False def __init__( self, out_size: int, in_size: int, rpu_config: RPUConfigGeneric, bias: bool = False, in_trans: bool = False, out_trans: bool = False, ): TileModule.__init__(self) RPUCudaSimulatorTileWrapper.__init__( self, out_size, in_size, rpu_config, bias, in_trans, out_trans ) def _create_simulator_tile( self, x_size: int, d_size: int, rpu_config: RPUConfigGeneric ) -> 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(self.get_data_type()) return meta_parameter.create_array(x_size, d_size, device_parameter)
[docs] def forward(self, x_input: Tensor) -> Tensor: """Torch forward function that calls the analog forward""" return AnalogFunction.apply( self.get_analog_ctx(), self, x_input, self.shared_weights, not self.training )
[docs] def joint_forward(self, x_input: Tensor, is_test: bool = False, ctx: Any = None) -> Tensor: """Perform the joint forward method. Args: x_input: ``[N, in_size]`` tensor. If ``in_trans`` is set, transposed. is_test: whether to assume testing mode. ctx: torch auto-grad context [Optional] Returns: torch.Tensor: ``[N, out_size]`` tensor. If ``out_trans`` is set, transposed. """ return self.tile.forward( x_input, self.analog_bias, self.in_trans, self.out_trans, is_test, self.non_blocking )
[docs] def backward(self, d_input: Tensor, ctx: Any = None) -> Tensor: """Perform the backward pass. Args: d_input: ``[N, out_size]`` tensor. If ``out_trans`` is set, transposed. ctx: torch auto-grad context [Optional] Returns: torch.Tensor: ``[N, in_size]`` tensor. If ``in_trans`` is set, transposed. """ return self.tile.backward( d_input, self.analog_bias, self.out_trans, self.in_trans, self.non_blocking )
[docs] def update(self, x_input: Tensor, d_input: Tensor) -> None: """Perform the update pass. Args: x_input: ``[..., in_size]`` tensor. If ``in_trans`` is set, ``[in_size, ...]``. d_input: ``[..., out_size]`` tensor. If ``out_trans`` is set, ``[out_size, ...]``. Returns: None """ return self.tile.update( # type: ignore x_input, d_input, self.analog_bias, self.in_trans, self.out_trans, self.non_blocking )
[docs] def set_learning_rate(self, learning_rate: Optional[float]) -> None: """Set the tile learning rate. Set the tile learning rate to ``-learning_rate``. Note that the learning rate is always taken to be negative (because of the meaning in gradient descent) and positive learning rates are not supported. Args: learning_rate: the desired learning rate. """ if learning_rate is not None: self.tile.set_learning_rate(learning_rate)
[docs] def get_learning_rate(self) -> float: """Return the tile learning rate. Returns: float: the tile learning rate. """ return self.tile.get_learning_rate()