PyTorch Implementation of the LCA Sparse Coding Algorithm

LCA-PyTorch (lcapt) provides the ability to flexibly build single- or multi-layer convolutional sparse coding networks in PyTorch with the Locally Competitive Algorithm (LCA). LCA-Pytorch currently supports 1D, 2D, and 3D convolutional LCA layers, which maintain all the functionality and behavior of PyTorch convolutional layers. We currently do not support Linear (a.k.a. fully-connected) layers, but it is possible to implement the equivalent of a Linear layer with convolutions.

Installation

Dependencies

Required:

• Python (>= 3.8)

Recommended:

• GPU(s) with NVIDIA CUDA (>= 11.0) and NVIDIA cuDNN (>= v7)

Pip Installation

pip install git+https://github.com/lanl/lca-pytorch.git

Manual Installation

git clone [email protected]:lanl/lca-pytorch.git
cd lca-pytorch
pip install .

Usage

LCA-PyTorch layers inherit all functionality of standard PyTorch layers.

import torch
import torch.nn as nn

from lcapt.lca import LCAConv2D

# create a dummy input
inputs = torch.zeros(1, 3, 32, 32)

# 2D conv layer in PyTorch
pt_conv = nn.Conv2d(
  in_channels=3,
  out_channels=64,
  kernel_size=7,
  stride=2,
  padding=3
)
pt_out = pt_conv(inputs)

# 2D conv layer in LCA-PyTorch
lcapt_conv = LCAConv2D(
  out_neurons=64,
  in_neurons=3,
  kernel_size=7,
  stride=2,
  pad='same'
)
lcapt_out = lcapt_conv(inputs)

Locally Competitive Algorithm (LCA)

LCA solves the $\ell_1$-penalized reconstruction problem

$\underset{a}\min \lvert|s - a * \Phi \rvert|_2^2 + \lambda \lvert| a \rvert|_1$

where $s$ is an input, $a$ is a sparse (i.e. mostly zeros) representation of $s$, $*$ is the convolution operation, $\Phi$ is a dictionary of convolutional features, $a * \Phi$ is the reconstruction of $s$, and $\lambda$ determines the tradeoff between reconstruction fidelity and sparsity in $a$. The equation above is convex in $a$, and LCA solves it by implementing a dynamical system of leaky integrate-and-fire neurons

$\dot{u}(t) = \frac{1}{\tau} \big[b(t) - u(t) - a(t) * G \big]$

in which each neuron's membrane potential, $u(t)$, is charged up or down by the bottom-up drive from the stimulus, $b(t) = s(t) * \Phi$ and is leaky via the term $-u(t)$. $u(t)$ can also be inhibited or excited by active surrounding neurons via the term $-a(t) * G$, where $a(t)=\Gamma_\lambda (u(t))$ is the neuron's activation computed by applying a firing threshold $\lambda$ to $u(t)$, and $G=\Phi * \Phi - I$. This means that a given neuron will modulate a neighboring neuron in proportion to the similarity between their receptive fields and how active it is at that time.

Below is a mapping between the variable names used in this implementation and those used in Rozell et al.'s formulation of LCA.

LCA-PyTorch Variable	Rozell Variable	Description
input_drive	$b(t)$	Drive from the inputs/stimulus
states	$u(t)$	Internal state/membrane potential
acts	$a(t)$	Code/Representation/External Communication
lambda_	$\lambda$	Transfer function threshold value
weights	$\Phi$	Dictionary/Features
inputs	$s(t)$	Input data
recons	$\hat{s}(t)$	Reconstruction of the input
tau	$\tau$	LCA time constant

Examples

• Dictionary Learning Using Built-In Update Method

  • Dictionary Learning on Cifar-10 Images
  • Fully-Connected Dictionary Learning on MNIST

• Dictionary Learning Using PyTorch Optimizer

  • Dictionary Learning on Cifar-10 Images

License

LCA-PyTorch is provided under a BSD license with a "modifications must be indicated" clause. See the LICENSE file for the full text. Internally, the LCA-PyTorch package is known as LA-CC-23-064.