Implicit Representation with High Order Layers

Implicit representation of various things using PyTorch and high order layers. The network uses high order layers as implemented here. Implicit representation is creating a function that approximates your data (cuve fitting). The function can be a compact representation of the original data and also provides an interpolation of that data. Below we show example functions for images.

PIP install of library functions

pip install high-order-implicit-representation

and

poetry add high-order-implicit-representation

if you run into problems installing triton with poetry, this is a hack I’ve had to
do for certain packages

poetry shell
pip install triton

Implicit Representation of Images

Train a model

python examples/implicit_images.py mlp.hidden.width=10 mlp.hidden.layers=2 lr=1e-3 mlp.n=3 mlp.periodicity=2.0 mlp.layer_type=continuous mlp.hidden.segments=2 mlp.input.segments=100 mlp.output.segments=2 batch_size=256

Evaluate a model example

python example/implicit_images.py train=False checkpoint=\"multirun/2021-01-10/18-31-32/0/lightning_logs/version_0/checkpoints/epoch=49-step=145349.ckpt\" rotations=2

Alternatively, model results are also plotted for each result in tensorboard

Examples

Piecewise Continuous

The example below uses piecewise quadratic polynomials. The input layer is the x, y position where there are 100 segments
for each input connection. There is 1 hidden layers with 40 units each and 2 segments. There are 3 outputs representing the RGB colors, where each output has 2 segment. In total there are 40.8k parameters,
The raw image can be represented by 2.232e6 8bit parameters.

python examples/implicit_images.py -m mlp.hidden.width=40 mlp.hidden.layers=1 lr=1e-3 mlp.n=3 mlp.periodicity=2.0 mlp.layer_type=continuous mlp.hidden.segments=2 mlp.input.segments=100 mlp.output.segments=2 batch_size=256 mlp.input.width=4 rotations=2

Fourier Series

similarly with a fourier series network

python examples/implicit_images.py -m mlp.hidden.width=40 mlp.hidden.layers=1 lr=1e-3 mlp.n=3 mlp.n_in=31 mlp.layer_type=fourier batch_size=256 mlp.input.width=4 rotations=2

Piecewise Discontinuous

and discontinuous polynomial

python examples/implicit_images.py -m mlp.hidden.width=40 mlp.hidden.layers=1 lr=1e-3 mlp.n=3 mlp.periodicity=2.0 mlp.layer_type=discontinuous mlp.hidden.segments=2 mlp.input.segments=100 mlp.output.segments=2 batch_size=256 mlp.input.width=4 rotations=2

Implicit Neighborhoods

Train interpolator / extrapolator

python examples/implicit_neighborhood.py mlp.hidden.width=50 mlp.hidden.layers=2 lr=1e-3 mlp.n=2 mlp.periodicity=2.0 mlp.layer_type=continuous mlp.hidden.segments=2 mlp.input.segments=50 mlp.output.segments=2 batch_size=256

create output with trained filter

python examples/implicit_neighborhood.py train=False checkpoint=\"outputs/2022-06-29/15-22-09/lightning_logs/version_0/checkpoints/'epoch=23-step=68448.ckpt'\" images=["images/jupiter.jpg"]

Training on the image of the newt and applying the filter repeatedly to the image of jupiter gives
the following results.

Applying to random noise produces

Associative Dictionary

This approach currently does not work so I’ll need to think about it for a while, but it
does run!
This is an attempt to store more than one image in a network based on text embedding and associated image. In principle it could also be a generative model if you ask for something not in the dictionary, but we’ll see what happens. I’m using the Pick-a-Pic so you’ll need to download those parquet files - the idea here is not (yet) to train on an enormous dataset but maybe use 10s to 100s of images.

python3 examples/text_to_image.py batch_size=2000 optimizer=sparse_lion max_epochs=10

Random Interpolation (A Generative Model)

This model picks random pixels and also the pixels locations relative to a target pixel as the training set. The random pixels also have location information while the target pixel is always at (0,0) as all other pixels are measured relative. The model learns to predict the
pixel value from these random samples.

python examples/random_interpolation.py mlp.hidden.width=10 mlp.hidden.layers=2 mlp.n=3 mlp.periodicity=2.0 mlp.hidden.segments=2 mlp.input.segments=100 mlp.output.segments=2 batch_size=1

and with an image folder

python examples/random_interpolation.py mlp.hidden.width=10 mlp.hidden.layers=2 mlp.n=3 mlp.periodicity=2.0 mlp.hidden.segments=2 mlp.input.segments=100 mlp.output.segments=2 batch_size=256 folder=/mnt/1000gb/celeba/img_align_celeba

and run evaluation

python examples/random_interpolation.py train=false checkpoint=\"outputs/2022-06-21/08-39-19/lightning_logs/version_0/checkpoints/epoch=49-step=19800.ckpt\"

Example generated image from celeba dataset. This is a WIP as I try and figure out the right parameters to get this working - currently suffering some mode collapse.