LibSPN Keras

LibSPN Keras is a library for constructing and training Sum-Product Networks. By leveraging the Keras framework with a TensorFlow backend, it offers both ease-of-use and scalability. Whereas the previously available libspn focused on scalability, libspn-keras offers scalability and a straightforward Keras-compatible interface.

Contents

• API Reference

Documentation

The documentation of the library is hosted on ReadTheDocs.

What are SPNs?

Sum-Product Networks (SPNs) are a probabilistic deep architecture with solid theoretical foundations, which demonstrated state-of-the-art performance in several domains. Yet, surprisingly, there are no mature, general-purpose SPN implementations that would serve as a platform for the community of machine learning researchers centered around SPNs. LibSPN Keras is a new general-purpose Python library, which aims to become such a platform. The library is designed to make it straightforward and effortless to apply various SPN architectures to large-scale datasets and problems. The library achieves scalability and efficiency, thanks to a tight coupling with TensorFlow and Keras, two frameworks already in use by a large community of researchers and developers in multiple domains.

Dependencies

Currently, LibSPN Keras is tested with tensorflow>=2.0 and tensorflow-probability>=0.8.0.

Installation

pip install libspn-keras

Note on stability of the repo

Currently, the repo is in an alpha state. Hence, one can expect some sporadic breaking changes.

Feature Overview

• Gradient based training for generative and discriminative problems
• Hard EM training for generative problems
• Hard EM training with unweighted weights for generative problems
• Soft EM training for generative problems
• Deep Generalized Convolutional Sum-Product Networks
• SPNs with arbitrary decompositions
• Fully compatible with Keras and TensorFlow 2.0
• Input dropout
• Sum child dropout
• Image completion
• Model saving
• Discrete inputs through an IndicatorLeaf node
• Continuous inputs through NormalLeaf, CauchyLeaf or LaplaceLeaf. Each of these distributions support both univariate as well as multivariate inputs.

Examples / Tutorials

1. Benchmark: libspn-keras and Einsum Networks.
2. Image Classification: A Deep Generalized Convolutional Sum-Product Network (DGC-SPN).
3. Image Completion: A Deep Generalized Convolutional Sum-Product Network (DGC-SPN).
4. Understanding region SPNs
5. Samping with convolutional SPNs
6. More to come, and if you would like to see a tutorial on anything in particular please raise an issue!

Check out the way we can build complex DGC-SPNs in a layer-wise fashion:

import libspn_keras as spnk
from tensorflow import keras

spnk.set_default_sum_op(spnk.SumOpGradBackprop())
spnk.set_default_accumulator_initializer(
    keras.initializers.TruncatedNormal(stddev=0.5, mean=1.0)
)

sum_product_network = keras.Sequential([
  spnk.layers.NormalizeStandardScore(input_shape=(28, 28, 1)),
  spnk.layers.NormalLeaf(
      num_components=16,
      location_trainable=True,
      location_initializer=keras.initializers.TruncatedNormal(
          stddev=1.0, mean=0.0)
  ),
  # Non-overlapping products
  spnk.layers.Conv2DProduct(
      depthwise=True,
      strides=[2, 2],
      dilations=[1, 1],
      kernel_size=[2, 2],
      padding='valid'
  ),
  spnk.layers.Local2DSum(num_sums=16),
  # Non-overlapping products
  spnk.layers.Conv2DProduct(
      depthwise=True,
      strides=[2, 2],
      dilations=[1, 1],
      kernel_size=[2, 2],
      padding='valid'
  ),
  spnk.layers.Local2DSum(num_sums=32),
  # Overlapping products, starting at dilations [1, 1]
  spnk.layers.Conv2DProduct(
      depthwise=True,
      strides=[1, 1],
      dilations=[1, 1],
      kernel_size=[2, 2],
      padding='full'
  ),
  spnk.layers.Local2DSum(num_sums=32),
  # Overlapping products, with dilations [2, 2] and full padding
  spnk.layers.Conv2DProduct(
      depthwise=True,
      strides=[1, 1],
      dilations=[2, 2],
      kernel_size=[2, 2],
      padding='full'
  ),
  spnk.layers.Local2DSum(num_sums=64),
  # Overlapping products, with dilations [2, 2] and full padding
  spnk.layers.Conv2DProduct(
      depthwise=True,
      strides=[1, 1],
      dilations=[4, 4],
      kernel_size=[2, 2],
      padding='full'
  ),
  spnk.layers.Local2DSum(num_sums=64),
  # Overlapping products, with dilations [2, 2] and 'final' padding to combine
  # all scopes
  spnk.layers.Conv2DProduct(
      depthwise=True,
      strides=[1, 1],
      dilations=[8, 8],
      kernel_size=[2, 2],
      padding='final'
  ),
  spnk.layers.SpatialToRegions(),
  # Class roots
  spnk.layers.DenseSum(num_sums=10),
  spnk.layers.RootSum(return_weighted_child_logits=True)
])

sum_product_network.summary(line_length=100)

Which produces:

Model: "sequential"
_________________________________________________________________
Layer (type)                 Output Shape              Param #
=================================================================
normal_leaf (NormalLeaf)     (None, 28, 28, 16)        25088
_________________________________________________________________
conv2d_product (Conv2DProduc (None, 14, 14, 16)        4
_________________________________________________________________
local2d_sum (Local2DSum)     (None, 14, 14, 16)        50176
_________________________________________________________________
conv2d_product_1 (Conv2DProd (None, 7, 7, 16)          4
_________________________________________________________________
local2d_sum_1 (Local2DSum)   (None, 7, 7, 32)          25088
_________________________________________________________________
conv2d_product_2 (Conv2DProd (None, 8, 8, 32)          4
_________________________________________________________________
local2d_sum_2 (Local2DSum)   (None, 8, 8, 32)          65536
_________________________________________________________________
conv2d_product_3 (Conv2DProd (None, 10, 10, 32)        4
_________________________________________________________________
local2d_sum_3 (Local2DSum)   (None, 10, 10, 64)        204800
_________________________________________________________________
conv2d_product_4 (Conv2DProd (None, 14, 14, 64)        4
_________________________________________________________________
local2d_sum_4 (Local2DSum)   (None, 14, 14, 64)        802816
_________________________________________________________________
conv2d_product_5 (Conv2DProd (None, 8, 8, 64)          4
_________________________________________________________________
spatial_to_regions (SpatialT (None, 1, 1, 4096)        0
_________________________________________________________________
dense_sum (DenseSum)         (None, 1, 1, 10)          40960
_________________________________________________________________
root_sum (RootSum)           (None, 10)                10
=================================================================
Total params: 1,214,498
Trainable params: 1,201,930
Non-trainable params: 12,568
_________________________________________________________________

TODOs

• Structure learning
• Advanced regularization e.g. pruning or auxiliary losses on weight accumulators