Create deep neural networks based on very different kinds of graphs or use deepstruct to extract the structure of your deep neural network. Deepstruct can automatically create a deep neural network models based on graphs and for purposes of visualization, analysis or transformations it also supports graph extraction from a given model.
Interested in neural network visualizations, pruning, neural architecture search or neural structure in general?
See examples below or read the docs.
- With pip from PyPi:
pip install deepstruct - With poetry (recommended for projects) using PyPi:
poetry add deepstruct - With conda in your environment.yml (recommended for reproducible experiments):
name: exp01
channels:
- defaults
dependencies:
- pip>=20
- pip:
- deepstruct- From public GitHub:
pip install --upgrade git+ssh://[email protected]:innvariant/deepstruct.git
deepstruct provides two major tool approaches to pytorch models:
- Based on a graph structure, it allows you to automatically construct a deep neural network model.
- Given a (pre-trained) model, deepstruct provides options to extract different notions of a graph from it as to further visualize or analyze it.
The simplest implementation is one which provides multiple layers with binary masks for each weight matrix. It doesn't consider any skip-layer connections. Each layer is then connected to only the following one.
import deepstruct.sparse
mnist_model = deepstruct.sparse.MaskedDeepFFN((1, 28, 28), 10, [100]*10, use_layer_norm=True)This is a ready-to-use pytorch module which has ten layers of each one hundred neurons and applies layer normalization before each activation. Training it on any dataset will work out of the box like every other pytorch module. Have a look on pytorch ignite or pytorch lightning for designing your training loops. You can set masks on the model via
import deepstruct.sparse
for layer in deepstruct.sparse.maskable_layers(mnist_model):
layer.mask[:, :] = Trueand if you disable some of these mask elements you have defined your first sparse model.
Specify structures by prior design, e.g. random social networks transformed into directed acyclic graphs:
import networkx as nx
import deepstruct.sparse
# Use networkx to generate a random graph based on the Watts-Strogatz model
random_graph = nx.newman_watts_strogatz_graph(100, 4, 0.5)
structure = deepstruct.graph.CachedLayeredGraph()
structure.add_edges_from(random_graph.edges)
structure.add_nodes_from(random_graph.nodes)
# Build a neural network classifier with 784 input and 10 output neurons and the given structure
model = deepstruct.sparse.MaskedDeepDAN(784, 10, structure)
model.apply_mask() # Apply the mask on the weights (hard, not undoable)
model.recompute_mask() # Use weight magnitude to recompute the mask from the network
pruned_structure = model.generate_structure() # Get the structure -- a networkx graph -- based on the current mask
new_model = deepstruct.sparse.MaskedDeepDAN(784, 10, pruned_structure)import torch
import deepstruct.recurrent
import numpy as np
# A sequence of size 15 with one-dimensional elements which could e.g. be labelled
# BatchSize x [(1,), (2,), (3,), (4,), (5,), (0,), (0,), (0,)] --> [ label1, label2, ..]
batch_size = 100
seq_size = 15
input_size = 1
model = deepstruct.recurrent.MaskedDeepRNN(
input_size,
hidden_layers=[100, 100, 1],
batch_first=True,
build_recurrent_layer=deepstruct.recurrent.MaskedLSTMLayer,
)
random_input = torch.tensor(
np.random.random((batch_size, seq_size, input_size)),
dtype=torch.float32,
requires_grad=False,
)
model.forward(random_input)Define a feed-forward neural network (with no skip-layer connections) and obtain its structure as a graph:
import torch
import deepstruct.sparse
from deepstruct.transform import GraphTransform
model = deepstruct.sparse.MaskedDeepFFN(784, 10, [100, 100])
# .. train the model or load a pre-trained
# Define a random input tensor which is required to analyse the structure
input_random = torch.randn((1, 20))
functor = GraphTransform(input_random)
result = functor.transform(model)
What's contained in deepstruct?
- ready-to-use models in pytorch for learning instances on common (supervised/unsupervised) datasets from which a structural analysis is possible
- model-to-graph transformations for studying models from a graph-theoretic perspective
Models:
- deepstruct.sparse.MaskableModule: pytorch modules that contain explicit masks to enforce (mostly zero-ordered) structure
- deepstruct.sparse.MaskedLinearLayer: pytorch module with a simple linear layer extended with masking capability. Suitable if you want to have linear-layers on which to enforce masks which could be obtained through pruning, regularization or other other search techniques.
- deepstruct.sparse.MaskedDeepFFN: feed-forward neural network with any width and depth and easy-to-use masks. Suitable for simple and canonical pruning research on zero-ordered structure
- deepstruct.sparse.MaskedDeepDAN: feed-forward neural network with skip-layer connections based on any directed acyclic network. Suitable for arbitrary structures on zero-order and on that level most flexible but also computationally expensive.
- deepstruct.sparse.DeepCellDAN: complex module based on a directed acyclic network and custom cells on third-order structures. Suitable for large-scale neural architecture search
- deepstruct.recurrent.MaskedDeepRNN: multi-layered network with recurrent layers which can be masked
- zero-th order: weight-level
- first order: kernel-level (filter, channel, blocks, cells)
- second order: layers
There is various evidence across empirical machine learning studies that the way artificial neural networks are structurally connected has a (minor?) influence on performance metrics such as the accuracy or probably even on more complex concepts such as adversarial robustness. What do we mean by "structure"? We define structure over graph theoretic properties given a computational graph with very restricted non-linearities. This includes all major neural network definitions and lets us study them from the perspective of their representation and their structure. In a probabilistic sense, one can interprete structure as a prior to the model and despite single-layered wide networks are universal function approximators we follow the hypothesis that given certain structural priors we can find models with better properties.
Before considering implementations, one should have a look on possible representations of Sparse Neural Networks. In case of feed-forward neural networks (FFNs) the network can be represented as a list of weight matrices. Each weight matrix represents the connections from one layer to the next. Having a network without some connections then means setting entries in those matrices to zero. Removing a particular neuron means setting all entries representing its incoming connections to zero.
However, sparsity can be employed on various levels of a general artificial neural network. Zero order sparsity would remove single weights (representing connections) from the network. First order sparsity removes groups of weights within one dimension of a matrix from the network. Sparsity can be employed on connection-, weight-, block-, channel-, cell-level and so on. Implementations respecting the areas for sparsification can have drastical differences. Thus there are various ways for implementing Sparse Neural Networks.
We provide some simple utilities for artificial function approximation.
Like polynomials, neural networks are universal function approximators on bounded intervals of compact spaces.
To test, you can easily define a function of any finite dimension, e.g.
import numpy as np
import torch.utils.data
from dataset import FuncDataset
from deepstruct.sparse import MaskedDeepFFN
# Our artificial landscape: f: R^2 -> R
# Have a look at https://github.com/innvariant/eddy for some visual examples
# You could easily define arbitrary functions from R^a to R^b
stier2020B1d = lambda x, y: 20 + x - 1.8 * (y - 5) + 3 * np.sin(x + 2 * y) * y + (x / 4) ** 4 + (y / 4) ** 4
ds_input_shape = (
2,) # specify the number of input dimensions (usually a one-sized tensor if no further structures are used)
# Explicitly define the target function for the dataset which returns a numpy array of our above function
# By above definition x is two-dimensional, so you have access to x[0] and x[1]
fn_target = lambda x: np.array([stier2020B1d(x[0], x[1])])
# Define a sampling strategy for the dataset, e.g. uniform sampling the space
fn_sampler = lambda: np.random.uniform(-2, 2, size=ds_input_shape)
# Define the dataset given the target function and your sampling strategy
# This simply wraps your function into a pytorch dataset and provides you with discrete observations
# Your model will later only know those observations to come up with an approximate solution of your target
ds_train = FuncDataset(fn_target, shape_input=ds_input_shape, size=500)
# Calculate the output shape given our target function .. usually simply a (1,)-dimensional output
ds_output_shape = fn_target(fn_sampler()).shape
# As usual in pytorch, you can simply wrap your dataset with a loading strategy ..
# This ensures e.g. that you do not iterate over your observations in the exact same manner
# In case you sample first 100 examples of a binary classification dataset with label 1 and then another
# 100 with label 2 it might impact your training .. so this ensures you have an e.g. random sampling strategy over the dataset
batch_size = 100
train_sampler = torch.utils.data.SubsetRandomSampler(np.arange(len(ds_train), dtype=np.int64))
train_loader = torch.utils.data.DataLoader(ds_train, batch_size=batch_size, sampler=train_sampler, num_workers=2)
# Define a model for which we can later extract its structure or impose sparsity constraints
model = MaskedDeepFFN(2, 1, [50, 20])
# Iterate over your training set
for feat, target in train_loader:
print(feat, target)
# feed it into a model to learn
prediction = model.forward(feat)
# compute a loss based on the expected target and the models prediction
# ..Have a look into our positioning paper on arxiv and related articles. We're glad if you cite our work
@article{stier2022deepstruct,
title={deepstruct -- linking deep learning and graph theory},
author={Stier, Julian and Granitzer, Michael},
journal={Software Impacts},
volume={11},
year={2022},
publisher={Elsevier}
}
@article{stier2019structural,
title={Structural analysis of sparse neural networks},
author={Stier, Julian and Granitzer, Michael},
journal={Procedia Computer Science},
volume={159},
pages={107--116},
year={2019},
publisher={Elsevier}
}
@phdthesis{stier2024structures,
author = "Julian Stier",
title = "Structures of Artificial Neural Networks - Empirical Investigations",
school = "University of Passau",
year = "2024"
}