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Feb. 15, 2019
Jul. 1, 2018

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Hypergraph is machine learning training scheduler and hyper-parameters optimizer. It has been developed to provide a high level of abstraction when developing machine learning and deep neural networks. In this framework, everything rotates around graphs where nodes are atomic operations of a certain process that has to be optimized. The connections between nodes play the crucial part, these can be optimized through meta-heurisitic optimisation algorithms (e.g. genetic algorithms). The result is a network of nodes composed by "moving parts" (called tweaks) which can be tuned by optimization algorithms. The global optimization algorithms currently available are Genetic and Tree-structured Parzen Estimator. The Tree-structured Parzen Estimator (in short TPE) implementation is inherited from the outstanding hyper-parameter optimization library Hyperopt.

The purpose of the project is purely experimental and we are willing to accept any contribution and comment.

Getting Started with Hypergraph


To install Hypergraph the following command can be used. Hypergraph is compatible with Windows and Linux operating systems. It supports Python 3.6 or superior.

pip install git+

Hypergraph and Keras in action

The core data structure of Hypergraph is a directed graph. Each graph consists of a number of nodes. The information in form of python objects, flows from the inputs, gets transformed and continues toward the single output that each node has. Methods for creating nodes and adding them to a graph are demonstrated in the next sections. We start with a relatively simple example where we use our framework to optimize the structure and some parameters of a neural network implemented through Keras. Despite Keras has been used in all examples related to neural networks, Hypergraph is completely agnostic to the various deep learning frameworks.

Creating Nodes

Nodes are instances of the class hg.Node. However, there a number of shortcuts and tricks to define nodes using standard python functions. Let's, for instance, declare a Keras model where some parameters and connections between the layers are dynamic. Here is a code snippet showing the declaration of the first node (note that node is meant in the hypegraph context, layer instead is used to distinguish Keras' parts):

import hypergraph as hg
from keras.layers import Dense, Dropout, GlobalAveragePooling2D, GlobalMaxPooling2D

# Declare the first tweak as a uniform choice between two types of global pooling
@hg.decl_tweaks(global_pool_op=hg.UniformChoice((GlobalAveragePooling2D, GlobalMaxPooling2D)))
# the second tweak is the dropout rate which will be a uniform value between 0 and 0.5
@hg.decl_tweaks(dropout_rate=hg.Uniform(0, 0.5))
def classifier_terminal_part(input_layer, class_count, global_pool_op, dropout_rate):
    Create the terminal part of the model. This section is composed by a global pooling layer followed by a dropout
    and finally a dense layer. The type of global pooling is chosen automatically by the hyper-parameters optimization
    algorithm, the same also applies to the dropout rate.
    :param input_layer: The input layer which is the output of the node connected right on the top of this
    :param class_count:
    :param global_pool_op: The type of global pooling, this parameter is handled directly by hypergraph
    :param dropout_rate: The dropout rate, this parameter is handled directly by hypergraph
    :return: The output layer of this section of network
    net = global_pool_op()(input_layer)
    net = Dropout(rate=dropout_rate)(net)
    return Dense(class_count, activation='softmax')(net)

First of all, to declare a functional node we define a function decorated with @hg.function(), this is just necessary to install Hypergraph's fine machinery around the function. The tweaks related to the current function are then declared using the decorator @hg.decl_tweaks(). Here the variable associated to the tweak is passed alongside its prior distribution. The framework will then call the function with the parameters sampled according to the optimization strategy. The input parameters that are not declared as tweaks are instead retrieved by Hypergraph from the inputs to the node.

graph and tweaks example

Figure 1 The node created by classifier_terminal_part with its internal tweaks and their interaction with the various parts.

Similarly we define all the other nodes, for a complete source code please follow this link

Putting all together, the graph

Finally, it is time to put together the various nodes. The decorator @hg.aggregator() is meant for this purpose. Again we define a function and we invoke the nodes functions as regular python functions. The magic that is happening here is that the invocations are intercepted by the framework and the returned values are not the actual values but rather expressions. This allows hypergraph to understand the structure of the statements and at the moment of the real execution, substitute the tweaks and invoke the functions along the active path.

import hypergraph as hg

def model_graph():
    input_layer = input_layer_()
    top_section = features_extraction_net(input_layer=input_layer)
    bottom_section = classifier_terminal_part(input_layer=top_section)
    model = compile_model(input_layer=input_layer, output_layer=bottom_section)
    return model
graph1 = model_graph()  # create a graph
hg.tweaks.dump_tweaks(graph1)   # dump the tweaks config for inspection

The key difference between functions annotated with @hg.function() versus @hg.aggregator() is that in the first case the parameters and invocations within the function body handle the real objects and values that are part of the information flow among nodes. In the latter instead, the invocations return expressions involving the type hg.Node.

Here is the output of the dump_tweaks from the last code snippet. It is interesting to notice how the tweaks are collected and uniquely identified by the framework.

Tweak id Config
model_graph.classifier_terminal_part.dropout_rate 'type': 'Uniform', 'space': {'type': 'continuous', 'boundaries': (0, 0.25)}
model_graph.classifier_terminal_part.global_pool_op 'type': 'UniformChoice', 'space': {'type': 'categorical', 'size': 2} 'type': 'LogUniform', 'space': {'type': 'continuous', 'boundaries': (1e-05, 0.1)}
model_graph.compile_model.optimizer 'type': 'UniformChoice', 'space': {'type': 'categorical', 'size': 2}
Invoke the optimization algorithm

Once the graph structure is ready we instantiate the graph and run the optimization algorithm on its tweaks. At this point we need a measure of performance to be applied to each 'tweaked' graph. This measure is provided by the user-defined function objective. The optimizer goal is to minimize the objective. The objective function also takes care of the execution of the model. The code snippet below shows the simple steps necessary to define an objective and run an evolutionary algorithm. In this case, we are employing a genetic algorithm, this is just for demonstration purposes, indeed the framework can be easily extended and other optimization methods will be included.

graph1 = model_graph()  # create a graph

def objective(individual):
    The objective function that is minimized by the optimizer.
    :param individual: A set of tweaks for the graph.
    :return: The score achieved by the tweaks provided as argument.
    print(f'Trial, tweaks={individual}')
    model =, tweaks=individual)
    history =, y=y_train, epochs=4, validation_data=(x_test, y_test))
    # The number of epochs here could be handled by resources allocation algorithms such as Hyperband.
    # This feature will be soon available on hypergraph.
    # We take the opposite of the maximum validation accuracy achieved as
    # measure to be minimized.
    return -np.max(history.history['val_acc'])

history = History()     # the history callback records the evolution of the algorithm
best = hg.optimize(algo='genetic', graph=graph1, objective=objective, callbacks=[ConsoleLog(), history],
                   generations=20, mutation_prob=(0.1, 0.8), lambda_=4)     # these are algo specific parameters
print("best:" + str(best))     # print a dictionary containing the tweaks that determined the best performance

The optimizer is invoked through the call hg.optimize. This is a unique function that can be used to invoke any of the optimizers provided by the library. When the optimization algorithm reaches its stop condition it returns the best set of tweaks. Given a set of tweaks we can execute the graph with the configuration applied through the call, tweaks=best).


Figure 2 The evolution of the fitness over 20 generations.

As shown in this example it is also possible to use Hypergraph to optimise training parameters (such as queue size, batch size and the number of workers) to optimise the training time of a Keras model.

Beyond hyper-parameters optimization

Driven by the insatiable desire of exploring new scenarios we extended our framework with Cartesian Genetic Programming algorithms (CGP). In the domain of reinforcement learning, Cartesian Genetic Programming has recently been shown to be a competitive, yet simple, alternative approach for learning to play Atari games (Wilson et al. 2018). Hypergraph is very well suited for evolving such solutions which have motivated its implementation. Additionally, a gym adapter is provided so that OpenAI's gym environments can be easily assessed. A full example of a Hypergraph implementation of CGP for the CartPole(v1) gym environment is provided here. The following animation is an example of the results from running this example.


Figure 3 A perfect solution of the OpenAI CartPole environment obtained through Hypergraph CGP.

It should be noted that both the CGP and optimisation routines are general and can be easily tailored for a given problem by specifying a suitable set of operations and an appropriate objective function.


Figure 4 The evolution of the CGP's score with two different optimizers: genetic and TPE. Notably, in this case, genetic algorithms seem to reach the target score faster than TPE.