Algorithm for selecting edges in a neural network without weights and biases?

[quantumadmin]

In a neural network without weights and biases, you are essentially dealing with a graph structure where nodes represent neurons, and edges represent connections between neurons. The absence of weights and biases implies that the connections are binary (either present or absent) rather than having specific numerical values.

Here's a simple algorithm for selecting edges in a neural network without weights and biases:

Initialize Neurons: Create a set of neurons where each neuron corresponds to a node in the graph.

Connect Neurons: For each pair of neurons, decide whether to create a connection (edge) between them. This decision can be based on various criteria, such as proximity, similarity of function, or domain-specific knowledge.

Topology and Connectivity: Define the desired topology of your neural network. This could be a fully connected network, a sparsely connected network, or any other topology that suits your problem.

Connection Criteria: Determine the criteria for connecting neurons. Some possibilities include:

Proximity: Neurons that are physically close or adjacent in a layer might be connected to each other.

Functional Similarity: Neurons that have similar roles or functions in the network might be connected.

Task-Specific Knowledge: If you have domain knowledge about the problem you're solving, you can use that knowledge to guide the connectivity decisions.

Connection Strength: Since you don't have weights, you could consider using a binary strength indicator for connections. For example, you could have strong (1) and weak (0) connections based on the strength of the relationship between neurons.

Connectivity Algorithm: Based on your criteria, iterate through all possible pairs of neurons and decide whether to create a connection between them. You can use a threshold to determine whether a connection is strong enough to be established.

Construct Graph: Create the graph representation of the neural network using the selected connections as edges between neurons.

Network Analysis (Optional): Once you've constructed the graph, you can analyze its properties using graph theory techniques. This might provide insights into the network's structure and connectivity.

Task-Specific Evaluation: Evaluate the constructed neural network on your specific task to determine its performance. Depending on the task, you might need to refine the connectivity criteria and topology.

Remember that working with neural networks without weights and biases is quite different from traditional neural networks with learnable parameters. The lack of weights means that the network's behavior is more dependent on the connectivity patterns you define. The success of your network will largely depend on your ability to design meaningful connections that capture the relationships needed for your specific problem.