Building upon the concept of self-replicating neural networks (Gabor et al., 2019), this research explores the integration of auxiliary functional goals alongside the primary objective of self-replication. The aim is to create networks that can not only reproduce their own weights but also perform useful computations or interact meaningfully with an environment simultaneously.

The study introduces a methodology for dual-task training, utilizing distinct input/output vectors to manage both the replication process and the execution of a secondary task. A key finding is that the presence of an auxiliary task does not necessarily hinder self-replication; instead, it can sometimes complement and even stabilize the replication dynamics.

Further investigations were conducted within the framework of an "artificial chemistry" environment, where populations of these dual-task networks interact:
- The impact of varying action parameters (related to the secondary task) on the collective learning or emergent behavior of the network population was examined.
- A concept of a specially designed "guiding particle" network was introduced. This network influences its peers, demonstrating a mechanism for potentially steering the population's evolution towards desired goal-oriented behaviors.
This work provides insights into how functional complexity can be integrated with self-replication in computational systems, offering potential pathways for developing more sophisticated artificial life models and exploring guided evolution within network populations. (Gabor et al., 2021)