Unexpected Benefits of Self-Modeling in Neural Systems

TL;DR

The hypothesis that self-modeling is more than simply a network learning to predict itself is supported, which may help explain some of the benefits of self-models reported in recent machine learning literature, as well as the adaptive value of self-models to biological systems.

Abstract

Self-models have been a topic of great interest for decades in studies of human cognition and more recently in machine learning. Yet what benefits do self-models confer? Here we show that when artificial networks learn to predict their internal states as an auxiliary task, they change in a fundamental way. To better perform the self-model task, the network learns to make itself simpler, more regularized, more parameter-efficient, and therefore more amenable to being predictively modeled. To test the hypothesis of self-regularizing through self-modeling, we used a range of network architectures performing three classification tasks across two modalities. In all cases, adding self-modeling caused a significant reduction in network complexity. The reduction was observed in two ways. First, the distribution of weights was narrower when self-modeling was present. Second, a measure of network complexity, the real log canonical threshold (RLCT), was smaller when self-modeling was present. Not only were measures of complexity reduced, but the reduction became more pronounced as greater training weight was placed on the auxiliary task of self-modeling. These results strongly support the hypothesis that self-modeling is more than simply a network learning to predict itself. The learning has a restructuring effect, reducing complexity and increasing parameter efficiency. This self-regularization may help explain some of the benefits of self-models reported in recent machine learning literature, as well as the adaptive value of self-models to biological systems. In particular, these findings may shed light on the possible interaction between the ability to model oneself and the ability to be more easily modeled by others in a social or cooperative context.

Figures (4)

• Figure 1: A schematic depiction of the self-modeling auxiliary task applied to an MNIST classifier. The red arrow indicates the selected layer to form the target of self-modeling. Evaluation is done by comparing classification outputs to the correct digit and the self-modeling outputs to the true activations of the network during its forward pass.
• Figure 2: Results for networks performing the MNIST classification task. A. Y axis shows width of the distribution of weights in the final layer measured in standard deviation (SD). X axis shows training epoch ($1-50$). Data from baseline network with no self-modeling and from five networks that differ in self-modeling weights (AW $1-50$). Data are from the network architecture with a hidden layer size of $512$. Lines show mean of $10$ runs and $95\%$ CI. B. The width of the distribution of weights in the final layer (Y axis) as a function of the size of the hidden layer (X axis), for baseline network with no self-modeling and for networks with self-modeling at five weights. Data are from epoch $50$ of training. Points and error bars show means of $10$ runs and $95\%$ CI. C. The RLCT measure of network complexity (Y axis) as a function of the size of the hidden layer (X axis), for baseline network with no self-modeling and for networks with self- modeling at five weights. Data are from epoch $50$ of training. Lines show mean of $10$ runs and $95\%$ CI. D. Accuracy (% correct) on the MNIST classification task (Y axis) as a function of the size of the hidden layer (X axis) for baseline network with no self-modeling and for networks with self-modeling at five weights. Data are from epoch $50$ of training. Lines show mean of $10$ runs and $95\%$ CI.
• Figure 3: Results for networks performing the CIFAR-10 classification task. A. Y axis shows the width of the distribution of weights in the final layer measured in standard deviation (SD). X axis shows training epoch ($1-250$). Data from baseline network with no self-modeling and from networks with three different self-modeling weights (AW). Lines show mean of 10 runs and $95\%$ CI. B. The RLCT measure of network complexity for a baseline network and for three self- modeling networks that varied in AW. Data are from epoch $250$ of training. Bars show mean of $10$ runs and $95\%$ CI. C. Accuracy (% correct) on the CIFAR-10 classification task for a baseline network and for three self-modeling networks that varied in AW. Data are from epoch $250$ of training. Bars show mean of $10$ runs and $95\%$ CI.
• Figure 4: Results for networks performing the IMDB classification task. A. Y axis shows the width of the distribution of weights in the final layer measured in standard deviation (SD). X axis shows training epoch ($1-500$). Data from baseline network with no self-modeling and from networks with two different self-modeling weights (AW). Lines show mean of $10$ runs and $95\%$ CI. B. The RLCT measure for the baseline network, a self-modeling network with AW $= 100$, and a self-modeling network with AW = $500$. Data are from epoch $250$ of training. Bars show mean of $10$ runs and $95\%$ CI. C. Accuracy on the IMDB classification task for the baseline network, a self-modeling network with AW $= 100$, and a self-modeling network with AW $= 500$. Data are from epoch $500$ of training. Bars show mean of $10$ runs and $95\%$ CI.