Harmonizing Program Induction with Rate-Distortion Theory

Many aspects of human learning have been proposed as a process of constructing mental programs: from acquiring symbolic number representations to intuitive theories about the world. In parallel, there is a long-tradition of using information processing to model human cognition through Rate Distortion Theory (RDT). Yet, it is still poorly understood how to apply RDT when mental representations take the form of programs. In this work, we adapt RDT by proposing a three way trade-off among rate (description length), distortion (error), and computational costs (search budget). We use simulations on a melody task to study the implications of this trade-off, and show that constructing a shared program library across tasks provides global benefits. However, this comes at the cost of sensitivity to curricula, which is also characteristic of human learners. Finally, we use methods from partial information decomposition to generate training curricula that induce more effective libraries and better generalization.

Modelling continual learning in humans with Hebbian context gating and exponentially decaying task signals

Humans can learn several tasks in succession with minimal mutual interference but perform more poorly when trained on multiple tasks at once. The opposite is true for standard deep neural networks. Here, we propose novel computational constraints for artificial neural networks, inspired by earlier work on gating in the primate prefrontal cortex, that capture the cost of interleaved training and allow the network to learn two tasks in sequence without forgetting. We augment standard stochastic gradient descent with two algorithmic motifs, so-called "sluggish" task units and a Hebbian training step that strengthens connections between task units and hidden units that encode task-relevant information. We found that the "sluggish" units introduce a switch-cost during training, which biases representations under interleaved training towards a joint representation that ignores the contextual cue, while the Hebbian step promotes the formation of a gating scheme from task units to the hidden layer that produces orthogonal representations which are perfectly guarded against interference. Validating the model on previously published human behavioural data revealed that it matches performance of participants who had been trained on blocked or interleaved curricula, and that these performance differences were driven by misestimation of the true category boundary.

Episodic memory for continual model learning

Both the human brain and artificial learning agents operating in real-world or comparably complex environments are faced with the challenge of online model selection. In principle this challenge can be overcome: hierarchical Bayesian inference provides a principled method for model selection and it converges on the same posterior for both off-line (i.e. batch) and online learning. However, maintaining a parameter posterior for each model in parallel has in general an even higher memory cost than storing the entire data set and is consequently clearly unfeasible. Alternatively, maintaining only a limited set of models in memory could limit memory requirements. However, sufficient statistics for one model will usually be insufficient for fitting a different kind of model, meaning that the agent loses information with each model change. We propose that episodic memory can circumvent the challenge of limited memory-capacity online model selection by retaining a selected subset of data points. We design a method to compute the quantities necessary for model selection even when the data is discarded and only statistics of one (or few) learnt models are available. We demonstrate on a simple model that a limited-sized episodic memory buffer, when the content is optimised to retain data with statistics not matching the current representation, can resolve the fundamental challenge of online model selection.