Modular Growth of Hierarchical Networks: Efficient, General, and Robust Curriculum Learning

Structural modularity is a pervasive feature of biological neural networks, which have been linked to several functional and computational advantages. Yet, the use of modular architectures in artificial neural networks has been relatively limited despite early successes. Here, we explore the performance and functional dynamics of a modular network trained on a memory task via an iterative growth curriculum. We find that for a given classical, non-modular recurrent neural network (RNN), an equivalent modular network will perform better across multiple metrics, including training time, generalizability, and robustness to some perturbations. We further examine how different aspects of a modular network's connectivity contribute to its computational capability. We then demonstrate that the inductive bias introduced by the modular topology is strong enough for the network to perform well even when the connectivity within modules is fixed and only the connections between modules are trained. Our findings suggest that gradual modular growth of RNNs could provide advantages for learning increasingly complex tasks on evolutionary timescales, and help build more scalable and compressible artificial networks.

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.

Predictive, scalable and interpretable knowledge tracing on structured domains

Intelligent tutoring systems optimize the selection and timing of learning materials to enhance understanding and long-term retention. This requires estimates of both the learner's progress (''knowledge tracing''; KT), and the prerequisite structure of the learning domain (''knowledge mapping''). While recent deep learning models achieve high KT accuracy, they do so at the expense of the interpretability of psychologically-inspired models. In this work, we present a solution to this trade-off. PSI-KT is a hierarchical generative approach that explicitly models how both individual cognitive traits and the prerequisite structure of knowledge influence learning dynamics, thus achieving interpretability by design. Moreover, by using scalable Bayesian inference, PSI-KT targets the real-world need for efficient personalization even with a growing body of learners and learning histories. Evaluated on three datasets from online learning platforms, PSI-KT achieves superior multi-step predictive accuracy and scalable inference in continual-learning settings, all while providing interpretable representations of learner-specific traits and the prerequisite structure of knowledge that causally supports learning. In sum, predictive, scalable and interpretable knowledge tracing with solid knowledge mapping lays a key foundation for effective personalized learning to make education accessible to a broad, global audience.