Konstantin Nikolaou

Samuel Tovey, Christoph Lohrmann, Tobias Merkt et al.

This work introduces SwarmRL, a Python package designed to study intelligent active particles. SwarmRL provides an easy-to-use interface for developing models to control microscopic colloids using classical control and deep reinforcement learning approaches. These models may be deployed in simulations or real-world environments under a common framework. We explain the structure of the software and its key features and demonstrate how it can be used to accelerate research. With SwarmRL, we aim to streamline research into micro-robotic control while bridging the gap between experimental and simulation-driven sciences. SwarmRL is available open-source on GitHub at https://github.com/SwarmRL/SwarmRL.

Konstantin Nikolaou, Sven Krippendorf, Samuel Tovey et al.

Scaling laws offer valuable insights into the relationship between neural network performance and computational cost, yet their underlying mechanisms remain poorly understood. In this work, we empirically analyze how neural networks behave under data and model scaling through the lens of the neural tangent kernel (NTK). This analysis establishes a link between performance scaling and the internal dynamics of neural networks. Our findings of standard vision tasks show that similar performance scaling exponents can occur even though the internal model dynamics show opposite behavior. This demonstrates that performance scaling alone is insufficient for understanding the underlying mechanisms of neural networks. We also address a previously unresolved issue in neural scaling: how convergence to the infinite-width limit affects scaling behavior in finite-width models. To this end, we investigate how feature learning is lost as the model width increases and quantify the transition between kernel-driven and feature-driven scaling regimes. We identify the maximum model width that supports feature learning, which, in our setups, we find to be more than ten times smaller than typical large language model widths.

Samuel Tovey, Sven Krippendorf, Konstantin Nikolaou et al.

A theory of neural networks (NNs) built upon collective variables would provide scientists with the tools to better understand the learning process at every stage. In this work, we introduce two such variables, the entropy and the trace of the empirical neural tangent kernel (NTK) built on the training data passed to the model. We empirically analyze the NN performance in the context of these variables and find that there exists correlation between the starting entropy, the trace of the NTK, and the generalization of the model computed after training is complete. This framework is then applied to the problem of optimal data selection for the training of NNs. To this end, random network distillation (RND) is used as a means of selecting training data which is then compared with random selection of data. It is shown that not only does RND select data-sets capable of outperforming random selection, but that the collective variables associated with the RND data-sets are larger than those of the randomly selected sets. The results of this investigation provide a stable ground from which the selection of data for NN training can be driven by this phenomenological framework.