Manu Srinath Halvagal

Manu Srinath Halvagal, Sebastian Lee, SueYeon Chung

Reinforcement Learning (RL) has long served as a model for goal-directed animal behavior in neuroscience. Modern deep RL has shown remarkable success across many domains, further strengthening this connection. The ability to learn abstract representations of high-dimensional state spaces underlies much of this success. However, theoretical understanding of these learned representations remains limited, hindering direct comparisons between models and animal learning. We address this gap by analyzing deep RL representations through the lens of MDP reduction theory. Investigating canonical RL algorithms in a navigation task, we find that even when performance is comparable, the value-based method (DQN) learns representations that are invariant to MDP homomorphism symmetries, while the policy-gradient method (PPO) learns representations invariant to action symmetries. These differences emerge consistently across domains, have downstream consequences for transfer learning, and appear in LLMs in a prompt-dependent manner. Our findings provide a principled approach to comparing learned representations across RL algorithms, with demonstrated practical implications and possible insights for neural coding in the brain.

Manu Srinath Halvagal, Axel Laborieux, Friedemann Zenke

Non-contrastive SSL methods like BYOL and SimSiam rely on asymmetric predictor networks to avoid representational collapse without negative samples. Yet, how predictor networks facilitate stable learning is not fully understood. While previous theoretical analyses assumed Euclidean losses, most practical implementations rely on cosine similarity. To gain further theoretical insight into non-contrastive SSL, we analytically study learning dynamics in conjunction with Euclidean and cosine similarity in the eigenspace of closed-form linear predictor networks. We show that both avoid collapse through implicit variance regularization albeit through different dynamical mechanisms. Moreover, we find that the eigenvalues act as effective learning rate multipliers and propose a family of isotropic loss functions (IsoLoss) that equalize convergence rates across eigenmodes. Empirically, IsoLoss speeds up the initial learning dynamics and increases robustness, thereby allowing us to dispense with the EMA target network typically used with non-contrastive methods. Our analysis sheds light on the variance regularization mechanisms of non-contrastive SSL and lays the theoretical grounds for crafting novel loss functions that shape the learning dynamics of the predictor's spectrum.