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Alexandra Maria Proca

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3 papers

1 author row

ICLR Conference 2025 Conference Paper

From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks

Clémentine Carla Juliette Dominé
Nicolas Anguita
Alexandra Maria Proca
Lukas Braun
Daniel Kunin
Pedro A. M. Mediano
Andrew M. Saxe

Biological and artificial neural networks develop internal representations that enable them to perform complex tasks. In artificial networks, the effectiveness of these models relies on their ability to build task specific representation, a process influenced by interactions among datasets, architectures, initialization strategies, and optimization algorithms. Prior studies highlight that different initializations can place networks in either a lazy regime, where representations remain static, or a rich/feature learning regime, where representations evolve dynamically. Here, we examine how initialization influences learning dynamics in deep linear neural networks, deriving exact solutions for lambda-balanced initializations-defined by the relative scale of weights across layers. These solutions capture the evolution of representations and the Neural Tangent Kernel across the spectrum from the rich to the lazy regimes. Our findings deepen the theoretical understanding of the impact of weight initialization on learning regimes, with implications for continual learning, reversal learning, and transfer learning, relevant to both neuroscience and practical applications.

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ICML Conference 2025 Conference Paper

Learning dynamics in linear recurrent neural networks

Alexandra Maria Proca
Clémentine Carla Juliette Dominé
Murray Shanahan
Pedro A. M. Mediano

Recurrent neural networks (RNNs) are powerful models used widely in both machine learning and neuroscience to learn tasks with temporal dependencies and to model neural dynamics. However, despite significant advancements in the theory of RNNs, there is still limited understanding of their learning process and the impact of the temporal structure of data. Here, we bridge this gap by analyzing the learning dynamics of linear RNNs (LRNNs) analytically, enabled by a novel framework that accounts for task dynamics. Our mathematical result reveals four key properties of LRNNs: (1) Learning of data singular values is ordered by both scale and temporal precedence, such that singular values that are larger and occur later are learned faster. (2) Task dynamics impact solution stability and extrapolation ability. (3) The loss function contains an effective regularization term that incentivizes small weights and mediates a tradeoff between recurrent and feedforward computation. (4) Recurrence encourages feature learning, as shown through a novel derivation of the neural tangent kernel for finite-width LRNNs. As a final proof-of-concept, we apply our theoretical framework to explain the behavior of LRNNs performing sensory integration tasks. Our work provides a first analytical treatment of the relationship between the temporal dependencies in tasks and learning dynamics in LRNNs, building a foundation for understanding how complex dynamic behavior emerges in cognitive models.

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ICLR Conference 2024 Conference Paper

Discovering modular solutions that generalize compositionally

Simon Schug
Seijin Kobayashi
Yassir Akram
Maciej Wolczyk
Alexandra Maria Proca
Johannes von Oswald
Razvan Pascanu
João Sacramento

Many complex tasks can be decomposed into simpler, independent parts. Discovering such underlying compositional structure has the potential to enable compositional generalization. Despite progress, our most powerful systems struggle to compose flexibly. It therefore seems natural to make models more modular to help capture the compositional nature of many tasks. However, it is unclear under which circumstances modular systems can discover hidden compositional structure. To shed light on this question, we study a teacher-student setting with a modular teacher where we have full control over the composition of ground truth modules. This allows us to relate the problem of compositional generalization to that of identification of the underlying modules. In particular we study modularity in hypernetworks representing a general class of multiplicative interactions. We show theoretically that identification up to linear transformation purely from demonstrations is possible without having to learn an exponential number of module combinations. We further demonstrate empirically that under the theoretically identified conditions, meta-learning from finite data can discover modular policies that generalize compositionally in a number of complex environments.

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