Clémentine Dominé

Clémentine C. J. Dominé, Nicolas Anguita, Alexandra M. Proca et al.

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.

Nicolas Anguita, Francesco Locatello, Andrew M. Saxe et al.

Pretraining and fine-tuning are central stages in modern machine learning systems. In practice, feature learning plays an important role across both stages: deep neural networks learn a broad range of useful features during pretraining and further refine those features during fine-tuning. However, an end-to-end theoretical understanding of how choices of initialization impact the ability to reuse and refine features during fine-tuning has remained elusive. Here we develop an analytical theory of the pretraining-fine-tuning pipeline in diagonal linear networks, deriving exact expressions for the generalization error as a function of initialization parameters and task statistics. We find that different initialization choices place the network into four distinct fine-tuning regimes that are distinguished by their ability to support feature learning and reuse, and therefore by the task statistics for which they are beneficial. In particular, a smaller initialization scale in earlier layers enables the network to both reuse and refine its features, leading to superior generalization on fine-tuning tasks that rely on a subset of pretraining features. We demonstrate empirically that the same initialization parameters impact generalization in nonlinear networks trained on CIFAR-100. Overall, our results demonstrate analytically how data and network initialization interact to shape fine-tuning generalization, highlighting an important role for the relative scale of initialization across different layers in enabling continued feature learning during fine-tuning.

Daniel Kunin, Allan Raventós, Clémentine Dominé et al.

While the impressive performance of modern neural networks is often attributed to their capacity to efficiently extract task-relevant features from data, the mechanisms underlying this rich feature learning regime remain elusive, with much of our theoretical understanding stemming from the opposing lazy regime. In this work, we derive exact solutions to a minimal model that transitions between lazy and rich learning, precisely elucidating how unbalanced layer-specific initialization variances and learning rates determine the degree of feature learning. Our analysis reveals that they conspire to influence the learning regime through a set of conserved quantities that constrain and modify the geometry of learning trajectories in parameter and function space. We extend our analysis to more complex linear models with multiple neurons, outputs, and layers and to shallow nonlinear networks with piecewise linear activation functions. In linear networks, rapid feature learning only occurs from balanced initializations, where all layers learn at similar speeds. While in nonlinear networks, unbalanced initializations that promote faster learning in earlier layers can accelerate rich learning. Through a series of experiments, we provide evidence that this unbalanced rich regime drives feature learning in deep finite-width networks, promotes interpretability of early layers in CNNs, reduces the sample complexity of learning hierarchical data, and decreases the time to grokking in modular arithmetic. Our theory motivates further exploration of unbalanced initializations to enhance efficient feature learning.

Marco Pegoraro, Clémentine Dominé, Emanuele Rodolà et al.

Antibody-antigen interactions play a crucial role in identifying and neutralizing harmful foreign molecules. In this paper, we investigate the optimal representation for predicting the binding sites in the two molecules and emphasize the importance of geometric information. Specifically, we compare different geometric deep learning methods applied to proteins' inner (I-GEP) and outer (O-GEP) structures. We incorporate 3D coordinates and spectral geometric descriptors as input features to fully leverage the geometric information. Our research suggests that surface-based models are more efficient than other methods, and our O-GEP experiments have achieved state-of-the-art results with significant performance improvements.