Oğuz Kaan Yüksel

Oğuz Kaan Yüksel, Etienne Boursier, Nicolas Flammarion

Due to its empirical success in few-shot classification and reinforcement learning, meta-learning has recently received significant interest. Meta-learning methods leverage data from previous tasks to learn a new task in a sample-efficient manner. In particular, model-agnostic methods look for initialization points from which gradient descent quickly adapts to any new task. Although it has been empirically suggested that such methods perform well by learning shared representations during pretraining, there is limited theoretical evidence of such behavior. More importantly, it has not been shown that these methods still learn a shared structure, despite architectural misspecifications. In this direction, this work shows, in the limit of an infinite number of tasks, that first-order ANIL with a linear two-layer network architecture successfully learns linear shared representations. This result even holds with overparametrization; having a width larger than the dimension of the shared representations results in an asymptotically low-rank solution. The learned solution then yields a good adaptation performance on any new task after a single gradient step. Overall, this illustrates how well model-agnostic methods such as first-order ANIL can learn shared representations.

Oğuz Kaan Yüksel, Rodrigo Alvarez Lucendo, Nicolas Flammarion

This paper introduces a high-order Markov chain task to investigate how transformers learn to integrate information from multiple past positions with varying statistical significance. We demonstrate that transformers learn this task incrementally: each stage is defined by the acquisition of specific information through sparse attention patterns. Notably, we identify a shift in learning dynamics from competitive, where heads converge on the most statistically dominant pattern, to cooperative, where heads specialize in distinct patterns. We model these dynamics using simplified differential equations that characterize the trajectory and prove stage-wise convergence results. Our analysis reveals that transformers ascend a complexity ladder by passing through simpler, misspecified hypothesis classes before reaching the full model class. We further show that early stopping acts as an implicit regularizer, biasing the model toward these simpler classes. These results provide a theoretical foundation for the emergence of staged learning and complex behaviors in transformers, offering insights into generalization for natural language processing and algorithmic reasoning.

Oğuz Kaan Yüksel, Enis Simsar, Ezgi Gülperi Er et al.

Recent research has shown that it is possible to find interpretable directions in the latent spaces of pre-trained Generative Adversarial Networks (GANs). These directions enable controllable image generation and support a wide range of semantic editing operations, such as zoom or rotation. The discovery of such directions is often done in a supervised or semi-supervised manner and requires manual annotations which limits their use in practice. In comparison, unsupervised discovery allows finding subtle directions that are difficult to detect a priori. In this work, we propose a contrastive learning-based approach to discover semantic directions in the latent space of pre-trained GANs in a self-supervised manner. Our approach finds semantically meaningful dimensions comparable with state-of-the-art methods.