arXiv subjects

Oğuz Kaan Yüksel

Publications and source records attributed to Oğuz Kaan Yüksel.

4 recordsLinked to original sources

arXiv2026

Incremental Learning of Sparse Attention Patterns in Transformers

This paper studies simple transformers trained on a high-order Markov chain, where the model must incorporate information from multiple past positions, each with different statistical importance. We show that transformers learn the task incrementally, with each stage corresponding to learning how to copy information from a subset of positions via a sparse attention pattern. Notably, the learning dynamics transition from a competitive phase, where all heads focus on the statistically most important positions, to a cooperative phase, where different heads specialize in different patterns. We model these dynamics with simplified differential equations and prove stage-wise convergence of the resulting system. Functionally, these stages correspond to a sequence of increasingly expressive misspecified models, with the full model class reached only at the end. Overall, we give a theoretical account of how structured attention patterns and head specialization emerge in stages without an explicit curriculum, with implications for generalization in sequential tasks.

cs.LG↗

arXiv2025

Long-Context Linear System Identification

This paper addresses the problem of long-context linear system identification, where the state $x_t$ of a dynamical system at time $t$ depends linearly on previous states $x_s$ over a fixed context window of length $p$. We establish a sample complexity bound that matches the i.i.d. parametric rate up to logarithmic factors for a broad class of systems, extending previous works that considered only first-order dependencies. Our findings reveal a learning-without-mixing phenomenon, indicating that learning long-context linear autoregressive models is not hindered by slow mixing properties potentially associated with extended context windows. Additionally, we extend these results to (i) shared low-rank representations, where rank-regularized estimators improve the dependence of the rates on the dimensionality, and (ii) misspecified context lengths in strictly stable systems, where shorter contexts offer statistical advantages.

stat.ML↗

arXiv2024

First-order ANIL provably learns representations despite overparametrization

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.

cs.LG↗

arXiv2021

LatentCLR: A Contrastive Learning Approach for Unsupervised Discovery of Interpretable Directions

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.

cs.LG↗