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 rates with respect to dimensionality, and (ii) misspecified context lengths in strictly stable systems, where shorter contexts offer statistical advantages.

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

Recent research has shown great potential for finding interpretable directions in the latent spaces of pre-trained Generative Adversarial Networks (GANs). These directions provide controllable generation and support a wide range of semantic editing operations such as zoom or rotation. The discovery of such directions is often performed in a supervised or semi-supervised fashion and requires manual annotations, limiting their applications in practice. In comparison, unsupervised discovery enables finding subtle directions a priori hard to recognize. In this work, we propose a contrastive-learning-based approach for discovering semantic directions in the latent space of pretrained GANs in a self-supervised manner. Our approach finds semantically meaningful dimensions compatible with state-of-the-art methods.