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Learnability and Competition in High-Dimensional Multi-Component ICA
Eser Ilke Genc, Samet Demir, Zafer Dogan
Independent Component Analysis (ICA) is a foundational tool for unsupervised representation learning, yet its high-dimensional theory remains largely limited to single-component re…
Learning Beyond the Gaussian Data: Learning Dynamics of Neural Networks on an Expressive and Cumulant-Controllable Data Model
Onat Ure, Samet Demir, Zafer Dogan
We study the effect of high-order statistics of data on the learning dynamics of neural networks (NNs) by using a moment-controllable non-Gaussian data model. Considering the expre…
Implicitly Normalized Online PCA: A Regularized Algorithm with Exact High-Dimensional Dynamics
Samet Demir, Zafer Dogan
Many online learning algorithms, including classical online PCA methods, enforce explicit normalization steps that discard the evolving norm of the parameter vector. We show that t…
Optimal Attention Temperature Improves the Robustness of In-Context Learning under Distribution Shift in High Dimensions
Samet Demir, Zafer Dogan
Pretrained Transformers can perform in-context learning (ICL) from a few demonstrations, but this ability can fail sharply when the test distribution differs from pretraining, a co…
How Data Mixing Shapes In-Context Learning: Asymptotic Equivalence for Transformers with MLPs
Samet Demir, Zafer Dogan
Pretrained Transformers demonstrate remarkable in-context learning (ICL) capabilities, enabling them to adapt to new tasks from demonstrations without parameter updates. However, t…
Asymptotic Study of In-context Learning with Random Transformers through Equivalent Models
Samet Demir, Zafer Dogan
We study the in-context learning (ICL) capabilities of pretrained Transformers in the setting of nonlinear regression. Specifically, we focus on a random Transformer with a nonline…