Laura Balzano July 24, 2018

Streaming PCA Review Article

The Proceedings of IEEE posted our review article today on Streaming PCA and Subspace Tracking with Missing Data. It was a great experience to work with Yuejie Chi and Yue Lu on this survey. You can also find a less pretty version on the arxiv.

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Analyzing Out-of-Distribution In-Context Learning

May 29, 2025 By Laura Balzano

We posted a new paper on arxiv presenting analysis on the capabilities of attention for in-context learning. There are many perspectives out there on whether it’s possible to do in-context learning out-of-distribution: some papers show it’s possible, and others do not, mostly with empirical evidence. We provide some theoretical results in a specific setting, using linear attention to solve linear regression. We show a negative result that when the model is trained on a single subspace, the risk on out-of-distribution subspaces is lower bounded and cannot be driven to zero. Then we show that when the model is instead trained on a union-of-subspaces, the risk can be driven to zero on any test point in the span of the trained subspaces – even ones that have zero probability in the training set. We are hopeful that this perspective can help researchers improve the training process to promote out-of-distribution generalization.

Soo Min Kwon, Alec S. Xu, Can Yaras, Laura Balzano, Qing Qu. “Out-of-Distribution Generalization of In-Context Learning: A Low-Dimensional Subspace Perspective.” https://arxiv.org/abs/2505.14808.

SDP Relaxation paper in SIMAX

April 19, 2025 By Laura Balzano

I’m excited that our paper “A Semidefinite Relaxation for Sums of Heterogeneous Quadratic Forms on the Stiefel Manifold” has been published in the SIAM Journal on Matrix Analysis and Applications. https://doi.org/10.1137/23M1545136. We were inspired to work on this problem after it popped up inside the heteroscedastic PCA problem. It’s a fascinating, simple, general problem with connections to PCA, joint diagonalization, and low-rank semidefinite programs. Applying the standard Schur relaxation to this problem gives a trivial (and incorrect) solution, but one minor change makes the relaxation powerful and even tight in many instances. You can find the code for experiments here.

Sarah Goddard Power Award

February 11, 2025 By Laura Balzano

I am honored to have received the Sarah Goddard Power Award, an award given to those who contribute to the advancement of women in scholarship and academic leadership. Right now this work is critically important in my field, as technology in machine learning, artificial intelligence, and computing changes our world on a daily basis. Technology is often thought of as an objective pursuit, where the goals are clear and well-defined, and only those who are “math geniuses” can make a contribution. This couldn’t be further from the truth – we are constantly defining the goals and values of our technology, and diverse voices are key to creating technology that lifts us up as a whole society.

Streaming PCA Review Article

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Analyzing Out-of-Distribution In-Context Learning

SDP Relaxation paper in SIMAX

Sarah Goddard Power Award

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