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- Holden Lee, Rong Ge, Andrej Risteski, Tengyu Ma, Sanjeev Arora
- COLT
- 2017

Deep neural nets have caused a revolution in many classification tasks. A related ongoing revolution—also theoretically not understood—concerns their ability to serve as generative models for complicated types of data such as images and texts. These models are trained using ideas like variational autoencoders and Generative Adversarial Networks. We take a… (More)

- Holden Lee
- Archive of Formal Proofs
- 2014

- Rong Ge, Holden Lee, Andrej Risteski
- ArXiv
- 2017

In the last several years, provable guarantees for iterative optimization algorithms like gradient descent and expectation-maximization in non-convex settings have become a topic of intense research in the machine learning community. These works have shed light on the practical success of these algorithms in many unsupervised learning settings such as… (More)

- Shishir Agrawal, Eva Belmont, +12 authors William Wright
- 2011

- Sanjeev Arora, Holden Lee
- 2015

M = ∑ λiuiu T i . A 3-D tensor M is a n × n × n array. Extending linear algebra to tensors is nontrivial. Many problems regarding tensors are NP-hard, like rank (which is not straightforward to define). Today we are interested in tensors that we are guaranteed have a representation like M = ∑ λiu ⊗3 i , where the ui are orthogonal. We don’t know the ui’s… (More)

- Eva Belmont, Holden Lee, ALEXANDRA MUSAT, Sarah Trebat-Leder
- 2012

Folsom, Kent, and Ono used the theory of modular forms modulo ` to establish remarkable “self-similarity” properties of the partition function and give an overarching explanation of many partition congruences. We generalize their work to analyze powers pr of the partition function as well as Andrews’s spt-function. By showing that certain generating… (More)

- Holden Lee
- ArXiv
- 2015

An open problem in complexity theory is to find the minimal degree of a polynomial representing the n-bit OR function modulo composite m. This problem is related to understanding the power of circuits with MODm gates where m is composite. The OR function is of particular interest because it is the simplest function not amenable to bounds from communication… (More)

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