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2:00pm to 3:00pm - 340P Rowland Hall - Combinatorics and Probability Shihao Zhang - (UCSD) Provable Post Training Quantization and Its Error Compensation for Large Language Models Post-training quantization (PTQ) has become a crucial tool for reducing the memory and compute costs of modern deep neural networks, including large language models (LLMs). Among PTQ algorithms, GPTQ has emerged as a leading method due to its computational efficiency and strong empirical performance. Despite its widespread adoption, GPTQ lacks rigorous quantitative theoretical guarantees. In this talk, I will discuss the first quantitative error bounds for both deterministic and stochastic variants of GPTQ. We also proposed a novel LoRA adaptation method for PTQ, which can achieve near-optimal guarantees on layer-wise reconstruction error. |
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1:00pm to 2:00pm - RH 340N - Dynamical Systems Dr. Alexandro Luna - (UCI) A Survery on Recent Methods in Dynamical Rigidity Abstract: We discuss the so-called “matching functions” technique, recently formulated by Gogolev and Rodriguez-Hertz to prove rigidity results for expanding maps, codimension one Anosov diffeomorphisms, and codimension Anosov flows. We compare this to the classical method of “matching measures” first introduced by de la Llave, to prove rigidity results for surface Anosov diffeomorphisms with matching periodic data. |
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3:00pm to 3:50pm - RH 340P - Logic Set Theory Nam Trang - (University of North Texas, Denton) Towards the consistency of the ABCD hypothesis (cont.) The ABCD hypothesis, formulated by Chan, Jackson and Trang, is the conjunction of $ZF$ and the statement: (*) given four infinite cardinals $A, B, C, D$, then $|A^B| \leq |C^D|$ if and only if $A\leq C$ and $B\leq D$. Recently W. Chan shows that $AD^+$ implies (*) holds below $\Theta$. We sketch a scenario to improve this result and show the full ABCD hypothesis is consistent. This is not a complete proof as it relies on conjectures about the structure theory of Nairian models but presents the most plausible path towards the consistency proof. |
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3:00pm to 3:50pm - RH 306 - Analysis Ming Xiao - (UCSD) ObstrucObstruction flatness and Bergman logarithmic flatness of circle bundles Let \(\Omega \subset \mathbb{C}^n\) be a smoothly bounded strictly pseudoconvex domain. The boundary \(\partial\Omega\) is said to be obstruction flat if the log singularity (the obstruction function) in the logarithmic potential of the complete K\"ahler--Einstein metric on \(\Omega\) vanishes. It is called Bergman logarithmically flat if the logarithmic singularity in the Fefferman expansion of the Bergman kernel vanishes. Both notions of flatness depend only on the local CR geometry of the boundary and can be defined for any strictly pseudoconvex real hypersurface.
In this talk, we consider real hypersurfaces arising as unit circle bundles of negative Hermitian line bundles over a complex manifold \(M\). We study the relationship between obstruction flatness and Bergman logarithmic flatness of these circle bundles and the K\"ahler geometry of the induced metric on \(M\). The talk is based on joint work with Peter Ebenfelt and Hang Xu. |
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11:00am to 12:00pm - RH 306 - Nonlinear PDEs Arghya Rakshit - (U. Toronto) Solutions to the Monge-Ampère equation with singular structures We construct examples of solutions to Monge-Ampère equations with point masses whose singular sets exhibit polyhedral structures. We also construct solutions to Monge-Ampère equations whose Monge-Ampère measures contain singular components supported on lower-dimensional sets, and study the regularity of such solutions away from these singular sets. To motivate these constructions, we present examples arising from optimal transport where the potentials of the optimal transport maps satisfy Monge-Ampère equations similar to the ones we study. In particular, we focus on planar optimal transport problems where the target domain is nonconvex. |