arXiv subjects

Shiyu Shen

Publications and source records attributed to Shiyu Shen.

23 records · Page 2Linked to original sources

arXiv2023

Bayesian Domain Invariant Learning via Posterior Generalization of Parameter Distributions

Domain invariant learning aims to learn models that extract invariant features over various training domains, resulting in better generalization to unseen target domains. Recently, Bayesian Neural Networks have achieved promising results in domain invariant learning, but most works concentrate on aligning features distributions rather than parameter distributions. Inspired by the principle of Bayesian Neural Network, we attempt to directly learn the domain invariant posterior distribution of network parameters. We first propose a theorem to show that the invariant posterior of parameters can be implicitly inferred by aggregating posteriors on different training domains. Our assumption is more relaxed and allows us to extract more domain invariant information. We also propose a simple yet effective method, named PosTerior Generalization (PTG), that can be used to estimate the invariant parameter distribution. PTG fully exploits variational inference to approximate parameter distributions, including the invariant posterior and the posteriors on training domains. Furthermore, we develop a lite version of PTG for widespread applications. PTG shows competitive performance on various domain generalization benchmarks on DomainBed. Additionally, PTG can use any existing domain generalization methods as its prior, and combined with previous state-of-the-art method the performance can be further improved. Code will be made public.

cs.LG↗

arXiv2023

High-Throughput GPU Implementation of Dilithium Post-Quantum Digital Signature

Digital signatures are fundamental building blocks in various protocols to provide integrity and authenticity. The development of the quantum computing has raised concerns about the security guarantees afforded by classical signature schemes. CRYSTALS-Dilithium is an efficient post-quantum digital signature scheme based on lattice cryptography and has been selected as the primary algorithm for standardization by the National Institute of Standards and Technology. In this work, we present a high-throughput GPU implementation of Dilithium. For individual operations, we employ a range of computational and memory optimizations to overcome sequential constraints, reduce memory usage and IO latency, address bank conflicts, and mitigate pipeline stalls. This results in high and balanced compute throughput and memory throughput for each operation. In terms of concurrent task processing, we leverage task-level batching to fully utilize parallelism and implement a memory pool mechanism for rapid memory access. Considering the impact of varying repetition numbers in Dilithium on the overall execution time and hardware utilization, we propose a dynamic task scheduling mechanism to improve multiprocessor occupancy and significantly reduce execution time. Furthermore, we apply asynchronous computing and launch multiple streams to hide data transfer latencies and maximize the computing capabilities of both CPU and GPU. Across all three security levels, our GPU implementation can concurrently compute ten thousand tasks in less than 32 miliseconds for signing and 15 miliseconds for verification on both commercial and server-grade GPUs. This achieves microsecond-level amortized execution times for each task, offering a high-throughput and quantum-resistant solution suitable for a wide array of applications in real systems.

cs.CR↗

arXiv2022

Complex K-theory of moduli spaces of Higgs bundles

We establish an isomorphism of complex $K$-theory of the moduli space $\check{\mathcal{M}}$ of $``SL_n"$-Higgs bundles of degree $d$ and rank $n$ (in the sense of Hausel--Thaddeus) and twisted complex $K$-theory of the orbifold $\hat{\mathcal{M}}$ of $PGL_n$-Higgs bundles of degree $e$, where $(n,d)=(n,e)=1$. Along the way we prove the vanishing of torsion for $H^*(\check{\mathcal{M}})$ and certain twisted complex $K$-theory groups of $\hat{\mathcal{M}}$. We also extend Arinkin's autoduality of compactified Jacobian to a derived equivalence between $SL_n$ and $PGL_n$-Hitchin systems over the elliptic locus. In the appendix we develop a formalism of $G$-sheaves of spectra, generalising equivariant homotopy theory to a relative setting.

math.AG↗

arXiv2021

OSKR/OKAI: Systematic Optimization of Key Encapsulation Mechanisms from Module Lattice

In this work, we make \emph{systematic} optimizations of key encapsulation mechanisms (KEM) based on module learning-with-errors (MLWE), covering algorithmic design, fundamental operation of number-theoretic transform (NTT), approaches to expanding encapsulated key size, and optimized implementation coding. We focus on Kyber (now in the Round-3 finalist of NIST PQC standardization) and Aigis (a variant of Kyber proposed at PKC 2020). By careful analysis, we first observe that the algorithmic design of Kyber and Aigis can be optimized by the mechanism of asymmetric key consensus with noise (AKCN) proposed in \cite{JZ16,JZ19}. Specifically, the decryption process can be simplified with AKCN, leading to a both faster and less error-prone decryption process. Moreover, the AKCN-based optimized version has perfect compatibility with the deployment of Kyber/Aigis in reality, as they can run on the same parameters, the same public key, and the same encryption process. We make a systematic study of the variants of NTT proposed in recent years for extending its applicability scope, make concrete analysis of their exact computational complexity, and in particular show their equivalence. We then present a new variant named hybrid-NTT (H-NTT), combining the advantages of existing NTT methods, and derive its optimality in computational complexity. The H-NTT technique not only has larger applicability scope but also allows for modular and unified implementation codes of NTT operations even with varying module dimensions. We analyze and compare the different approaches to expand the size of key to be encapsulated (specifically, 512-bit key for dimension of 1024), and conclude with the most economic approach. To mitigate the compatibility issue in implementations we adopt the proposed H-NTT method.

cs.CR↗

arXiv2018

On the Kirwan map for moduli of Higgs bundles

Let $C$ be a smooth complex projective curve and $G$ a connected complex reductive group. We prove that if the center $Z(G)$ of $G$ is disconnected, then the Kirwan map $H^*\big(\operatorname{Bun}(G,C),\mathbb{Q}\big)\rightarrow H^*\big(\mathcal{M}_{\operatorname{Higgs}}^{\operatorname{ss}},\mathbb{Q}\big)$ from the cohomology of the moduli stack of $G$-bundles to the moduli stack of semistable $G$-Higgs bundles, fails to be surjective: more precisely, the "variant cohomology" (and variant intersection cohomology) of the stack $\mathcal{M}_{\operatorname{Higgs}}^{\operatorname{ss}}$ of semistable $G$-Higgs bundles, is always nontrivial. We also show that the image of the pullback map $H^*\big(M_{\operatorname{Higgs}}^{\operatorname{ss}},\mathbb{Q}\big)\rightarrow H^*\big(\mathcal{M}_{\operatorname{Higgs}}^{\operatorname{ss}},\mathbb{Q}\big)$, from the cohomology of the moduli space of semistable $G$-Higgs bundles to the stack of semistable $G$-Higgs bundles, cannot be contained in the image of the Kirwan map. The proof uses a Borel-Quillen--style localization result for equivariant cohomology of stacks to reduce to an explicit construction and calculation.

math.AG↗